Constant mean curvature hook face construction method based on normal mean

Abstract

The invention discloses a constant mean curvature hook face construction method based on a normal mean. The method comprises the following steps that: firstly, reading a grid, and calculating the unitnormal vector of each surface of the grid and the average unit normal vector of a neighbor surface; then, according to the unit normal vector of each surface and the average unit normal vector of theneighbor surface, constructing a rotation matrix; then, calculating the Laplacian matrix of the vertex of the grid, utilizing the rotation matrix to calculate a coordinate matrix after the vertex ofthe grid rotates, and utilizing the Laplacian matrix and the coordinate after the vertex of the grid rotates to solve a linear equation set to obtain the practical new coordinate of the vertex; finally, updating a grid vertex coordinate, and outputting a display grid so as to finish one-time iteration; and judging a termination condition, stopping iteration if a condition is conformed to obtain afinal output model, and otherwise, and taking a current output grid as input to return to execute the first step. The method exhibits good robustness and adaptation and high efficiency, and the problem of poor adaption, low efficiency and surface patch overturning in a current constant mean curvature hook face construction method can be effectively solved.

Description

technical field

[0001] The invention belongs to the technical field of three-dimensional grid processing, and in particular relates to a method for constructing a constant average curvature surface based on normal vector averaging. Background technique

[0002] A surface whose mean curvature is constant everywhere is called a constant mean curvature (CMC) surface, and a minimal surface is a special case of a CMC surface whose mean curvature is zero everywhere. In many architectural designs and engineering creations, CMC surfaces are popular due to their high aesthetic value and structural stability, and tension membrane structures in buildings can be modeled as minimal surfaces. Inflatable buildings, including inflatable domes and shells, were also modeled as CMC surfaces.

[0003] CMC surface construction is a challenging problem in computer graphics. There are many ways to construct CMC. The commonly used CMC surface modeling method is to optimize some energy function, s...

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