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Showing posts from April 29, 2019

Morphing point clouds algorithm

In some sense, point cloud is an universal medium for representing 2D and 3D vector objects and raster images/volumes. Namely, each 2D or 3D raster (image/volume) can be treated at least in two opposite ways: as a grid of points, where each point posess the color and opacity, without overlapping. as a set of points, where each point has pure grayscale, reg, green or blue color, and almost transparent. So many points overlapped additively and get required colors.  Of course, there are possibilities between this polar cases. Each 2D or 3D vector object (curve/surface) can be filled points so dense, that when viewing it on a rester display, it looks like just vector object. Such representation of an objects from a "sand" points gives opportunities of free morphing objects. So, consider the following problem. Let A and B are two point clouds of size N of equal color and transparency. It's required to create bijective mapping k_i, that {A_i}->{B_