ACS Algorithms for Complex Shapes with Certified Numerics and Topology Piecewise Linear Kernels for Simultaneous Approximation of Implicit and Mesh Surfaces from Point Cloud Data

We investigate a new method to compute a piecewise linear representation of a surface in R or R from a set of sample points from the surface. As implicit surface functions we use the weighted sum of piecewise linear kernel functions centered at the surface points. For such a function we can partition R or R in such a way that these functions are linear on the subsets of the partition. For each subset in the partition we can then compute the zero level set of the function exactly as the intersection of a hyperplane with the subset. This method works in principle, but is costly for large problems. Furthermore, the resulting mesh representation can be very irregular.