In-Depth Perspective

Description

In-Depth Perspective is a spreadsheet with unique capabilities that allows artists to create accurately proportioned depth in their perspective drawings using exact measurements directly on their paper, with no mathematics required. It gives them the ability to easily find the exact distance to measure directly from any point on their paper towards a vanishing point (VP) anywhere on the horizon, corresponding to the distance in the scene they are drawing. In the 500 years that artists have been using perspective in their drawings, this capability has never been available until now. The spreadsheet also allows the artist to position the primary vanishing point (VP1) and it calculates the position of the secondary vanishing point (VP2). As an added bonus, it also calculates the position of the vanishing point for lines that are sloped from the horizontal. A scaled diagram is provided that displays the distances in the scene and the VP’s in relation to the size of your drawing paper. See a picture of the spreadsheet by scrolling to the right from the logo above.

 There are many excellent sites and videos that describe the use of vanishing points for drawing in perspective so this site assumes that you are familiar with these concepts and I am just presenting this spreadsheet as a tool to make it easy to portray precise depth in your drawings.

Features

• A standard ruler is all that is required for all measurements on the drawing (no special rulers). A standard metric ruler is recommended since it is marked in 10ths corresponding to the input and output of the spreadsheet.
• You define the drawing paper size and orientation and where the horizon is located on the paper.
• You choose where to place the primary vanishing point (VP1) on the horizon with two optional methods.
• You decide on the angle of view for the whole drawing as an equivalent 35mm camera lens focal length. Most people can relate to a wide angle, normal, or telephoto view and sample lenses are listed. Any focal length can be used.
• The secondary vanishing point (VP2) is calculated based on the angle of view and paper size for a two point perspective.
• You decide the scale for the whole drawing by placing a vertical line anywhere on the drawing with a height that corresponds to the height of an object in the scene. You enter these two heights and the location on the paper of the bottom of the line (called the Origin) into the spreadsheet.
• Scene distances and dimensions can be in any units, such as feet or metres, as long as the same units are used throughout. The input to the spreadsheet is in decimals (10ths and 100ths) of those units.
• For each entry in the spreadsheet you can press CALCULATE to see the results on the scaled diagram.
• You can decide whether depths in the drawing are calculated and displayed towards VP1 or towards VP2.
• There is an option to calculate and display the location of the vanishing point for lines at an incline (which you decide) to horizontal.
• You can enter up to 9 scene distances from the origin towards VP1 or VP2 in any order and when CALCULATE is pressed, the corresponding distances on the drawing are shown in the table and displayed in the diagram.
• You can transfer the Origin to anywhere on the drawing paper with a newly calculated scale to maintain the exact same overall proportions.
• Distances from this new Origin can be calculated and displayed in any direction from there.

Benefits

• You can head out from any starting position on the paper towards any heading for any distance in the scene you choose and the spreadsheet gives you the exact corresponding distance to measure on the drawing.
• You can either start from a known layout or draw from your imagination on the fly.
• The spreadsheet uses 15 significant digits for calculation so your drawing can be as accurate as the tip of your pencil.
• The correct spacing of objects in depth is usually required for architectural subjects but can be useful for power poles, fence posts, tree lines, or just laying out items in a scene.
• The capability and ease of use of this spreadsheet opens new opportunities to create accurately proportioned drawings.
• The items in the scene do not have to be equally spaced or in multiples of a certain distance as is required in other methods that also require construction lines which have to be erased.
• There is no need for graphical projections through planes.
• There are no special rulers.
• There is no need for construction lines to create measuring points or any other graphical aides so your drawing paper does not get messy with erasing.
• You can have several buildings at different angles to the line of sight with the precise proportion of dimensions for true perspective.
• The calculated distances can also be used for 3 point perspective by those who are familiar with those more intricate drawings.

Limitations

• The In-Depth Perspective spreadsheet requires you to have Microsoft Excel on a computer, preferably a laptop close to your drawing paper. It will not work on smart phone or tablet versions of Excel.
• The expiry date is shown at the bottom of the table but I have set it to 31 December 2100 so it is now available for free indefinitely!

 Why Did I Create In-Depth Perspective

There are many web sites, videos, and books dedicated to showing how to graphically construct a perspective drawing using projection through a plane, find increments of a certain distance towards a VP, or construct a widely spaced ruler for a single set of parameters. All these methods are tedious and result in numerous construction lines that have to be erased, making a mess of your drawing paper. You cannot readily change any of the parameters to see the results. There are several software packages now available for architectural illustrators and 3D CAD programs that will produce perspective views but these can be quite expensive and require specialised learning to create entire buildings before obtaining the view required. You then have to transfer that to paper.

The most logical way of producing a perspective drawing is to start at one place on the paper and measure in the direction you want to go but to arrive at those measurements requires complex math and trigonometry. No one seems to have solved this problem so I took the challenge.

Who am I ?

My name is Hugh Templin and I am an engineer living in Nova Scotia, Canada. I am very adept in trigonometric calculations and have had an interest in the geometry of perspective for many years.