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Add safety distance calculation about celeritas HOT 4 OPEN

sethrj avatar sethrj commented on July 3, 2024
Add safety distance calculation

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Comments (4)

hahnjo avatar hahnjo commented on July 3, 2024 1

From #291:

Maybe the safety could be approximated with a few iterations with steepest descent?

The most promising literature that I could find to date is ON THE DISTANCE FROM A POINT TO A QUADRIC SURFACE. What we need for safety is a sort of "conservative" estimate, ie the returned value can be too low but it must never be too large, I think.

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sethrj avatar sethrj commented on July 3, 2024

This is a blocking task for #181 to calculate the step length.

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sethrj avatar sethrj commented on July 3, 2024

#406 implements the CalcSafetyDistance algorithm, which works for spheres, planes, and cylinders, since the gradient of those surfaces points to the nearest point on the surface. For any other surfaces, the safety distance is zero (ultra-conservative). For "complex" volumes (those with internal surfaces) the safety distance will be unnecessarily conservative near those internal surfaces.

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sethrj avatar sethrj commented on July 3, 2024

I finally rediscovered this reference: Hart, Sphere Tracing: A Geometric Method for the
Antialiased Ray Tracing of Implicit Surfaces
which in Appendix A (pp 5-109–5-110) discusses distance to plane, sphere, cylinder, cone, torus. Distance to an ellipsoid requires solving a sixth degree polynomial.

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