The problem considered here is how to arrive at the fastest and an accurate measure of distance in perspective drawing to enhance creative drawing. Most artist and all architects are familiar with linear perspective that allows them to render very realistic drawings. There are many approaches to this method with various degrees of accuracy. Typically, most artist use perspective intuitively to give their subjects some degree of realism, however, in some cases, a composition requires a greater degree of accuracy and this is what is addressed here. Therefore, some measuring is required by this solution, but if you have used the most common measuring method, then you will see that this method is faster and has less measuring with the same accracy as the common.
This solution assumes you are familiar with perpcetive drawing and basic terms, so a few terms will suffice here to explain the solution. Terms:
PP or Picture Plane: This is the actual 2D picture surface such as a 18" X 24" drawing paper.
SPL or Scaling Plane Line: This is the bottom of the Picture Plane which runs horizontally across the entire paper.
HL or Horizon Line: This is the line that represents the horizon on the Picture Plane where the sky meets the ground.
SP or Scaling Plane: This is the horizontal plane that runs from the Scaling Plane Line to the Horizon Line and is the same elevation for the entire distance.
CSPLP or Central Scaling Plane Point: This is the point located at the center of the Picture Plane on the Scaling Plane Line.
CVP or Central Vanishing Point: This is the central point on the Horizon Line. A perpendicular line can be drawn to connect the CVP and CSPLP.
Lines of Reccession: These lines connected to any line segment in the picture plane and which recede to a vanishing point represent equal size of the original line segment although each line segment as it recedes on the Picture Plane actually gets smaller and smaller.
The solution to Square the Scaling Plane:
Take a peice of paper. Draw a Horizon Line at the center. You can draw the Horizon Line below or above the center, but for this example, just start at the center. Then draw lines of recesssion from the far left and right corners of the Scaling Plane Line to the Central Vanishing Point. This is a basic set up for a perspective drawing.
The Scaling Plane Line represents some actual distance, therefore, at some distance between the Scaling Plane Line and the Horizon Line along the Lines of Recession there is a distance which respresents the Scaling Plane Line has been squared. At that point a line segment that runs parrallel to the Scaling Plane Line and connects the two Lines of Reccession will be drawn. This is the first square and the distance can be determined using Squaring Angles from the Central Scaling Plane Line Point (CSPLP). The first Squaring Angle is 50 Degrees. Simply take a protractor and mark a 50 Degree Angle on the right side of the CSPLP and connect a line to the Right Line of Recession. At that intersection is the first square. All the remaining squares of the Scaling Plane Line follow the same rule, but with different Squaring Angles. This holds true for any Horizon Line level or size paper.
1) 50 Degrees
2) 67.5 Degrees
3) 74 Degrees
4) 78 Degrees
5) 81 Degrees
6) 82 Degrees
7) 83.5 Degrees
8) 85 Degrees
9) 85.5 Degrees
10) 86 Degrees
11) 86.5 Degrees
12) 87 Degrees
13) 88 Degrees
14) 88.5 Degrees
15-25) 88.75 - 90 Degrees