new perspective systems

NEW PERSPECTIVE SYSTEMSSeeing the total picture.One through six point perspective.

Authored and published by Dick Termes.

Copyright© 1998 Dick Termes.

Rt 2Box 435B, Spearfish SD 57783

All rights reserved.

for helping me find the way

for suggesting I needed to show where six point comes from,

hanging in therewith me, and

for helping me with the design of this book.

Dedicated to:Victor Flach

Ken Scholz

MarkieLangKabe

Bill Fleming

IN T RO D U C T I O N .….5NO N-PE R S P E C T I V E .….8

ON E PO I N T PE R S P E C T I V E ….10T WO PO I N T PE R S P E C T I V E ….14

TH R E E PO I N T PE R S P E C T I V E ….16FO U R PO I N T PE R S P E C T I V E ….18

FO U R PO I N T CO N T I N U O U S PE R S P E C T I V E ….21FI V E PO I N T PE R S P E C T I V E ….26

SI X PO I N T PE R S P E C T I V E ….30TH E GR I D S ….33

Contents:

4 • T E R M E S • NEW PERSPECTIVE SYSTEMS

Seeing the total picture • T E R M E S • 5

Have you everbeen in placeswhere you go crazytaking photo-graphs but whenyou get back homeand develop the

photos you just don't feel theyeven come close to capturingwhat you saw? I would like youto be able to walk into a won-derful environment that is excit-ing in every direction and knowyou can capture it TOTALLY

in your drawing. Thismanual gives you new waysto see and draw the world

all around you. By firstbuilding upon traditional one

and two point perspective, youwill be able to expand and cap-

ture more and more of your visu-al landscape surrounding you.Surprising as it may seem, whenyou finish this manual, you willhave the insights to draw every-thing from top to bottom and allaround.

Webster's Dictionary defines per-spective "as the science of paint-ing and drawing which representsobjects in their natural shape andappearance, the true relationshipof objects or events to one anoth-er." Most people have observedthat: 1) objects diminish in size asthey recede farther from the eye;2) that parallel lines appear toconverge; and 3) that in generalthe appearance of objects differsfrom the reality. The rules gov-erning these differences are deter--


mined by the principles of per-spective. Linear perspective, onwhich we are focusing, is used notonly by artists for drawings andpaintings, but by architects, andinterior designers to help capturethe visual world in a very realway.

I believe an integral aspect oflearning to draw with perspectiveis the use of background grids.These grids, which are includedin the manual, will help you learnmore easily the six systems of per-spective. Feel free to copy thegrids in this manual, but pleasedo not copy the manual.

Drawing on a sheet of typing orcopy paper taped over the gridswill show the flow of the projec-tion direction and help you tolearn quickly where the cubicallines should project. The gridswill help you learn the system ofone through six point perspective

Throughout this manual, I will usethe directions of the compass totalk about the different vanishingpoints as they are found aroundus: North, East, South, West,Zenith (above or top) and Nadir(below or bottom). These direc-tions could be any six equal dis-tance points around us but for thesake of keeping it simple I will staywith the compass directions.

The basic rules of traditional-ly defined perspective wereformulated in the fif-teenth century in Italyby Piero dellaFrancesca, LeonBattista Alberti andothers. In the fif-teenth century view, ifthe horizon around youwas imagined as 360degrees, two point perspec-tive drawings and paintingsheld 90 degrees of the visualworld. In other words, their

paintings could capture everythingbetween the North point on thehorizon to the East point. I haveexpanded this discovery of perspec-tive in order to allow the artist tocapture more and more of this visu-al world. With six point perspec-tive, drawings and paintings reveal atotal view encompassing the full360 degrees in all directions.


My way of learning and teaching perspective focus-es on the cube because most of our constructedworld grows from this geometric shape. Our citiesare organized on a 90 degree cubical order.Buildings are typically cubical, as are the roomsconstructed within. Extending that further, we fillour cubical rooms with cubical-shaped objects -couches, television sets, radios, tables. We haveindeed built some incredible structures with thesimple cube. When I began my study of perspec-tive, I was fascinated by the changes that tookplace in the lines of the cube as they took on moreand more vanishing points. I discovered that thelines that construct the cube start to curve whenyou reach four point perspective.

To follow this logic, let us first analyze the cubewhen it is not in perspective. The cube or hexahe-dron, is made up of three sets of parallel lines.When these cubical lines are projected out fromthe cube, they go in six directions (fig. 1a). Oneset projects to the North and to the South, anoth-er set projects to the east and to the West; and thethird set of lines projects Up (Zenith) and down(Nadir)(fig. 1b).

Included in this manual is a NON-PERSPECTIVECUBE GRID (fig. 2). Notice three sets of parallellines, these will help you with your drawing.

Practice drawing groups of cubes on a sheet ofpaper placed over the cube grid on page 34

To do this, tapea sheet of typingor copy paperover the gridpaper. As thegrid lines showthrough onyour paper,begin drawingcubes.Experiment with thelength of the cubes.These cubes can be long or short cubes or anylength you can come up with. The grid can havelines added between them wherever you want.Remember to use the same three sets of parallellines shown on the grid for all cubes.

Try to have all of your cubes consistent through-out your drawing - you are either looking down atthem all or you should be looking up under them.This is very simple, but it teaches you the sixdirections cubes can project in space within thedrawing. Later, this thinking will help you to cre-ate very complex perspective drawings.

Another exercise you can try is to subtract cubicalholes from some of these cubes. Use the samethree sets of parallel lines but use them to subtractrather than add to turn them into realistic objects.Remember when you learn to draw the cube, youare also learning to draw the many thousands ofobjects that use the structure of the cube: televi-sions, radios, books, houses, desks, shelves, furni-ture, and the like.


One point perspective (fig. 4) takes one of the three sets of paral-lel lines of the cube and projects them to a point, a VANISHINGPOINT. We will say this is the North direction. The other twosets of lines of the cube continue to run parallel and unaltered.This vanishing point can also be considered where your eye islocated in relation to the objects found on this page. This loca-tion of the eye or (vanishing point) becomes the place wherecubes shift across in space to show their opposite side, from rideto left and from above you to below you (fig. 5, pg 12).

Lay a sheet of paper over the one point perspective grid (pg. 35).As you are drawing a group of cubes, start with the front squareside of the cube. Add the rest of the lines back from the cornersof the square (fig. 6).

On another sheet of paper, draw an inside (fig. 7, pg. 13) or out-side (fig. 8, pg. 13) scene. Non typical views, such as drawing ascene of a room through the transparent floor, can also comefrom this grid (fig. 8b).


Fig.5

Notice how the sides of the cubes shift asthey move by the single vanishing point.

A one point perspective drawing of a persondrawing his complete room.


Two point perspective uses two ofthese three sets of parallel lines of the cube. It projects one setof parallel lines to the North point and the second set of parallellines to the East vanishing point. In two point perspective, thethird set of lines continues to run parallel. In this case, they runstraight up and down. Notice the two points we are using.North and East, are 90 degrees of our horizon. This HORIZONLINE is also the EYE LEVEL LINE. The eye level is better touse because if you are underground or in outer space there is nosuch thing as a horizon but there always is a location of your eyes(eye level).

Practice using the two point perspective grid (fig. 9) to drawsome cubical objects (fig. 10). Continue on with creating aninside or outside cubical scene (fig. 11a and 11b). The two pointgrid is on page 36.

Fig. 9Horizon line is fine if you are on Earth but from outer space, eye level is all you have.

Fig. 10


Fig. 11aInside scene2 point perspective

Fig. 11bOutside scene2 point perspective


Three point perspective uses all three sets ofparallel lines of the cube. Similar to two point perspective, one of the setsof parallel lines aims toward the North point and the other set aims towardthe East point. The third set of lines project toward the Nadir point (belowyou) (fig. 12) or the Zenith point (above you) (fig. 13a). Either Zenith orNadir can be used with the same grid just by spinning the three point per-spective grid 180 degrees. You can project all of these lines with a straightedge.

Which direction you use the grid would determine whether you want to belooking up or down at the cubes in your drawing. This drawing is mostproper if held to the triangle shaped canvas or paper. First try to draw agroup of cubes with the three point grid on page 37 (as illustrated in fig.13b). When you have an understanding of this, play with an outside (fig.14a) or inside (fig. 14b) realistic scene. If you go outside the line betweenthe points you'll discover some distortion. You might, however enjoy thisdistortion.

Some three point grids can beturned so the cubes can be seen

from above or below.


Four point perspective can be thoughtof in a couple different ways. First, we use the same logic it takes toget to three point perspective. But if the cube we are looking at isvery tall and it projects above you and also goes below your eye level,these up and down lines must project toward two points (fig. 15).Not only does the cube look far in the middle, it also seems to getsmaller as it goes above and below your eye level. These lines, whichused to be the up and down parallel lines of the cube, are now curv-ing in like a football coming together at the Zenith and Nadirpoints. If you were on the twentieth floor of a skyscraper, lookingout the window at another skyscraper, forty stories high, you wouldsee this type of effect.

Two practice, slip the four point perspective grid under your paperand draw some cubes using the grid on page 38 (see fig. 16). Nowmake some cubes into a city scene. Notice the examples (fig. 17a,17b, and 17c).

Notice two sets of lines still run straight liketwo point perspective but the up and down

lines project toward two points

fig.15 fig.16fig.17aIllustration by Jan Stevenson


Another way to think of four point perspective is what I callthe continuous four point perspective. This system keeps the Zenith and Nadir lines ofthe cube actually parallel, and curves the North to South and East to West lines of thecube (fig. 18).

Try drawing cubes using the grid on page 39 (see fig. 19). Notice the North, East andSouth vanishing points. The grid covers 180 degrees of the horizon around you. You canalso try making two copies of this pattern, taping them together edge to edge so; you cancapture the directions of North, East, South, West and back to North (fig. 20). This dou-ble grid allows you to stand anywhere in any cubical room and produce a 360 degree stripof the room. It misses, however, some of the floor below and the ceiling directly aboveyou.

The results of drawings made from this longgrid paper can be displayed on the flat sur-face or cylindrically. It can be rolled up andtaped together to show the total wraparoundview. To achieve this total view, you'll needto start and end with the same spot on theeye level line. You can view it from theinside or from the outside of the cylinder(fig. 21a). Note the outside scene (fig. 21b,pg. 23) or inside room (fig. 22, pg. 25)makes a full revolution.

Something else to look at in the room exam-ple is how the ceiling tile and floor patternsfit together. In Figure 21c, (pg. 24) you canstart with a North direction and you turn tothe East, South, West, then back to North,East and South again. You turn around inthis drawing one and one half times. If youlook closely at the repeated walls, you alsowill find you are seeing the walls from differ-ent locations within the rooms (fig. 23b, pg.25).

Using these two continuous four point per-spective grids, draw an inside and an outsidescene (see fig. 23a, pg 24 and fig. 21b atright). If you want a drawing which shows aroom where you are rotating in many circles,tape more and more grids together. Eachrevolution can show time passing almost likea moving picture (fig. 21c, pg. 24).


Fig. 21bThis shows a full view of rotation 360 degreesaround you. As you can see, the right side of theClosely at the repeated walls, you also will find youare seeing the walls from different locations withinthe rooms (fig. 23b, pg. 25)

Using these two continuous four point perspectivegrids, draw an inside and an outside scene (see fig.23a, pg. 24 and fig. 21b). If you want a drawingwhich shows a room where you arerotating in many circles, tape moreand more grids together. Each rev-olution can show time passingalmost like a moving picture(gig. 21c, pg 24).drawing fits with the leftside. Notice the onlystraight lines are theup and downlines.


Fig. 21b

This shows a

full view of

rotation 360

degrees

around you/

As you can

see, the right

side of the

drawing fits

with the left

side. notice

the only

straight lines

are the up

and down

lines.


Continuous four point perspective uses a curvedline grid. The grid helps to show you which lines

curve and how much. It is important to notehow the floor and ceiling tiles fit. Walls bulge

out and corners are the furthest away like itwould be in a real room.


Fig. 23b Notice how objects repeat but are seen from a different position. This technique implies either that the viewer is "everywhere at once" or is moving through time (the fourth dimension). Student drawing by Jan Stevenson.

Fig. 22


This system of perspective, using fivepoints, creates a circle on a piece of paper or canvas. You nowcan illustrate 180 degrees of visual space around you. It cap-tures everything from North to South and from Nadir toZenith. Think of yourself inside a really exciting visualenvironment like St. Peter's Basilica in Rome. Youbring a transparent where along with you. When youfind a spot in the Basilica where any direction youlook is visually exciting, you place the sphere thereand imagine you could somehow step inside thistransparent ball. With one eye you look from thevery center of the sphere at the Basilica all aroundyou. Now paint what you see outside the sphereonto the inside surface (fig. 24a, pg. 30).

A five point perspective scene would stop at half ofthe sphere (one hemisphere). This five point gridwill allow you to do the same thing. One of thepoints, North we'll say, is in the middle of the circleand four other points are equal distant around theoutside edge of the circle on the same horizontal linethat the North vanishing point is. The other twopoints are directly above and below the North point onthe top (Zenith) and bottom (Nadir) edge of the circle(fig. 24b, pg. 27).

A cube or cubes drawn in this space project with straight linesinto the center point like a one point perspective The second set oflines curve from the West point to the East point. Depending on where thecube is located within the circular sheet of paper, these lines change their shapefrom a straight line, if it is located in the center of the circle, to more and moreof a curving line as it moves out to the edge of the circle. The other set of linesdo the same, but project from the Zenith point to the Nadir point (fig. 24d). Inother words, the lines of the cubes drawn have two sets of the parallel lines curv-ing, and the other set projecting straight to the center point. A fish eye lens hasthis kind of effect.

Draw a group of cubes within this circle grid to see if you understand this fivepoint concept (fig. 24d). If these small cubes were made into individual houses,you would have an example of an outside scene (fig. 24e). To create an insidescene, start with the basic inside cube room. It is easiest to start with the dis-tant rectangular wall first (fig. 25a). Next, draw lines out from the four cornersof the rectangle. Now add doors and windows and other details to these insidewalls. All windows and doors and the thickness of the windows and doors usethe same projection vanishing points as the walls use (fig. 25b). Notice how fig-ure 27 on page 28 shows you how the center vanishing point of this room couldbe straight down. The center point could also be the ceiling or the north, east,south or west wall. Try any outside cubical scene (see fig. 28, pg. 29).


Fig. 24d, 180 degrees of your view above, below to the east north and west.

Five point perspective is a hemisphere of view.

fig.25a fig25b


Fig. 27 Looking straight down

on the floor from a ceiling view. Student draw-

ing by Jan Stevenson.


The sixth (South) point is missingfrom five point perspective drawings. With five point we get half, or ahemisphere, of the visual world around us. If you wanted to get the restof the picture, the whole picture that is, you must add that last vanish-ing point. You would have to turn around and look at the roomBEHIND you to see the rest of the room and to find that last point. Ifyou were back in the transparent sphere in St. Peter's Basilica you wouldhave to copy not only what you see in front of you, but everything behindyou as well (fig. 24f).

Staying with the flat surface, a very interesting way to create the rest ofthe visual world is to continue the drawing from the outside edge of thecircle around to the back side of the piece of paper.

Start by cutting out your original circular drawing from the five point per-spective exercise (fig. 25b). Now move the grid paper around to the otherside of the drawing paper. The gird paper is now sandwiches to the origi-nal drawing side. The clear side of the drawing paper is facing you.With the grid attached, hold the paper up to the light of a window youcan see the grid. Make sure the grid points are overlapping the first draw-ing's points. Lightly tape these two sheets together.

We are going to use this same grid to help us organize this new side, butit must be organized to the first drawing. The center point, which isshowing through is now the South (or the sixth) vanishing point.Continue the four lines of the basic room, which run off the circle ofyour paper (fig. 25c). These lines now must aim toward the new Southvanishing point. You can also add the South wall of the room to thisnew side. Make it either closer to you or farther away. This gives yourtotal room more variety and helps to make your room more interesting(fig. 25d).

What if you were inside St. Peter's Basilica and

could get inside of a clear ball? With one eye in

the center of that sphere, you copy onto the

inside surface everything you see all around you.

Now move outside the sphere to see the total

picture you have drawn.

This is how one side of

the sphere would look…


Notice any details in the original five pointdrawing (couches, chairs, television cabinets,etc.) that disappeared at the edge of the circle.These images can now continue around to thenew drawing to complete them (fig. 25e).

To make this flat six point perspective conceptmore exciting the next time you do one, youshould make sure there are many objects onthat edge to be brought around. This adds tothe excitement of the concept. You now have asix point perspective drawing (fig. 26 and fig.27, pg. 32).

You can hang the two sided drawing with astring from the top vanishing point. If youused two sheets of appear, they can be glued toa circular piece of foam and hung from the ceil-ing.

Fig. 25c

Turn sheet over and continue the four lines from

the back wall around the edge of the paper to

the back of the sheet.

Fig. 25e

Finish South part of room.

Extend windows from North

(opposite) side.

Fig. 28(also front & back cover of book)Both sides of total visual world.

Here have repeated the back sidefour times (top, left, right and bot-tom) on each of the four corre-sponding vanishing points to showhow this drawing entitled "The SixSenses" uses the vanishing pointsto focus on each sense (sight,taste, touch, hearing, smell, andintuition).


Being able to enclose total visualenvironments is a very rewardingaccomplishment. Your next job is tothink of and express ideas which fitthis concept. What are truly sixpoint perspective concepts?

This way of thinking is what led meto use the sphere as my canvas since1969. I call my paintingsTermespheres. To date I have paint-ed over one hundred and fifty ofthem. The Termespheres hang androtate from ceiling motors. Subjectson the spheres range from geometricto surrealistic to a series on famousinteriors from around the world.They range in size from 12" to 7 ½feet in diameter.

Lately I have found a system to repro-duce my spherical paintings. Theseare silk screened limited editionspheres. How these spherical paint-ings were accomplished will beexplained in the next manual.

See the inside back cover of thisbook for more information


The painting, Escher3" takes Escher's "Hand With Reflective Sphere" and spreads it out around an actual sphere (shown here in six different rotations.) Thewindow and the table are added on the back sides. The distortion on the edge of the mirrored ball becomes much more readable when organized with the sixpoint perspective system.


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new perspective systems

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