Hình họa chì, luật xa gần

ft should — | be pla cod wear the vertical scale œ the horizonas Shown, ay out the separate widths of the units on His horizontal line Tas 1s the horizontal sca/e How to draw variable

ALL DRAWING STEMS FROM ONE OR MORE OF THESE FORMS

Think of your paper as representing open space, not as a

two-dimensional surface, but as if its edges were the boun-

daries of an open window You look at all of life and nature

through this paper window

Attempt either to set forms into this space that exists be-

fore you or to give a feeling of actuality to forms which you

create from a knowledge of the laws of nature We study

nature for effects and set them down

This involves dimension, contour, viewpoint (meaning per-

spective), and lighting Only through light, which pro-

duces all tone, color, and appearance, can we produce a

true image of life

Really to draw, we cannot think only of any single aspect

of drawing, such as contour, without the other essentials,

but must seek to unify all aspects into a complete and

organized whole

15

THUMBNAIL ROUGHS

The habit of setting down your mental concep-

tion of a subject in miniature roughs can play

a most important part in your development

as an artist The best way is to shut your eyes

CHARACTER The specific qualities of individual units of your subject in light

CONSISTENCY All the essentials of construction, lighting, and pattern, organized as a unit

EVERY DRAWING HAS A HORIZON

of the picture It may be above or below the pic- the artist cannot depend upon the camera He ture plane or may cross it at any point We must —_—s must know perspective

EVERY DRAWING IS A PROBLEM OF DIMENSIONS

H-Haght chosen ter drawing

‘A A- Quarter pauls it direction

iy, mn B-Lighth points lip and down

i - When drawiig trom life,

her all, '2ovÉz check on your daw,

you Know the proportious are correct

.———

23

SIDE-OF-THE-LEAD STROKES

Good drawiig bequs with a search tor simple basic pores

7 41 the basic torus established, we

can then bucld on the surface fom

Veen, since only light cau

efuce form, we must st,

does as tt travels across

Lhe SU FACES, noting the

areas light, halftone

aud shadow

Ay the form turns away trout the light it produces bulftoue asd

shadow ‘Ike Ligktuess or darkness of tee hadlltoue t bee resulbof the 2⁄2 plane ta relation to the direction of bee Light Shadows occur only when bee hight cannot reach he p Laue

26

THE SQUARE AND THE CUBE Let us start with the beginning of all good draw-

ing, proportion and dimension The square with

its equal dimensions is extremely important, as

the following pages show From the square we

can construct nearly all other forms in perspec- tive The square is a basic means of measure- ment We must first learn to divide the square

poocnt of bee Sguare

^2⁄ 2 pepe cular line ct the same pout of Cross

a square (or ay rectangle) tuto four equal parts YOM

thivegs wll deve lop Airct we construct the cube tow the square,

ie observe that two diagonals will locate Lhe utidd/e

Niece all objects will Kt urtto 2 box,we must know how to construct be cube or block

tA perspect ve Knowing 4e overa// Aine SOK of object, we constvuct 2 box whick would tit around it, Then we build the object within t Even vousud objects tit hee cube or block fo draw the cube, we must establish 2 horizon (or evyeleve/)ard two vescishong 2z MU sides of Kee cubes vecede toward Meese veasshing pout

The drawing above shows the square laid flat on spective In the drawing above there is some the ground All ground plans begin with this

We can now build the cube on the square The

sides of the cube are divided like the squares at

the top of the page, but now are shown in per-

30

distortion because the vanishing points had to be placed a little too close in order to show them both on the page Try drawing some cubes cor- rectly

THE CIRCLE AND THE CYLINDER

By means of the divided square and the cube, ellipse quite accurately by using the divided

we can draw the circle and the cylinder We use _ square drawn in perspective This is valuable in

a compass to draw the circle The circle in per- _ drawing all round or cylindrical forms

spective becomes an ellipse We can draw the

By adding diagonals be the quarters of the sguare, we construct another Sgdare

whese corners touch the tmiddle of bee tour sides By placiug 2 pots half

way between Aland B,we cau judge about where the atc 4 bee circle cutr across Lhe tagorvall, cohich helps as to draw the e/z2e

THE CYLINDER IN PERSPECTIVE

To draw a circle in perspective, we first lay out cube or block, we construct a cylinder in per-

a divided square We draw the arcs around the _ spective The vanishing points for a small object four sides, making the arcs cut just short of the should be spaced wide apart For large objects, halfway points between A and B Now by draw- _ they can be spaced closer

ing ellipses on the top and bottom sides of a

31

THE CIRCLE AND THE CONE The cone is built on the circle in perspective, built with the cone as the basic form, such as and the circle in perspective is of course con- the wine glass, horn, etc

structed within the square Many objects are

Remember that both vanish:

ng points must be located ou ¬ the same truly te horizon

32

THE CIRCLE AND THE SPHERE Since a circle fits within a square, a sphere will Then draw the circle plan on the upright diag- fit within a cube First divide the cube, then _ onal planes The length of these planes is deter- draw the circle plan in perspective horizontally mined by the perimeter of the horizontal circle across the middle section of the cube (Fig 1)

THE DRAWING BELOW SHOWS

THE CIRCLE PLAN LAI D OUTON

THE MID-HORIZONTAL PLANE FIGURE TWO

AND ONE OF THE DIAGONAL PLANES THE CIRCLE PLAN LAID ON ALL PLANES

THUS PRODUCING A DIVIDED SPHERE

FUNDS Liana: MhovuUMUc Vit

ROUND FORMS WITHIN THE BLOCK What is true of the cube and the sphere is also

true of any elongated block that will fit around

any rounded form Any such form can be drawn

in accurate perspective by using this basic ap- proach First draw plans of the middle planes

THE BLOCK APPLIED TO ROUND OBJECTS

The circle and the block can be applied in any object in any position within your subject drawing many different objects If you can draw Draw the block to equal the height, width, and the block in perspective, you can draw almost depth of the form

“— 222 the ellipses treehatd

the disk 0 flat version of the cylis-

der Siuce tt has many uses, isu)

to Know #42 the Cp ses Should be

2⁄2 Lo Kit 2⁄⁄ olyect atany /⁄⁄⁄

poll and tO 2⁄ eyeleve/

HOW TO CONSTRUCT THE BLOCK CORRECTLY

In case you are having trouble in drawing blocks

correctly, the drawings below will help you Re-

member that ellipses narrow as they near the

eye level Studying a real object will help you

How to coustvucta block of: given

Or derived Sireusiowus

24 xeed/a | sguare anda “zz⁄4 Extabhish @ hortZzort or eyeleve/ Drew a perpendicular @, “2/54 heigl ated width fb/ock @ox the

perpenddicusar jhe depth of 4 of

the topside in perspective Dis op-

tional Through the points ertab-

lished atends of hue ® caw connect

Mg lixes@end © ty be vanrshisig punt above then daw the eh he oder wudicated, by beer HUMLBOPS

BLOCKS OF SPECIFIED DIMENSIONS Here are two ways of constructing blocks of

specified dimensions In the drawing at the left,

the dimensions are laid out on the middle line

or axis, using the procedure shown on the pre-

UNITS ARE PROJECTED TO THE FRONT

PLANE OF THE 6LOCK

When you can produce a block of specified di-

mensions, you have the basis for drawing any

object accurately You are urged to practice this

until you can do it, because it is a procedure that

6 LAY QUT IN UNITS AND PROJECT TO BASE LINE

you will use for the rest of your life We pro- gress from this to other methods of measurement

in perspective.

MEASURING DEPTH BY MEANS OF DIAGONALS

The drawings below show how to space off

equal units in perspective within both horizontal

and vertical planes This is valuable in drawing

evenly spaced units that recede toward the hori-

zon It will enable you to space correctly such

ve OF DIAGONALS HORIZON

the horizontal plate

The cagovals of units ov

a hovizoutal plave wel!

vanish ina pout on the

things as units of rug designs, fence posts, tele- phone poles, trains, window panes, blocks in sidewalks, building blocks, bricks, roofing, wall- papers, ete

ing it, Hts perspective dept parges

trom such @ taut or area When thetirtt uni

by rauning 2 diagonal through aha

Bo lie aa Jerse Mes ae

beat plane Lither hagonel may be sed

222e2/2⁄4qe t affected by

ahh every Step we take toward or allay

The vertical plaxe vVQHE shiteg port of

we wiust Set tte ?22⁄/20đ/12 2⁄4 d⁄a/⁄/É

the Jirbatece froth which We ae view-

fis estab ithed, we repeat tt

Jha tut ot the writ toetther bee

Abe text unjlas ottrovighe I to 2,2/03,e.

DRAWING TO SCALE Every artist should know how to draw to a scale

Scale drawings usually require the division of

vertical and horizontal planes into square feet or

square units By the plan shown here, we can

quickly divide such planes into squares of any

Tne dotted lines mdicate chagonals and

sicbseguent divisions of the Mat Get Paces

) _ 2860Fr

.K! V3 Tr 2 = —a— v — : LA Ay Li 2 =a

2 L‡ tÍP EBECT PEBPEMÔICULART AT AC,

POINTS WHERE THE A THROUGH

° ° DIAGONALS ACH THR GROUND LINE the measurmert

a al — doubles whexever

>aF lở = ee a diagonal ts ex-

5 a = feuded tromA L7 JZ eg = through each’

z PA ee Part on Lhe Le-

= — — s<— -^” z Z “ S + a > sử secting line, 0

MORIZON TAL EASURIN ne tee ground line

How to scale a vertical aud a horizontal (plaice

We uusk first establish avertical aad a hovizontal MCOBSUP MG Lue, touching each other at right anges, (point zero) On both lines we lay out so egua/ usucts to represent /o feet The size ofa unit cr optional lhe horizou is buen setat any cesired heotght on the vertical MEASUIIG lite We then erbablith a varshirg pots anywhere on bee horizon, Connect pots 0, Hand AteVP fstablish optional depth of ble

tirst foot Then draw liner bromall foot units toward VP Diagonal othirst

hotlOC) marks of vertical Aivirtous of foot units axtd algo hee kirst/0

fe unit at point C Diagonal A tivough Blox the bisecting Lite) to D marks off 20ft on Lee ground line When AB lo LE is 40 Fz and 50 04% ک untinetyr

39

DIAGONALS IN SINGLE-POINT PERSPECTIVE

It is very important to understand what is meant

by a single-point perspective and two-point per-

spective and how the planes and their diagonals

operate in each The basic plan for single-point

perspective is shown below Although we do not need all the diagonals for purposes of meas- urement, we should know how to choose the ones we need

and therefore have none In single-point

perspective there is only one main vanish-

8T!

zon cannot converge to a vanishing point pranes vertical line drawn through the main van-

ishing point

40

DIAGONALS IN 1W(O-LUVHIMIK + RAV dan ốc

drawing below, while it appears to be com-

ated, is simple when you understand it We

e divided a block into sections of four units

_ side and carried all the diagonals to their

IATONALS OF

BRYICAL SIDES

proper vanishing points This is seldom neces- sary, but it illustrates the basic plan for diag- onals in two-point perspective, and is important

to know

DIAGONALS OF VERTICAL sous 47

WSS Note that the ;enx/20/0y /094/7 of gore

NÀY X`& a vertical line Craw tere Lhe „2 J;

` LỚN outer vanishing pouty of the block 7, 7 04

The vanishing point of the diagonals of the

horizontal planes is located on the horizon What

is true of diagonals on vertical planes also ap-

plies to inclined planes, as we learn later, for

their vanishing points also fall on a vertical line

through the vanishing points of the vertical planes It is necessary to study the drawing care- fully to locate the diagonals of any particular section Try drawing this

41

EQUAL SPACING OF SOLIDS IN PERSPECTIVE

By the same method of measuring depth by _ row of objects that are constructed within equal means of diagonals we can also repeat a solid blocks Remember that all objects can be drawn block, as shown below This is valuable in draw- _ within blocks

ing buildings of repeating dimensions or any

ve HORIZON ~~ mm N

| 7 ` - \

ou may use the hagonals of the whole a \

side(AAAA), or half of it (BBAA),produc- “>> * a

ing the same resul either way \ ` NI SA

Tue dé / of de of Lhe block may be used for X

ee a oe osc creme AB ghd CO ave sim-

Lar Leagouals oA peralle! planes of equal size ` ae cal

42

UNEQUAL SPACING OF SOLIDS IN PERSPECTIVE

Measurement of unequal depths in perspective an angle can be attached to any object, thus becomes very simple if we use a vertical and a _ setting up a scale of measurement for all vari- horizontal scale The scale is a right angle at —_ able heights and widths

tached to the near corner of the first block Such

How to draw units ofvariable

AMmMeHSIOMS tt POF IPer ⁄z2r⁄e

"a Measuring pont if erlablisheed

~ in ovder to project MeasurenteHts

==- es trom the horizontal scale to bhs

bare line of the uruts ft should

— | be pla cod wear the vertical scale

œ the horizonas Shown,

ay out the separate widths of the units on His horizontal line

(Tas 1s the horizontal sca/e)

How to draw variable spaciugs withtK a

single block or unct

lay out and project aff measurements trom

* he measuri int cax be

]) placed tothe right or left of the

ay vertical scale, but sos

ETS F : a HORIZONTAL SCALE

Measurements for all spaces may be set by They are then projected in perspective in the choice or taken from a plan or scale elevation manner shown in this drawing

and laid out on the vertical and horizontal scale

43

SIMPLE PROJECTION IN PERSPECTIVE Here is a very simple method

mensions and spacings in perspective The top

drawing shows the front and s

a house The dimensions of these create a ver-

of projecting di-

ide elevations of

ings are projected to the base lines by means of two measuring points The vertical spacings are transferred to the vertical scale of the perspec- tive drawing and projected to the vanishing

wo first draw the trout and

= < — ——— side elevations of abuilding L| = TỊ [| oF QUHCHS(OHS OF

Drop 22 al/ Xe =Ú 3)/21L2Ì655/8i0⁄E

ows to the Hagia ante! #4 |

vertica/ scale lay outthe

hecokts on tue vertical scale

Extend base lines te vanishing

potxts ot both right and left

The potntr on the horizontal scale are a// connected to the

two measuring pocuts trough the base lines lua thes way

the spactugs are carried back to te building [hen by

running pape eae up the walls at teese points, we

Cetermiiine the

ofthe vertical scale are carried out

lateral spaciugs in perspective the ports

, e vancshiing pacts,

thus establirhing the vertical spactngs on the perper-

44

PROJECTING THE VERTICAL SCALE The vertical scale can be projected to any part — corner of the steps, along the base line to the

of a drawing In the drawing below it is more middle line, which has been projected down practical to place the scale in front of the mid- _ from the front elevation to the measuring line dle of the building, so we move it from the front — or horizontal scale

Draw atront anda side elevation of a building

POINTS OF FRONT ELEVATION 4 POINTS OF SIDE ELEVATION

HORIZONTAL SCALE (OR MEASURING LINE )

45

ARCHITECTS’ PERSPECTIVE This is the way an architect renders ground

plans and elevations in perspective This knowl-

edge makes it possible for an artist to draw any

building to scale Both vertical and horizontal

Draw lines trom the station ott to the horizon so thud

they are pearalle/ to Lhe sides

of the ground (plate 2c ef

will make a right arigle at the

Station pot and will locate the vanishes powcts where hey cross the MOV-LZ0K

fi f/f pierure PLANE

| | lị HORIZON

St os -I-=-H-

a

re Vertical measurements are

⁄2/cc(ed trom elevations to

lhe measuring live aud then

to Lie vanishing ,2⁄⁄⁄:

the statiou pont represents the '02////2/ of the observer first we

lay outa ground, (plan aud place ttat whatever angle we hoose toview the building We drop avertical line dows tron the close comer Ht Yas corner we also draw ahortzortal line tovepreseHtl

thee picture plane horizon canbe establijied at any height 2Á2/ 4 2⁄2 “xe, áo crosstg Hever tical, bus vertical

LECOMCS 2 ⁄42////4/ lie, Jela station pot below the 2⁄2⁄⁄Z

line Lines aiming at the station 002/2 2 to te roused

plant te lee picture plane Mi spacisg ts then projected to the base lites

46

ARCHITECTS’ PERSPECTIVE

In this drawing we have a rather complicated _ this odd shape We are concerned here with set- ground plan But remembering that “any form tỉng the ground plan on the ground plane, using can be built within a box,” we make use of this _a single over-all height for the building truth to simplify the rendering in perspective of

Mt complicated exteriors of A421, a/2(Lt1tO⁄r ⁄r( Ác

exéexơeœ to the baselines, or the linetohich rust out be

the two vesashisg potty trou the front corner of 4e

Á¿⁄⁄⁄2 this amount bo placirg the build ucg within

evrectargiular block The division pouts are brought

gous trom the picture plane to the base limes teex

carried back to the vanishing poids Study thes

STATION POINT

47

SCALING YOUR PICTURE This is an answer to perhaps the greatest puzzler set up in square feet, or other units, for the

in perspective drawing By this method the ˆ whole picture area This gives both vertical and base line of the picture may be set at any dis- — horizontal scaling

tance from the observer and an accurate scale

will gue! cach Wher I2FT M

THE PLAN E PLAN IN PERSPECTIVE

trom lhe geometrical truth here showt, we learu that one hal} the piclure wee ofthe ground plane ts taken up by adistance equal be twice the heigl of the weupotne Example: liken viewtyg the horizon trom aheight of six feet ig), one halk the

vertical distance te the horizon willbe taken up by the tirst twelve feet,

EXAMPLE OF SINGLE- POINT PERSPECTIVE SCALING

SHOWING A GROUND PLANE VIEWED FROM A HEIGHT OF EIGHT FEET

Drawing may be vị |s LA H—Z Picture avea may be

done tt reverse zlzL |x†+ F\ 271 LZ chosen with bs limsrts

Ground plan ẹ a LÌ placed as desired

be Se and z 6 | TT TY L2 : pes ee ae

12/21 l || al ON NE ese eatncieg ' " L~ L W/fill by uing diagonals,

©l¿ La ƒ L1 LALA S| | 0 Seale of origina!

A— t + B Srawtyg was

Since the vertical : LA L ee %4“ ¿ /+c*

height re(ec(Π4)> / TINY 5 mee

8H, the line AB ề | W444 4 Af} 4 a

“(tCÁ C¥OSSES L⁄ % 3

rete seoleat ev ý WV = ˆ Z Z 7 ƒ f — ¬ x \

FAI, all cao "0P 7-7 Z7 Lo

aicetle 2 depth ` GROUND UNITS ARE EXTENDED HORIZONTALLY FROM POINTS ON THE BASE LINE

of lé Ft OL Lhe if 2/- 3f a/ sf «} 2Í a} \ \ \ \

WORIZONTAL SCALE ground, (plane

Select height ror a viewpoint Litabluh a horizon through the viewpout Construct

ahorizonte! and avertica/ scale poth equal te the height of riewpout, these, with the horizon, wil complete asguare Mark off ae z2 œ⁄40o⁄ scases Draw the horizontal AB through hee hallway pont of vertical scale Connect all uutts to the vanishing point (iH thts Case the viewpowtt ) Lrect perpendicular

where lue ABevosses base line Keduce areas to square teet by using diagonals

48

SCALING YOUR PICTURE Scaling the ground plane for two-point perspec- seale is practical when placed at the near corner tive requires the usual two vanishing points set of the first square The horizon can be set at any wide apart The horizontal scale is set on orbe- height you choose

low the bottom line of the picture The vertical

TWO - POINT PERSPECTIVE

The vertical scale és used only Whe vertical scale can be projected

hor measuring uprights so that | to any point on the ground plane

they wll hea scale with the ies

ground units, Units of both scales Xa aceon

me vPÌOF OIAđG£ mp HORIZON ¢ —

“itablith two measuring potnts,one on each side of the vertical stale, evenly

spaced on the kovizon, (op) rom poiutzero establih base lines to both vase sh

tng pots Connect horizontal scale units to reach baselues on both sides by

lines poiatiug al Ps Thismarks off units in perspective on both hase lnes

Extend there units to both vanishing pots, After you have established some

square!, you can locate the vanishing pont of the dceagonals on the horizon More

tquares wll be marked off as the diagonals crass untt lines to the vanishing points

4 George Fox College Lioraty : Newberg, Oregon

SCALING THE INSIDE PLANES OF THE BLOCK

The vertical and horizontal scales can be used

to scale any plane Once we have the unit lines

running in one direction, the diagonal of any

square in crossing these lines marks off the units

running in the other direction, for width or depth as the case may be All diagonals of sim- ilar squares or units will have the same vanish- ing point

SINGLE- POINT PERSPECTIVE

VE the dhawug above the rollowtng problert ts worked out

2⁄44) a root /8 by27by late at worntal cyeleve/, wite Lwo

figures standing as ttapart, ix single-point perspective

Solution: Establish a vertical rcale on ahovrizontal sae

Mark bhese off ix foot units tobe equal ou bolhe scales Jet the

horizon at shght lecr ban bvertical feet Set van ishing

pot at uterrection of horizon and vertical scale Cox-

nect horizontal units to VP Erlablish depth ot first square

foot Draw diagonal te horizon leis establishes VP of đc

⁄⁄2z2⁄2⁄4 for al, receding untts a/ olfo veates a att

s49 Repeat Bas unt with dhagonals as Show te.

SCALING THE INSIDE PLANES OF THE BLOCK

Here the previous problem has been changed to _to a theoretical position to the right of the fig- two-point perspective This amounts toa change _ures Only two walls are now visible The full

of viewpoint Instead of looking straight down _length of the room cannot be shown

the middle of the room, the observer has moved

TWO - POINT PERSPECTIVE

a — ~——

TƯ — a —

—— - BOTTOM LIMIT OF PICTURE

' 2 HORIZONTAL SCALE If DROPPED BELOW BOTTOM LIMIT OF PICTURE

the Squaring off of the grouxd plane, the drawing above, is made 4⁄⁄⁄

establishing too MERSUUG points, one Lo the left and one to the right of

the vertical scale the near comer of be roone i dropped below the bot: tom lim of the picture Units on bee horizontal scale ave projected

up ? the base luaes of the Hoor by connecting them to tee two weas-

uring pots by the use of diagonals,we can mark 2⁄//2////2 ants

51

SCALING AN INTERIOR FROM ELEVATIONS The importance of being able to scale inside — within an interior, keeping all things in scale or walls and floors should be obvious to anyone in- _ proportion to each other, and you know what terested in good drawing When you can do this, _ size a figure should be at any spot in the room you can draw any interior and any furnishings

Establish avertical scale Mark off height of iutended wall si treet: Establish a horizon cutting vertical scale at desived hetgkt

kitablish vanishing points at right aud lett Draw the base line for

Left wall t right vanishing point: Cnnectvertical divisions to the varnishing point Establish depth of kirrt square Use tue diagonal of the ' thirst spuare to wtark off 8 squares further dagonals will esta blithe

| aM other units Do the Sane with rear wal, using lett vanuishisg pout

ee SS HO maRK OFF FLOOR IN SQUARE FERT, SIMOLY

——— “—“——— ———S DRAW LINES FROM BOTH VANISHING POINTS

— — THROUCH ALL POINTS ON THE BASE LINES

————-TOC EXTENDO ÄCRO// THE FLOOR

—_

52

HOW TO DRAW A CURVED SURFACE IN PERSPECTIVE The problem of drawing a curved surface in which can be scaled off in units, from which the correct perspective is often puzzling A simple curve can then be put into perspective solution is offered below A ground plan is made,

Lay oul a plana the curve

block oth a sguate Utes

Wark apont wherever the curve crosses Lee horizontal

Place stmt/av pots

on Lhe 2⁄22, (plan laid out /#⁄/ ve

We set the plan on the Gtovusd plate wt tie usual manner, te either Siigle or

two „2é perspective We establish ascale of hecght at the Sole €H0 Of

the 2e Vertical uits are thes vguared off 2⁄4 a thraight wall at

oxe side of the ground, (plak 4eect a perpendicular at VOY, pootiel where

the curve crosses ahovrizoutal Sivision of the ground eats, Deawa bir tzonte/ out to meeteach perpendicular trom the lop of tle side wall 4

establishes the height of the curved plane at that pont Uusts woay

be bisected where KECeSSary 2 Shows tt Lee tivst uait 2đ

53

SIMPLE PROJECTION This is a simple but very valuable bit of working

knowledge Any drawing or design can be

squared off and projected in perspective on

/

either a vertical or a horizontal plane This is

practical for such things as lettering in perspec- tive, wall and floor designs, or placement of any

in in any flat plane of your subject

TO LOCATE POINTS INTHE DESIGN, LETTER THE x x

LINES IN ONE DIRECTION AND NUMBER THEM Ñ AI `

/ }N THE pee") THUS £3 1S THE CENTER OF CIRCLE \ SN

You Cas pre la“ hea points of y

the squares to any size by Ầ

REPEATING A DESIGN IN PERSPECTIVE Any design can be repeated in perspective readily approximate the position of the points Simply square off the design The squares serve on the divided rectangle in perspective Draw

as guide lines for the points to be followed By _ diagonals to repeat the blocks

laying out such points on the squares, you can

Draw 2a block arouvd the c&/⁄7⁄4 ad subsvide tt

INCLINED PLANES IN PERSPECTIVE The ground plane is always considered as a level

plane stretching out to the horizon All other

The vanishing ae 7P potuts of \ \ “Yo Ì / / / ft ' V722 z opty PP <

inclined planes do wot fall ! A , Viger” ZL Coa at

on the horizon of the grou 7 UNẾ, :

plane, but ona vertical line

through avanitung point

ofa Lorient aces the

vantihing point of ar as

ccuding plane will be

above the horizon, Cua of

a descending plane és

below the horizon

INCLINED PLANES Drawing roofs is a problem to one who does not

know perspective A roof, being an inclined

plane with two edges parallel to the ground, has

two vanishing points, The edges parallel to the

ground plane vanish on the horizon at the van-

IN PERSPECTIVE ishing point of the building The inclined edges vanish above or below the horizon on a vertical line drawn through the vanishing point of the building Many artists do not know this

Here we have three buildings Note that the re of the

root of building Dis at right angles to the otter two,

Coorner the visible edge of this root wclexes toward our let, Tkerefore d must vanish tx alive draws

through the left vesishing pout ot lhe building (ole

arrow) The visible sides of the roots of buildings @ and

© are cxclined toward the vight, so they vatush Ut a

vertical line drawn trough the right %8 22⁄4 point

We cousider bke near of vistble plases of the roofs

as sloping upward avd the tar or wresthle places 47

lopiug down were lhercfore the former vartesh a

bove tee hovizon asd tue labler below the posttiow `

of the vanishing pots on the vertical lie is deter:

(re angle of oe tage 1 flatter roof

e

wotld vaHtth Hearer HOPCZO

57