There are some 3D applications which can cast shadow or silhouette below 3D models. They render pretty fast and smooth. I wonder what kind of technology is the standard procedure to get 3D model shadow/silhouette.
For example is there any C++ library like libigl or CGAL to get shadow/silhouette pretty fast? Or maybe GLSL shading is used? Any hint would be appreciated on the standard technology stack.
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Computing shadows is a vast and uneasy topic. In the real world, light sources are extended and the shadow edges are not sharp (there is penumbra). Then there are cast shadows, and even self-shadows.
If you limit yourself to punctual light sources (hence sharp shadows), there is a simple principle: if you place an observer at the light source, the faces he will see are illuminated by that light source. Conversely, the hidden surfaces are in the shadow.
For correct rendering, the shadowed areas should be back-projected to the scene and painted black.
By nature, the ray-tracing techniques make this process easy to implement.
For rendering, it's trivial. Just project the vertices to the surface (for the case of the XY plane, this just entails setting the Z coordinate to 0) and render the triangles. There'll be a lot of overlap, but since you're just rendering that won't matter.
If you're trying to build a set of polygons representing the silhouette shape, you'll need to instead union the projected triangles using something like the Vatti clipping algorithm.