gill_2pt_persp - VERTICAL PLANE. 1. VERTICAL PLANE. 2. 1...

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Unformatted text preview: VERTICAL PLANE. 1. VERTICAL PLANE. 2. 1 Terms used in perspective projection SE ELEVATION. END ELEVATION. PLAN. 10 Related views of a rectan- gular prism. HORIZONTAL PLANE. The most important thing to understand from the beginning is that a ‘. I V perspective drawing can show only that which can be seen from a specific viewpoint. A perspective drawing is a technical drawing, un- . 3 like the artist’s drawing, which is his own interpretation of what he 0 sees. It is because a perspective drawing is a technical drawing that if. an accurate system of setting up is necessary. The system shown “ here is considered the most accurate yet evolved, and produces as ‘I‘ nearly as possible a drawing of a three-dimensional object which- coincides with the actual view of the object seen from the chosen viewpoint. ' ) ' The first requirement when setting up a perspective view of an " ‘ object is to obtain accurate information. This information is usually in the form of plans, elevations and sections. It is from the plan, usually, that the perspective view is projected (a plan of suitable size should be obtained), and heights etc. are measured from the elevations and sections. For the purpose of explanation the plan and elevations of a simple rectangular prism are shown in i Fig. 10, using orthographic projection. Orthographic projection is simply the method of drawing three- dimensional objects in two dimensions by means of related views 11 Orthographic projection: pro- jecting both horizontally and vertical- ly on to co-ordinated planes (planes at right angles to one another). I” '''''''' " called plans, elevations and sections. This means a parallel or per- I run-:— pendicular projection. Most buildings, furniture and fitting designs : LuuL i are prepared in this way. : [END I If the object is placed so that its sides are parallel to the co- . :ELEVAT'°’€' {ELEVAT'W- ordinated planes, as shown in Fig. 1 1, the faces of the object (in this i l I' case a rectangular prism) can be projected back onto the planes L———4— - - — - -—- parallel with the faces and the plans and elevations can be drawn. To explain the next step fully it is necessary to imagine that the co-ordinated planes are 'hinged’. The horizontal plane is swung downwards through 90°, and the vertical plane 2 is swung round through 90° so that the three planes, i.e. the projections, will lie in the same plane, which allows the draughtsman to work in two dimensions when portraying three-dimensional objects. In actual 13 '4 HORIZONTAL PLANE. [I . PLAN OF OBJECT. 13 Selection of station point in 12 The sections used in orthographic . _ relation to an object. projection, and their relationship to the actual object. HORIZONTAL SECTION. I (USUALLY A PLAN.) 14 VERTICAL SECTION. I CROSS SECTION.) practice the projection is made by first drawing the plan, then the front face (elevation) immediately above and the end elevation beside the front elevation. This is known as ’first-angle’ projection, and it means that each view is so placed that it represents the face of the object remote from it in the adjacent view. The first-angle projection is used in the British Isles and in Europe generally, Holland being the exception. The Dutch, like the Americans, use what is known as 'third-angle' projection, in which the plan is immediately above the elevation of the front face of the object. The end elevation, which is placed next to the front elevation, is of the adjacent end. In practice, architects often combine both first- and third-angle projections, so that the plan is located as in first- angle projection and end elevations are placed as in third-angle projection. This arrangement is recommended for general use. Sections A section is a view of an object when it has been cut straight through in (usually) either a vertical or horizontal direction. The most-used sections are illustrated in Fig. 12 but they by no means cover all the possibilities. The horizontal section is the plan (sectional plan), and usually there is a plan or horizontal section at each floor level in a building, including the foundations and the roof. If the object is cut longitudinally and vertically the view is called a longitudinal section, or long section. If the object is cut across and vertically, the view is known as a cross section. VIEW 1 J21 ’ STATION Paint—c VERTICAL SECTION. (LONGITUDINAL SECTIONJ VIEW 2. Sections are used in orthographic projection to show interior details and/or details of construction. Therefore sections should be taken through important parts of objects and buildings. Station point This is the chosen point from which the object is to be viewed. It is also known by other names, such as the 'observer', 'viewing point' or ‘eye position’, but 'station point’ is preferred by most authorities. The station point should always be chosen in relation to the nature of the object. A station point chosen too close to an object will give a dramatic appearance to the perspective drawing which is seldom acceptable. It is usually advisable to avoid this effect by moving a little further back from the object. Selecting a suitable station point is a matter of judgment and ex- perience, and it should never be finally chosen until its position has been checked with the 'cone of vision’ and also the size of the final drawing considered. (See Cone of Vision, p. 16, and Picture Plane, p. 19.) It is often advisable, when selecting the position of a station point, to look at a similarly-shaped object: if you are drawing a rectangular prism, look at a cigarette packet or a matchbox, as a check. Unless otherwise stated, the height of the eye above the ground at the station point is taken as 5 ft. In Fig. 13, view 1 shows a perspective drawing of a rectangular prism resulting from a badly chosen station point. Distortion is clearly evident, which makes this view unacceptable. The remedy in this case is simply to move the station point further back from the object. View 2 shows another perspective drawing of the same rect- angular prism resulting from a much better position for the station point. The lack of distortion makes this view acceptable. 15 ‘ 2 OUT OF FOCUS: — MAXIMUM CONE OF — VISION FOR PERSPECTIVE AWING . . . . . 1 [15:8 “St/2;):ng {Jigsand centre 16 .Cone of Vision in plan (top) and SENATOR ‘ CENTRE LINE OF mm 9 - CENTRE OF INTEREST. Elevat'on' ETATION POiNr. CENTRE LINE CF VISION.3\ ‘ ‘ CENTRE LINE OF VISION.—-, ACTUAL RANGE \ _ a: VISION. flour 0F Focus: . [MORE THAN 0 [:I: STATION PO'NTA ‘ r 150') fl STATION POINT—"l #5 ~ ' 0W 0" FOCUS—4:7 MAXIMUM DONE 0F 15 Station point and centre :EfJiON EVISligggEngSE DRAWING. - - - - - CENTRE LINE OF VISION, line of vrsron (elevation). WTATOR I CENTRE LINEDF “51% OR STATION POINT. OBJECT. m GROUND PLANE, I _ _ i [a , 17 Two alternative station pomts, figfiTfingggmfiL a and what is seen from them. RANGE 0“ “Sim-J V—* Centre line of vision ‘ -—-~\ \ ’z \ \ / \ ‘ I ‘ / \\ 0F CONE OF \\ I . . . . . . . ~ EXTENT / The centre line of wsuon, or, as It is sometimes known, the ‘dlrect i ,’ \ VlSlON (STATION POINT 1.) \ . . . , , . . . , . . . . ‘ V \ line of Visuon or the direct line of sight in perspective drawmg IS a' ‘ I/ \ \ \ e n . a n u "‘ \ line from the station pomt to the centre of interest of the object — i l‘ + : \ \ \ I / in other words, the point on which the eye is fixed. This line is al- \ . I \ \ / I ways represented as a vertical line in perspective drawing. When the L ' " $35155 0F V‘smUV'GLWI // station point is located and the direction of the view (centre line of \ STATIONEQNT 1_ / vision) is decided upon, the plan should be turned round until the 1 [I \ // centre line of vision is vertical, and usually with the station point at i W \ EENTEOW/ the bottom. This is done for convenience, to make it easier to pro- ; ' i \ r) I] . l duce a perspective drawing using a T-square and a set-square. The " 4 ll EXTENT OF CONE 0F \\ ' l/l centre line of vision is always taken to be parallel to the ground ‘ \ PVISIDN (STATION POINT 2.1 \\ // plane, which is shown as a horizontal plane for the purpose of ‘\ W perspective drawing (see Ground Line, p. 31). i \ / ‘1‘; WV // STAWN NT 2. , \\\ // Cone of vision \\\‘___,,/’/ The field of vision is known to be more than 180° but it is not pos- , sible to see clearly over this whole range. The normal maximum As can be seen from the diagrams, any object or part of an object range within which it is possible to see clearly and easily is accepted ’ which would not normally be seen clearly because of its lying out- as being a cone of less than 90° and is seldom if ever shown as more side this cone of vision will be distorted if we try to draw it. To ob- than 60°. For the purpose of perspective drawing it is usually limited I tain a wider coverage with the cone of vision it is necessary to move to 60° or less. Where possible, the student is advised to use a cone of :‘ back from the object; it is not enough simply to widen the cone of vision of much less than 60°, say 45° or even 30°, as these will nor- vision. When deciding on the position from which to view the ob— maiiv be adequate for his purposes and will give a much more satis- ject it is necessary to fit the whole — or the part which is to be in- factory result than a wider cone of vision. cluded in the drawing — inside the cone of vision. This fact governs 17 .gfieokfw From examination of Fig. 18 a number of points can be learned. #30?th $5332?" 53331: '3; RtEfitfi-‘T'ON / The first of these is that the smaller the angle for the cone of vision, PM” VT” /’ \\ ,//l the greater the distance required between the object and the station /Goo CENTRE “NE 0F v.90” \\\ ,//// g point to obtain the same coverage. The second is that even though WES 0F V'S'UN- \\ \ g //// the plan of the cone of vision appears to confirm the location of the ' \ \ \ / // station point, when this is checked in the elevation it can be seen that GROUND LINE \\ \W l/ l in each case the station point must be moved further back from the CENTRE LINE OF VISION‘ mm" mm “1765/ l’ __ object. (For the purposesuof illustration it is intended to use a 45° ' \ \Ls7 // cone of vision for the examples in this book.) STATION PO'NT 2-H / r The elevation of the 45° cone of vision shows the station point L B ND NE \ ,l E] repositioned so that the whole of the object falls within the cone 45° CONE 9F VlSlON. \ ' ’ " of vision. (The repositioned figure is shown in black.) This means I :T’fi . . . CENTRE .LINE OFflON W that a perspective drawing made using the new confirmed station \ mm" mm 3. y point will not contain distortions. PLAN OF OBJECT WITH THREE It can be seen that it is the cone of vision that governs the dis- 30° CONE OF VISION. GROUND LIME. 33553355 455$??th 36?'%T§NE%ASEE ? r tance of the station point from the object. ignorance of this fact ELEVATIONS SHOWING LOCATIONS OF THE THREE VlSlON- is responsible for many of the badly distorted perspective drawings POSSIBLE STATION POINTS LOCATED ON THE PLAN. \ that are produced. \ \\ / , \\ // Picture plane \ \ / v CONE OF VIS'ON‘4\ \ ' ,l ' This is an imaginary vertical plane on which the perspective drawing \\ \\ _ / l/ is supposed to be done. The perspective drawing is in fact the plotting \\ \\ // / of the positions where the visual rays from the eye (station point) \ W // ‘ through the points of the object intersect the picture plane. Imagine a fixed eye position looking through a sheet of glass (eg. a window). \-, It would be possible to trace the shape of the object on the glass STATION POINT.—————¥ (ACCEPTABLE, exactly as It IS seen. As shown m Fig. 19, this prinCIple remains true PLAN OF WlTH Whether the picture plane is placed in front of Or the Object. ‘8 cone 0f Vim": examples °f “5 use t° '°°ate STAT'ON POINT US'NG A 45° CONE In perspective drawing the picture plane is an imaginary plane, the I'm'“ of a drawng' OF VIS‘ON' 1?‘ normally at 90° to the ground plane, on which the perspective draw- / ing is supposed to be made. The picture plane can be inclined to the ground plane for special views, which are dealt with later (see the distance from which one should view the object. When a station Aerial View, p_ 35), but in What are known as Ione-point' and 'two. point is being considered and its position checked with the cone of ~ point’ perspectives the picture plane is always taken to be perpen- vision, it should be checked on the plan and also on the elevation. - _ dicuhr, The reasons for this will be obvious when the object is, for example, From Fig_ 19 it can be seen that the picture plane may be placed a tall building. in front of, behind or, if necessary, even through the object. In The centre line of this cone is the centre line of vision. This line other words, the location of the picture plane is a matter of personal is represented in plan by a vertical line and in elevation by a hori' I; choice and convenience, so long as it is perpendicular and at 90° to 18 zontal line. The apex of this cone is the station point. t the centre line of vision. I 19 20 . . _ VISUAL ms .‘ I: 5 19 The prInCIpIe of the picture I‘L. 2 plane in relation to the object and V 1:“. . . . hI I III I; FD<ED EYE the eye. POSITION. OBJECT. SHEET CF GLASS. (PICTURE PLANEI PICTURE PLANE IN FRUIT CF (BJECI'. PICTURE PLANE BEHIND OBJECT. The exact situation shown in the diagram can be drawn in plan where the plan of the object, the station point (spectator) and the centre line of vision are prepared for perspective drawing as pre- viously described. The plan view of the perpendicular picture plane will be represented by a straight line drawn in a selected position at 90° to the centre line of vision. It will be obvious that the picture plane cannot remain perpen- dicular, as shown in Fig. 20, when a perspective drawing is being done on a flat sheet of paper. As explained on p. 12, a plane can be 'hinged’ so that a vertical plane can be brought into the same plane as the horizontal plane for drawing purposes. This can be done without altering the image of an object drawn on the plane. By using vertical projection, distances marked on the plan of the picture plane can be projected either above or below the plan of the picture plane to a selected position where the perspective draw- ing is to be made. This is explained more fully in Fig. 21. The upper diagram in Fig. 21 shows the visual rays from the spectator (station point) passing through the points of the object and meeting the picture plane. From Fig. 19 it can be seen that by joining these points where the visual rays meet the picture plane the perspective view can be drawn. Also shown are the plans of the visual rays from the station point through the points of the plan of the object and meeting the picture plane. From this it can be seen that lines projected up from the points where the plans of the visual rays meet the picture plane coincide with the points of the perspective of the object. This simply means that by working 20 The spectator and the object in their relation to a selected picture plane. PICTURE PLANE. CENTRE LINE OF VISION. ~ _ SPECTATOR. ‘IIIIIIIIIIIIIIIIIIIIII GROUND PLANE. DIAGRAM SHOWING A SPECTATOR LOOKING AT AN OBJECT WITH A PICTURE PLANE PLACED BEHIND IT. PLAN OF PICTURE PLANEI 90° ‘4me LINE OF VISICN. STATION POINT I SPECTATOR. I PLAN OF OBJECT SET UP AS SHOWN IN THE DIAGRAM, PICTURE PLANE. CENTRE LINE OF VISION. PLAN OF '7\ CENTRE LINE OF wsnP‘fiBfl?“ PLANE WHEN IT HAS BEEN BRUJGHT INTO THE SAME PLANE AS TI-E PLAN FOR DRAWING PURPOSES. DIAGRAM SHOWING THE METHOD OF RELATING THE ACTUAL TO THE REQUIREMENTS FOR PREPARING A PERSPECTIVE DRAWING. 21 ION POINT. 1—61” DIAGRAM SHOWING FOUR DIFFERENT POSITIONS FOR THE LOCATION CF THE PERSPECTIVE DRAWING OR THE PICTURE PLANE I ELEVATION). II THIS POSITION IS PREFERRED AND IS USED IN 'THE DIAGRAMS AND EXPLANATIONS UNLESS OTHERWISE SPECIFIED. I rVERmAL LINES : IHWH POINTS OF INTERSECTION OF Tl~E VISUAL RAYS AND THE PLAN 0: THE PICTURE , PLANE. ‘ MITRE LINE OF VISIOI. PICTUFE PLANE I PLAN.) l I "'"-"-'1 PICTURE PLANE. PERSPECTIVE OF OBJECT. GROUND LINE. I I l I ELEVATION OF THE PICTURE PLANE. GROLND LINE. PLAN (F PICTURE PLANE. PICTLRE PLANE I SI‘ATION POINT. VISUAL RAYS AND THEIR PLANS. PERSPECTIVE OF OBJECT PLANS OF VISUAL RAvs ‘ 21 The picture plane brought into the same plane as the plan, to allow for a perspective drawing to be made. 22 PCENTRE LINE OF VISION. i ~$TATION POINT, IENTIFICATION OF PLAN OF PICTURE PLANE. A 90" e \\ I I I PICTURE PLANE 1. CENTRE LINE N VISION. PICTURE PLANE ‘l. PICTURE PLANE 2. PICTURE PLATE 3. PICTURE PLANE L. B__.____.__ \ v / ' A\ ‘ I 3 PICTURE PLANE 5. T ‘ ‘.““l—“——" P.P.2. \ \\ 1’ l A‘ 3 I ’3 PICTURE PLANE s. \ \\ 4 I / I i I I3 _ PICTURE PLANE 1 RP.3. P.P.1.. \\\\ .IFI VISUAL RAVS. ® \‘\.I/ \ II P'P'G' PPS. STATION POINT 223 The effect of moving the picture plane: only the size of the drawing is changed. with a plan of the object together with a plan of the picture plane it is possible to locate the vertical lines on which the points of the object will be located on the elevation of the picture plane. When the picture plane is swung down so that it falls in the same plane as the plan, as shown in the lower diagram of Fig. 21, it can be seen that the same situation occurs as described in the first diagram. In this second diagram the picture plane (elevation) is located above the plan of the picture plane but it should be understood that the picture plane (the position where the perspec- tive drawing is to be made) can be placed above, below or even on top of the plan of the picture plane. Once the principles of the picture plane are understood it is no longer necessary to refer to the plan of the picture plane. In per- spective drawing this line is usually referred to simply as ’the picture plane’, and this is the name which will be used in diagrams and text from this point on. The location of the picture plane is a matter of choice, conveni- ence or control of the size of the perspective drawing required. The closer to the spectator the picture plane is located the smaller the drawing, and, naturally, the further away the larger the drawing. However, it is only the size of the drawing which is affected; the view of the object remains the same. Fig. 22.3 explains this. By drawing the visual rays from the station point through the points of the object to the selected picture plane the over-all size of the perspective drawing can be measured. A check on the finished size of the perspective drawing to be made at this point can save a 23 24 ~CENTRE LINE OF VISION. 22b The effect of moving the station point: both the size and the view of the object are changed. \\ \ //l \\ \ //l \ \ +1-—<STATION POINT 2. \ \ ,1 \ \ \ \il/I \\ STATION POINT 3. -I \ I I STATION FUN L. STATION POINT 3. VIEW OF OBJECT FROM STATION FONT 1, gym POlNT 2. STATION POlNT 4. great deal of effort and time. The complete control of the size of the finished perspective drawing from the beginning is a valuable aid to anyone preparing any type of perspective drawing. Fig. 223 shows seven different locations for the picture plane, chosen at random. PointsA and B are the extreme ends of the object seen from the station point shown. These two points can be located as shown on each picture plane, and measurement of the distance be- tween them will give the over—all length of a perspective drawn using each location for the picture plane. By contrast, using a fixed picture plane and different station points changes not only the size of the drawing but also the view of the object. The diagram in Fig. 22b has four station points locat- ed at different distances from the object along a common centre line of vision. (For the purpose of illustrating this point the cone of vision has been ignored in the views from station points 1, 2 and 3.) By com- paring the views of the object seen from the‘different station points it can be seen that they differ considerably from one another even when allowance is made for the obvious distortions in the view from station point 1. A thorough understanding of these facts will enable the student, from the beginning of a project, to control the drawing size and fit a perspective drawing into any given size without difficulty. 23 Why the vanishing point is at the obser- ver's eye level. CENTRE LIFE (F VISION. VANISHING POINT. EYE LEVEL. VANISHING FONT FOR RAILWAY TRACKS. The position where it is intended to draw the perspective on the paper is the picture plane in elevation. This can be clearly understood by referring to Fig. 21, where the actual construction of the perspec- tive drawing can be seen on the picture plane behind the object. Vanishing points Any two or more parallel lines will, if extended indefinitely, appear to converge and meet at a point. This point is known as the vanishing point. Regardless of direction, each set of parallel lines will converge towards its own vanishing point. In perspective drawing it is necessary to locate exactly the vanish- ing points for parallel lines. To do this, the relationship between parallel lines and sight lines must be understood. When a spectator looks along railway lines, the centre line of vision is in fact parallel to the tracks. (The centre line of vision is parallel to the ground plane.) Because these lines are parallel they will converge until they meet at a common vanishing point. The second diagram in Fig. 23 shows how the angle between the centre line of vision and the visual rays decreases as the distance between the spectator and the point observed increases. From this it can be seen that the visual rays will 25 26 24 The method of ob- taining the vanishing points for a simple rectangular prism, and the actual vanish- ing points in relation to their plan positions. VP 1. I PICTURE PLANE. SIGHT LINE PARALLEL TO SIDE A - B IS DRAWN FROM THE STATION POINT T0 INTER- SECT THE PICTURE PL A NE AT V. P 1. STATION POINT. VANISHING POINT I IV.P.1.) IS THE POSITION IN PLAN CF THE VANISHING POINT FOR SIDE A-B AND ALL SIDES AND LINES PARALLEL TO IT. VPI. PICTURE PLANE. SIGHT LINE PARALLEL T0 SIIJE B-C T0 LOCATE V.P.2. STATION POINT. VANISHING POINT 2 IV.P.2I IS THE POSITION IN PLAN OF THE VANISHING POINT FOR SIDE B-C AND ALL SIEES AND LINES PARALLEL TO IT. PICTURE PLANE. .L-CENTRE IBE OF VISION. ‘ SIGHT LINE. \ \1 -;,\\ SPECTATCN. SIGHT LINE PARALLEL TO SICE 0F_§‘BLI_EQI.._.———-—‘ STATION POINT. PLAN U: SIGHT LINE PARALLEL TO THE SIDE OF THE OBJECT IN PLAN. finally coincide with the centre line of vision, which means that the vanishing point will be on the eye level. Therefore the vanishing point for the railway lines is at the point at which the sight line (the centre line of vision in this case) parallel to them intersects the picture plane. Because the sight line, which is parallel to the railway lines, vanishes to the same vanishing point as the railway lines it can be assumed that all lines parallel to the railway lines will converge to the same vanishing point. From this it can be assumed that in all cases where a sight line parallel to a object meets the picture plane (in plan), that point line or side of an 25 The method of obtaining vanishing points for two objects at different angles to the picture plane. STATION POINT. will be the vanishing point for the line or side of the object and all lines parallel to it. Once the principle of locating vanishing points has been under- stood it can be applied to perspective drawing. It has been estab- lished in Fig. 23 that a sight line (the centre line of vision in the case of the spectator looking along the railway lines) parallel to a side of an object vanishes to the same vanishing point as all lines which are parallel to that side. This means that the method of finding the vanish- ing point for a side of an object is a simple matter of drawing a sight line parallel to the side. The point of intersection between the picture plane and the sight line is the vanishing point in plan. By reference back to the explanation of the picture plane (p. 19) it can be seen that the actual location of the vanishing points will be above or below their plan position (depending on the location of the elevation of the picture plane). Also from the explanation, and from Fig. 23, it is known that the vanishing points for lines parallel to the ground plane will be on the eye level. (This is further explained in Fig. 29, p. 30.) For objects at an angle to each other, since it has been established that each set of parallel lines will converge to a single vanishing point, by treating each object separately the vanishing points for each side can be found and each object drawn in perspective. This is also true for objects with more than four sides or irregularly-shaped objects. The important thing to remember is that each set of parallel lines will have its own vanishing point, so it does not matter how many differ- ent directions are included in any one object or group of objects. Provided the vanishing points are found for each set of parallel lines in each direction, any shape can be drawn in perspective. Height lines The height line in perspective drawing is the line used for measuring all vertical heights. These heights are measured using the same scale as that used for the plan and elevations. The location of this line is 27 PICTURE PLANE. PICTURE PLANE. FENTRE lNE (I: VISION. HEIGHT LINE. SIGHT LINES PARALLEL T0 SITES OF THE DBJEC . A l-ORIZONTAL PLANE UUWN THROUGH THE EYE LEVEL TO MEET TIE PICTURE ACTUAL HEIGHT 07 TIE OBJECT ON THE PICTURE PLANE. 28 A horizontal plane through the spectator's eye level intersecting the picture plane at the horizon line. 26 Locating the height line: a side of the object is project- ed to meet the picture plane. HEIGHT LINE inEBIATIVE HEGHT LINES. . j 1 l V actual fact a continuation of the side being measured. This remains PICTURE PLANE. ' . . . true for all the SldeS of the object, therefore the most convenient side should be chosen to be projected either backwards or (if the pic- ture plane is in front of the object) forwards to the picture plane to locate the height line. Fig. 27 shows the alternative locations for the height line when other sides are extended. It can be seen that any side can be extend- srmou pom. ed but it should also be obvious that a convenient side should be used to locate the height line, otherwise inaccuracies can be expected. This is explained more fully later on in this book, but generally the side chosen should be one prominent in the view of the object from the selected station point, and for preference it should be on the side which has the greater distance between the centre line of vision and the vanishing point. HEIGHT LINE, _ PlC1URE PLANE. V592 SIDE PROJECTED BACK TO MEET THE PICTURE PLANE. STATION INT. 27 Location of the height line in plan, with alternative locations shown dotted, and with the picture plane in front of and behind the object. Eye level or horizon line found by projecting a line as the continuation of a side of the object When the spectator’s centre line of vision is parallel to the ground, I in plan either backwards or fon/vards, as necessary, to meet the plan the eye level coincides with the horizon line. This means that if a I of the picture plane. From this point a vertical line can be drawn on 1 horizontal plane is drawn through the spectator’s eye level it will I the elevation of the picture plane and it is on this line that vertical I meet the picture plane, producing a straight horizontal line parallel heights can be measured. Fig. 26 shows graphically therelationship ‘ , to the ground plane and the same distance above it as the spectator’s between the plan and the actual side of the object projected back to eye. The line produced on the picture plane by the intersection of meet the picture plane and the plan. From this it can be seen that the horizontal plane through the eye level of the spectator is known the top and bottom of the extended side meet the picture plane on as the eye level or the horizon line. (In perspective drawing, the the line projected up from the plan location of the height line and term 'horlzon line’ is preferred, and will be used from here on.) because the top and bottom lines are parallel the distance between L The important fundamental in perspective drawing is the height them is the same as the height of the object. Therefore actual heights 5 of the eye level above the ground plane. As previously described, 28 can be measured on the height line because the height line is in the elevation of the picture plane can be located as convenient 29 IE T INE. w L LGENTRE LINE OF VISION. HORIZON LINE 29 Locating the vanishing points on the‘horizon line. Note that the various alternative locations for the horizon lines (opposite) do not alter the relationship between the vanish- ingpoints, the centre line of vision and the height line. Any of the alternative locations would be satisfactory for draw- STATION T. . VP, . . . . .. H NE. mg the perspective VIeW of the _, ORIZON Ll V VP; object WHEN THE HORIZON LINE IS LOCATED THE ACTUAL VANISHING ' POINTS CAN E LOCATED BY PROJECFING UPIIN THIS CASE) (R DOWN FROM THEIR PLAN POSITIONS LOCATED ON THE PLAN I]: THE PICTURE PLANE. HEIGHT LINE. [—CENTRE LINE OF VISION. v.91. HORIZON LINE (AL ERNATIVE). ’ vez. v.91. PICTLRE PLANE. mm LINE [—CENTRE LINE OF VISION. _Lv.e1. STATION v.21. HORIZON LINE . _‘_ (AL ERNATIVE) v.ez*_ r—-F HEIGHT LINE. (within certain limits), so wherever the horizon line is drawn can be assumed to be the elevation of the picture plane — in other words, the position where it is intended to draw the perspective view. This is usually directly above or sometimes below the plan of the picture plane, whichever is more convenient. It is necessary in per- spective drawing to project up (or down) from the plan of the pic- ture plane to locate the vanishing points and the height line on the horizon line. ' The positioning of the horizon line on the elevation of the picture plane is a matter of convenience. The position is limited only by the equipment and space available (i.e. the size of the drawing board and the length of the set square to be used for the vertical projections). A few important points regarding the horizon line and its use are worth remembering. The horizon line in a perspective drawing shows the position of the spectator’s eye level. It is advisable to draw ob- jects using an eye level normally used for viewing that object in reality unless some special viewing position is required for some spe- cific reason. Generally a horizon line placed towards the top of the picture or above it means a high eye level, sometimes called a ‘bird's- eye view’. This is often used in perspective drawing when the top of the object is important. The horizon line placed about the centre of the picture usually means a normal eye level lie. 5 ft. above the ground). A low horizon line (near the bottom of the picture) usually means a low eye level or 'worm's-eye view’. When locating the horizon line on the picture plane it should be decided at what height the eye level is to be, so that space can be provided either above or below the horizon line as may be neces- sary for the perspective drawing to be done. Ground line The ground plane is a horizontal plane representing the ground on which the spectator and the object are supposed to stand or to which they are supposed to be related. The eye level of a spectator is measured as some distance above (or below) the ground, depend- ing on the spectator’s position relative to the ground, 9.9. a spectator standing on the top step of a ladder will have a higher eye level than a spectator standing on the ground. PICTURE PLANE. HEIGHT LINE. HORIZCN LINE . GROUND [me/4" .4 -, 3,63011nn‘: .RLA'NE; J: 3/ \gi ' r 7 30 The relationship between the ground line and the horizon line. The ground line is the intersection of the ground plane and the picture plane. This is explained graphically in Fig. 30, where the object and the spectator are shown in relation to the ground plane and the picture plane. The spectator is standing on the ground in what is known as the 'normal' position, that is to say the eye level is assumed to be 5 ft. above the ground. Unless something different is specified, this assumption is always made. The ground line is seen to be a horizontal line parallel to the hor- izon line. In perspective drawing, the ground line is located (Fig. 31) by measuring down from the horizOn line the distance of the select- ed eye level (using the same scale as that used for the plan and eleva- tions) and at this point a horizontal line is drawn, representing the ground line. This places the ground line at the required distance be- low the horizon line or the spectator's eye level. In other words, the horizon line and the ground line are related to each other so as to produce a perspective drawing of an object when looked at from this specific eye level. The location of the horizon line is a matter of convenience but the ground line is always located in relation to the horizon line, therefore they should be thought of as inseparable, and when the horizon line is located the ground line should be located with it. r..- g V.P.1. HORIZON LINE. GROUND LINE. - PICTURE PLANE. V.F!1 INE CF VISION. STATION POINT 31 The distance between the horizon line and the ground line, as it would be measured on the height line in setting up a perspective drawing. In practice the ground line need be located only where it inter- sects the height line, which means that the height line should be used to measure the distance between the horizon line and the ground line. The reason for this will become obvious as the method of drawing the perspective view is described. 33 34 HORIZ N LINE. v.91. ECTURE PLAIE. l V.P1. HORIZON LlNE. PICTURE PLANE. 32 Top, one-point perspective. Bottom, two-point perspective. D3 LCENTRE UIE ‘ a: VISION. 4-STATIO‘I FONT. LCENTRE LINE - OF VISION. l 'LSTATION POINT. V.P.Z. 2 Drawing the perspective: one- point and two-point With the location of the ground line the preparations for drawing the perspective view are complete. All that remains is for the actual per spective view to be drawn, but before proceeding to this it is necessary to understand the various types of perspective drawing in general use. There are three types of perspective drawing. Each type has a dif- ferent relationship between the lines of the object and the picture plane. In perspective drawing, any set of parallel lines may be paral— lel to, at right angles to, or oblique to the picture plane. Lines which are parallel to the picture plane remain parallel in the perspective. A set of lines which are at right angles to or oblique to the picture plane vanish to a vanishing point in perspective. The three types of perspective drawing are distinguished by the number of vanishing points required by each type. One-point perspective has two sets of lines parallel to the picture plane and a third set at right angles to it. Since a set of parallel lines not parallel to the picture plane converges to a vanishing point, this set-up will require only one vanishing point and is called 'one—point' perspective. V Two-point perspective has one set of lines parallel to the picture plane (the vertical lines only) and two sets oblique to it. Parallel lines oblique to the picture plane converge to a vanishing point, which means that this set-up will require two vanishing points. Three—point perspective has three sets of lines oblique to the pic’ ture plane, thus requiring three vanishing points. Three-point per- spective is more difficult to construct than the other two types and is not used as frequently as the others. It is not illustrated at this stage, but is dealt with later (p. 71). The most-used type of perspective drawing is probably two-point perspective; because of this, the explanations used so far have been illustrated with two-point principles, but as will be seen these prin- ciples remain true for each of the three types of perspective drawing. 35 EZICI ELEVATDN. EM) ELEVATDN. C3 PLAN. m-IOGRAPHIC PROJECTION (F A RECTANGULAR ISM USED TO ILLUSTRATE THE CONSTRUCTION ' A TWO~POINT PERSPECTIVE 'EP 1. - OBTAIN INFORMATION. ENTRE LINE OF VISION / \\ I / \ ' Leone Ir VISICN. rLJ lLS' IN ms use) \'/ STATION NT. YEP l..- CHECK TIE LOCATION OF E STATION PONT WITH Tl-E CONE : VlSlQN‘ 33 Two-point perspective drawv ing: steps 1-5. \-CENTR€ LINE CF VISKN. % \ lhcerrms uNE \ , W VISION. STATION PM I mm mm. vim AND THE DIRECTION OF VIEW ' STEP 3.- CENTRE IN VISION TO BE VERTICAL. PICTIRE PLANE. Lemme LINE Ir VIsnu. STATION JOINT. STEP 5.- LOCATE THE PICTURE PLANE AT 90" T9 CENTRE LINE (I: VISION. Two-point perspective drawing Figs. 33—35 show the steps for the preparation of a plan and the set- ting up of conditions for the drawing of a perspective view of an ob ject. If these steps are followed in the sequence shown here, it will be found that perspective drawings can be prepared quickly and accurately. Step 1. Either obtain or prepare information regarding the object, i.e. plan, elevations and, if necessary, sections. For the purposes of illustration the same rectangular prism is used as for the pre- ceding explanations, and it is shown in orthographic projection. Step 2. Select the direction of the view and the station point, i.e. the centre line of vision and the position from which it is pro- posed to view the object. Step 3. In perspective drawing, the plan of the centre line of vision is always drawn as a vertical line, so it is necessary to rotate the plan and the station point until the centre line of vision is vertical. 34a Two-point perspective drawing: steps 6 and 7. V.P.I. PIERRE PLANE. __’_ VRZ LINE PARALLEL TO THE SIZE OF THE OBJECT. LIIE PARALLEL T0 STEP 6.- LOCATE VANISHING POINTS. VPJ.‘ PICTlRE PLANE IEIGHT LINE. CDITINUATION CF STATION POINT. STEP 7.“ LOCATE THE l-EIGHT LINE. Step 4. The location of the station point should be checked at this stage with the cone of vision. (The cone of vision suggested in the earlier explanations was 45°.) If the whole of the object intended to be included in the drawing falls Within this cone of vision, the position of the station point can be taken as confirmed. If not, it will be necessary to move the station point back from the object. (It is not sufficient to simply widen the cone of vision: see Figs. 16-18, Cone of Vision.) Step 5. Locate the picture plane in the desired position. The picture plane is always drawn at 90° to the centre line of vision. (See Figs. 19—22 for an explanation of the picture plane.) Step 6. Locate the two vanishing points required for the perspec. tive drawing of this object from this station point. From the station point draw lines parallel to the sides of the object to meet the picture plane. Where these lines and the picture plane inter- sect are the required vanishing points. (See Figs. 24 and 25 for an explanation of the vanishing points.) Step 7. Locate the height line by projecting a convenient side of the plan of the object to meet the picture plane. (See Fig. 27 for an explanation of the height line.) 37 38 34b Two-point perspective drawing: steps 8 and 9. STAT t FONT. STEP fl. - LOCATE THE l-DRIZON UN§ AND PROJECT LP TO LOCATE VANISHlNG POINT 04 THE l-KJRIZON LINE. V31. 5m Pout STEP 9. - LOCATE THE GROUND LINE: _____________._—————- Step 8. Locate the horizon line in a convenient position either above or below the plan. In this example it is intended to draw the perspective view above the plan, so the horizon line is drawn at a convenient height above the picture plane. Project up from the plan the positions of the vanishing points and the height line in the picture plane (plan) to locate them on the horizon line. (See Figs. 28 and 29 for an explanation of the horizon line.) Step 9. Locate the ground line at the required distance below the horizon line. (See Figs. 30 and 31 for an explanation of the ground line.) The next step is to draw the perspective view of the object. Once the set-up has been completed (steps 1 to 9), the actual drawing is done using visual rays, vertical projections and perspective lines, 35a Two—point perspective drawing: step 10. HEKBHT LINE. FEIGHT (I: CHEW. HGTlZON LINE. STATDN FONT. STEP 10.~ LOCATE HEIGHT OF OBJECT ON THE HElGHT LIFE AND TOP AM) WTTOM LlNES (1: DE A-B IN THE PERSPECTlVE VIEW. i.e. lines to the vanishing points, in the sequence shown in Fig. 35. Opinions may vary as to the sequence used in the drawing of the perspective view. Any sequence can be used; for instance, some people prefer to locate the base of the object in the perspective view first. But whichever sequence is adopted the student is advised to follow it and only deviate from it when absolutely necessary, otherwise he can easily become confused in the early stages of his studies in perspective drawing. Many needless, time-consuming mistakes in perspective drawing are made because the wrong line 0r point is used. The student is advised to name each line clearly as soon as it is located. Similarly, as each point is located it should be identified so that it can easily be followed through the construction, and any mistakes quickly found and rectified. Step 10. It is usually advisable to draw first the perspective view of the side of the object which is used to obtain the height line. To do this it is necessary to locate the height of the object on the height line. From the elevations the height of the object can be measured. Measuring from the ground up, the height of the ob— ject is located on the height line. From vanishing point 1 a line is drawn through the intersection of the height line and the ground line. The bottom line of the side of the object which was projected back to find the height line will be located on this line. (See Fig. 27.) From vanishing point 1 a second line is drawn through the measurement of the height of the object on the height line. The top line of the side of the object which was used to locate the height line will be located on this line. 39 'HomloN LINE VP 35b Two-point perspective drawing: steps 11 and 12. STEP 11. - VISUAL RAYS USED TO LOCATE POINTS ‘A' AND ‘8' IN THE PERSPECTIVE VIEW ()3 THE OBJECT. STEP 12. - VISUAL RAYS AM) PERSPECTIVE LINES TO C(NPLETE THE PERSPECTIVE VIEW 0: Ti-E (BJECT. Step 11. From the station point visual rays are drawn through the points of the object, i.e. the ends of the side used to find the height line, to meet the picture plane. From the points where these visual rays meet the picture ‘plane, vertical lines are pro- jected up to the lines representing the top and bottom lines of the side in perspective. With the location of the vertical lines at each end of the side of the object in perspective the side can be drawn as it will appear to a spectator looking at the object from the selected station point. Step 12. By drawing the visual rays from the station point through the remaining points of the object and projecting up vertical lines from the points where they meet the picture plane the draw- ing of the object in perspective can be completed. From the diagram it can be seen that vanishing point 2 is used for the sides at right angles to the side drawn first. Vanishing point I is used lament LINE. MRI. PICTIRE PLAN. V.P 36 An alternative method of setting up a perspective construction and drawing. .R‘l. WIZON UlE. ELEVATICN (f WECT. for the side parallel to the side drawn first. It will be seen from the diagram that the point at the back of the object need not be sighted (that is to say, the visual ray need not be drawn) as this point can be located by drawing lines back to the vanishing points from the established sides of the object. However, it is often advisable to sight this point when accuracy is required. The method shown here (Figs. 34 and 35) is considered the easiest and most convenient but in some cases, e.g..objects with a very complex elevation, it is preferable to place the plan as shown in Fig. 36 and to project directly across to the height line. As can be seen, the result is exactly the same as for the previous method. The horizon is placed below the plan (as in the preceding method, any location can be used so long as it is directly above or below the plan of the picture plane.) The construction is identical to that shown in Fig. 34. When the ground line has been located an elevation is then set up (on whichever side is the more convenient) so that its ground line coincides with the ground line in the perspective con- struction. The height of the object is located on the height line simply by projecting a horizontal line across from the top line of the elevation of the object to intersect the height line. The perspective view of the object can now be drawn as shown in Fig. 35b. One-point perspective The second of the more commonly used types of perspective drawing is the one-point perspective. In a number of ways one-point perspec- tive is easier and quicker than the two-point but the principles are I very much the same. The principles explained in-Figs. 13 to 21 apply 41 )—CENTRE LM CF VISKN ELEVATION. em ELEVATION ml; \ \ / . \ / cone or VISION-1 FLA” ) ILS' TN 11415 use) ’ UHOGRAF'HIC Peoiecrlou or A aemmtm Jr \ / arsu r-"n. m ILLUSTRATE me omsTnmnou * = A View pspseecnve. swam pom. STATION mum. fl_‘; TAIN INFORMATION. STEP 2.- LOCATE STATION POINT STEP 3.- CIECK TIE SP. AND THE CENTRE LINE (33 VISIQEI WITH THE CCNE G: VISM. 37a Onepoam perspective Mildew.- drawing: steps 1-3. to one~point perspective even though the more common two-point perspective has been used to illustrate them. The main differences between the two types of perspective are in the selection of the station point and, because of this difference, in the number of vanishing points required by each. In two-point perspective the station point is positioned so that the centre line of vision is at an angle to a side of the object, so that all four sides of a rectangular prism are at an angle to the spectator. This means that two vanishing points will be required to draw the object in perspective from this station point. In one-point perspective, on the other hand, the station point is ) located so that the centre line of vision is at right angles to a side of the object. This means that this side and all‘lines parallel to it will be parallel to the picture plane, therefore they will remain parallel in the perspective drawing, and not converge to a vanishing point. In the rectangular prism used to explain the method of draw- ing an object in one-point perspective, the sides parallel to the pic- ture plane are at right angles to the centre line of vision. In this case the centre line of vision is a sight line parallel to a side of the object, therefore the vanishing point for these sides parallel to the sight line will be located at the intersection of this sight line and the picture plane (plan). (See Figs. 23 and 24, Vanishing Points.) A height line as such is not required in one-point perspective. The method used for locating the height line in two-point perspec- tive (Fig. 27) can be applied in one-point perspective but when the sides of the rectangular prism used here are projected (back, in this case) to meet the picture plane it is possible to link up the points projected back and produce a true elevation of the object. Once this particular aspect of one-point perspective is fully , ) understood it can be used to save a considerable amount of time and effort. This is discussed further in the section dealing with interior perspective, where it is shown to be a distinct advantage to locate a side of the obiect in the picture plane so that one wall of the interior can be drawn in the perspective as a true elevation. STEP 1.. - LOCATE Tl~E PICTLRE PLANE AT PM PLANE. PICTLRE PW. W? CENTRE LE (I VISIfN L" (Y VISIN 90°TOTHE CENTRE | I LINE (I: VISION. l swim POINT sm'm Pom §IEP 5- LOCATE THE VAnglm gm F95 THE SIDES OF THE OBJECT mgugi, TQ 37b One-point perspective drawing: THE ENTRE LINE 0: VISIW' M Steps 4 and 5. The method used for setting up a one-point perspective is shown in Fig. 37, and again it is emphasized that if the set-up is done in sequence it will be found easy to follow. Step 1. Either obtain or prepare information regarding the object, i.e. plan, elevations and, if necessary, sections. For the purposes of illustration the same rectangular prism is used as for the preceding explanations and the two-point perspective. Step 2. Select the direction of the view and the station point, i.e. the centre line of vision and the position from which it is proposed to view the object. In one-point perspective the centre line of vision will be at right angles to one of the sides of the object. As 'with two-point perspective, )the centre line of vision is always drawn as a vertical line, so it is necessary to rotate the plan and the station point until the centre line of vision is vertical. Step 3. The location of the station point should be checked at this stage with the cone of vision. (The cone of vision suggested in the earlier explanations was 45°.) If the whole of the object intended to be included in the drawing falls within this cone of vision, the position of the station point can be taken as confirmed. If not, it will be necessary to move the station point further back from the object. (It is not sufficient to simply widen the cone of vision; see Figs.16— 18, Cone of Vision.) Step 4. Locate the picture plane in the desired position. The picture plane is always drawn at 90° to the centre line of vision. (See Figs. 19—22 for an explanation of the picture plane.) Step 5. Locate the vanishing point required for the perspective draw- ing of this object from this station point. As previously described, the centre line of vision is used as the sight line parallel to the sides of the plan of the object. Where this sight line and the picture plane intersect is the vanishing point for all lines parallel to the 43 l4 HORIZON LINE. VJ? V. R up i-lfiN'TRE LINE OF VISION STAT ION STEP 6.- LOCATE THE HORIZON LINE AND PROJECT LP TO LOCATE THE VANl HIN PUNT ON THE HORIZON LINE. PICTURE PLANE, 37c One~point perspective drawing: steps 6-8. HORIZON LINE. VP. GROUND LINE. PIERRE PLAlE. i—CENTRE LINE CF Vlsm smoulpomt W HEIle LIFE. VP YRLE ELEVATK‘N GRIND LINE OF ‘ PICTURE PLANE. LCENIE LM 0F VISDN STATDN fPOINT. STEP 8.- LOCATE TRUE ELEVATION (F OBJECT CN ELEVATION 0: PICTURE PLANE. centre line of vision, i.e. all lines at right angles to the picture plane (See Figs. 24 and 25 for an explanation of the vanishing point.) Step 6. Locate the horizon line in a convenient position either above or below the plan. In this example it is intended to draw the per- spective view above the plan, so the horizon line is drawn at a con- venient height above the picture plane. Project up from the plan the position of the vanishing point in the picture plane (plan) to locate it on the horizon line. (See Figs. 28 and 29 for an explana- tion of the horizon line.) Step 7. Locate the ground line at the required distance below the horizon line. (See Figs. 30 and 31 for an explanation of the ground line.) ,Step 8. No height line as such is required in, one-point perspective but it is necessary to locate the elevation of the object on the ele- vation of the picture plane. The simplest method of doing this is 383 step 9. One-point perspective drawing-1 HORIZON LINE. WND LITE. Hcrune PLANE. l l—CENTRE LINE CF VISDN. STATION‘lTPOlNT. STEP 9.- FROM THE VANISHING POINT DRAW PER CTIVE LI THR THE POINTS OF TH ELEVATI N. to project up from the plan, as shown in the diagram. The height of the object can be measured on the elevation and located on the elevation of the picture plane (measurement is set out from the ground line up). From this measurement the top line of the object can be drawn, thus completing the elevation of the ob- lect. The next step is to draw the perspective view of the object. Once the set-up has been completed (steps ‘I to 8), the actual drawing is done using visual rays, vertical projections and perspective lines, i.e. lines to the vanishing point. Fig. 38 shows the sequence used for drawing the perspective view of the object, and if this or any other logical sequence is followed, time and wasted effort can be minimized. ln one-point perspective, as.in the two-point method, lines and points should be identified and named as soon as they are located. Acquiring this habit from the beginning will eliminate many of the time-consuming mistakes which, more often than not, are the result of using the wrong line or point. V Step 9. it is usually advisable to draw first the perspective lines of the object, i.e. lines from the vanishing point through the points of the elevation of the object on the picture plane. It will be on these lines that the lines of the object which are at right angles to the picture plane will be located. Step 10. From the station point visual rays are drawn through the points of the front face of the object, i.e. the ends of the front face, to meet the picture plane. From the points where the visual 45 ‘V" 46 HORlZDN LINE. V.P. HORIZON LINE. VB I \ - [I \l I I \ , I t l I l I \\ I [LVISUAL RAY. \‘ I Il—wsum. an. \\ II \\ l \t' V ‘l’ 5; STATION PDlN'l’. snrm Pom. STEP 10.- VISUAL RAYS USED TO LOCATE STEP 11- VISUAL RAYS USED TO LtXJATE THE F NT FACE OF THE OBJECT IN THE REAR FACE OF THE OBJECT IN THE PER§PECTIVE VIEW THE PE CTlV VIEW PlCTURE PLANE 38b One-point perspective drawing: steps 10 and 1 1 . ncrune PLANE. 39 One-point perspective drawing: an alternative method of setting up. ELEVATDN CF CB£CT rays meet the picture plane vertical lines are projected up to the lines representing the top and bottom lines of the ends of the ob- ject in perspective (the perspective lines located in step 9). Horizontal lines are drawn from the points of intersection and result in the outline of the front face of the object in the pers- pective drawing. Step 11. By drawing visual rays from the station point through the two remaining points of the plan of the object (rear face) and pro- jecting up vertical lines from the points where they meet the pic- ture plane, the drawing of the object in perspective can be com- pleted. The method shown in Figs. 37 and 38 is considered the easiest and most convenient, but in some cases, e.g. objects having a very com- plex elevation, it is preferable to place the plan as shown in Fig. 39 MlZON Llw. KRIZN LINE, VP. I I \ \ ’ l I - I l ‘ \ ‘ \ ‘ \ I , \\\ I cam-f7, use or VISION. \\\ camps" LINE or vrsnou. \\\\ centre UNE or wsm. \\ l/l/ \\ . l/ \\ ’ Il/ \\ I I I ‘\\ II \‘\ i ,I \ . I \\ ’I \\ . I/ “l I ll \‘ ,l’ \l I I’ \ III-VISUAL RAYS. \‘\ [,1 VISUAL RAYS, \\\ [III—WSW“. RAYS. ‘ I . l . \ I/ . \‘ [I] \i\ l ,5" ‘1 ,l’ i _II \.I/ V, W \I smell mm. 5mm mm. STATION FONT. 40 Three different locations for thepicture plane, with fixed positions for the object and the station point. and project directly across to the elevation of the object on the pic- ture plane. in this method, the horizon line is placed below the plan (as in the previous method any location can be used so long as it is directly above or below the picture plane). The construction is iden- tical to that shown in Fig. 37. When the ground line has been located an elevation is then set up (on whichever side is more con- venient) so that its ground line coincides with the ground line in the perspective construction. The height of the object is located in the perspective view by projecting a horizontal line across from the top line of the elevation of the object. The perspective view of the object can now be drawn as described in Fig. 38. As can be seen, the result is exactly the same as for the previous method. Fig. 40 shows three examples of one-point perspective drawings resulting from three different locations for the picture plane. As with two-point perspective, only the size of the perspective is affected by moving the picture plane; the view of the object remains the same. (The greater the distance between the station point and the picture plane the larger the resulting perspective drawing and, naturally, the smaller the distance the smaller the perspective drawing.)- The location of the picture plane is a matter of choice, conven- ience or regulation of the size of the perspective drawing. The three positions for the location of the picture plane shown in the diagram either coincide with a face of the object or pass through it. It will be 48 seen that the relationship of the plan of the object to the picture plane is maintained in the relationship of the perspective view and the ground line: that is to say, if the plan of the object is in front of the picture plane the perspective drawing of the object will be in front of the ground line, and vice versa. An understanding of this will help in setting up a perspective drawing because it will enable the student to locate the horizon line and the ground line in such a position as to allow enough room for the perspective drawing to be done with— out overlapping work already completed. Onepoint and two-point perspective constructions combined One—point and two-point perspectives are each treated as a separate type of perspective drawing but, as can be seen from the examples and explanations so far, they are based on exactly the same prin- ciples and are in fact interchangeable in a sense. The only difference between the two types is the angle of the centre line of vision to the side of the object at which the spectator is looking. Fig. 41 shows a spectator looking at two objects, one of which is parallel to the picture plane and‘wilI be drawn in one—point perspective. The other object is at an angle to the picture plane, so it will be drawn in two- point perspective. The station point, the centre line of vision and the picture plane are common to both objects, so that if each object is treated separately — the object parallel to the picture plane being drawn first as a one-point perspective and then the object at an angle to the picture plane as a two-point perspective — the resulting combination will show each object as the spectator would see it and each object will be in its correct relation to the other. When producing a drawing containing more than one object or one set of vanishing points it is advisable to work on one object or one set of vanishing points at a time, to avoid confusion. That one-point and two-point perspectives can be combined in one drawing is important because it allows for a wide variety of drawings which can be simply and quickly set up without the long and laborious sets of projections that are sometimes necessary to obtain the same results if only one type of perspective construction is used. Fig. 42 shows another perspective view containing both one-point and two-point perspective constructions. In this example one object is located inside the other. The larger object is placed parallel to the picture plane and is therefore drawn as a one-point perspective. The v3}. rel HEIGHT LINE (Bl. WIZON LINE. GROUND LINE. Vfll. (BI Bl V.P1. a) i jve‘lA H.L. 8) PICTURE PLANE, v.92. l I “ A. l / l / / / I / / / / LVISUAL RAvs. l , / / / / / I / / / I / I / l/ // STATION POINT. 41 Set-up combining one-point and two-point perspective construction. 42 - use CF VISICN. / L—VIsUAL RAYS. Another combination: two-point perspective inside a one-point perspective. HORIZON LINE. GROUND LINE. PICTWE PLANE. 49 /\. 50 smaller object, which is positioned inside the larger one, is located at an angle to the picture plane, therefore it will be drawn as a two- point perspective. From this example it can be seen that this com- bination is very useful when working on interior perspectives of rooms etc. Interior perspectives using one-point construction Interior perspectives can be either one-point or two-point perspectives and in many cases both are used in one drawing, but it is usually the one used to set up the room which is the main construction that iden- tifies the type of perspective used. The selection of a one-point or a two-point perspective for a specific drawing is often a matter of personal choice but it should be understood that while both types are accurate, one-point interiors are usually quicker and easier to set up and draw. This aspect can be only partly appreciated at this stage but it should become clearer as the student becomes more proficient at drawing perspective views of objects. Another reason for the popularity of the one-point perspective for interior views is that it is easier to 'control', which means that there is iess likelihood of unfortunate angles 'appearing' and other mistakes or accidents occurring which may not become evident in a two—point perspective construction until the drawing is well advanced. As with most things, experience is important in perspective drawing when it comes to controlling what is likely to happen; time spent in the beginning of a project ’controlling’ as much as possible is seldom wasted. Fig. 43 shows the set-up and perspective view of a simple room. To avoid confusion, it is shown without furniture or any details such as skirtings, architraves or light fittings. The method used for setting up the perspective view of the room is exactly the same as for any other one-point perspective but in this case the station point is located within the object to be drawn, which means that the wall be- hind the spectator will not be visible to him and therefore it will not appear in the perspective view. It will be found that the use of the maximum angle for the cone of vision (60°) is advisable in interior perspectivesxparticularly of small rooms, because the recommended small angles (30°—45°) will be found much too restricting. Once the main room is set up in the perspective view it is neces- sary to locate the positions of the door and the window. Because 43 A simple one-point interior per- spective set-up and drawing. the end wall of the room coincides with the picture plane it is drawn in the perspective view as a true elevation, which means that measurements can be made on it using the same scale as that used for.the plan. As the height of the door in the left—hand wall and the height of the top and bottom lines of the window in the right hand wall are known (obtained from the plan, elevations and'sections of the room, not shown here) they can be measured on the end wall. Because the door is in the left-hand wall lat right angles to the picture plane) it will be necessary to locate the measurement on the left- hand end of the end wall to allow this height to be projected back along the left-hand wall. The top line of the dobr will be located on this line. To locate the door it is necessary to sight its position in the plan in the usual fashion. (From the station point draw a visual ray through the sides of the door and from the points of intersection of these visual rays and the picture plane project vertical lines up to the wall in the perspective view. Using these vertical lines and the perspective line at the height of the top of the door, the actual door can be drawn in the perspective view.) ‘ The window in the right-hand wall is located and drawn in the same way as the door. In this case, the height of the top and bottom lines of the window are set out on the right-hand end of the wall to allow for these heights to be projected back along the right-hand 51 ...
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This note was uploaded on 05/15/2010 for the course ARCH 202 taught by Professor Quinn,k during the Winter '10 term at University of Michigan.

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gill_2pt_persp - VERTICAL PLANE. 1. VERTICAL PLANE. 2. 1...

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