The ellipse is then approxi- sion of the minor axis. With the rough approximation complete, centerline can eliminate distortion in the draw- the major and minor axes can be approximated ing of circular forms in perspective, and allows to aid in refinement. The minor and major axes for freehand sketching of ellipses as well as should not be confused with the diagonal divi- construction of complex linear perspectives. In perspective drawings, circles are drawn as ellipses. The major axis is found at the widest diameter of an ellipse.
The minor axis is found at the narrow diameter and is always at 90 degrees to the major axis. The centerline of a cylinder is drawn as an extension of the minor axis also at 90 degrees to major axis. When found on a horizontal plane such as a floor, the major axis is horizontal. Our view of the ellipse varies according to the location of our eye level horizon line ; elliptical templates are used to easily approximate the various views.
Based on their geometry, as shown at the top of the figure, ellipses can be esti- mated by creating an enclosing plane and plotting locations on diagonals: 1. Create an enclosing plane that appears square in perspectve; divide the plane with diagonals as in diagonal division. Mark the center as located by the diagonals. From the center mark, extend lines vertically and horizon- tally; these lines will define midpoints of the enclosing plane. Mark the locations where these lines are tangent to touching the enclosing plane.
Divide each half of the diago- nal into thirds and make marks at these locations. Sketch the ellipse by locating the mark two-thirds from center and drawing con- necting curvilinear lines from the two-thirds mark to the adjacent midpoint mark.
Refine the ellipse by visual assess- ment. Note: quarter divisions of the square are not the major and minor axes. These divisions are for estimation purposes only. The major axis is actually slightly forward of center dashed line. The central leg of this table is formed by a center line extend- ing from the top minor axis to the lower minor axis.
A full cylinder can be sketched using an enclosing cube to Many designers use elliptical templates to perhaps the single most effective tool in free- create the forward and rear planes; these are then used to create accurate ellipses and curvilinear forms.
It is worthwhile for form the required ellipses. The use of elliptical templates is based on the students to practice by filling pages with 9.
Refine the final drawing by locations of the major axis, the minor axis, and boxes drawn to look square in two-point per- visual assessment. When templates are spective. Once this skill has been developed, used, the two-thirds estimating method is not the box is drawn as an enclosing form, like a employed. Starting with a simple box, and adding square-looking box accurately. Employing the cube is employed to construct items that are principles of perspective mentioned thus far quite different in form from the original en- allows for better drawing and for the use of closing cube.
Sketch a box that approxi- mates the dimensions of the object. Make sure the vanish- ing points are generously spaced. Create a measuring line at the front corner of the box. Mark equal divisions of the measuring line these can be eyeballed or estimated with diagonal division.
Use the measuring line and diagonal division to rough out details and proportions. Overlay with clean tracing paper and refine details. Use a clean overlay for a final drawing; a combination of freehand and drafted lines often look best. Drawing by Leanne Larson. Drpic, Ivo.
Sketching and Rendering Interior Space. New York: Whitney Library of Design, Forseth, Kevin, and David Vaughn. Hanks, Kurt, and Larry Belliston. Rapid Viz. Los Altos, Calif. McGarry, Richard, and Greg Madsen. Pile, John. Perspective for Interior Designers. A square drawing that work well in the creation of accu- that serves as the back wall of the room can rate, beautiful drawings.
However, it is impor- then be drawn that is 10' by 10' in any appro- tant to note that all of the most accurate and re- priate scale or eyeballed. The horizon line fined methods of perspective drawing require a should bisect the square at its vertical mid- great deal of time, ranging from one hour to point.
Next, a single vanishing point is located eight hours or more. These may be appropriate on the horizon line slightly left or right of cen- for final design development presentations, but ter. Perspective lines indicating depth are cre- time constraints require designers to develop ated by drawing lines from the vanishing point quick sketching techniques in order to use through all four corners of the square.
The drawings throughout the design process. Quick overall depth of the room is simply estimated. The depth must be estimated in a way that The easiest method of quick sketching in- makes the room look square. This is the tricky terior environments has as its foundation the part — which takes some practice. Once this is box-sketching techniques discussed previ- accomplished, architectural elements can be ously.
This estimated method allows us to cre- drawn by using measurements found on the ate a perspective of a ten-foot-square room by back wall the original square and estimating drawing a giant ten-foot-square box in one- depth. Diagonal bisection of planes can be point perspective. Figure is a quick refer- used to find depths of walls and correspon- ence to this estimated one-point perspective ding objects. Divide the square using diago- nals. Draw a horizontal line through the center.
This is the horizon line H. Place a van- ishing point on the horizon line slightly left or right of center. Draw perspective lines from the V. Now estimate the depth of the room — make it look square.
Use diagonals to divide the original square see Figure , which is now the back wall. If necessary, a grid can be estimated through diagonal division. On side walls, verti- cals are located where height lines intersect diagonals.
Use measuring increments created in step 4 or a grid to locate objects and architec- tural elements. Use a clean overlay to create a line drawing. To raise or lower the ceiling, simply draw lines from the V. Diagonal exten- sions can be used to enlarge the room see Figure Curves are found by plotting and sketching in appropriate locations.
This is cess of this method. The lo- appropriate dimension to the back wall the cation of the single vanishing point is impor- original square and extending the walls to the tant because walls and objects located very desired height.
It is useful to draw a few quick this method allows for the original 10' by 10' thumbnail sketches of the space, using the es- square to serve as the starting point for a room timation method, to locate the vanishing point of another shape. Dividing and adding to the and visualize the space being drawn. Thumb- room using diagonal bisection allows for the nail sketches aid in the location of an appro- creation of a variety of room sizes.
Once again, priate view of the space and the location of the the ability to see and create the original square vanishing point. Figure and modifying it. Figures elongated to set up the structure Ca, b, c show the process of of the larger environment in this color-rendering this drawing. With the basic proportions of the environment complete, furnishings and additional elements can be roughed in. Measurements are based on rough ap- and design development phases of a project proximations.
For example, the horizon line is prior to the completion of a full set of ortho- placed at roughly five feet in height, providing graphic drawings. Figures a, b, c, a, b, c, a view of the space from a five-foot eye level. Practice generating these types We can imagine that most pieces of furniture of drawing can provide the skills necessary fit into a inch-high packing crate.
Therefore, for drawing quickly and directly in client much of the furniture is roughed in as inch- meetings with simple pens and no tools Fig- high boxes. Human figures drawn to scale ures a and b. Most of the more refined should be included in interior perspectives and methods of linear perspective require com- are best placed with eye levels at or near the plete scaled plans and elevations, thus necessi- horizon line. More information regarding scale tating that the design be complete prior to the figures can be found in Appendix 4.
The This method of quick sketching, using more refined perspectives are useful as a rough approximations, allows designers to means of presentation but are not as helpful draw space as they design it. It also allows as a quick means of exploring design options perspective drawing to be integrated into the or brainstorming.
The bold lines in this drawing indicate FIGURE C the back wall of the orignal 10' x A final clean copy of the drawing 10' room; dashed lines indicate can be traced and readied for the areas in which the ceiling rendering if necessary. Figure was altered, in this case to indi- C is a color rendering of this cate a shed roof in a small New drawing. Mexico cabin. With the basic pro- portions of the environment com- plete, furnishings and additional elements can be roughed in. The bold lines in this drawing indicate the back wall of the orignal 10' x 10' room; dashed lines indicate the areas in which the room was altered, in this case to create a much larger exhibition space.
Sig- nage can be generated, photo- copied, and pasted onto the draw- ing. Fig- ure illustrates this drawing as manipulated digitally. This group of drawings was sketched in less than ten minutes using ink pens. One-point interiors are helpful and easy to cre- In the two-point method a 10' by 10' square ate but are limited in use because of problems room is drawn first as a guideline for further with distortion, particularly in drawing furni- development.
Figure is a quick reference for ture and freestanding objects. Because of the the estimated two-point perspective method. Draw a single vertical line to serve as a measuring line. Divide the line into four equal segments. At the midpoint, draw a horizontal line; this is the horizon line H. Place two vanishing points on the H. Draw lines from each V. This creates floor and ceiling lines. Now estimate the depth of room — make it look square. To create a grid, draw diago- nals on each wall.
Then, at the intersection of the diagonal and each height line, draw a vertical. Use the grid to estimate archi- tectural elements and objects. Note: grids are not always nec- essary; for simple spaces it is best to simply estimate meas- urements. Use a clean overlay for tracing and refining the drawing.
Raise or lower the ceiling by estimating the desired height. Extend the room using diagonal division see Figure Curved surfaces are estimated by using a grid. This vertical measuring line The originally estimated square room can be serves two important functions: first, it is the modified to create a lower or higher ceiling by only true measuring device in the drawing; sec- simply extending or reducing the dimensions of ond, it can become the back corner of the the original vertical measuring line and extend- room s being drawn.
A horizontal line is then ing lines to the vanishing points. The walls of the drawn through the middle of the vertical line room can be reconfigured easily by diagonal bisecting it at the five-foot mark. This is the subdivision and extension. One should be located fairly close ronment is the key to the success of this method.
The second should complicated items and architectural elements are be located far from the vertical measuring line; easiest to draw when placed on the wall created this is referred to as the far vanishing point. This is because the Next, draw a line from the near vanishing wall generated by the near vanishing point tends point to the very bottom of the vertical meas- to become distorted. A common distortion prob- uring line and extend it forward, creating the lem in two-point perspective drawing is caused floor line.
Repeat the process with the far van- by locating the two vanishing points too close to ishing point. Lines are then drawn from each each other. This creates a distorted, unnatural- vanishing point to the top the tenth increment looking view of the space.
If in the process of of the vertical measuring line and extended using this method your drawing becomes dis- forward, creating the ceiling line. The depth of the room must now be a few thumbnail sketches of the space to locate estimated. The overall room depth is approxi- the vanishing points and visualize the space mated by visually assessing the room and cre- being drawn.
Thumbnail sketches allow for the ating a square-looking box of a room. As with location of an appropriate view of the space and one-point estimation, this is the tricky part. The the proper positioning of the vanishing points. Measurements With the use of this method, architectural are based on rough approximations. For exam- elements and freestanding objects are located ple, the horizon line is placed at roughly five by measurement and estimation.
The vertical feet in height. This gives the drawing the over- measuring line can be used to find vertical all view at eye level of the viewer. We can measurements; these are taken from the van- imagine that most pieces of furniture fit into a ishing point through the vertical measuring inch-high packing crate.
Therefore, much of line and plotted on the appropriate wall. In the furniture can be sketched into the space as cases where objects are freestanding, heights inch-high boxes.
Human figures drawn to can be determined by extending a line from the scale should be included in interior perspectives vanishing point through the appropriate height and are best placed with eye levels located at or on the wall to the location of the object. Depths near the horizon line. This method of estimat- are estimated using diagonal division and ex- ing two-point perspective drawings perspective tension — dividing the walls with diagonals allows drawing to be integrated into the design and finding the midpoint of the room at the in- process during the schematic design and de- tersection of the two diagonals.
The bold lines in this drawing indicate the back wall of the orignal 10' x 10' room; FIGURE D dashed lines indicate the areas in which the room A final clean copy of the drawing can be traced and was elongated to the left and the ceiling was low- readied for rendering if necessary.
In preparing this ered to roughly eight feet above the floor. Visualization skills are funda- tive drawings. The more refined perspectives mental to the design of interior environments.
Refined, measured linear perspective require complete scaled plans and perspectives are most useful as a means of elevations, thus necessitating the design to be presentation for clients, end users, real estate complete prior to the creation of the perspec- professionals, investors, and the general public.
The bold lines in this drawing indicate the back wall of the orignal 10' x 10' room; dashed lines indi- cate the areas in which the room was elon- gated to the left and the ceiling was lowered to roughly eight feet above the floor.
The drawing is then contin- ued by adding necessary details and refining design elements FIGURE C A final clean copy of the drawing can be traced and readied for rendering if necessary. In preparing this more refined drawing, tem- plates and tools were used. The bold lines in this drawing indicate the back wall of the orignal 10' x 10' room; dashed lines indicate the areas in which the room was elongated to the rear of the origi- nal square.
This particluar drawing was done very early in the design process and was used to consider the entire volume of the retail design. Type was printed and pasted into the signage area as a means of understanding scale isues. In prepar- ing this more refined drawing, some elements were drawn free- hand while tools were used for others. The type shown in the pre- vious figure was modified by C hand to relate directly to the right vanishing point.
The plan projection The perspective drawing concepts and skills method requires a completed scaled floor plan covered thus far can help us gain valuable visu- and scaled elevations, which means the project alization skills. These skills are easily trans- must be well resolved for this method of draw- ferred to the refined, measured methods of lin- ing to take place.
Figures a and b illus- ear perspective. Therefore, the ability to draw trate step-by-step plan projection instructions. The ability to create refined perspective pres- Although it is useful and highly accurate, it entation drawings is useful for all environmental can be confusing at first because it requires designers.
Most firms have at least one employee going back and forth from plan view to per- and often several who is considered to be a per- spective view. To minimize confusion, one must spective drawing or rendering specialist. Such understand that the floor plan is used to set up individuals are often called upon to do much of the final perspective elements and measure- the detailed perspective drawing and rendering ments.
In this method the floor plan is manipu- for the firm. These drawings are generally cre- lated to provide information that is projected ated well into the design process and are not onto the perspective drawing.
It is also To begin this method, decisions must be quite common for firms to hire professional de- made as to what view of the space is desired, the sign illustrators and renderers to create highly location of the viewer, and the cone of vision. Firms often select a particular within a degree cone of vision. This points to the fact that there is never a the orientation of the viewer, the plan is set up single way to illustrate space; there is a range of against the picture plane also drawn in plan.
The plan setup must also include the loca- A wide variety of methods of measured tion of the viewer in plan; this is known as the perspective drawing are used in practice. I station point, but I like my students to think of have found that certain methods work best for it as the head of the viewer in plan. The station certain people. People who draw well in meas- point, or location of the viewer, is extremely ured perspective employ the particular method important to the success of this method.
The that works best for them. For this reason a va- location of the station point dictates the view riety of methods are discussed briefly and il- of the space, as well as the cone of vision and lustrated in the following sections.
Students other key elements, such as the location of the should experiment with the described methods vanishing points. A the plan, to the picture plane, and then pro- comparable method is used commonly for ex- jected onto the perspective drawing. Draw a horizontal line; this is the picture plane P. Select the desired angle of view and orient the plan so that the rear corner touches the picture plane. Locate the station point S. Locate the station point one to three times the height of the interior space from the focal point of the drawing.
Draw lines from the S. Draw a horizontal line below the plan setup; this is the hori- zon line H. Project the location of V. Project a line from the rear corner of plan vertically to the H. It can be measured in scale to match plan ; it will also be the back corner of the room. The horizon line must be located at 5' to 6' in scale on the M. These are the wall and floor lines.
Repeat this step with V. Next, draw lines from the S. Project these locations vertically onto the drawing. Project these locations object and extend them to the P. Project these 3. Find the height of objects by drawing a line from vertically onto the drawing.
To find a floor location, first transfer the furniture height on the M. Then draw 4. The object is completed with lines drawn to the available elevation.
Next project locations on the P. But it can be time-consuming and the picture plane and 2 those then projected sometimes leads to unexpected distortion, re- from the picture plane to the perspective draw- quiring the entire process to be completed a ing. Measurements of width and depth are pro- second time. I find that the method works best jected from the picture plane onto the perspec- for environments based on simple geometric tive drawings.
Heights are taken from the forms rather than those based on complex or measuring line or elevation s and tranferred to organic forms. Figures a — j delineate the appropriate location. In beginning the drawing, the desired view must be selected. In this case the plan is ori- ented to provide a view of the rear corner of the kitchen to include the kitchen cabinets.
The picture plane should pass through the rear corner of the plan with the walls you wish to include in the drawing on the left and right. Create a station point directly below the rear corner of the plan there are other ways to do this, but this is the easiest. The station point indicates the location of the viewer. This point should be located roughly 2—3 times the height of the room in the same scale as the plan.
Draw a line dashed here from the station point to the picture plane; this line must be paral- lel to the back walls of the A room in plan. The actual perspective drawing was created. It is helpful to 8. A horizontal line is now drawn 9. Wall and ceiling lines can now or above the plan. The line projected in 5 now the perspective drawing.
In ing point to the appropriate becomes the measuring line. This line is drawn to the located at eyeball height, in this desired height of the room in case 5'5".
The vanishing points this case nine feet , in the should be projected vertically same scale as the original plan directly from the picture plane onto this new horizon line. Wall and object locations are found by locating the item on the plan and projecting a line from the station point to the location on the plan, onward to the picture plane, and down onto the drawing.
In this case a line is drawn from the station point to the cabinet, onward to the picture plane, and then projected verti- cally from the picture plane to the drawing. Note: If your drawing looks weird, you are not projecting consistently down from the picture plane.
The height of the lower cabi- nets is found by counting off the measuring line, in this case 3'. Some people prefer to obtain the height dimensions by transferring them from the adjacent elevations. The sink location is found by drawing a line from the station point to the front corners of the sink, onward to the picture plane, and then onto the drawing.
The dishwasher is found by drawing a line from the station point to the front corners of the dishwasher, onward to the pic- ture plane, and then onto the drawing. To find the heights of the wall cabinets it is necessary to first locate the height on the origi- nal measuring line in this case the height information is transferred from the adjacent elevation. Because the cabinets are recessed into the wall see plan , it is necessary to draw a line from the station point to the rear edge of the cabinet, onto the picture plane, and project C this location onto the drawing.
The lower cabinets are com- pleted when lines are drawn from the edges of the cabinets to the appropriate vanishing points. The angled portion of the lower cabinets is created by drawing a line from the station point to the edges of the angled portion onward to the picture plane, and then the lines are projected onto cabinets in the drawing. The location of the stove is found by draw- ing a line from the station point to the front corners of the stove, onward to the picture plane, and then down onto the drawing.
This piece of furniture is located by draw- ing lines from the station point to the three visible edges of the object, onward to the picture plane, and then onto the drawing. The height of the object is determined by locating it on the measuring line and then transferring, by use of the vanishing point dashed lines. The upper cabinets can be completed by working from the measuring line and the vanishing points, similarly to step 3 above.
The island, which is freestanding, is drawn using a combination of projected lines. Because the item is freestanding, its height and actual floor location must be deter- mined by transferring the object location onto walls in plan setup dashed lines in plan.
Lines are then drawn from the station point to the plan wall locations found in 2 above, onward to the picture plane, and then onto the corresponding walls in the perspective drawing.
Now, working on the perspective drawing, lines are drawn from the left van- ishing point to the location where the wall projection done in 2 meets the floor, and these lines are extended foward to the cor- ners of the island.
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