Continuous point projection to planar freeform curves using spiral curves
We present an efficient algorithm for projecting a continuously moving query point to a family of planar freeform curves. The algorithm is based on the one-sided Hausdorff distance from the trajectory curve (of the query point) to the planar curves. Using a bounding volume hierarchy (BVH) of the planar curves, we estimate an upper bound (h) over bar of the one-sided Hausdorff distance and eliminate redundant curve segments when they are more than distance (h) over bar away from the trajectory curve. Recursively subdividing the trajectory curve and repeating the same elimination procedure to the BVH of the remaining curves, we can efficiently determine where to project the moving query point. The explicit continuous point projection is then interpreted as a curve reparameterization problem, for which we propose a few simple approximation techniques. Using several experimental results, we demonstrate the effectiveness of the proposed approach.
continuous point projection hausdorff distance bounding volume hierarchy curve reparameterization axis-aligned bounding box line swept sphere minimum distance culling geometric algorithms