A Non-Gradient and Non-Iterative Method for Mapping 3D Mesh Objects Based on a Summation of Dependent Random Values

The manuscript presents a novel non-gradient and non-iterative method for mapping two 3D objects by matching extrema. This innovative approach utilizes the amplification of extrema through the summation of dependent random values, accompanied by a comprehensive explanation of the statistical background. The method further incorporates structural patterns based on spherical harmonic functions to calculate the rotation matrix, enabling the juxtaposition of the objects. Without utilizing gradients and iterations to improve the solution step by step, the proposed method generates a limited number of candidates, and the mapping (if it exists) is necessarily among the candidates. For instance, this method holds potential for object analysis and identification in additive manufacturing for 3D printing and protein matching.