Complex curved surface optimization flattening method based on spring mass point model

Abstract

The invention relates to a complex curved surface optimization flattening method based on a spring mass point model. The method comprises the following steps: (1) dispersing a three-dimensional curved surface; (2) constructing a triangular network model; (3) determining a flattened triangle to obtain an initial flattened position; (4) searching adjacent triangular belts through topology, and constructing a spring mass point model equation; and (5) searching adjacent triangles according to the flattened triangles, and flattening the triangles one by one in neighborhoods until all triangles are flattened. The method is based on the discrete grid triangle, automatically searches the central processing triangle, gradually releases the elastic energy according to the spring mass point model, provides a simple and convenient triangle folding processing scheme, and is simple in algorithm step, high in flattening efficiency and high in stability.

Description

technical field [0001] The invention relates to a method for unfolding a three-dimensional curved surface to a plane, in particular to an optimized flattening method for a complex curved surface based on a spring mass point model. Background technique [0002] In the field of product design and manufacturing, such as shells of ships, automobiles, and aircraft, shoe uppers and clothing, plate-shaped materials are required for stamping and cutting. The shape of these products is a non-developable surface in the mathematical sense (Gaussian curvature K≠0). Usually, it is often necessary to flatten these complex three-dimensional surface modeling to a two-dimensional plane to obtain the contour map. In the field of computer graphics, due to the complexity of the surface itself, some operations on the surface need to be realized with the help of the planar expansion results of the surface, such as surface parameterization, texture mapping, etc. Therefore, the research on the two...

AI Technical Summary

Problems solved by technology

Although the above method solves most of the surface expansion problems, there are still some problems when dealing with complex surfaces with large changes in surface curvature.

For example, when the initial geometry of the discrete surface is unfolded, the triangular mesh cannot be formed; when the spring-mass model is used to perform mechanical correction on the initial unfolded plane, the phenomenon of oscillation divergence and non-convergence occurs; the folded triangle cannot be effectively processed, etc.

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