Browse Prior Art Database

Estimating Projected Area

IP.com Disclosure Number: IPCOM000078865D
Original Publication Date: 1973-Mar-01
Included in the Prior Art Database: 2005-Feb-26
Document File: 3 page(s) / 56K

Publishing Venue

IBM

Related People

Appel, A: AUTHOR [+2]

Abstract

There are several situations wherein the area of a projected image of a solid object is required. Examples of such situations are: in the field of radiant heat transfer where the amount of heat absorbed by a solid is determined by the amount of radiant energy that is intercepted, the design of space craft, nuclear reactor design, the determination of gas dynamics in a vacuum, solar cells, and the design of tanks and aircraft for minimum vulnerability to cannon fire wherein the components of engines are The task of estimating the projected area of a single flat plane is relatively trivial, such projected area being the true area of the surface multiplied by the cosine of the angle between the surface and the direction of projection.

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Estimating Projected Area

There are several situations wherein the area of a projected image of a solid object is required. Examples of such situations are: in the field of radiant heat transfer where the amount of heat absorbed by a solid is determined by the amount of radiant energy that is intercepted, the design of space craft, nuclear reactor design, the determination of gas dynamics in a vacuum, solar cells, and the design of tanks and aircraft for minimum vulnerability to cannon fire wherein the components of engines are The task of estimating the projected area of a single flat plane is relatively trivial, such projected area being the true area of the surface multiplied by the cosine of the angle between the surface and the direction of projection. However, for complex arrangements of planes wherein one plane may be hidden by another, the problem becomes quite complicated and it is quite difficult to measure the area of overlap of the many projected images.

There is described herein a method wherein the projected area in aforementioned complicated situations can be readily estimated. This method has been found to be accurate to within 2% and even further accuracy can be achieved with a slight increase in computation time.

Considering the described method, there are known programs whereby shaded pictures of solids can be drawn. Thus, the program known as LEGER is disclosed in the publication "Techniques for Shading Machine Renderings of Solids", Spring Joint Computer Conference, 1968, by Arthur Appel, and the program known as SIGHT disclosed in the above-mentioned publication, produce a shaded picture by rendering on a digital plotter a uniformly spaced array of symbols, there symbols suitably being plus signs or dots. Utilizing the above- mentioned programs, the size of the plus sign or the intensity of the dot is calculated as a function of the surface that it falls on. In this connection, reference is made to Fig. 1 wherein there is shown a three-dimensional object, wherein plus signs are utilized as the graphic shading element. In this figure, it is assumed that the angle A, not shown, is the angle between the surface and the source of light. The plus sign to plus sign spacing is the same. If dots were to be utilized rather than plus signs on an illuminated surface, such as surface 12, the dot size would be equal to H(MAX) x (1-Cos A). 0n a surface such as surface 14, i.e., a nonilluminated surface wherein there is desired to provide shadows, the plus signs would be of larger size. The dot size would be equal to H(MAX).

In Fig. 2 there is shown the typical shadows cast by a remote light source (at infinity). In th...