When I was first introduced to the concept of linear perspective, I was fortunate because it wasn't in a dry, boring geometry lesson but in an art history class. Perspective drawing handbook / Joseph D'Amelio ; illustrations by In Perspective Drawing You Draw What You See, Not Your Idea or Mental Image of the. Seventeen reproductions of ancient and modern art plus more than instructive figures complement this functional approach to perspective drawing. The first.

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The Theory and Practice of Perspective by G. A. Storey. No cover available. Download; Bibrec Download This eBook. To get a more realistic looking drawing, a distortion called foreshortening is used. This is the basis of perspective drawing. Examples of different ways that. Read "Basic Perspective Drawing A Visual Approach" by John Montague available from Rakuten Kobo. Sign up today and get $5 off your first download.

No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means - graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems - without written permission of the author. Perspective is found in all types of printed matter. In all instances drawings depicting ideas or real objects are communicated to a wide variety of viewers. Perspective has been with us for a long time. Adding overlap and a single vanishing point gave the illusion of objects gradually getting smaller as they went farther away. Two and three point perspective brought about new possibilities as it became necessary to show what objects and buildings would look like before they were manufactured or constructed. Designers then began to find better ways to develop their perspectives that would use less construction - resulting in faster solutions. Also, new tools such as ellipse guides and perspective grids have been introduced to help quicken this process. There have been several good textbooks which have each made a contribution to help us understand these processes. Unfortunately, they are now out of print.

In all instances drawings depicting ideas or real objects are communicated to a wide variety of viewers. Perspective has been with us for a long time. Adding overlap and a single vanishing point gave the illusion of objects gradually getting smaller as they went farther away. Two and three point perspective brought about new possibilities as it became necessary to show what objects and buildings would look like before they were manufactured or constructed. Designers then began to find better ways to develop their perspectives that would use less construction - resulting in faster solutions.

Also, new tools such as ellipse guides and perspective grids have been introduced to help quicken this process. There have been several good textbooks which have each made a contribution to help us understand these processes. Unfortunately, they are now out of print. I have taught perspective for many years and have not found a comprehensive textbook.

I solved this by writing a supplement in syllabus form. The syllabus eventually grew until it replaced the text. Use these forms to practice the short cut Measuring System.

After selecting which system you want to use, develop the objects using a light construction line and then heavy-up the object lines to make them stand out. Do at least one for each system, i. Right or 2-Pt. Left, 2-Pt. Measuring System. This allows you to draw in full size or scale and measure everything in true length. A great deal of depth is still possible. Another advantage is that circles are still circles and can be easily VP HL.

In later chapters we will cover the circle as it turns from our line of sight and becomes elliptical. The drawing below was constructed using a modular application of a cube that was multiplied to double the proportion. Details were measured in true length on the front surface. Before creating your finest drawing ever, become familiar and at least 1 piece turned at Find its VPs on the with the 3 different ways to find the MP.

Then try to draw HL. It is always best to draw a plan view of your several different sized boxes on the same floor plan. Make room first. They can represent rooms or objects 3. Draw a cube and multiply to a large structure. Make like furniture. Develop a Floor Grid of any size. Place several vertical above.

Construct or trace a large letter facing you. Take all line of sight and at 90 to you. Give 6 inch thickness to edges to a VP. Pick a letter depth and measure remaining these walls.

Place several pieces of furniture on the grid depth details. This is taken down to point B. As you can see from this construction, the MP is approx. This technique involves strenuous construction and uses a large area of space below the view which is usually unavailable on a small sheet. This creates a single vanishing point and all other lines are either horizontal or vertical.

Unlike Two-Point Perspective where the Vanishing Points are distant from the view, this Vanishing Point is now inside the view or its proximity. This distance must be far enough to give a 60 Cone of Vision. Without this quideline, distortions will appear at the outer edges of the view. Drawing shows how squares distort as they pass beyond the circle. Draw HML in size and scale needed. Establish HL and extend to right or left side. Establish HL and extend to right or left.

Move a horizontal line up and down until it appears to represent a square lying on a horizontal surface. Draw a diagonal to find MP. This moves the observer forward and back until it looks visually correct and gives a way to vary the depth.

HL VP. Pick a MP at a random distance from the VP. Draw the HML anywhere within this circle. The object will not be distorted. Be careful at this stage because the looks of the entire drawing will be effected by this depth and the location of the VP.

Draw a line to MP from the most distant point on the grid 12 here. This will cross the VP line from O to give 12 deep. Begin to grid the square by drawing depth lines using the equal measurements along the HML to the VP. Finish the grid by drawing horizontals where these depth lines cross the diagonal to MP at dots. Increase the depth to 17, 24 or any additional depth by using diagonals wherever the measurement is needed.

Establish a Vanishing Point VP off center and connect ground lines to front two corners. Establish MP at twice the distance of long diagonal VP-A this will give a short cut solution for a 60 Cone of Vision and will not be distorted.

If the room is made wider, a new MP should be found. Connect all other corners to VP. Construct a grid by connecting measurements along HML to the VP and drawing horizontal depth lines through their 15 foot back wall. Construct back at 15 feet deep using verticals at corners. Project fireplace, stairs and table using grid and measured heights along each wall from the elevation MP view.

Only 1 MP is shown here, but there are always 2 MPs. Either or both MPs can be used for depth measurements. For other degrees of rotation each corner of the object is located on the perspective grid first and then lines are drawn through the respective corners to locate their VPs. This semidetailed view of a shopping mall shows how a 1-point view might be used to develop a design solution. Depths and elevations are changed at random until the ultimate solution is found.

Eye level here is at 10 feet. A single block is multiplied to gargantuan proportions, if necessary, or can be divided down into minuscule increments. Many times it is necessary to construct a drawing of an object that does no yet exist and whose dimensions are not yet known. In this case it is a good idea to construct forms from building blocks called cubes. These are the same dimension in height, width and depth. If the proper number of cubes can be placed together in the right numbers, any proportion in height, width and depth can be constructed.

The following steps show how a cube can be constructed in 2 Point Perspective from its square elevation. This elevation can be placed in the right scale and the correct distance from the HL for desired eye level. To avoid distortion it works best if the front corner of the cube is near the center between the VPL and VPR or placed within a 60 cone circle.

The system works by assuming that the Horizontal Diagonal HD is a true horizontal. This is only true at the center of VP's, and is not always the case in other methods. The 2-Point Center, Left or Right Method discussed in Chapter 3 can be used also to construct a cube if measuring points are used. Measuring Points defeat the purpose of Multiplication or Division since measurements of any size can be made directly.

Note that this method works for a cube only. Construct HL with both VP's as wide apart as practical 4. Find front corner of cube by projecting lines from for your paper size and work surface. Place side elevation square of needed scale within the 5. Draw a vertical at the found front corner. Cone of Vision and near center of the VP's and at desired distance below eye level. Find Horizontal Diagonal HD by taking the vertical diagonal of the square to the horizontal base line.

This gives the Horizontal Diagonal Plane in true length. This works at this location because the Horizontal Diagonal is a horizontal line at center of VP's only. Take outside corners to both VP's. Finish the cube by taking a vertical through the found back corners. Now the cube can be multiplied to other sizes. In orthographic views the divisions are made by using diagonals to find the center of each surface and then lines parallel to the sides will divide the surface in half. The same method works in perspective.

The height is divided into the number of equal steps needed and the diagonals do the rest for you. Radiate lines from a chosen Radiate lines from a chosen of form. Pick an enlargement of form. Pick an enlargement to original view. The cube is used as a building block for the larger object.

Once the cube is divided by diagonals to find its center, it can then be multiplied into any proportion wanted. This can be accomplished in different ways depending on which multiplication is done first. What makes this method so great, is the option of changing the size quickly, without having to start all over again.

The cube side is divided by crossing diagonals. A line through midpoint is taken to VPL and used to multiply the cube to the left two times using half diagonals making the width 3 deep.

Cube is multiplied in height by taking the half diagonal to the extended front vertical line of the original cube. Be careful about using exact points, as noticeable error can occur. Check the doubled height, by using a ruler or similar device. The cube can be multiplied to 4 one cube at a time or by using full diagonals of the doubled height. The horizontal plane can be multiplied also by using horizontal diagonals as first constructed on the original cube. This is the best approach if the object covers a large horizontal surface.

An overall grid can be constructed in this manner and will be discussed in the following section. Draw additional Horizontal Diagonals through the far edge of each found square. In this method the height of the doubled cube is found taking the full diagonal dashed line from the second horizontal square. You can enlarge each side in proportion by drawing a diagonal from a common corner Z across each side.

The second diagonal will give you the depth of the second side at Y. VPL X Y. The common corner picked will remain stationary. This means that if you want the top to remain the same distance below HL, pick the top corner instead of the bottom. Once the back two walls are developed and divided equally in the back corner, the wall heights are projected outwards and diagonals give the vertical divisions. Develop the grid on the walls first and then the floor.

This grid has a good application for an interior showing a corner of a room. The figure adds scale with eye level at 5'. Once the cube is developed, there is a square in 2-Point Perspective on the horizontal plane. This square can be multiplied as in previous exercise by using the HD of many multiplied squares. What appears here is a horizontal plane that is divided into squares using 2 different methods.

Each multiplication represents a square in 2-point perspective. The vertical measurements are taken along the VML which is the vertical multiples of the original square used to set up the grid. This Grid could be used to make many different drawings with objects placed in many different locations.

This makes it possible to use any corner as the leading corner of a view or a detail within a larger drawing. Figure below shows the development completed. Each at any depth in by measuring or can be reversed. Multiply that distance vertically 45 construction shown. Figure below shows the 1 Point Perspective Grid with a stack of smaller squares using the height the same dimension as its base at that depth in the drawing.

Different grids have interior or exterior orientations. These are examples of tracing grids that were developed for small consumer product drawings and large interior layouts. There are many "ready-made" grids available. They can be very helpful, but in many cases are not very accurate and allow for over distortion. It is much better to develop your own trace grids that meet your specific needs. Any of the Measuring Systems will work in both 1 and 2 Point Systems. Figure drawing scares many people needlessly.

You might begin by tracing figures from pictures in newspaper and magazine ads.

Learn to simplify features and show relaxed stances. Once you have a style that works, try these steps for more originality. Each step is traced from the other.

Establish eye level. Block in main body parts and line in arm and leg positions, keeping good proportion. Outline main head, arm and body features. Tighten details, using simplified face and hands. This might take several steps.

Add accessories to meet the requirements of the drawing and increase interest. Figures can easily be changed, so keep your originals on file. Enlarge or reduce using photo copies. The view is moved to the outermost VP either side and allowed to distort slightly beyond the Field.

The resulting system looks very similar to a OnePoint Perspective except that all horizontal lines are not parallel and go to a distant VP. This is appealing because the resulting view is more realistic as long as the distortion is kept under control and not over done.

One-Point Perspective is often thought of as being rather static and uninteresting and not the way we ordinarily see things. Draw a Horizon Line 5' here and near one margin measure above and below in even increments making the height 8' 10' is OK.

On the other margin make the same measurements in slightly smaller increments. Connect each measurement line across to its corresponding measurement on the other side. Draw a line 45 from the vertical at the lower corner. Connect a vertical where this angle reaches the top line. This will give the first vertical measuring square representing 8' x 8'. Multiply the first 8' x 8' using half diagonals through the 4' Now draw diagonals for each square and place verticals where height.

Take these multiples out as far as your scale allows. Pick a VP near the center of the first square. This is now a completed Vertical MeasurThree is considered to be best. Make smaller if necessary. This is a chosen point representing the distance of the observer from the picture plane as in many other systems. This means that moving the DVP to the left is the same as backing away from the view.

This makes the floor appear shallower. Moving to the right makes the floor appear deeper. You now have outlines of 8' x 8' squares on the horizontal plane. STEP 9 8 8. Draw all depth lines through all points on the ground plane forward from the VP. This gives the width lines of the grid and begins the wall on the right hand side also a vertical measuring plane.

Using the DVP crossing points with the depth lines, draw the horizontal lines of the grid. Portions here were left out to show how each line is referenced. They can be drawn to the full width as well as all verticals drawn to full height.

This would be a lot of work for just one drawing. The idea is to do a solid job, even in ink, and use it over and over again as an underlay for drawings. It can be flopped to make the near "wall" on the left side. Actually, these are not walls, but measuring planes. It is possible to measure behind the Vertical Measuring Plane by counting where the DVP crosses each depth line just like the 1-Point Perspective floor grid.

Each grid square represented 1'-0". Notice that the walls do not necessarily fall at the vertical measuring plane and can be in front or in back of this plane. There is much distortion as the form gets closer to the right measuring wall. If this is a problem, move farther inward.

This will give less distortion to the right hand side. This would mean that they are constructed with a consistent radius of a specific size about a center point. Actually we seldom see a circle this way.

The only time would be when the circle is at eye level and perpendicular to our line of sight. Our perception of a circle, then, is not a true circle at all, but an ellipse that varies considerably from a perfect circle to an ellipse that is so tight that it becomes a straight line.

This can happen on the horizontal and vertical plane as well as any other plane at any angle. The circle is so commonplace when you are working with drilled holes in surfaces, circular knobs protruding from a surface, radius edges, rounded corners, cylinders of various types, cones and circular lines on spheres.

What we need for our purposes is the relationship of the Minor Axis diameter of the smaller circle and the Major Axis diameter of the larger circle. Every ellipse has a Major and Minor Axis. It is their variations that give the ellipse its perceptual difference. The above construction is very reliable for constructing large ellipses on an orthographic plane.

Other methods are necessary to find ellipses in perspective. First make a square that joins a vertical side of the perspective square. Construct a true circle within the square and draw its diagonals. Then project the lines where the circle crosses the diagonals into the perspective view. This will give 4 points around the circle in addition to the 4 midpoints of the square.

This is done on a vertical plane first and then projected to a horizontal plane if needed. A cube composed of 3 squares in perspective. The problem is to place a full circle on each surface. The projections can be taken to the next side using VPR not shown and repeated. A square and circle are attached to the vertical side.

Projections can be taken to the top horizontal surface in the same manner. Construction square and circle can now be removed. This can be accomplished on an orthographic view as well as a view in perspective. The same constructions can be done in perspective.

Use your VP's and diagonals to divide into 16 squares. The rest is just the same. The 12 points connected will give an ellipse that represents a circle within the perspective square on both horizontal and vertical planes. Orthographic construction is as follows: Divide the square into 16 smaller squares following the constructions above. Then draw the diagonals of the outside sets of four squares. Draw circle through points found at the crossing of the first grid line from each corner.

If it is rectangular, you will be constructing an ellipse in perspective - not a circle. EQUAL done infrequently. Their best application is for circles that are large. For smaller circles it is more convenient to use ellipse guides. If done correctly, this method is quite accurate and becomes very easy with a certain amount of practice. Ellipse guides are available individually and in sets of 4 or more depending on how many ellipse angles you want.

Below is a set of 4 with ellipse angles of 15, 30, 45 and 60 degrees. Each angle has a series of different ellipse sizes. Combination ellipse guides have all 4 angles on one guide.

The more Ellipse Angles you have to work with the better. Trace templates are available. Below is a circle construction on a horizontal plane using 1 point perspective. The rules for ellipse alignment can be quite simple. Shown below is the 8-point circle construction. If you overlay the drawing with an ellipse guide of the correct size and angle, you can determine the major and minor axis of the ellipse used.

When the actual minor and major axis of each ellipse is drawn, you will discover several relationships of the ellipse to the surface it is resting on. They can't be fooled.

Circles must look like circles lying on whatever plane they are on. The ellipses below were constructed using correct alinement and angles. They show the use of minor axis alignments perpendicular to the surface they are resting on.

Ellipses on the inclined plane use HL2. We have used our best judgement up to this point as to alignment and angle.

From these observations we can see that all the ellipses are the same vertically and change gradually as they move horizontally across the plane. Therefore, the only thing they have in common is a vertical line running through the ellipse center. This vertical line must somehow give us a measured ellipse angle. Since the HL crossing will only give the same angle anywhere within the circle, the only other crossing point is at the Field of Vision edge. Once this is taken to VPL for circles on planes facing left we discover that the angle the vertical centerline makes VPL with the line to VPL is the same as the ellipse angle on the ellipse guide.

This is true for surfaces facing right as well. Their angles use the VPR. Here we see that the four commonly used ellipse angles make their corresponding angles on each protractor.

The angle formed with that vertical is the ellipse angle of the circle anywhere along the vertical line. Now, align the ellipse using minor axis to opposite VP. This is a horizontal line at center.

If this point is taken to either VP, it will give the angle of the ellipse. This works for any location within the Field of Vision. This diagram shows 3 different angles and how they were found. It also points out a very interesting fact about any angles over It appears to suggest that when looking horizontally, we cannot see angles that are greater and stay within the Field of Vision. To get larger we must look downward or rotate the surface.

VPL 0. Take the horizontal centerline to the vertical of the circle, then to either VP. The angle that this line makes with the HL is the ellipse angle used within the square. Fit by size the square and then rotate to a vertical minor axis alignment to correct distortion.

This box will give the height and depth of the circle. One would think that all you would have to do is put an ellipse inside this box and that would be it. The problem is that each box requires a certain angle to fit it exactly. This angle might be 32 degrees or 53 degrees. You are limited to the size and scope of the set of ellipse guides you are using. Fitting each perspective square thus becomes impossible in many cases.

Since the ellipse is also a perfect ellipse and not a perspective ellipse, the fit is not exact because the ellipse on the guide is heavier or fuller on the back half. To make matters seem worse, the fore-shortening of the square many times makes the ellipse look turned into the surface or flat vertically.

This often occurs on plotted ellipses. One alternative in placing an ellipse on a surface in a certain location and size is to forget about the square that surrounds it and rely only on the vertical axis in the correct location and measurement. The correct ellipse angle will take care of the circle being as wide as it is high. So, the square gives a hint, but does not give exact angle needed. Ellipse guide circles rarely touch the square in the correct locations - that is the center of each side.

Hold the height at center and allow the ellipse to go outside the square if necessary so that it will visually appear to lie on the surface. Construct the perspective circle using the ellipse size and alignment that best fits the requirements making sure that the minor axis goes to VP.

Visually pick or measure the ellipse angle. If it looks indented or turned into the surface, try a fuller wider ellipse.

If it appears to be turned outward, try a tighter thinner ellipse. Each problem is noted. All the ellipses on this side are correctly chosen and aligned.

The illusion that is necessary to convey a cylinder is very similar to circles on flat planes. Any circle can be taken through this third dimension by using vanishing points or verticals, just like rectilinear forms. Cylinders are seen in almost any position relative to the viewer. They can be above, at or below eye level, and turned in any of degrees. Full circle within a square. Once the boxes of square cross-section are drawn in the location needed and to scale, the ellipses or circles at each end are drawn within the box and then connected with tangent lines.

Notice below that the same cylinder can be constructed by using either 1 or 2-point perspective. Either method works equally well. Each square horizontal plane gives an easy alignment of the ellipses using ellipse guides.

If the ellipse is slightly too full, allow the ellipse to extend beyond the back line at top and bottom always keeping the minor axis vertical. This time the Minor Axis goes to the opposite Vanishing Point. Use full circles in 1-point perspective where the cylinder is pointed toward the viewer. This extreme foreshortening can give very exciting views, but should be close to the VP to avoid over distortion. We learn from the box constructions that both top and In the same manner it is possible to construct ellipses on bottom ellipses share the same minor axis.

We also can see a horizontal plane using the minor axis to VP. Using a center vertical axis line makes it possible to construct a convincing cylinder without boxes. In this case VPR measurements are eyeballed. If you need measurements to give the right proportions, use a rectangle representing the height and diameter. This method is an exception to the rule, because it uses the major axis. The minor axis is still on a vertical line though the center. Both methods require a fuller ellipse at the bottom end.

The distance below eye level determines the fullness of both ellipses. You can always use Chapter 6 Ellipse Angle Measurement if you need to be exact. Note the various positions of the cylinders and their ellipse angles. Measured ellipse angles and boxes can also be used. As cylinders go above the eye level, the ellipse angles need the same distance above the HL as they do below.

For standing cylinders be careful not to work too close to the HL as very tight ellipses are needed. Even the 15 ellipse needs some distance below the HL.

The tire stack was created with a single ellipse angle of The sizes get smaller along the tread line to give foreshortening to the depth. The drawing construction was done using a minor axis to a distant VP. The VP will give the correct tilt for any distance below HL. The same drawing was repeated with a 90 rotation for th e horizontal tire. The overlap gives the illusion that one is above the other.

It is hard to perceive these as the same drawing. A super way to do this is by using elevation views along the bottom edge of the HML. This makes measurements easy. If you don't have these views or you don't want to take time to draw them, you can take the measurements from an actual camera. Lens cap is all Minor axis goes to VPR or is vertical.

Then you can add other objects to create interest and scale. Overlap forms and develop a strong composition by making the negative areas into interesting shapes. Draw all the inner detail lines using a medium line weight and then trace around the outside edge with a heavier line. Construct the circle ellipse Construct the circle ellipse using any method. Draw the using any method. Draw elevation of the circle with the elevation of the circle any number divisions wanted.

Each point is taken through on circles front half. Construct a Plan View showing how many steps there are in one revolution. This can vary depending on height requirements. With the use of 1-Point Perspective, transfer the Plan View onto the horizontal plane and number stations for each step. Add a VML to one side for each step riser. Project lines to the MP to find the riser height at the center of the cylinder.

Taking one step at a time. Trace the heights to their respective positions above the plan view. Add center cylinder support and trace their respective heights for each step. Or look at how the trees and hills in the landscape outside your window always seem to have stronger, warmer colors than objects in the distance, which appear fainter and cooler in color. You draw objects overlapping to make one appear closer than the other.

Play with scale so that objects that are supposed to be farther away are painted or drawn smaller in size than those in the foreground. Knowing the basics methods of linear perspective drawing is also key to creating the illusion of distance and space in your artwork. Three-point perspective, two-point perspective, and one-point perspective are all built on this approach, and each is named for the number of vanishing points used in the given situation.

For me, it all comes down to remembering that your best bet is to trust yourself and paint what you see. That and a little perspective know-how can make all the difference in your art, so enjoy your free access to Understanding Linear Perspective Drawing: Download now! Courtney Jordan. Thank you so much for your free e books!