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PERSPECTIVE DRAWING GUIDE Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 TABLE OF CONTENTS EXERCISE PAGE 1 CUBE IN ONE-POINT PERSPECTIVE 1-2 CUBE IN TWO-POINT PERSPECTIVE 3-4 CUBE IN THREE-POINT PERSPECTIVE 5-6 2 ONE-POINT PERSPECTIVE PLAN PROJECTION 7-8 3 DIVIDE AND PROPORTION 9 4 SHADOWS - SUNLIGHT 10 SHADOWS - RAY LIGHT 11 5 SHADOWS - FRONT AND BACKLIT 12 6 PYRAMIDS - STANDING/TIPPED 13 7 CIRCLES IN ONE-POINT PERSPECTIVE 14 CIRCLES IN TWO-POINT PERSPECTIVE 15 8 CYLINDER - STANDING 16 CYLINDER - ROLLED 17 BOX WITH SWINGING FLAPS 18 9 CONES - STANDING/TIPPED 19 DOME 20 10 INTERSECTING ROLLED CYLINDERS 21 COMPOUND FORM (PLAN PROJECTION) 22 11 COMPOUND FORM (3-D GRID) 23 12-POINT ELLIPSE 24 12 REFLECTIONS 25 13 FINAL PROJECT 26-27 Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 1: CUBE IN ONE-POINT PERSPECTIVE 1 The cube is the single most basic form in draft- ing, so it is easy to help begin the understanding of perspective. In one-point perspective, the face of the cube is always “true”, meaning it has the ac- tual height and width dimensions because this face is always coplanar to the picture plane. All other sides of the cube vanish to a single point, the van- 1 2 ishing point, to imply depth. To begin, ﬁrst a horizon/eye level (H/EL) is estab- lished and a cone of vision is created. The H/EL is simply the diameter of the cone of vision (CoV)- a semicircle. Where the H/EL intersects with the CoV are the diagonal vanishing points (DVP), and the midpoint of the H/EL is the center of vision (CV). Follow the steps, use light construction lines initial- ly, then darken the completed object with the ap- propriate line weights. This setup will apply to all 3 4 exercises that follow. 1) Complete the set up above 2) Locate a square within the cone of vision 3) Connect all four corners of the square to the CV 4) Connect the corners to the opposing DVPs 5) Draw vertical lines where the lines from step 3 and 4 intersect - this establishes the depth 6) Connect the lines in the back and complete the cube 5 6 Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 1: CUBE IN ONE-POINT PERSPECTIVE 2 This exercise is to construct six cubes that share the same vanishing point, and placed throughout one single cone of vision to provide a variety of views. The objects shown here are modiﬁed cubes, by proportion and subtraction. Notice the objects that are the farthest away from the center of vision (or clos- est to the edge of the cone of vision), they appear distorted due to the fact that the frontal surfaces remain “true” while the rest are in perspective, this gives the objects an awkward and skewed appearance. Therefore, one- point perspective drawings are not used most often. They are, however, the simplest and easiest to construct. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 1: CUBE IN TWO-POINT PERSPECTIVE 3 Unlike in one-point, a two-point perspective cube does not align with the picture plane. Therefore, there is not a face that is of true measurement. However, There is one side/edge that is coplanar to the picture plane, and it is the only edge that is “true”. This edge is determined on the location of the cube in the cone of vision, and it is the deter- mining factor of the height for the remaining cube. 1 2 To begin, set up the cone of vision in the same man- ner as in one-point perspective. However, instead of the DVPs, those points will be labeled as RVP and LVP, as in right and left vanishing points. The base/plan of the cube (or the object) should be de- termined so it can be arranged and projected into the perspective, hence the method’s name of “plan projection.” 1) Start a line from each of the VPs and intersect them anywhere along the CoV. This should form a 3 4 right angle and should be then form the base of the cube 2) Establish a ground line (GL). This is the ground on which your cube will be rested. The closer it is to the horizon, the more you are looking at the cube from eye level. Then project the front corner of the square onto the horizon line, establishing the CV, and the outer corners to the GL 3) Connect the center/front line at GL to the RVP and LVP. Then connect the corners at GL to the CV. Where they intersect the ﬁrst two lines in this 5 6 step will establish the edges of the cube Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 1: CUBE IN TWO-POINT PERSPECTIVE 4 4) Swing an arc the same distance as one side of the base on the front edge to establish the height of the cube. Then connect the end of this line to each of the VPs 5) Fill in the vertical lines and connect each to the VPs as the cube slowly takes shape 6) Establish the back of the cube Two-point perspective is most com- monly used because of its ease of construction and relative accuracy. Note that the farther away from the H/ EL the more apparent the distortion, because there is still a third dimen- sion (or axis) being disregarded. So it is still not a perfect depiction of reality, but it is an ideal compromise between difﬁculty and accuracy. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 1: CUBE IN THREE-POINT PERSPECTIVE 5 The most accurate depiction of reality is three-point perspective, because it takes into consideration all three dimensions (x,y,z). Since all three axis are in perspective, there is no “true” surface or edge. To begin, set up the cone of vision (CoV) as in two- point perspective. 1) Find the midpoint on the H/EL and label it m. Locate and label point X anywhere along the H/EL. Connect this point vertically downward to intersect with the CoV, this will be the vertical measuring line (vmp). The intersection should be labeled SPx. Lo- cate any point n along the vmp and draw lines to both the LVP and RVP. Extend the two lines from n to intersect with the CoV and label the points Y and Z. 2) Draw lines connecting the LVP to Z and RVP to Y. Extend these lines and they should intersect along the vmp line. This intersection is the third vanishing point (VP3). Now all three horizons and measuring lines are established. 3) Find the midpoint on each of the two other mea- suring lines, from LVP and RVP to VP3, and label each point m. Draw an arc from each point m that connects the VPs. Label where the arc intersects at line RVP-Z point SPz, and at LVP-Y point SPy. The SPs (x,y,z) indicate the corners of the cube. Simply connect each to the opposing VPs and the cube will slowly appear. 4) To eliminate the distortion of the large cube (rep- resenting its closeness to viewer), it is proportioned Illustrations from Jay Doblin’s Perspective: A New System For Designers. and divided into a smaller and more usable one. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 1: CUBE IN THREE-POINT PERSPECTIVE 6 In the smaller picture is a three-point perspective cube that is at a perfect 45-degree on all three horizons. It is much simpler to construct but uncom- mon in real life applications. 1) Compose a perfect circle (CoV) and label the center n 2) From n draw three measuring lines outward at 120 degrees apart 3) Where these lines intersect with the CoV label the points RVP, LVP and VP3 3) Draw a circle at n, and where it intersects with the three measuring lines will be the corners (x,y,z) of the cube 4) Connect these corners to the op- posing VPs and the complete the cube Three-point perspective is the most accurate depiction of reality. How- ever, its accuracy does not justify the difﬁculty and the time it takes to con- struct. Therefore, it is often preferred over by two-point perspective. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 2: ONE-POINT PERSPECTIVE PLAN PROJECTION 7 As a quick exercise to put the one- point perspective to a more practical use, a simple table is designed. First, the orthographics (two dimensional views) of the table is constructed. Using the plan view, a picture plane (PP) is deﬁned. This the plane on which the view is taken and where all measurements are “true”. Next, es- tablish (again on the plan) a station point (SP). Imagine this point as the PP eyes relative to the object. Lastly, vertically below the SP, establish a central vanishing point (CVP). SP To begin constructing the perspective, setup the drawing as shows, with the CVP side view to the side and the plan view above the ﬁnal perspective. Project from the plan above each point of the table directly to the SP. Where the lines intersects the PP is where it will appear in perspective. In this case, since the front of the table is directly on the PP, the true table front can be copied into the perspective view. The rest of the table will converge toward the CVP. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 2: ONE-POINT PERSPECTIVE PLAN PROJECTION 8 Once the orthographics for the room is constructed, create a grid system as shown. This two dimensional grid will be translated into three to help the construction of the room. The follow- ing ﬁve steps are the guidelines for all plan projection perspective drawings: 1) Construct the orthographics for the object, which includes the top/plan view, the side and the front view 2) Set up the drawing. Place the plan within the cone of vision, and align the orthographics accordingly on the layout. Be sure to place the side/front views along the ground line 3) Transform the plan into three-di- mension using the same method as creating the base of a cube 4) Use the elevations (front/side views of the orthographic to project the height of the object to the picture plane 5) Construct the object using all available views in the same manner as creating the cube In this one-point perspective room, there is one single vanishing point to which all depth converges. In the case of a two-point, the objects will converge to the opposing vanishing points along the horizon. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 3: DIVIDE AND PROPORTION 9 A cube is the most basic and simplest form, and it is quite boring. However, simply by dividing and proportioning it one can create more complex objects. As a matter of fact, most shapes can be broken down into cubes, or partial cubes. A simple cube can be divided into smaller cubes. For example, by con- necting the diagonals, a face can be divided into quadrants, and each quadrant can be divided into more by doing the same, and so forth. Or as shown on the right, one can be divided into nine squares, and so forth. Simi- larly, by combining multiple cubes, the same effect can be achieved. Shown on the far right are a couple of examples of creating objects from dividing and proportion, a set of steps and a diamond. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 4: SHADOWS - SUN LIGHT 10 Sunlight is also referred to as paral- lel light, because it comes from the same direction for all objects [within the same view]. Therefore the shad- ows of each object will be cast in the same opposite direction. The most simple method of cast- ing a shadow is to break down the object into its composition, the lines or “sticks”. By casting each line at a time, the projected image will form naturally. The angle of the sun must be deter- mined at ﬁrst. On the right (top), the angle is set at 45. Simply project the top of the segment onto the ground at 45 degrees, where this projection intersects the base of the segment is the end of the shadow. To help keep the lines distinct, especially on more complex objects, label each point on the object and their corresponding shadow, and in the end simply con- nect the shadow points in the same order as in the object. If an object is ﬂoating, establish the ground ﬁrst, and project all lines to that ground. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 4: SHADOWS - RAY LIGHT 11 light source Ray light is a projecting light, or re- ferred to as artiﬁcial light such as a light bulb. Similar to sunlight, shad- ows for ray light are determined by the same two factors - altitude (angle) and direction of the light source. Un- like sunlight however, ray light can be placed in a manner which multiple ob- jects in a single view can have shad- plan light ows in various directions (as shown on right). First establish the angle and direction, they must be align vertically. Then project the light in the same manner as in the sunlight exercise. Label the points as necessary to help keep them organized. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 5: SHADOWS - FRONT AND BACKLIT 12 Front and backlit shadows simply im- ply the direction from which the light source casts the shadows. Front lit objects have the light source in front, thus the shadows are cast behind the objects. Contrarily, backlit objects have the light source from behind, casting shadows in front of them. All the shadows are constructed in the same manner as the previous exer- cises, with addition attention paid to the location of the light source to pro- duce the desired effects. On the right, the two diagrams illus- trate the ideal altitude and direction of light to create shadows, indicated by the hatched areas. Below are two more diagrams illustrating the front and backlit setup for sunlight. Note that the shadow vanishing point (SVP) must be located on the H/EL, with the auxiliary vanishing point (AVP), the angle of the light, directly above or be- low. In the case of ray light, the SVP can be above or below the H/EL. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 6: PYRAMIDS - STANDING/TIPPED 13 A pyramid is another form that can be derived from a simple cube. It is sim- ply a square base that converges into a single point at a certain height. A standing pyramid is quite basic, simply follow the steps in drafting a cube but only establish a single point to which the base will connect. How- ever, a tipped cone is much more challenging. To be able to draft in perspective accurately the slope of the tipped surface, the orthographics must be constructed. First draft the orthographics of the standing variation. Then draw an arc with the same length of the sloped surface from the corner to the side in which the pyramid is to be tipped. This arc establishes the new “base” of the tipped object. Simply ﬁnish the object by drawing the arc length from the new tip back in the original direc- tion, and another arc with the length of the original base to establish the ﬁnal corner. Finish the plan view and proceed to project it into two-point perspective. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 7: CIRCLES IN ONE-PERSPECTIVE 14 A circle in perspective (CIP) is simply an ellipse. First create a grid in one- point perspective. Begin to ﬁll in the ellipse and use the grid as a guide. The vertices intersect the midpoint [in perspective] of each box. Perfect freehand drawing the shape of an el- lipse simply by repetition and practice. Notice the gradual rotation and elon- gation of the ellipses as they move further away from the center of vision. This is due to distortion and should be avoided. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 7: CIRCLES IN TWO-PERSPECTIVE 15 Constructing a circle in two-point per- spective is similar to that in one-point. First create a cube, and include the orthogonal lines as guides. Again, practice freehand drawing the el- lipse forms and ﬁll in the ellipses onto the surfaces. Note in the examples that the central axes of the cubes are shown; they connect to the cor- responding vanishing points. For the majority, these axes double as the mi- nor axes of the ellipse. The concept is that the minor axis converges to the vanishing point and the major axis is perpendicular to the axis of the form. Only exception is when the surface is so close to the edge of the view that is becomes distorted, and should be avoided. These axes can be very helpful in creating the correct ellipse. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 8: CYLINDER - STANDING 16 A standing cylinder is simply an ex- truded circle. Instead of using the previous hand-sketch method of cre- ating the CIP, here is a point-by-point method that is more accurate. This method requires the use of a grid on the plan view. Select points along the circumference, equally spaced is more desirable, and create a grid us- ing such points. Using the plan pro- jection method, convert the circle and the grid into a three-dimensional plan. Once the plan is converted, simply connect the corresponding points within the grid to form the circle - now an ellipse. Project a second plan at a set height, and repeat the same process for the top of the cylinder. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 8: CYLINDER - ROLLED 17 A rolled cylinder is simply a cylin- der standing on its side. The point- to-point method used to construct a standing cylinder will be used here. Start by creating a grid over the ortho- graphics. Translate this grid in three- dimension ﬁrst to the front face of the cylinder, therefore place this grid vir- tually. Duplicate this grid for the rear face of the cylinder. Connect the two faces by their tangents and the cylin- der is complete. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 8: BOX WITH SWINGING FLAPS 18 This exercise is to use the concept of circles in perspective to locate a point (or object) along an arc, such as a open door. Orthographics must ﬁrst be construct- ed, and the angle of the ﬂaps are de- termined. An arc is drawn to indicate the “swing” of the ﬂap. A grid is then imposed to deﬁne the arc. Simply draw the box and add the ﬂaps on using the point-by-point method as in the rolled cylinder exercise, except here only a portion of the circle (the arc) is necessary. Once the point for the ﬂap is locate, repeat the process to deﬁne the other end of the ﬂap and connect the two. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 9: CONES - STANDING/TIPPED 19 The cone is a similar form to the pyra- mid. Instead of a square base, it has a circular one. For a standing cone, simply draft the base, a circle, in per- spective and converge into a single point at a certain height. A tipped cone is much more complex. To be able to draft in perspective ac- curately the tipped surface - the circu- lar base, the orthographics must be constructed. Follow the steps for tip- ping the side views of a pyramid. First impose a grid on the perfectly circular base of the standing cone. Using the side views, translate this grid onto the plan view. Note on the true plan view, the circular base is an ellipse due to the sloped orientation. To construct the perspective, simply convert the plan grid into three-di- mension, and project the height using the orthographics. Finally, connect all the points for the CIP and converge its tangents to the tip of the cone. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 9: DOME 20 The dome is simply half a sphere, and since a sphere is a perfect circle in all perspective, a dome is easily a perfect semi-circle. Construct the orthographics for the dome. Create a grid on both the plan and side views, then translate the plan grid into three-dimension. Once this is completed, use translate the side view grid into the perspective at the diameter (or quadrant) of the circle. Do this twice at 90 degrees apart, this will deﬁne the main axes of the dome, also the highest point, along its diam- eter. Once the two semi-CIP (arcs) are drafted, simply use a compass and connect to your best ability a perfect arc that passes through all points - the two vertices on the plan and the inter- section of the two arcs. You will notice that it is impossible for a single arc to intersect with all these points. How- ever, there should be two that come very close. Simply converge the two for a close ﬁt. This discrepancy is due to the fact that this is a two-point perspective, where the third (vertical) vanishing axis is disregarded, thus creating this minor distortion. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 10: INTERSECTING ROLLED CYLINDERS 21 Intersecting two cylinders is an intro- duction to more complex and com- pound objects. For this exercise, two rolled cylinders are used. As with many of the exercises, the or- thographics are crucial and essential in order to construct the perspective drawing. Here, the object must be draw and their intersection properly located, as desired, in plan and side views. Follow the same steps for the single rolled cylinder exercise and place a grid on each individual cyl- inders. It may be beneﬁcial for both circles to share grid lines, however, depending on the size differences, it may be necessary to use a smaller grid for the smaller circle. The second and most important part process is identifying the actual inter- section of the cylinders, in this case - the plan view. Carefully translate the intersection points from the side and front views to the plan view. Once all the intersection points are estab- lished, continue with the typical steps and construct the perspective draw- ing. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 10: COMPOUND FORM (PLAN PROJECTION) 22 As an introduction to compound forms, an object is designed to be drawn us- ing the plan projection method. The object simulates a vehicle, with a dome as the main body and several intersecting cylinders as the wheels. As with previous exercises, the ortho- graphics of the vehicle are drawn, and grids are constructed over the circu- lar forms. The plan is then translated into three-dimension, and the height is then projected to form the ﬁnal ob- ject. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 11: COMPOUND FORM (3-D GRID) 23 Another method of constructing per- spective drawings is through the use of a three-dimensional grid. The con- cept is to create a grid in the ortho- graphics, then directly translate this grid in perspective, so the ﬁnal object can be drawn by deﬁning location of its individual component without the use of the plan. In the sample drawing, a simply race car is constructed in the orthograph- ics. A grid is imposed over the views to deﬁne the location of each line and shape. The grid is directly translated into the perspective in three-dimen- sion. Note the omittance of the plan in three-dimension. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 11: 12-POINT ELLIPSE 24 This method of drawing an ellipse (CIP) is a short- cut to the point-by-point method. Instead of having to create a grid on the orthographic view, and hav- ing to translate that grid in three-dimension, a grid is directly created in perspective as guidelines for the ellipse. 1) Divide the surface into quadrant by ﬁnding its center 1 2 2) Divide each quadrant into more quadrants in the same manner 3) Connect the diagonal lines between the outmost quadrants as shown 4) Connect all the points at various intersections as shown Notice the ellipse is much more facetted than one that would be constructed from the point-by-point method, simply because this method provides much fewer points for connection. Use this method only as a guideline, sketch over with a smoother ellipse by hand afterwards. 3 4 Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 12: REFLECTIONS 25 Reﬂection is simply the mirror image of an object on a different surface. The following steps apply when creating simply reﬂections on a surface that is par- allel to the object and perpendicular to the ground. 1 2 1) Establish the reﬂecting surface in relations to the object 2) Locate the midpoint of the object and extend it through the “mirror” to the vanishing point. Where this line intersects with the mirror will deﬁne the midway distance between the mirrored and actual object 3) Extend the sides of the object to the same van- ishing point. Draw diagonal lines from the corners crossing through the intersecting point. Extend the 3 4 diagonal lines to establish the corners of the mir- rored object 4) Extend the top edges of the object into the mirror and connect them with the base lines established in step 3 and deﬁne the front face of the object 5) Repeat steps 3 and 4 for the rear face 6) Attach the two faces and the object is now re- ﬂected 5 6 Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 12: REFLECTIONS 26 Setting up the objects correctly is key to creating interesting reﬂections, they should be fairly close to one another. Sloped and angled surfaces are more difﬁcult for constructing reﬂections. In order to establish the correct reﬂec- tions, orthographics of these objects must ﬁrst be created. The purpose of the orthographics is to help deﬁne the perpendicular relationship between the object and the mirror, without them, it is impossible to ﬁnd the per- pendicular in perspective. Once the perpendicular is established, it can be translated into the perspec- tive drawing. Simply follow the same steps as the simple reﬂections, using the perpendicular line (instead of the vanishing line) as the axis of which the object is reﬂected. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005 EXERCISE 13: FINAL PROJECT 27 The ﬁnal project is a combination of all the previous exercises. It is a small, portable USB hard drive. The object is a composition of many different el- ements, including a dish (reversed dome), a partial cone, a half-cylinder and other rectilinear forms. Many details are added to the object as well to improve its appearance. The edges are rounded to provide smoothness and ﬂuidity. Parting lines are drawn to establish some realism. Slices (section lines) are added on the object to better illustrate its form. Lastly, a ray light, backlit shadow is created. Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005