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How to Draw drawing and sketching objects and environments from your imagination
How to Draw drawing and sketching objects and environments from your imagination
Scott Robertson and Thomas Bertling
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How to Draw is for artists, architects and designers. It is useful to the novice, the student and the professional. You will learn how to draw any object or environment from your imagination, starting with the most basic perspective drawing skills. Early chapters explain how to draw accurate perspective grids and ellipses that in later chapters provide the foundation for more complex forms. The research and design processes used to generate visual concepts are demonstrated, making it much easier for you to draw things neverbeforeseen! With a combined 26 years of teaching experience, Scott Robertson and Thomas Bertling bring you the lessons and techniques they have used to help thousands of their students become professional artists and designers. This book is indispensable for anyone who wants to learn, or teaches others, how to draw.
Jahr:
2013
Verlag:
Design Studio Press
Sprache:
english
Seiten:
211
ISBN 13:
9781933492735
Datei:
PDF, 286,35 MB
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Am meisten angefragte Begriffe
bertling^{165}
grid^{144}
scott robertson^{143}
ellipse^{122}
thomas bertling^{110}
sketch^{105}
vertical^{99}
vanishing^{96}
lens^{89}
axis^{84}
vanishing point^{66}
grids^{65}
it's^{65}
centerline^{63}
drawings^{62}
minor axis^{57}
perspective grid^{52}
sketching^{52}
ellipses^{51}
guidelines^{48}
sketches^{48}
rectangle^{46}
wing^{45}
ing^{43}
wheels^{43}
define^{39}
cone of vision^{39}
planes^{38}
thi^{37}
width^{36}
underlay^{36}
mirrored^{34}
bounding^{33}
squares^{33}
marker^{32}
lvp^{31}
diagonal^{31}
mirroring^{30}
intersection^{30}
vertical line^{29}
vanishing points^{29}
horizontal^{29}
silhouette^{29}
robertson i thomos^{28}
proportions^{28}
surfaces^{28}
curves^{27}
convergence^{27}
thomos bertling^{26}
intersect^{26}
converge^{26}
visual^{26}
perpendicular^{25}
volumes^{25}
draft^{23}
let's^{23}
vehicles^{22}
bounding box^{22}
vertical lines^{22}
pencil^{22}
2 comments
Mutungii
A literal gold mine! Loved It!
05 April 2021 (17:38)
ak1neo
One of the few books thats almost essential to all beginner artists!
14 April 2021 (10:11)
Sie können die Buchrezension schreiben oder über Ihre Erfahrung berichten. Ihre Meinung über das gelesene Buch ist interessant für andere Leser. Unabhängig davon, ob Sie das Buch mögen oder nicht, kann Ihre ehrliche und ausführliche Beschreibung anderen Leuten beim Suchen von Büchern helfen.
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HOW TO DRAWING and SKETCHING OBJECTS and ENVIRONMENTS fr om YOUR IMAGINATION DRAW by $coH Robertson w ith Thomas Bertling designstudiolpRESS D ~ DEDICATION This book is for those with a passion for drawing and learning . Never stop! BEYOND THIS BOOK: It [!] . Stepbystep videos are an integral part of the How To Draw educationa l experience! Use a smartphone or tablet to open a OR Reader app and scan thi s OR code. It links to the Design Studio Press imagerecognition app needed to play the videos. Download the DSP app, scan Scott's photograph from page 008 and an introductory video will load. All of the pages in thi s book th at link to educational videos have a "play button" at the bottom , like thi s: 0 No smartphone or tablet? No worries. Go to page 206, type in the URL on a ny computer to gain access to th e entire links li st. Copyright © 2013 Design Studio Press. All Rights Reserved. All text and artwork in thi s book are copyrig ht © 20 13 Scott Robertson, Thomas Bertling unless done by one of th eir former students or as noted th roug hout the book. No parts of thi s book may be reproduced or transmitted in any form or by any mean s, electronic or mechanical , including photocopyi ng , xerogrophy, and videography recording without wr itten permission from the publisher, Design Studio Press. Copy Editors: Melissa Kent, Erika G . Bertling, Heather K. Dennis, Jessica Hoffmann I Graphic Design: Cecilia Zo Publi shed by Design Studio Press Address: 8577 Higuera Street, Culver City, CA 90232 Printed in China I First Edition, November 20 13 10 9 8 7 6 5 4 3 2 1 Library of Congress Control Number: 2013943344 004 I Website: www.des ignstudiopress.com I Email: info@desig nstud iopress.com I Hardcover ISBN·13: 978193349273 5 I Paperback ISBN·13: 978193349 2599 TABLE OF CONTENTS INTRODUCTION CHAPTER I PAGE 008 01 Drawing Materials and Skills I PAGE 010 012 013 014 015 016 017 018 019 CHAPTER 02 Perspective Terminology I PAGE 020 022 023 024 026 027 CHAPTER CH; APTER 03 Perspective Drawing Techniques 04 Creating Grids ("1' S> I Choosing Your Drawing Materials Choosing Pens and Paper The Craft of Drawing Practicing Freehand Straight Lines XYZ Coordinate System Practicing Freehand Smooth Curves Practicing Freehand Ellipses Drawing an Ellipse on the Minor Axis Defining the Perspective by the Viewing Position Cone of Vision  COV Finding Vanishing Points on the Picture Plane Physical Parallel Lines Converge to a Common Vanishing Point Horizon Line Relative to Position I PAGE 028 030 032 033 034 036 037 040 042 043 Division and Multiplication of Dimen sions in Perspective Multiplying and Dividing Rectangles Dividing into OddNumbered Proporti ons Mirroring in Perspective Mirroring Tilted Planes Mirroring Rotated , Tilted Planes Mirroring 2D Curves Mirroring a 2D Curve on a Tilted Surface Mirroring 3D Curves in Perspective: The 2Curve Combo 046 048 049 050 051 053 054 057 058 061 062 068 Perspective Grid Types Perspective Grid Con struction Diagonal Vanishing Point, Station Point Method 2Poi nt Grid Construction with Vanishing Points on the Page Rotated 2Point Grids with SameSized Squares Transferring Scale in Perspective The Brewer Method : Constructing a Grid with Vanishing Points off the Page Creating a Grid of Squares, without Diagonal Vanishing Points When to Use a ComputerGenerated Underlay Other Benefits and Ways to Use an Underlay Not All Perspective Grids Are Created Equal Assembly and Exploded Views PAGE 044 4;:' I ScoM Robertson I Thomas Bertling I HOW TO DRAW 005 CHAPTER 05 Ellipses and Rotations ~ I PAGE 070 I " , CHAPTER CHAPTER CHAPTER 006 072 073 074 074 075 076 078 079 Ellipse Basics and Terminology Placing a Circle in Perspective or Drawing Ellipses Creating a Cube Using Ellipses Offsetting Ellipses Hinging and Rotating Flaps and Doors Subdividing Ellipses Shortcuts to Dividing Ellipses Placing a Circle on a Sloped Surface 082 084 085 086 088 089 090 092 093 094 096 100 102 Planning Before Perspective Orthographic Views, a.k.a. Orthogonal Views or Draft Views Transferring a Side View into Perspective Putting It All Together : XYZ Section Drawing Extending the Sections 2Curve Combo Cutting Volumes Adding Radii and Fillets Wrapping Graphics Detailing and Sculpting Surfaces More Tips for Modifying Complex Volumes Contour Lines, Overlapping and Line Weight XYZ Section Drawing Applied 06 Working with Volume I PAGE 080 07 Drawing Environments I PAGE 104 08 Drawing Aircraft     Scott Robertson I I Thomas 108 110 112 115 116 1 18 120 Photo Underlay Site Planning Thumbnail Sketching NonPhoto Blue, Then Ink SciFi Environment StepbyStep Warp That Grid with a WideAngle Lens! Outdoor Environment Sketch StepbyStep 124 126 128 130 132 133 137 142 146 Airplane Anatomy Visual Research Drawing from Observation Loose Concept Sketching "Paper Plane" Ideation "Paper Plane" Perspective Grid Drawing a Paper Plane, StepbyStep Using a 3D Underlay Final Airplane Drawing StepbyStep PAGE 122 Bertling I HOW TO DRAW CHAPTER 09 Drawing Wheeled Vehicles I PAGE 152 154 157 160 164 166 169 170 174 175 176 178 180 186 CHAPTER 10 Sketching Styles and Mediums I PAGE 188 190 191 192 193 194 195 196 197 198 199 200 201 Glossary Index Ballpoint Pen Copic Marker + Ballpoint Pen Graphite Pencil Colored Pencil Pilot HITEC Pen on Newsprint Copic Marker + Pilot HITEC Pen NonPhoto Blue Colored Pencil + Marker + Brush Pen Pentel Pocket Brush Pen Copic Marker + Pen + Gouache Gouache on Illustration Board Toned Paper + Mixed Med ia Digital: Sketchbook PRO I PAGE 202 I PAGE 203 Additional Resources Video Links Bios Visual Research Have an Idea or a Goal Before Starting to Sketch Some Basics on Vehicle Packaging and Architecture Flexing Your Creativity Grids, Grids, Grids! Drawing a Side View in Perspective Drawing a Stylized Side View in Perspective Basic Body Sculpting Drawing the Windshield and Greenhouse Wheel Wells, Wheels and Tires in Perspective Common Automotive Lines Car Drawing Construction, StepbyStep Grid Vehicle Sketching with a WideAngle Lens I I PAGE 204 PAGE 206 I PAGE 207 Special Thanks I PAGE 208 Scott Robertson I Thomas Bertling I HOW TO DRAW  007 INTRODUCTION Drawing is almost a magical power. It enables you to communicate in a different way than spoken or written language. Perspective drawing lets you convey how things work and how they look. You can inspire others w ith something as simple as a pen and a napkin! When I created Design Studio Press, this is the first book I ever intended to write. Well DSP turned 10 years old this past March . With 55 other books already in print, so much for Plan A! Finally, with the help of my good friend and longtime coteacher, Thomas Bertling, I bring you the drawing knowhow I've taught for over 18 years in my own workshops and at Art Center College of Design. Organizing this book was like a sport where you train for years in order to compete at a high level for a few seconds. We combed through over a decadeandahalf of demos and lectures to formulate the pages we now present to you. Once you master these manageable perspectivedrawing exercises, you wi ll have the knowledge to sketch anything from your imagination, to think like a designer and draw things the world has never seen! Books are great for looking at beautifully printed reproductions of original drawings and reading about the th oug hts and methods behind those drawings, but video might be even better for stepbystep demonstrations. For that reason, many pages of this book link to online tutorials. Check out page 004 for a full explanation of how to use the Design Studio Press app. Almost all of us drew when we were kids and some of us never stopped. While it takes practice to master the techniques in this book, it's worth the effort. Humans have been drawing for over 40,000 years so you're about to acquire one of the oldest forms of communication. Jump in and do the basic exercises at the beginning of this book with passion. As you master th ese ancient skills, pass along th e knowledge and teach others the wonders of perspective drawing from their imagination . Let's draw! May 31 , 2013 Los Angeles, California 008 Scott Robertson I Thomos Bertling I HOW TO DRAW 0 009 010 Scott Robertson I Thomas Bertling I HOW TO DRAW CHAPTER DRAWING MATERIALS AND SKilLS In this chapter you will learn about all the basic tools needed to get started with drawing. There are two categories: material s and skills . It is important to know how to pick the right materials for the job at hand. As the topic and intent of the sketch changes, so w ill the materials needed . Quick loose sketches require a good flow of ink to paper and sometimes strokes should be very light to find "happy accidents" in the drawing. Tight drawings need a lot of attention. Optimally, one pen is used to generate varying thicknesses of lines. To achieve the best workflow, match different kinds of paper to d ifferent pens. When you find your favorite pen, make sure to buy several! Sometimes that beloved pen goes out of production way too fast. 01 Building up mechanical drawing skills is an important factor in creating great drawings. It might seem simple, to draw a straight line, ellipse. or curve. But these skills must become ingrained in muscle memory so that concentration can be spent on construction versus thinking about how to create the lines in the construction. Also , these skills will help create clean drawings that can be done quickly and passed along the production line easily. Not having to use multiple tools will also speed up the drawing process. Building muscle memory takes time and practice, so be patient! Take on the exercises one at a time, and soon your skills will improve. o Scott Robertso n I Thomas Bertling I HOW TO DRAW  011 CHOOSING YOUR DRAWING MATERIALS In th e beginning , a lot of money does not need to be spent o n ma teri a ls. All that is reall y needed are pens, paper and a few basic tools. Brand na mes don 't matter much , so let's get i nto th e cri teria for choosi ng materia ls. Basic tools 1. Circle template 4. Equal spacing divider A circle template is quite useful to clean up circles, especially in side vi ews. A compass is nice to have, but the circle template is fa ster to use. An equal spac ing divider is a su perhandy tool that divides any di stance into even segments . 2. Sweeps 5. Straightedge Th e sweeps pi ctured above conta in the most co mmo nly sketched auto motive curves. But don't rel y o n them to dictate y o ur design . A lways d raw your lines freehand and th en use the sweeps to clean Use a straightedge to construct grid s for underlays . them up . Use ellipse templates to clean up ellipses. Alvin or Pickett are recom mended brands since they w ork for most situations. A good set of ellipse guides is a n investment, but worthw hile because it wil l last decades. 3. Cotton pad, paper towel or tissue To avoid ink glo bs on the page , da b the ballpoint pen freq uently. 012 Scott Robertson I Tho mas 6. Ellipse template set Bertl ing I HOW TO DRAW CHOOSING PENS AND PAPER Match the pen to the paper in order to create drawings with different line weights. Ideally, yau want to be able to draw both construction lines and contour lines without switching your drawing tool. Pens Ballpoint pens When choosi ng a ballpoint pen, test it on the paper that you plan to use most frequently to see how much ink builds up on the tip as multiple lines are sketched. A pen that ca n sketch at least 10 lines without forming an ink glob on the tip is best. No erasing! Being able to erase is not an advantage in this style of drawing. There are so many intersecting construction lines that it is nearly impossible to erase anything without disrupting these valuable shortcuts that help to explain your drawing. Plus, erasing slows down the drawing process a lot. Pads So what can be done when erasing is not possible? Draw lightly. It's as simple as that. Sure, some lines might be incorrect, but you can clean up the drawing later with an overlay. Refer to the last chapter of this book, page 188, for examples of combinations of materials used for various types of drawings. Choose a paper th at works well with your preferred drawing tool. A rougher paper will be able to produce both thin and thi ck lines wi th fa ster flow ing bal lpoint pen s. Types of paper Try many combination s of pens and paper until a favorite is found. Anything from cheap cop ier paper to speci alty papers will work. There ore a couple of specialty papers that work well with markers as well as pens. Be aware that there are two sides to these papers: one side is waxed and the other is raw. Always draw on the raw side . The waxed side is there to prevent markers from b leed ing through to the next page and it's terrible to draw on with markers. Paper Softness of the Drawing Surface This is not referri ng to the paper itself, but how it is used. Drawing on a soft surface enables the best line quality. Do not work on a hard surface with a single piece of paper! Have at least 15 pages under a drawing to get the best line quality possible . . ~ .c~ y ~ Working with underlays Look for paper that is transparent enough so than an underlay can show through, but not so transparent that the table shows through when you present your drawing s. Scott Robertson I Thomas Bertling I HOW TO DRAW  013 THE CRAFT OF DRAWING Drawing requires full concentration! Initially you'll spend most of your energy on craftsmanship and construction and very little on design . The more craftsmanship and construction skills become muscle memory, the more design can become the focus . The first step in this process is to practice the basic craft of drawing lines : straight lines, controlled curves and ellipses. This book has several good exercises for practicing these skills . As skills increase , the need to practice these exercises will diminish . Let's start with some warmup drawings . Set up a workspace Clear the space! In order to stay focused , it's best to clear enough F _ ~ ___ ~ __ _ space and time to commit fully to the drawing. Have a clear work surface with tools at the ready. Flow will be broken when a pen or straightedge can 't be found! The worst part is that the rhythm is lost for that drawing and what was clear ten minutes ago will take another ten minutes to understand again . Have a soft pad to draw on with at least 15 pieces of paper underneath the drawing for best _~.J"fj lineweight results . Being able to draw straight lines from point to point and in a grid is essential for all of the techniques in this book. These exercises may seem simple, but to do them well means burning through some paper to build the necessary muscle memory. Learn to draw one straight line Let's look at the body mechanics that are necessary to achieve a consistently straight line. You only need to learn how to draw one straight line. After that rotate the paper to change the line direction. Without this technique, keeping the paper in a fixed position would lead to having to learn how to draw an infinite number of straight lines. Draw with the whole arm! For long lines, use the elbow and shoulder joints; it's almost impossible to achieve this by only using the wrist. Draw slowly! Lines need to be repeatable and controlled. Draw each line once and do not trace the same line over and over again . Ghost the line! Go through the movement with the pen hovering above the paper. When the correct orientation is found , drop the pen 1 ~== on the paper and draw. "' Is the line arching? 1. Muscle memory might have to be rewired when a line that feels straight while drawing results in an arch (red line). 2 . The best way to counterbalance is to draw a line that feels like the opposite arch (green line). 3. After some practice the feeling of drawing a straight line and the result will match up (blue line) .   . 014 Scott Robertson I Th o mas  Bertl ing I HOW TO DRAW PRACTICING FREEHAND STRAIGHT LINES Drawing parallel lines same length and spacing. Draw lightly. These are the fundam entals for drawing construction lines. Start off with shorter lines, so mething in th e 3inch range, and work up to the full length of the paper_ Make sure to engage the entire arm and that li nes are drawn con sciously; th ey should be re peatable at th e       Aiming lines point to point Th e seco nd exerci se is to draw lin es that meet in one point . Start to draw at any point outside of th e center, draw a lin e through th e Below are two ways of practi cin g_ First, draw a co uple of po ints o n th e page and co nnect them _ Remember to ro ta te the paper to orien t on e stra ig ht line that th e body knows how to d raw_ It's fin e to overshoot th e points sligh tly to improve flow_ cen ter, a nd co nti nue. / I / I  _.~ \ Drawi ng boxes in perspective Draw through , w hich mean s to draw even the edges that would no t be seen, because they are behind the box. Draw the complete box with light constru cti on lines, then darken the in sid e edges and the o utlines of the box. The outlines shou ld be darkest. Trace lines aga in and aga in to a ch ieve differen t line wei ghts. A fun way to practice draw ing straight lines is to draw boxes in lpoint perspective. Draw a Horizon Line (HL) and choose a Vani shing Point (VP) . Draw a rectangle and connect each corner to the VP. Draw another rectangl e in th e distance between these lines a nd you have a box ! HL VP         =F <   ./ ; iI //~7J//.';l ~/ /  /' ./ v LI ! /  ___ /i I / r/ ;:r/ ~ I _ I ScoM Robertson I Th o ma s Bertlin g I HOW TO DRAW     015 XYZ COORDINATE SYSTEM Z Axis Sketching in perspective requires understanding the XYZ coordinate system. Each axis points toward a Vanishing Point. Each plane is perpendicular to its axis. Stay in control of your drawing by always knowing on which plane you are sketching. This system is used not only to sketch boxes, but for all complex forms. To draw a box where no side is perfectly perpendicular to the viewer, 2point perspective is needed. Y Plane X Axis X Plane  Z Plane Y Axis Drawing a box In 2Point perspective HL   .          1. Draw the Horizon Line (HL) . Then draw the front corner of a box. This establishes the X, Y and Z Axes. LVP HL  ~ 2. Extend the X Axis and the Y Axis lines from the bottom of the vertical , until they intersect the Horizon Line. The intersections of these lines create the Left Vanishing Point (LVP) and Right Vanishing Point (RVP) for the drawing. X Axis          "" LVP Y Axis RVP HL , =43. Drow lines from the top of the vertical , to the Left and Right Vanishing Points. Then add two verticals at any distance. LVP HL    .~~~~ 4. Close the box by drawing lines from the ,,~ :::~ top of the two new verticals to the Left and , .... Right Vanishing Points. Add the resulting hidden vertical in the back. =   = RVP ~ =,.~:;;.,."..  .....  l LVP HL ~5. Darken the visible edges of the box. The drawing still shows the light construction lines . This is what it means to "draw through," which is very helpful to control your drawings. 016 Scan Robertson I Tho mas Bertling ""    I HOW TO DRAW RVP , , . ::.= __ 7'1 PRACTICING FREEHAND SMOOTH CURVES Drawing requires not only straight lines, but curves too. There is a skill to drawing smooth, accelerating curves. When working in side view you determine how the curves flow; in perspective, the construction dictates how the curves flow and it can sometimes be surprising how radically some curves move in perspective. Drawing curves through multiple points Practice drawing accelerating curves through multiple preexisting points . A smooth, graceful curve is optimal. This is done best by drawing the curve in segments, using the guide points as waypoints , not end points . Otherwise, the segments will have to be redrawn multiple times and that causes fuzzy/hairy lines. Keep practicing curves to prevent this from happening. DO DO NOT DO NOT Place points that follow your intended de Create a curve with edges and corners. sign , then create a smooth curve through those points. Rotate the page while drawing and use the natural curves your wrist and fingers draw. It's fine to draw the curve in segments; it's not necessary to draw it as one continuous line. Avoid this by seeing the points as waypoints rather than endpoints. Create a fuzzy line. Stay focused and methodical. Control the line as much as possible so that the task can be repeated over and over at a high quality. Scott Robertson I Thomas Bertling I HOW TO DRAW 017 PRACTICING FREEHAND ELLIPSES Ellipses occur frequ ently. They are essentially circles in perspective, and some obvious ellipses are wheels and gauges. But th ey are also needed in constructions to rotate doors and objects. To become comfortable placing ellipses, start by drawing a con trolled ellipse. In later exercises, placing a circle in perspective, w hich becomes an ellipse, will be explained. Drawing an ellipse and adding the minor axis Cy 1. Draw a freehand ellipse . Make sure to move the whole arm. 2. Draw with a light line. Later, the drawing can be cleaned up with an ellipse guide. Do not darken the lines too much by repeating the strokes. Even if you drew an incorrect ellipse, drawing over and over it will only make it more obvious . 3. Check that the ellipse has no flat spots and is not lopsided . ./ .' ./ / r '. Too dark and too many lines .... Good line weight 4. Place the minor axis on the ellipse. The minor axis is the line that divides it in half across the narrow dimension of the ellipse making each half equa l to the other. The minor axis plays an important role in placing the ellipse in perspective, so finding and controlling it is essential. 5. Doublecheck with an ellipse guide or fold the paper along the minor axis and check that the two halves line up on top of each other by holding the paper up to the light. '\ ) Round Draw minor axis /  (,," \ . Clean up with Ellipse Template ~~t· \ ;  Fold ellipse along minor axis on top of itself. 018     Scott Robertson I Thomas Bertling I HOW TO DRAW 0 I / DRAWING AN ELLIPSE ON THE MINOR AXIS Now switch it up. Draw the minor axis first and then place the ellipse over it. Align the hand correctly by rotating the paper to get the best angle. Make sure that the ellipse is symmetrical. Check that it is on axis. The minor axis needs to be centered and perpendicular to the drawn ellipse. \ Minor axis first ... ... then draw the ellipse Perpendicular, but not symmetrical Ellipse is not perpendicular to axis \ \ / ! ' / \ Drawing ellipses defined J \ J by the minor axis and width Draw the minor axis, then a line to the left and the right of it. Make sure these outer lines are symmetrical or it will be impossible to draw ellipses that fit. Place the ellipses on the minor axis and match them to the width of the two additional lines. Vary the degree (how narrow or wide they are) as well. \ \ \\ \ \ \ '" \ ~  > ~ \ \ ", \ \ \ ~ ~. ~, " \ \ Scott Robertson I Thomas Bertling I HOW TO DRAW  0 19 . .:c   ,, /' / 020 Scott Robertson I Thomas Bertling I HOW TO DRAW 60 deg COV IS deg VP / 30degVP 60 deg VP /'  / StabonpolOt CHAPTER PERSPECTIVE TERMINOLOGY Explore this chapter to familiarize and refresh your knowledge of perspective terminology. The focus is on the terms and principles that are essential to navigate perspective drawings and to design objects and scenes from your imagination. Remember, a true version of what is seen is not created , but rather emulated , since stereoscopic vision is not possible on paper. Humans have two eyes, which allows us to see in 3D . Drawing in perspective is a cheat, an approximation of how we see the world . This chapter will explain the rules that exist to create the best illusion on paper. Once the rules have been mastered , it's okay to break them intentionally. However, if they are broken accidently, it can sabotage what you are trying to convey to the viewer. For example, imagine 02 you want someone to view your fantastic landscape and house as someplace they would want to live. Instead, a nagging question comes to their mindsomething is odd and they cannot figure out what it is . This question is triggered by an inaccurate perspective in your drawing and shou ld not have happened , since the goal was to talk about the project, not perspective. This was unintentional and ended up distracting the viewer from the goal . Knowing the fundamental rules of perspective will allow you to join the discussion and exploration of perspective knowledge. There are many books that cover this terminology in depth , and doing additional research is encouraged. Join the community and start exploring your own questions and finding answers that allow for judging work and helping others. scan Robertson I Thomas Bertl ing I HOW TO DRAW 021 DEFINING THE PERSPECTIVE BY THE VIEWING POSITION Defining the viewing position is essential to controlling ·the perspective drawing. Keep in mind that photography is being replicated in the drawings; therefore, it is essential to define where one is standing , the viewing direction, and the lens being used . This knowledge will apply to the guessed perspective, the constructed perspective, and even to the computergenerated perspective. The rules need to be known so it becomes obvious when they are being broken. Defining Point of View  (POV) Let's look at the following situation. A great picture of a building is taken with a camera and displayed. Another person wants to take the same shot when visiting the same location. In order for this to happen , the second photographer needs to know the location, viewing direction and the lens to use. This is the same information needed to create a drawing. 1. Ground Plane Line of Sight Station Point 1. Ground Plane The position and direction where the photo was taken needs to be known. This could be on the street, on a bridge or on the sand at the beach. Whatever surface on which the photographer was standing or sitting is the ground plane. That's simple on Earth, but what about in outer space? In space it would still be considered as sitting or standing in a spaceship and this would determine the ground plane. What if the ship is removed from the equation? Then think of the ground plane as the extension of the soles of the feet. 2. Picture Plane Station Point· (SP) Now that the ground plane is established , the location and height of the cameraor in the case of a drawing, the eyeneeds to be disclosed. In a drawing this spot is called the Station Point. Think of the Station Point as a point in space that has no direction . Line of Sight The direction one is looking is the Line of Sight. The Line of Sight determines both the direction being looked and the incline. In the graphic, the Line of Sight is parallel to the ground. This creates a 1 or 2 point perspective in which all physical vertical lines are represented by vertical lines in the drawing. Tilting the line of sight (having it not be parallel to the ground) creates a 3point perspective or even a 5point perspective. For starters it is recommended to keep the Line of Sight parallel to the ground . This makes the construction considerably easier. 2. Picture Plane  (PP) The Picture Plane is the surface on which images are recorded. Imagine the Picture Plane being a plate of glass that is pinned perpendicular to the Line of Sight. It is time to capture the image. Close one eye and on the glass, start drawing what you see behind the plate of glass. The vision rays run from the eye to the object, passing through the picture plane. Record those transition points on the Picture Plane . This is perspective drawing. How far is th e Picture Plane from the Station Point? It doesn't matter for this construction . Pushing the Picture Plane away just creates a larger drawing, but will not change the proportions in the drawing itself. Historically, when the masters were really painting on glass, their arm length was the limiting distance factor. 022 Scott Robertson I Thomos Bertling I HOW TO DRAW CONE OF VISION  COV 1. Take a look at what was captured on the Picture Plane glass; specifically notice the squares on the ground . The squares closer to the box are less distorted than those that are closer to the vi ewer. The captured image is correct with a high or low amount of distortion, but the closer squares are much harder to understand. They may be squares, but they look more like long rectangles. 1. Coming back to the cam era analogy, it's time to choose the lens . This can be anything from wid e to telephoto. The particular lens determines how much of the area will be seen through the lens, which is wh at is included in the drawing. It's assumed here that the camera would take a square picture as defined by the square picture plane on the previous page. Stron distortion \ 90' COY 2. 60' COV 2. The optimal lens that creates an acceptable amount of distortion is a 50mm lens. Thi s translates into the drawing as a 60° Cone of Vision. How is this determined? Every lens has a degree of visibl e area assigned to it and 60° is close to what is seen throu gh a 50mm lens. This cone is green in the drawings. A 90° Cone of Vision is shown in red. 3. Going back to th e drawing, the Cones of Vision have been added. There are two circles. The inner circle represents the 60° Cone of Vision and the outer circle the 90° Cone of Vision. It becomes clear that the area within the 60° Cone of Vision has less distortion than the area in the 90° Cone of Vision. Cone of Vision degrees for different perspectives When drawing, it's best to maximize the space on the poge and not draw objects that are too distorted. Here are guidelines for the Cone of Vision degrees for different perspective constructions. lPoint Linear Perspective Cone of Vision: 50' lpoint perspective is very prone to distortions. To avoi d them altogether, stay within a 50° Cone of Vision in drawings. Going even as small as 40° is acceptable. Be aw are that going too small will flatten out the perspective like that of a telephoto lens. 2Point Linear Perspective Cone of Vision: 60' The Cone of Vision can be opened up more here. Be aware that around the edges, the distortion will increase, so it's best not to place any critical drawing elements near the edges . The 60° Cone of Vision will be the goto Cone of Vision for most drawings. 9~OV 3. 3Point Linear Perspective Cone of Vision: 60' Staying within the 60° Cone of Vision is still recommended . 5Point Curvilinear Perspective Cone of Vision: open choice In 5point perspective almost anything goes. Keep in mind that whatever is being drawn will be like a wideangleIens photograph at this point. To see examples of this jump ahead to page 047 . Perspectives can be created that allow more than the natural Field of View to be perceived. When this happens be extra mindful of th e construction . Make sure to doublecheck all lines since instinct can easily lead to a wrong direction. SeoM Ro bertson I Thomas Bertling I HOW TO DRAW  023 FINDING VANISHING POINTS ON THE PICTURE PLANE Let's emu late the "glass plate" experience on a piece of paper. Understanding where th e Vanishing Points are, and how they relate to one another, makes it easier to build perspective grids. Diag.1 HL LVP 1. When the parallel lines of the box are extended, each set converges to a Vanishing Point. Letters used in the Drawings : SP Station Point HL Horizon Line Center Vanishing Point CVP LVP Left Vanishing Point RVP Right Vanishing Point 45 VP 45" Vanishing Point, and other degrees Diag.2 LVP k  = == HL __ 2. To find the Vanishing Point for any set of parallel lines, use the top view and move one of the lines parallel until it intersects the Station Point. Next, find the point where that parallel line intersects the Horizon Line. This is its Vanishing Point. Top view Picture Plane HL  3. The next step is to abstract this construction to fewer lines to be able to find any Vanishing Point in the future. This drawing shows a combination of the top view and the Picture Plane. This is done to save space and is more efficient. It's called the Vi sual Ray Method for perspective drawings . Diag.3 ~~~P~____==========Fi~~==~F===~~V~ f  HL With both drawings combined , the two lines at the Station Point have a relative angle of 90°. This angle of 90° is what locates the two Vanishing Points on the Horizon Line needed for the construction of obiects with 90° corners in perspective. Going from the Station Point directly to the Horizon Line will yield a perpendicular line. The point where this line intersects with the Horizon Line is the Center Vanishing Point for this perspective construction. SP 024 Scott Robertson I Thomas Bertl ing I HOW TO DRAW Diag.4 4. To find a new set of 90° Vanishing Points rotate the two 90° lines together. The center of rotation is at the Station Point. Any degree of rotation can be chosen. Here the 90° lines were rotated clockwi se so that both intersect with the Horizon Line w hile still sta yi ng on the page. SP 5. To place another box with 90° corners use the new set of Vanishing Points. Both boxes sit on the same ground plane and are rotated at different degrees relative to the viewer. Diag.5 /' ~. \ A common error is to cause a rotated object to look like it's floating above the ground or is tilted. Thi s is cau sed by not matching the Vanishing Points to the same Cone of Vi sion . HL ~ SP 6. To find the degree of any Vanishing Point measure its deviation from the line that run s perpendicular to the Horizon Line and ends at the Station Point. To achieve a 90° box, the degrees of deviation of the Left and Right Vani shing Points will total 90' . Use them together as pairs and avoid mixing them with one another. Diag.6 63 VP ~~ 7. Up to now in this example, random Vanishing Point pairs have been found . Now it is time now to find a matching pair of VPs that are more common . Other than 1Point Perspective, very common VP combinations are 75 / 15, 60/ 30, and 45 / 45 . Take a second look at the 30° Vanishing Point. The edge of the 60° Cone of Vision runs through this Vanishing Point, while the center of the Cone of Vision is the Center Vanishing Point. 75 VP . 50VP HL SP Diag.7 OVP 4 VP 45 VP HL SP Seon Robertson I Thomas Bertling I HOW TO DRAW  025 PHYSICAL PARALLEL LINES CONVERGE TO A COMMON VANISHING POINT As a general rule, physical parallel lines converge to a common Vani shing Point, but like anything else there are exceptions! In linear constructions for lpoint and 2point perspective th ese exceptions are found. This is because lpoint and 2point perspective constructions are made more efficien tly by not having all physical parallel lines converge. lpoint perspective with some nonconverging lines In lpoint perspective, there is only convergence into the depth of the drawing. Any lines that are parallel to the Picture Plane or perpendicular to the viewer will scale, but not converge. In this drawing , neither the verticals nor the horizontals converge. In addition, all angled lines that are on a plane parallel to the Picture Plane do not converge either. This makes using lpoint perspective very attractive, since it is quick to set up and use. There is only one direction of convergence and only one Vanishing Point to consider. Drawing by: Danny Gardner View more of Danny' s nice work at: www.dannydraws.com 2point perspective with some nonconverging lines In 2point perspective, all physical parallel lines converge except the verticals. The verticals stay vertical and do not converge. Keeping the vertica ls perpendicular to the Horizon line makes it much easier and faster to draw in 2point perspective. The drawback is that the perspective can quickly become distorted if the 60° Cone of Vision is abandoned. A 3point perspective is needed to draw more dynamic views looking up or down. 026 Scott Robertson I Thomas Bertling I HOW TO DRAW HORIZON LINE RELATIVE TO POSITION Standing higher or lower with the Line of Sight parallel to the ground What happens to the Horizon Line when the Station Point is higher or lower? Let's review the setup of these scenes. There is a side view (left) and the corresponding view of the blue Picture Plane (right). In the Cone of Vision, the Line of Sight is parallel to the ground at different heights. On the object are 3 height lines. Each of the lines corresponds with the height of the viewer's eyes. Looking at these examples, notice that the corresponding height line is on the Horizon Line and flat, while the other height lines show convergence. Most important is that as the Station Point raises and lowers, so does the Horizon Line . The changes shown affect how much of the object can fit into the Cone of Vision while remaining in 2point perspective, with the verticals perpendicular to the Horizon Line. 1. Imagine standing on a large block and looking straight ahead. The corresponding height line is on the Horizon Line and level. Since the Cone of Vision moved up, less of the base of the object is seen. 2. Standing on the ground, the whole object can be seen in the Cone of Vision. The upper height line is converging, while the middle one matches with the Horizon Line. 1. PP \\ HL I  , "'t 2. / I HL 3. \ PP HL 3 . Standing in a hole, the corresponding height line matches the low Station Point. Now the upper part of the object is out of the Cone of Vision, but much more of the ground in front is visible. Tilting the head, or when the Line of Sight When the head is tilted , the Line of Sight, Cone of Vision and Picture Plane move in tandem . In a linear perspective there will be 3point perspective. Notice the verticals starting to converge. Then take a look at the height line! The line corresponding to viewing height is still on the Horizon Line, but the Horizon Line now has moved relative to the Cone of Vision and is not splitting it in half as it did when the Line of Sight was parallel to the ground. 4. Looking up, the verticals are converging and the base of the object is no longer seen. IS not parallel to the ground 4. / HL ( I ) \ \.\ _ I r 5. L ~ ~ 5. Looking down, the verticals are converging toward the bottom and the top of the object is no longer seen. HL Scott Robertson I Thom05 Bertling I HOW TO DRAW  027 \ \  /' . I / I .l. _ \ , 028 Scott Robertson I Thomas Bertling . I HOW TO DRAW  ' j / / / / I / /" :. ~ I / / ' t Y ' /~ /'  /? CHAPTER PERSPECTIVE DRAWING TECHNIQUES The drawing skills you acquired in the previous chapters are about to be put to good use! Construction techniques will be taught in this chapter that will provide a very powerful freehand sketching arsenal. One of the goa ls of perspective drawing is to be able to find any point in space. Connecting two points creates a line and connectin g multiple points can create a curve. Lines and curves are the building blocks to make objects of your imagination visible on the page. The ability to multiply, divide and mirror lines and objects in perspective is essential. These basic techniques will be explained so you can start to create more complex drawings. 03 Drawing lines lightly is essential, since a lot of lines will be created in a small area. Stick with a single pen and do not erase! Why one pen? Switching pens on ly slows you down and breaks your concen tration . Why no erasi ng? The drawings become so dense with lines that erasing can't be done without removing lines that are needed . Instead, draw lightly so that minor mistakes can be ignored. Work on the original drawing as long as possible . You can always create a clean overlay later. Scott Robertson I Thomas Bertling I HOW TO DRAW 029 DIVISION AND MULTIPLICATION OF DIMENSIONS IN PERSPECTIVE Being able to divide and multiply dimensions in perspective is one of the key building tools used to generate drawings. These rectangles provide the scaffolding to build upon. Dividing a rectangle In half, In No measuring required. This is a great advantage because it's quite laborintensive to measure in perspective. On the left are orthographic constructions and on the right are perspective examples. The techniques that work in the orthographic view also work in perspective. perspective 1. First, define the rectangle. Make sure to stay within the Cone of Vision to avoid unexpected results. 2. Draw the diagonals by connecting the opposite corners. Draw lightly, since these lines should disappear in the final drawing. 3. To divide the rectangle vertically, draw a vertical line through the intersection point of the two diagonals. In the orthographic view the rectangle is divided evenly. In the perspective view, the rectangle is also divided evenly, but in perspective. The distance between the closer two lines is wider than the distance between the ones further away. This is called foreshortening. 4. This works equally well when dividing horizontally. Make sure that the vertical and horizontal lines follow the perspective grid. I 5. Use this technique to find even subdivisions. This construction has been further divided into 1/4 as well as 1/16 (shaded pink). 030 Scott Robertson I Thomas Bertling I HOW TO DRAW Duplicating a rectangle, in perspective Reverse the technique used to divide a rectangle in order to duplicate any rectangle. This works great for building symmetrical objects, since the duplication line can be a centerline, too. 1. Define the rectangle and the direction to multiply toward. Since the height will stay the same, extend the lines that go toward the multiplication direction. 2. Find the midpoint of the multiplication axis. This point can be found with the diagonals or by estimating the halfway point when the dividing line is horizontal or vertical. 3. Draw a diagonal that connects the far corner of the initial rectangle through the midpoint until it crosses the extended line.  14. Draw a parallel line from the intersection to find the boundary of the duplicated rectangle. 0~~'< LI I TIP : Choose the shorter line (green) to draw! There are two possible diagonals but the shorter one is the better option, since shorter handdrawn lines are more precise. TIP : Multiplying in all directions is possible with this method. o Scott Robertson I Thomas Bertling I HOW TO DRAW 031 MULTIPLYING AND DIVIDING RECTANGLES Pay attention to your craft and make sure to draw light construction lines. The rectangles can be observed automatically foreshortening. Rotate the page to get the best position for your arm to draw those straight lines. Eventual ly there will not be a need to draw all the lines; some tick marks will suffice. \\ \\~ /~: \ / // / 'r es ' I / ~ . \ ,, <........ /~/ .... / n~ ! ,/ /" ' _.'\ 1. Draw a lower and an upper line toward a common Vanishing Point. 2. Create a rectangle with two parallel lines . 3 . Now that there is a base rectangle, multiply it either toward or away from you. The rectangles wil l foreshorten automatically in perspective . Watch out when making corrections . Avoid adding multiple lines to find the right one. It will only darken the lines and draw attention to the area of uncertainty. just draw one line and correct it by making an educated guess as to where the actual subdivision line should be . This will produce cleaner drawings and will be faster! Multiplying and dividing boxes More fun are the constructions wh ere you stack boxes on top of one another. Draw through! Show th e hidden edges of boxes where they are helpful. Th is is a way to doubl echeck the constructions automatically. Should lin es not meet at the expected intersectio n, go back and check wh ere things started to misalign. Being deliberate about this will increase learn ing speed . =r_~ . ' 1·, ~!  r/ 11 032 Seen Rebertsen I Themes Bertli ng I HOW TO DRAW r'r. DIVIDING INTO ODDNUMBERED PROPORTIONS What happens if there is a need to divide by 3 or more? This can be accomplished with a very fundamental technique of transferring a proportion into perspective. In this example let's subdivide a rectangle into 5 equal units. Perspective view Top view HL 1. Define the plane. 2. Draw a line parallel to the Horizon Line, starting at the front edge of the plane. Divide this line into 5 equal segments. HL 3. Connect the last subdivision point to the end of the plane and continue the line to the Horizon Line. All lines para llel to this line will converge at this same Vanishing Point. 4. Draw parallel lines in perspective from each segment point to the new Vanishing Point. VP HL VP HL '""' 5. Draw vertical lines at each of the intersection points to transfer the subdivisions. ,..... '""' ,..... VP HL You have divided a rectangle into 5 equal sections, in perspective. Sco~ Robertson  I Thomos Bertling I HOW TO DRAW     033 MIRRORING IN PERSPECTIVE It is essential to be able to mirror elements to draw symmetrical objects. To mirror any point in perspective, use one of these rectangle multiplication techniques . These techniques are very versatile and can be mixed and matched. Mirroring horizontal planes 1. Draw a rectangle and a perpendicular mirror plane. Extend the width lines of the rectangle toward the mirror plane until they intersect it. Draw diagonals in the rectangle to find its midpoint, and draw a line from that point, in perspective, to the mirror plane. 2 . Use the mirror point to mirror the closer line to the mirror plane with the multiplication technique, then move on to the far line. e  3. Mirror the far line by using the multiplication technique. 4. A mirrored plane has now been created. This technique can be applied for other parallel plane constructions. Remember this is all based on the multiplication technique! \ ...,L + / * \ I + 034 Scott Robertson I Thomas Bertling I HOW TO DRAW Mirroring vertical planes  • @ 1. Here, the same technique is used to mirror a vertical plane . Draw diagonals to find the midpoint of the mirror plane. 2. Extend the width dimension s of the rectangle for the expected position of the mirrored rectangle and find the centerpoint for mirrori ng. 3 . Complete the construction with the diagonals and find the height of the mirrored rectangle . Darken the lines of the res ulti ng recta ng le. Mirroring offset planes 1. Set up a plane that hovers above the ground or mirror plane. Extend the lines at each of the corners in the mirror direction. 2 . Mirror the front line by using the multiplication technique. ~· 7 3 . Comp lete th e pl a ne by following th e perspective grid a nd usin g th e vertical lines to define the size of the plane. / / I 4. Darken the outer edges . Scott Robertson I Th omas Bertling I HOW TO DRAW    035 MIRRORING TILTED PLANES Mirroring tilted planes uses the same technique of multiplying rectangles. These sidebyside examples illustrate this principle . They are separate constructions, mirroring different tilted planes. 1. Set up a tilted plane and the plane to be used as a mirror. Use a perspective grid to determine where both planes are located in space, relative to each other. This is essential to stay clear on the construction . 2. Choose a point (A) to mirror. Extend the tilted plane line (red line) and the mirror plane line to mark the intersection point (B) . Drop a vertical line from the top of the tilted plane to the ground plane (C) , if it is not already there as part of the construction . D• 3. Use the multiplication technique to mirror point A , to crea te point D. D A C B B D ~ 4. Draw a line between points Band D. The angle of the plane has now been mirrored in perspective. D~ A I B .B E D 5. To finish drawing, use the perspective grid guidelines going to the LVP to transfer a few more mirrored points (E and Fl. Connect these points to create the mirrored planes. C B 036 Scott Robertson I Thomos Bertling I HOW TO DRAW 'B MIRRORING ROTATED, TILTED PLANES Sometimes drawings require dealing with planes that have a more complex position in space. Three points define a plane. To create a rectangle, the fourth point needs to sit on the same plane. This is easy to forget when drawing. Things can be sketched that are not physically possible . Check out M . C. Escher; he did it on purpose. 1 . Take a look at all four points of the tilted and rota ted plane. Each of the points moves deeper into perspective. Only two 2point sets match up in height, but none match up in depth and width. I : ! ~  2 . Ta ke the topfront poi nt and mirror it across the mirror plane . Use the rectangle duplication technique . 3. Extend the tilted centerline and cross it with the extended tilted front edge. 4 . Connect the intersection point with the already mirrored topfront corner. Scott Robertson 5 . Draw a line from the lowerfront corner, perpendicular in perspective to the mirror plane. Where it intersects the lin e from step 4 is the lowerfront corner, mirrored . I Thomas Bertl ing I HOW TO DRAW  037 o \ , i I e 6. Now find the mirrored line on the ground. Start in the lowerfront corner and extend the lin e on the ground until it intersects wi th the mirror p lane. 7. Clip the line at the correct length by extending the line that is perpendicular to the mirror plane and runs to th e lower back edge of the rec tangle. This will cross th e mirrored directional line and determine the length of the line on the ground. 9 . Find th e end point of the upper edge by extending the upp er lin e in th e back 10. Connect the open edges. You have mirrored a plane that was tilted and rota ted. of the construc tion. 1 1. Darken the edges of the planes. f I 038 Scott Robertson I Thomos Bertling I HOW TO DRAW 8. Repeat the sam e technique to find the upper edg e direction and leng th. Practicing these constructions raises awareness of patterns in the environment. Mirroring planes seems like an abstract exercise, but becomes very applicable as soon as you want to draw a car or a jet plane. There are a lot of multipl ications in buildings too . In the photo, the green construction lines run through the same points on multiple arches, which is a big timesaver. After finishing this chapter and learning about mirroring curves, take another look at this construction and there will be increased understanding . Seon Robertson I Tho mos Bertling I HOW TO DRAW     039 MIRRORING 20 CURVES Mirroring curves gives you control over organic surfaces. The base construction still relies on straight lines and perspective control. 2D curves are by definition on a plane. This plane can be tilted in 3D space. Perspective View Orthographic View ./ First, define the plane on which the 2D curve is to be drawn. Box the plane into a rectangle and mirror this rectangle in the direction you want to mirror the curve . / \~ I l~ Technique 1: 1. Draw a V that is mirrored by using the corners of the rectangle and a common point on the centerline. 2 . Draw a horizontal line from the intersection of the curve and diagonal, until it crosses the mirrored diagonal. 3. Transfer multiple points that will define the mirrored curve. J Technique 2: Instead of drawing the diagonals to the corners of the rectangle, use the middle line that was generated by the original construction. r C~~ ____~~______+,D C~+ ____~________~D B 040 B Scott Robertson I Thomas Bertling I HOW TO DRAW Technique 3: 1. In this case decide which point to mirror on the curve (A). 2. Place a diagonal through that point to the centerline (B). 3. Add a horizontal line from points C to D. 4. Mirror the diagonal line by drawing a line from B to D. 5. Add an additional horizontal line from the intersection points A to E. t Crt'_ _..... D B Technique 4: The recta ng le dup lication method works here, too. 1. Define the point to mirror. 2. Draw a vertical and a horizontal line to crea te a recta ngle. 3. Duplicate the rectangle to use as the base to mirror the point. +/: All Techniques Combined: Here all methods have been combined to show how the points define the mirrored curve. ~/./ ~ ~ Which method shou ld be chosen? Pick the technique that provides the most points in the most efficient way, and combine techniques as needed . I  . ,,/ . \ I Scoij Robertson I Thomas Bertling I HOW TO DRAW  041 MIRRORING A 20 CURVE ON A TILTED SURFACE 1. Define the tilted surface. Draw a curve on it. 2. Use the plane mirroring technique to create the mirrored plane on which the mirrored curve will sit. G o 4. Draw a line in the perspective grid direction from the intersection point until it crosses the mirrored diagonal. 3. Draw a diagonal on both planes, so that the nearside diagonal intersects the curve. There are now three points for the mirrored curve: the start point, the endpoint and the new point just created. from 6. Repeat the previous the intersection of the centerline of the tilted plane to the curve. Transfer the information to the mirrored plane. step, but this time use the horizontal middle line to find the intersection with 5 . Draw a line G the curve. These lines can be moved to wherever the transfer point is desired. 042 Scott Robertson I Thomas Bertling I HOW TO DRAW MIRRORING 3D CURVES IN PERSPECTIVE: THE 2CURVE COMBO 1. Build a full construction of the 3D curve. This is done with the 2curve combo technique on page 089. Knowing where the line is in space is essential for these drawings . 2. Start with mirroring the starting point of your curve. The rectangle is being duplicated , but skip the vertical line since the vertical is not essential to the goal. Guessing the mirror point is possible here since there is very little perspective foreshortening in the vertical line. Q 3. Repeat th is process for th e rest of the points on the curve. Mirroring some strategic points instead of all points is an option here, but in the beginning add enough points so that the curve can be found with confidence. 4. Connect the points to find the mirrored curve and draw a smooth line. If one point seems off; just compensate as needed. 5. Once the curve is mirrored it's time to find the footprint of the curve . Drop in the verticals until they cross with the extended lines on the ground. 6. Now there are two mirrored curves: one 3D curve (green) and one flat curve (black). This technique creates a 3D volume at the same time it mirrors the curve. Sco~ Robertson I Thomos Bertling I HOW TO DRAW  043  ' hI    / / ./ / / / ",:::... . .~ /' _.~=====~  .. .  '>= ;.   00  1   / 044 Scott Robertson  I HOW TO DRAW I Thomas Bertling J.  ~~  . . . CHAPTER CREATING GRIDS This chapter focuses on constructing and understanding grids. The most commonly used perspectives have Vanishing Points that are off the page. Grids help aim lines toward those Vanishing Points . Grids come in very handy when working with complex drawings and multiple objects. Understanding the basics of grids is important in being able to decide how to use photographs or computergenerated underlays. When working without a grid, a lot of effort is spent trying to aim lines in the correct direction, with the worst part being not knowing whether or not the lines were on target. Having a basic grid alleviates this problem by aiming the lines. This makes it possible to concentrate on construction and later, on design , as drawing becomes more automated . 04 Eventually you can stop using grids for the easy things , but for difficult constructions with hinged parts, rotated elements, and multiple views of the same object, a base grid is very helpful. Grids can be reused often since they are not drawn on, but rather placed under the drawings. A grid used as an underlay should be as precise as possible, and it's important to choose the most effective way to create it, based on its particular use. It can be handdrawn with a straightedge, drawn in 2D software or generated by 3D software. Creating a process and updating it on a regular basis is part of being a designer and a problem solver. Scott Robertson I Thomos Bertling I HOW TO DRAW 045 PERSPECTIVE GRID TYPES Let's look at a couple types of perspective grids that are often encountered and that are useful for drawing. It's important when choosing a grid to consider the purpose of the final drawing. Some grids are better for the ideation of an environment than for products. To make things more complicated, it also depends on the user's comfort level. There is no absolute right or wrong. These are guidelines; not th e law! 1 lPoint Perspective Drawings The lpoint perspective grid is excell ent for ideation and adding perspective to a sideview sketch. It's easy to generate and the perspective from left to right and up to down is easy to control. This makes it simple to transfer proportions, since they are onetoone and just scale smaller wh en going deeper into the perspective. However, it is more difficult to control the depth of an object in this perspective. The depth can become very shallow and the perspective can compress a lot as it gets closer to the Horizon Line. 2Point Perspective Drawings The 2point perspective grid is one of the most commonly used grids. The grid changes with the orientation of the object to the viewer. Having an individual object in 2point perspective is rather basic , but when it comes to having two or more rotated objects on the same surface things become more tricky. A 2point perspective gives 046 Seon Robertson I Thomos Bertling I HOW TO DRAW the viewer a good idea of the orientation in space of the objects being shown. The effect is similar in a 3point perspective, but the drawing complexity increases since the verticals are not parallel to one another. Having the verticals perpendicular to the Horizon Line in this perspective grid makes drawing much easier. 3Point Perspective Drawings This perspective creates the most dynamic views, while nat being too diffi cult to construct and contro l. Of the linear perspective grids, the 3point perspective loaks the most natural. This perspective is seen a lot in computer games and SketchUp uses it too. It is recommended to either estimate the convergence of the verticals or use a 3D program to create the grid . Accurate construction by hand can take a lot of time compared to generating it with a comp uter. One challenge with 3point linear perspective is that it look s odd when the H or izon Line is c ross ed (see page 062). To put 3 point linear perspective to its best use keep the Horizon Line off the page or close to the top or bottom edge of the drawing.  ' r .". , \, \ \ .. /{ ," ' , 5Point Perspective Drawings or Curvilinear Perspective The 5point perspective grid can be seen when looki ng at fisheyeIens photography. Thi s grid allows for drawing above and below the Horizon Line with coverging vertical lines. The curvilinear perspective can be found in many variations and strengths. To have a truly curvilinear perspective, all vertical and horizontal straight lines arch. It's a difficult grid to generate by hand so it's recommended to draw over a photograph , use an existing grid or use 3D software to generate a grid. Scott Robertson I Thomas Bertling I HOW TO DRAW  047 PERSPECTIVE GRID CONSTRUCTION lPoint Grid Construction with Vanishing Points on the Page This exercise wi ll teach you to create a lpoint perspective grid of squares on the ground in the 60° Cone of Vision . The sq uares en able proportional transfers to be made from a n orthographic plan in to perspective. The goal for all grids is to find the correct convergence, and place squares in perspective upon that grid. (~P HL J / / \ 1. Establish the Center Vanishing Point, 60° Cone of Vision, 4SO Vanishing Point and Picture Plane relative to the Station Point by applying the knowledge from the Perspective Terminology chapter. / Add a horizontal line th rough the CVP, and a perspective plane defining three sides of a square (red lines). Line of Sight / Draw the Line o f Sig ht from the Station Point to th e Center Vanishing Point. 2. Since there is an established Cone of Vision and the leng th of one side of a square, there is on ly one solution to finding the length of the square that recedes into perspective. SP e" / HL / Draw a line fro m point A to the 45 ° Vani shing Point. The diagonal shows the length of the square in perspective. In thi s case th e 4Y Vanishing Point is th e Diagonal Vanishing Point for th e l poin t perspective square. SP / 3. Now that the initial square is establi shed , use the rectangle multiplication technique to create a grid on the groun d . Build the grid out only as far as needed for the drawing; there is no point in filling th e page w ith unnecessary squares . ~.5 HL This grid is now ready for use. There is an automatic foreshortening w ith this grid and it could be used for a street, product or interior. The size of the square could represent 50 feet or 5 inches . It' s your choice . SP / 048 Scott Robertson I Thomos Bertling I HOW TO DRAW DIAGONAL VANISHING POINT (OVP), STATION POINT METHOD f ) Line of Sight Top View: Draw a square. Consider one corner to be the Station Point. / 15 ~V\ Draw a diagonal line from the SP through the opposite corner, which places a diagonal at 45 ° to the sides. This diagonal has its own Vanishing Point specific to the rotation of the square, which is called the Diagonal Vanishing Point (DVP). There is one for every rotation of the square. To find the correct degree of the DVP, measure the angle between the diagonal and the Line of Sight. In thi s example, the diagonal line is converging to the 1SO VP. Perspective View: SP Below is a square in a 30/60 perspective grid. Draw a diagonal through two corners. Wherever that line intersects the Horizon Line determines the location of its DVP. HL  I  Estimating the rotation degree  ,..._       ....I 4  ==. 45" / / / / ,  .~     .. ~ ./ ./ / :/ L: Corner Point • • • • • Yt ~ • 1" • B • <;;> '\ J1. r D' Dividing a square in perspective provides opportunities to create other rotations in addition to the Diagonal Vanishing Point. Take a look at the orthographic construction above. The right side of the square was subdivided multiple times to create 1/2, 1/4 and 1/8 marks by using the technique of dividing in half.  ~ :::.: e· . ~ ~ __..;;,......    _ IS <> e       '  ._ .    1> O· Corner Point This technique's advantage is that it works in perspective as well. When the Corner Point connects to the diagonal corners it produces 5 radiating lines. The blue one is 0°, the purple rotated from the blue line followed by rotations of 1SO, 2SO and 4SO . r Use this technique to find angles in freehand drawings at r increments, which is precise enough for handdrawn constructions. Scott Robertson I Thomas Bertling I HOW TO DRAW  049 2POINT GRID CONSTRUCTION WITH VANISHING POINTS ON THE PAGE Setting up a 2point grid with squares is very similar to the lpoint grid. A 45/ 45 grid is being built in this example and the Center Vanishing Point becomes the Diagonal Vanishing Point. 1. Set up Vanishing Poi nts and a 60° Cone of 60· COV HL Jc ·5 LVP Vision via the Station Point. Establish three sides of a base square (red lines). Two parallel lines are infinite and converge to the LVP. The end cap converges to the RVP and its length is defined by the distance between the two parallel lines. / SP 2. Find the size of the square by drawing a diagonal that runs toward the Diagonal Vanishing Point, which for a 45 / 45 grid is the Center Vanishing Point. The intersection shows wh ere to draw the line toward the 4SO Right Vanishing Point to complete the square. " HL ) • • .x SP 3. Complete the grid by using the rectangle HL multiplication method. Two grids have now been created in the same Cone of Vi sion . Be aware that the squares on each of the grids are not the sa me size, they are just squares. SP ~ 050 Scott Robertson I Thomas Bertling I HOW TO DRAW u.S RVP ROTATED 2POINT GRIDS WITH SAMESIZED SQUARES Using the same size of square for each of the grids will make it possible to better estimate relative size . Thi s techni que is based on the idea that a c ircle is drawn in perspecti ve and then a square is rotated around it. HL 5 • _1, rVD + 1 . Set up the perspective based upon the Station Point projection for a set of Vanishing Points to be used for the rotation. A l po int grid and a 60/30 are used for thi s example. • \ \ )' HL \ ~5 1 HL HL ~5 (v? 2. Choose and build a square in the lpoint perspective grid as done earl ier. Now place an ellipse in side thi s sq uare. The minor axis of the ell ipse will point stra ig ht down. Make sure that th e ellipse fits the square perfectly. 3. Now expand the grid as much as needed. Only one additional square was added to this construction. 4. Trace the ellipse, the Cone of Vision and the Vani shing Points on an overlay. For this technique to work, these elemen ts must be traced prec isely. If the size of the overall grid ever needs to change, make su re to enlarge all of the elem ents at the same ratio . For example, scan it into the computer and enlarge or reduce it as needed. Scott Robertson I Thomos Bertling I HOW TO DRAW  051 5. Create a square around the ellipse with the 60/ 30 Vanishing Points by drawing a line that is tangent to the circle on the ground. This will result in a rotated square that has exactly the same size as the one in the lpoint perspective. Ex pand the grid as needed . In thi s example, the square was multiplied only once. cvp 1 6 . The two grids can be combined now. Line 3~ 4S HL 11 up the Horizon Line and the Cone of Vision precisely in the same position . These grids together allow for drawing objects that are rotated against one another on the same gro und plane . HL 7. By us ing these two grids, two boxes are placed on the same ground plane. They have the same footprint and height. With the availabi lity of samesized squares on the ground this becomes a quick construction . Read the next page to learn how the height of the box was transferred . / I ( \ I Thomas Bertling t /' \~~. ~ ~ r matching and that each grid is on a different piece of paper. They can be slipped under the page to tra ce over as needed . Scott Robertson \sv .,. 8 . Add more overlays to find more grids to rotate around the circle. Make sure that the Cone of Vision and Horizon Line are 052 \ , I HOW TO DRAW   / 1 . , 45 HL TRANSFERRING SCALE IN PERSPECTIVE Transferring the height of something in perspective is one of the simplest constructions, but too often it's done poorly. Never again! This section expla ins how to use a simple Reference Point (RP) to scale a figure from the foreground back into the distance . In the first example the figure stands on flat ground. In the second example as the figure is scaled back into the distance he stands in a hole and then on top of a box . 1. To transfer the height of any object as it moves around on a ground plane in perspective, draw a line from the base of the object, in the direction it will be moving , all the way to the Horizon Line (HL) . Thi s creates a Reference Point (RP 1) . __ H_L__~____~~~~__~____r__________~~RPl 2. Draw a line from the height of th e object to RP1. 3. Draw a vertical line anywhere that intersects both reference height lines. It will be the same height in perspective at that point. position 2 4. To move the figure even further away repeat the above steps, creating RP 2. 5. To move the figure left or right just draw height lines parallel to the starting position horizon from any figure position at all. Standing on a box in the distance Standing in a hole in the distance 1. Construct the height planes from the top of the figure to RP 1, across the top of the hole and through the box. 2. Decide where th e figure should be standing in th e top view of the box, and locate thi s point on the ground plane. 3. Transfer thi s point location straight up to the top of the box. 4. Take the height of the figure standing on th e ground plane at this position and tran sfer it up to standing on top of the box. Since the vertical lines are parallel in this case there is no need to worry about any vertical foreshortening. 1. Find the figure's height directly above the side wall where it intersects with the RP 1 ground line. 2. Transfer its height up from the bottom of the hole. Make it the same height as the line from the ground plane (green line). 3. To move the figure around in the bottom of the hole just repeat the same steps as the above example to crea te RP2. The only difference now is that the bottom of the hole is th e construction ground plane for this figure as was the top of the box for the figure standing on it. Now go ahead and draw that marching band on the football field you 've always wanted to do. RP 1 RP 2 o Scott Robertson I Thomos Bertl ing I HOW TO DRAW     053 THE BREWER METHOD: CONSTRUCTING A GRID WITH VANISHING POINTS OFF THE PAGE As we create drawings, sometimes the Vanishing Points are off the page. Constructing a grid with the Vanishing Points off the page is possible without having a computer, a giant piece of paper or a photocop ier, thanks to the Brewer Method. It's named after Bill Brewer, one of our teachers at Art Center College of Desig n, who originally taught us this method. " , " 2Point Grid using 4 esta blishi ng lines  The Brewer Method ..!~p ~ ~ "I To establis h a g rid, four basic lines are needed. 1. Draw a vertical line. Think of it as the front corner of a box. 2. Draw two lines that converge toward the right. Make sure that they converge off the page. Avoid parallel lines in this case . These two lines w ill establish the Right Van ishing Point and the position of the Horizon Li ne. How much should the lines converge? It depends on what view is being created. Feel free to consult a reference image or photograph with a desirable perspective and trace the lines. 3 . Draw a line from the bottom of the vertical line toward the Left Vanishing Point. 054 Scott Robertson I Thomos Bertling I HOW TO DRAW Take a look at the small sketch above . A perspective was established with the four lines placed on the page. Imagine if the lines to the right cross somewhere off the page a t the Right Vanishing Point. The RVP establishes th e position of the Horizon Line. The HL and the left lin e also would intersect somewhere off the page. Where they intersect is the missing Left Vanishing Point. The goal of the next few steps is to d raw a line from point A to the Left Vanishing Point that is off the page, withou t extending the page. The small sketches wi ll be kept on the bottom of each step to observe the process showi ng the entire grid. • C A '" " 4. Draw a vertica l line parallel to the existing vertical. Increase the precision of the drawing by keeping these lines as far apart as possible. : . c 5. Draw a rectangle with perfect 90° corners (red lines) starting from the height of the right vertical line. Where the bottom of the rectangle intersects the line going to the LVP (point BJ, draw a vertical which creates point C. _L~./ F~ L=r .... C A ." '" ''. .. . . . !.. B 6. Draw a line from point A through point C until the edge of the page is reached. The small drawing shows that this line would eventually hit the Left Vanishing Point. Now that this perspective has been established more grid lines are needed to make this grid useful. ... .:::..:: A. '. ,~ '. .. i '. I '. ', B 7. Divide all three vertical lines evenly. In this example they are divided into quarters, however there is the option of more subdivisions. To do this, measure using a ruler or an equal spacing divider tool. scan Robertson I Thomas Bertling I HOW TO DRAW 055 1 _===r1~ 1~  I ........ ~~. x. ...__.  ,j ~ f 8. Draw a line from each subdivision point on the center vertical line, through its correspondi ng point on each of the other vertical lines, toward the edge of the paper. 9 . Extending the grid is simple. If there is room toward the lower edge of the page, take one gridunit height of each of the verticals and add it to the bottom. Connect the new points as in step 8. I I I I'vp    .i,  ......... .........  I I I I I I I 10. The last step is to extend all the lines that lead to the Vanishing Points . This creates the final grid that can be used under future drawings. 056    Scott Ro bertson I Thomas Bertling I HOW TO DRAW 0 Make a few different grids that can be deployed as applicable. Use these grids as underlays and do not draw directly on them . This will allow for multiple uses of each grid . CREATING A GRID OF SQUARES, WITHOUT DIAGONAL VANISHING POINTS 1. Use the grid that was just created as an underlay. 2. Place the correct ellipse into the bounding area (red lines). ! \ ..., 3. Close it with a vertical tangent line (green line) . This creates a square in perspective that matches the current Brewer Grid. j 4. Extend the squares with the rectangle multiplication technique. I~ This makes a vertical plane with 3 squares. Any square can be expanded in either the Y (height) or Z (length) direction. / ' iI These squares enable orthographic transfer and provide control over the drawing proportions of future objects. I I I 5. Transfer one square to the ground plane. The starting point and width are already provided via the vertical square . 11 6. Place an ellipse on the ground plane and cap the square with a tangent line, (green line) . I 7. Expand the grid again. Mirror the square across the Xaxis (width) to make a symmetrical grid. If / ~ L  These grids are the foundation of most object drawings . Feel free to make a copy of any grid in this book to use as an underlay for future drawings. ScoH Robertson I Thomas Ber/ling I HOW TO DRAW     057 WHEN TO USE A COMPUTERGENERATED UNDERLAY Some of most significant advancements in perspective drawing are 3 D modeling programs that can aid in the basic layout of perspectivedrawing grids and larger volumes. Why not then have the computer do it all? In order to use these computer programs efficiently and effectively, it's important to learn how to construct handdrawn grids and volumes first. This combination of 2D and 3D tools can be very powerful to create awesome drawings. One of the most tedious parts of starting a new drawing is laying out the perspective grid with the larger volumes blockedin proportionally. It's tempting to rush this step, but it is important to make the foundation of the drawing as accurate as possible. For purely handdrawn grids, the POY often doesn't come out exactly as desired, or the amount of convergence is off and emulates the wrong camera lens. In that case you either carryon with the wrong POY, or start over. Above is a cityscape underlay modeled and rendered in MODO. The total time to model and render this image was 30 minutes, so the production advantages of working this way to get started are immediately evident. On the facing page (top), Mark Castanon built a 3D underlay of an interior scene in SketchUp, which is probably the simplest and least expensive of the 3D modeling and rendering programs with enough features to make it worthwhile to learn and use. Below is what he drew over the top of that underlay. This is a great example of modeling just enough of what is needed to establish 058 Scott Robertson I Thomas Bertling I HOW TO DRAW A 3D computer program is fantastic for quickly blocking out proportions of the large volumes, moving the POY around, and even trying different camera lenses before committing to doing section surfacing and detailing. However, when starting to use these types of programs, don't forget that you have drawing skills! It's easy to get sucked into modeling more than is needed, and to get carried away adding details or more complex forms that would be faster and easier just to draw. Hours can be spent messing around on the computer when all that was really needed was one good 3/4 view to get started. Like anything, using a new tool takes practice. The examples on the following pages were done by some of our former students at Art Center College of Design. All of these artists are now working professionals. a POY, proportions and a perspective grid before jumping into the final drawing. The amount of detail in the hand drawing, along with the varying line weights used to accentuate the overlapping objects in the scene and their respective silhouettes, makes this drawing more visually appealing than had the top image been finished only in the computer. Yiew more of Mark's fine work at: http://markcastanonportfolio.blogspot.com Scott Robertson I Thomas Bertling I HOW TO DRAW  059 Rustam Hasanov built the SketchUp model to the right and then did the overlay drawing below. Again , only a minimum amount of computer mode li ng was needed to rough out the scene before sketching over the top of it. When drawing over a computer underlay, it's easy to extend the guidelines from th e underlay information and repos itio n elements, as well as add new o nes. By varying the line weight, Rustam did a great job of helping the eye better understand the shapes in the scene. View more of Rustam 's ni ce work at: http: //cargocollective.co m/ ru stamhasanov 060 Scott Robertson I Thomas Bertling I HOW TO DRAW OTHER BENEFITS AND WAYS TO USE AN UNDERLAY When really getting into drawing from your imagination , especially once you are a professional designer, a big part of that job is to provide endless variations that visually solve the same problem ... and that mean s lots of sketches. In this series, John Park makes this repetition a little easier by copying or printing a very light version of part of his original drawing , then sketching over each one and working up different aesthetic options . The lines of the original are so light compared to the newer, heavier line work that they don 't distract from understanding the new concepts. View more of John 's handy work at: http ://www.jparked.blogspot.com Scoff Ro bertso n I Thomas Bertling I HOW TO DRAW  061 NOT ALL PERSPECTIVE GRIDS ARE CREATED EQUAL You might wonder about traditional drawing becoming obsolete with the popularity and ease of using 3D programs. The answer is not straightforward . In the worlds of architecture, industrial design, and entertainment, it's true that the most progressive development teams are utilizing a large dose of 3D tools to model their objects and environments in stead of drawing everything by hand, but the best use of these computergenerated renderings and how they are set up relies on having a deep knowledge of perspective drawing. Having strong perspectivedrawing skills opens up the many ways these types of renderings can be used . Looking ahead , all designers will need to have some 3D computer modeling and rendering ability, and the nature of how traditional media sketches are used will continue to morph and be abstracted and blended into a hybrid pipeline of digital and traditional skill sets. Looking at the imag es on these pages, there are two pairs of scenes. The first image in each pair was rendered in MODO with the camera set to an 18mm lens with no distortion, and a 90° field of view. The second image in each pair was rendered with a 0.1 lens distortion. You can see clearly what happens to the perspective grids in each case. The straightline perspective grids with no lens distortion are typical in videogame environments and 3D programs that don't have a lensdi stortion option. What the computer programs do is look at how much of the scene is above or below the Horizon Line, and then all vertical lines converge to a Vanishing Point located on the side that is being shown the most. This is a weird distortion, and the only place you ' ll ever see this effect is inside digital environments. In real life, when looking at a physical building projecting into the sky, the vertical lines converge to a Vanishing Point high in the sky, and the same building 's vertical lines cross below the Horizon Line and converge to a VP far below. This is clearly not the case in the videogame examples. In order for vertical lines to converge above and below the Horizon Line, lens distortion must be added. This lens distortion bends the appearance of the lines and creates curvilinear perspective grids. Why does this matter? If the goal is to draw an environment that has a more natural feel and more closely matches what is observed in photographs and with the naked eye, then a curvilinear grid would be used . But if the goal is to design game environments, a linear grid is needed. A good grasp of perspectivedrawing fundamentals allows for use of either grid as an underlay; then a program like Photoshop can be used to add details in perspective. If strong drawing skills are lacking, this forces everything to be created in the 3D modeling program with many possible errors. So the blending of 3D modeling , rendering , and then 2D drawing and painting over the top of these types of computergenerated imag es is currently the most productive way to work profess ionally. Linear perspective, found most commonly in digital videogome environments. Curvilinear perspective, found most common ly in photographed environments. Note how even with the Horizon Line close to the center of the image, the sky fills a slight majority of the frame versus the ground. This skews the convergence of the vertical line to above the horizon, making the vertical lines that continue below the horizon line divergent. To add an object like an airplane or a character in the foreground below the horizon, using this type of distorted perspective grid would look odd when viewed by itself but acceptable in relation to the surrounding scene. With cameralens distortion applied, as above, the horizon line has bent a little due to the fact that it is not exactly located at the center of the frame. If it were exactly centered, it would remain straight and horizontal. The reverse bend is happening in the image on the facing page for the same reason, but with a skew in that image to show mostly the ground instead of the sky. Also note that the vertical lines in it converge above and below the horizon line, as expected. 062 Scott Robertson I Thomas Bertling I HOW TO DRAW The complexity of sketching with a curvilinear grid , and the diverging vertical lines problem of the videogame grid, is the reason to draw with 1 and 2point perspective grids with simplified vertical lines that are truly vertical , even though both of these examples show that's not the case. When the entire frame is filled with the environment below the horizon or above it, use a 3point perspective grid. 1 and 2point perspective grids are really simplifications of perspective drawing that have a lot of limitations and their own distortion problems. However, they are simpler to draw and they work well enough , so they are the default grids for doing production work where speed is more important than true accuracy. The entire design team also understands that these simplified grids are not exactly truetolife but rather a kind of designer shorthand in creating the illusion of 3D perspective space on a flat surface. Scott Robertson I Thomas Bertling I HOW TO DRAW  063 Both pages drown by Roy Santua The 3point perspective grid for the above sketch is similar to what would be generated by a 3D computer program . From this POY it is very near to what would be observed in reality, without needing to add curvilinear perspective. 50 for this kind of view, a computergenerated perspective grid works great! The sketch on the opposite page (bottom) shows the influence of a perspective grid that came from a computer program, which is exactly what our former student Roy 5antua wanted for this interior space 064 Scott Robertson I Thomas Bertling I HOW TO DRAW he was designing for the digital world. It would feel odd to add a foreground obiect to this scene because the vertical lines would diverge below the Horizon Line . In that case, it would be advised to use a 1 or 2point perspective grid so the vertical lines could be drawn perpendicular (90°) to the Horizon Line. Drawing in perspective is never exactly perfect and tradeoffs will be encountered, so with an increased knowledge of these pros and cons you can make the appropriate decisions in your own work. Cutaway View DlNING AKEA Ro{ P. 5AI'ffiJ A Vl5c,oM 7 CA The drawing to the left is an excellent example of a cutaway view, an informative type of perspective drawing used to communicate one's design to others. Part of the foreground surface is literally cut away to expose what is behind or beneath it. As an example, Roy has cut away the roofing to expose the framework of the structure, and he has also cut away part of the roof and interior wall to reveal the arrangement of the furnishings and expose more of the rooms' interiors. These types of drawings provide a lot of bang for the effort as they communicate many things at once. View more of Roy's great work at: http:// rsantua.blogspot.com f. Scott Robertson I Thomas Bertling I HOW TO DRAW 065 Draft Views Draft views, also called orthogonal views, show an object without perspective. By getting rid of the perspective convergence, dimensions can be added to the drawing that make it possible to build it to any size. The goal here is the accuracy of dimensional information. Both of these draft views are of the exact same ship, in top view and in side view. It's often a great idea to draw draft views of an object before attempting to sketch it in perspective. Sketching a single draft view is much easier than doing it in perspective, but it's also easy to draw things in a draft view that will cause problems when trying to translate ...! the forms into the other views and ultimately into perspective. It's easier to concentrate on design when not worrying about perspective, but the disadvantage is that once the draft view is finished , there is only one view of the object. I ;/ I I I ~~ Both pages drow n by Roy Sontuo 066 Scott Robertson I Thomas Bertl ing I HOW TO DRAW ....__\ ~ nf I ', The advantage of sketching a perspective view of an object is that all of the draft views are actually being drawn, influencing design and form simultaneously. Here Roy has focused on sketch ing certain areas of the ship from a variety of different perspectives. All of the steps to do these drawings are the same. Start with build ing a good perspective grid , then work on the bigger surfaces, and add the smaller objects last. \ The scale of the object makes no difference and any size object can be drawn accurately using the same basic perspectivedrawing principles . Always start with a good set of guidelines. Use section lines to figure out the surfaces and silhouettes of the objects in the drawing . When constructions are rushed and guidelines not used , drawings become looser and less accurate. This is fine for quick sketches, but when a more precise drawing is required , just remember to take a deep breath and be patient while you work through the construction process . Scott Robertson I Tho mos Bertli ng I HOW TO DRAW     067 / ~I L'~ . . ~ ~,,J?, """"~~ ASSEMBLY AND EXPLODED VIEWS Both pages drawn by Roy Santua Assembly and exploded views communicate how things go together. These can be very specific. The drawing on this page shows a POV that communicates a lot about the assembly and arrangement of the props and furnishings in a sce ne. Accompa nying this in for mati ve a ssembl y d rawi ng a re tw o draft vi ew s o f the sa me main ob ject w ith th e cage highlighted with co lo r a nd a g raphic ex pl a ining the plann ed move me nt o f the cage . Also notice the backgrounds that Roy added which make the silhouettes of the objects pop out a little more than they would have if they had just remained on whi te paper. To add a backg round , eith er make a copy of the orig ina l d rawing and use markers to bl ock in th e va lu e a nd co lo r of th e backg roun d o r scan the original and do th e sa me thin g in a computer program like Sketchbook Pro , Painter o r Ph o tos ho p . Good exploded views like the d rawings to the right are abl e to communicate without notes and arrows, much like the informative drawings i n IKEA assembly directions . The POV is chosen not with an eye toward drama or making us feel like we are in the scene but purely for the best w ay to communicate how the objects are made, assemb led or arranged . If done well , these dra wings are wor th mo re th a n a th o usand wo rd s in any lang ua g e. Looki ng at Roy 's lin e wo rk , notic e how inside eac h draw ing he vari ed th e li ne we ig ht to he lp th e viewe r und e rsta nd th e smaller overlappin g eleme nts of each o bj ect. To construc t an exploded view, start by drawing the ob ject in its assembled position and then do an overlay using tracing paper while you move and slide the exploding parts by using perspective guidelines. Gen erally the exploded parts should not move diagona lly; instead, move the parts linearly in the perspective. M ove th e b igger p ieces fi rst and the n ex plode off the sma ll er parts fro m th ese larger o nes li ke the drawi ng o ppos ite (top). Use over laps a nd stro ng outlining wo rk to he lp communicate th e relati o nshi ps o f th e fl oating parts to each oth e r. It's not uncomm o n to end up w ith lots of layers of tra cingpape r o ve rl ays of the var io us pa rts when compos in g the se d raw ings. 0 68 Scott Robertson I Th o ma s Bertling I HOW TO DRAW Scan Robertson I Thomas Bertling I HOW TO DRAW _ 069 070 Scott Robertson I Thomas Bertling I HOW TO DRAW CHAPTER ELLIPSES AND ROTATIONS Ellipses are simply circles in perspective. The accuracy of a ell ipse can make or break a drawing so this entire chapter is dedicated to learning how to draw them properly. Drawing ellipses is the basis for hinging flaps, rotating objects and constructing spiral staircases. But best of all , drawing ellipses helps 05 to generate excellent perspective grids based on perfect squares multiplied in any direction. The ability to place a freehandsketched ellipse on any minor axis is the primary skill needed before moving into this chapter. Review this skill , and how to practice it, in Chapter 1 . Scott Robertson I Thomas Bertling I HOW TO DRAW  071 ELLIPSE BASICS AND TERMINOLOGY Minor Axis Ellipse anatomy The minor axis is the most important line in the construction of circles in perspective. An ellipse has a minor and a major axis. The minor axis divides the ellipse in half across its narrowest dimension and the major axis divides the ellipse in half across its longest dimension . Major Axis Ignore the major axis The minor axis always intersects the center of any foreshortened square drawn around it. The major axis almost never intersects the center of a foreshortened square drawn around it. For this reason , the major axis is of no help when placing an ellipse into perspective and can be ignored. Minor Axis ~   ~' The minor axis is key The minor axis has another important perspectivedrawing feature. It always points to the Vanishing Point that is perpendicular to the ellipse's surface being sketched . This makes the minor axis like th e axle of a wheel. Ellipse degrees I The degree of an ellipse is the measure of the angle of the Line of Sight into the surface of the ellipse . To better understand the degree, imagine looking straight ahead at a row of circl es on the ground , with your Line of Sight parallel to the ground plane . The degrees of the ellipses as they move toward the Horizon Line will be less than those directly below your feet. A 0 " ellipse would be on the Horizon Line . A 90" ellipse is a perfect circle directly below. The other degrees are found in between. • ! = , • • • + ~ I i 0° 15 ° 072 Sco~ Ro bertson I Thomos Bertli ng I HOW TO DRAW I I 0 20° 30° 50° 90° PLACING A CIRCLE IN PERSPECTIVE OR DRAWING ELLIPSES Placing ellipses on surfaces With the knowledge that the minor axis is actually a 3D element of the ellipse, we are ready to place circles on surfaces in perspective . Remember that the minor axis is like the steering column to the ellipse's steering wheel ; they are perpendicular to one another. THE MINOR AXIS IS ALWAYS PERPENDICULAR TO THE SURFACE ON WHICH THE CIRCLE WILL BE PLACED!!! 1. Define a vertical surface upon which to draw the circle in perspective. Draw a line that is perpendicular to this surface . This line will be the minor axis of the ellipse. 2 . Draw an ellipse around the minor axis and estimate the degree of ellipse . Then , draw a bounding box around the loose ellipse . The bounding box tests if the correct degree of the ellipse was drawn. / / 2.  .t~ ~ , V7\. 3. I I I ~! ~ I I J 3 . The side view of the circle on the surface shows the conditions that need to be met to find the correct degree of ellipse. There is only one circle that will fit between all these lines. Here are the conditions that the circle and the ellipse need to fulfill :  The circle touches the left vertical line halfway, (cyan point).  The circle touches the upper and lower line at points that are vertically aligned , (magenta points).  The circle touches the closing vertical line at the halfway point as well: Connecting the front and back points creates a parallel line to the upper and lower borders, (cyan line) . All three lines share the same vanishing point. 4 . Let's try this! Draw a light ellipse and check if it meets all conditions . Should it not meet all conditions adjust the degree of the ellipse to become larger or smaller until all conditions are met. Then clean up the drawing with an ellipse guide . 4. / ,/ \~ Degree too small Always ensure that the minor axis is correct. This is the condition that must be met before checking the other requirements . The vertical midpoint is not met (cyan point) and the touching points are not vertically aligned. The ellipse degree needs to be increased. Sketch a larger degree ellipse. Degree too big The touching points are not vertically aligned . The ellipse degree needs to be decreased. Sketch a smaller degree ellipse. Scott Robertson Degree correct All conditions are met. Closing off the back with the vertical line defines the back vertical halfway point. Connecting the two halfway points creates a (cyan) line that points to the correct Vanishing Point. Take the ellipse guide and clean up the ellipse! I Tho mas Bertling I HOW TO DRAW  073 CREATING A CUBE USING ELLIPSES Now that you know how to place circles in perspective as ellipses, it becomes possible to create cubes in perspective. This is very useful for both creating grids and also controling the proportions of objects in perspective. This technique assumes that you are proficient at drawing an ellipse and then drawing a perspective square around it. Practice over a grid until you are comfortable with the technique. Let's draw some cubes . . 1. Define the height and the fro nt corner of th e cube over a perspec tive grid . This establi shes the minor axis Vanishing Points for the ellipses. 2. Place an ellipse on each sid e, tangent to the corner. M ake sure to use the correct minor axis w hile drawing each ellipse and then adjust the degree and size to meet all conditions. Ellipse guides don 't a lways have th e perfect size or degree so some compensation for this might be required. 3. Add vertical lines tangent to the ellipses to define th e proporti ons of a cube. Add the top surface by following the perspective grid defined by the previous lines. OFFSETTING ELLIPSES Offsetting ellipses to create more complex assemblies becomes a lot easier once th e location of th e ellipses' minor axis is known . Use an ellipse guide to modify the size of the ellipse, while keeping the degree the same, as long as these smaller and larger ellipses are kept rather close together along th e minor axis. When moving far along th e minor axis into deeper perspective, remember to change the degree as well. Just redraw a defining perspective square to doublecheck the degree, as was explained o n page 073. 074 Scott Robertson I Thomas Bertli ng I HOW TO DRAW When drawing cars, make sure to know which way the wheels are tu rned. If they are aligned straighta head, th e minor axis of the wheel wi ll match th e grid of the car body itself. However, if the wheels are turned , the correct minor axis relative to the car body must be found before drawing the ell ipses. Always remember that drawing ellipses properly requires on ly two thing s, in this order: 1) a correct minor axis, followed by 2) the correct degree. If the minor axis is not correct no amount of adjustment to th e degree wi ll ever make the ellipse look right. HINGING AND ROTATING FLAPS AND DOORS ., Hinging and rotating elements are possible once ellipses can be accurately sketched in perspective . These drawings are shown in raw form , without cleanup, so that the construction of the rotations is obvious. Blue Lines: Entire construction grids can be rotated and redrawn by rotating as many points as are needed to help redraw the rotated surfaces. This is a bit more difficult than just rotating the flaps of a box but it's the same construction Green Lines: The minor axes, which are the hinges in the drawing , are marked in green. For each rotation, find the hinge that turns the object. Ellipses are drawn upon these hinges to calculate the rotated dimensions of the flaps. technique relying on the use of accurately drawn ellipses. Red Lines: The paths of the actual points that rotate in the drawings are marked in red. Sometimes these construction ellipses are not fully drawn since the entire ellipse is usually not needed to help construct the rotation. Be mindful when drawing by hand that these are still guesses, and can always be cleaned up with an overlay. o Scott Robertson I Thomes Bertling I HOW TO DRAW 075 SUBDIVIDING ELLIPSES Being able to subdivide an ellipse will help with drawing things like spiral staircases , equally spaced links on a tank tread , hour positions on a clock face, or teeth around a gear. l __ J / Keep your pencil and precision sharp to get the best results. 1. Set up the ellipse in perspective, which is to be subdivided . Take the vertical height of the ellipse and extend it to the side. Close the lines with a halfcircle. / .' / __  t 2. Add subdivision lines starting at the center of the semicircle by using a protractor. In this example the circle is divided into 22S increments. Here, only a quartercircle is subdivided , but feel free to add more increments as needed. p.   . l I 3. Draw horizontal, parallel lines through the intersection points of the circle over to the vertical line of the ellipse. At each of these points on the vertical line tangent to the ellipse, extend the lines into perspective . Make sure that these lines converge to the proper Vanishing Point. 4. Mark the intersection points of the parallel lines and the ellipse. Connect the intersection points of the ellipse through the center of the ellipse and continue them to the lower half. 076 Scott Ro bert son I Thoma s Bertl ing I HOW TO DRAW ............ \ t  ... ..... \ Spirals To create a sp iral, like a spiral staircase, use th e subdivision of ellipses. A sp ira l sta ircase has even "pie slices" for the stair treads th at are positioned at the same height increments to each other. Let's tackl e one thing at a time . • ._        • e • e / e \ e. 1. First, subdivide th e ellipse into the number of steps desired. The same subdividing technique is being used, but thi s time th e ellipse is on the ground. Therefore, use the horizontal width line tangent to the ellipse instead of the vertical height line. .   2. N ow, prepare to lift the stairs. Each step wi ll have a leve l surface, but each of its three corners are at different perspective depths. To construct this, mark lines that will help to find the correct height in perspective depth. First, mark the height of the steps in the center of the staircase. Then , transfer this height to the side (red lines), out of the way of the construction. Next, draw a vertical line and mark the intersection points. Finally, to extend the transferred height into perspective, add parallel lines tha