If you’re designing a mechanical part made from smaller three-dimensional pieces, you often want to display regions in which the pieces overlap. In many cases, such regions indicate design errors where parts of a machine interfere with each other. In the case of moving parts, this process can be even more valuable, because a search for interfering regions can be done through a complete mechanical cycle of the design. The method for doing this is complicated, and the description here might be too brief. Complete details can be found in the paper Interactive Inspection of Solids: Cross-sections and Interferences, byjarek Rossignac, Abe Megahed, and Bengt-Olaf Schneider (SIGGRAPH 1992 Proceedings).
The idea is to pass an arbitrary clipping plane through the objects that you want to test for interference, and then determine when a portion of the clipping plane is inside more than one object at a time. For a static image, the clipping plane can be moved manually to highlight interfering regions; for a dynamic image, it might be easier to use a grid of clipping planes to search for all possible interferences.
Draw each of the objects you want to check and clip them against the clipping plane. Note which pixels are inside the object at that clipping plane using an odd-even count in the stencil buffer, as explained in "Drawing Filled, Concave Polygons Using the Stencil Buffer." (For properly formed objects, a point is inside the object if a ray drawn from that point to the eye intersects an odd number of surfaces of the object.) To find interferences, you need to find pixels in the framebuffer where the clipping plane is in the interiors of two or more regions at once; in other words, in the intersection of the interiors of any pair of objects.
If multiple objects need to be tested for mutual intersection, store one bit every time some intersection appears, and another bit wherever the clipping buffer is inside any of the objects (the union of the objects’ interiors). For each new object, determine its interior, find the intersection of that interior with the union of the interiors of the objects so far tested, and keep track of the intersection points. Then add the interior points of the new object to the union of the other objects’ interiors.
You can perform the operations described in the preceding paragraph by using different bits in the stencil buffer together with various masking operations. Three bits of stencil buffer are required per pixel—one for the toggling to determine the interior of each object, one for the union of all interiors discovered so far, and one for the regions in which interference has occurred so far. To make this discussion more concrete, assume that the
1 bit of the stencil buffer is for toggling between interior and exterior, the
2 bit is the running union, and the 4 bit is for interferences so far. For each object that you’re going to render, clear the 1 bit (using a stencil mask of 1 and clearing to 0), then toggle the 1 bit by keeping the stencil mask as 1 and using the GL_INVERT stencil operation.
You can find intersections and unions of the bits in the stencil buffers using the stenciling operations. For example, to make bits in buffer 2 be the union of the bits in buffers 1 and 2, mask the stencil to those 2 bits, and draw something over the entire object with the stencil function set to pass if anything nonzero occurs. This happens if the bits in buffer 1, in buffer 2, or in both are turned on. If the comparison succeeds, write a 1 in buffer 2. Also, make sure that drawing in the color buffer is disabled.
