Determining whether a point in space is inside/outside of a given shape depends entirely on the shape’s topological properties. Shapes with holes and/or self-intersections do not have a mathematically guaranteed interior and exterior (by Jordan’s curve theorem). However, with sufficiently fine voxel outline of a given polygonal mesh, we can enclose the approximate interior and flood-fill the remaining voxels to achieve sign computation of our distancie field.
Category Archives: mathematics
The Fast Sweeping Algorithm
The distance function is a solution to a type of Eikonal equation. The fastest O(n) method for numerically solving Eikonal equations was introduced by H. Zhao in his 2005 paper called the Fast Sweeping Method.
Martin Cavarga 