Method for detecting umbilical point on triangle mesh curved surface

Abstract

The invention relates to a method for detecting an umbilical point on a triangle mesh curved surface, which comprises the following steps of: 1) preprocessing a triangle mesh, and estimating normal and shape operators; 2) performing local parameterization processing on shape operators of three vertexes of each triangle of the triangle mesh, constructing a corresponding umbilical point vector for each shape operator subjected to the parameterization, interpolating a zero-umbilical point vector on the three umbilical point vectors by using area coordinates, converting into a 2*2 linear equation system and solving the linear equation system; and 3) using the area coordinate of the zero-umbilical point vector in the triangle as a receiving umbilical point. The method is applied to the triangle mesh curved surface with any complex topological structure.

Description

technical field [0001] The invention belongs to the technical fields of differential geometry, computational mathematics, computer graphics and computer vision, and relates to a method for quickly detecting and calculating umbilical points on a triangular mesh surface with an arbitrary topology structure, which is useful in feature analysis, data registration, and face recognition , Meshing based on the principal direction field, 3D reconstruction, 3D shape retrieval, texture mapping, 3D animation modeling and other fields have important application value. Background technique [0002] The triangular mesh model is a general representation method for computers to represent the shape information of real-world objects. With the continuous improvement of shape information acquisition technology and computer processing capabilities, people need to analyze and process increasingly fine 3D mesh models for important applications such as feature extraction, data compression, shape ma...

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Problems solved by technology

[0004] The first type is to use the two principal curvatures of the umbilical point κ 1 with κ 2 equal properties, find out that |κ 1 -κ 2 | reaches the minimum point, but due to the discreteness of the grid, |κ 1 -κ 2 |Cannot really reach the zero value, it is generally only used as a necessary condition for mesh surfaces

[0005] The second type uses the property that the integral of the angle change rate of the main direction field around this point is not zero at the location of the general umbilical point. This type of method is more reliable than the first type of method; but for the reliability of the integral, it must be selected enough Many and evenly distributed sampling points, and this type of method can only estimate the vertices of the triangular mesh or the triangle as the umbilical point, and the real umbilical point generally exists inside the triangle

But the umbilical point is a local property, and the global parameterization will produce a large error; in addition, this method has great limitations on the topology of the triangular mesh manifold, for example, this method requires the triangular mesh to be homeomorphic to the disk or spherical, so their proposed method is not practical

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