Method for parameterizing quadrilateral grid in conformal mode

Abstract

The invention provides a method for parameterizing a quadrilateral grid in a conformal mode. The method is used for directly parameterizing a curved surface of the quadrilateral grid, and comprises the following steps that S11 a quadrilateral grid is input, S12 borders of the quadrilateral grid are parameterized with the length maintained to obtain a border condition, S13 an angle system of the quadrilateral grid is solved to obtain angle input of a conformal energy function, and S14 the conformal energy function is constructed, and the quadrilateral grid is grid-parameterized according to the conformal energy function. According to the method for parameterizing the quadrilateral grid in the conformal mode, the quadrilateral grid can be directly parameterized, not every quadrilateral needs to be divided to two triangles, and the curved surface is parameterized according to a triangular grid parameterizing method.

Description

technical field [0001] The invention relates to the technical field of computer graphics, in particular to a quadrilateral mesh conformal parameterization method. Background technique [0002] Mesh parameterization refers to mapping a mesh surface to the Euclidean plane, generally requiring the side length or angle to be kept constant. Mesh parameterization technology has a wide range of applications in texture mapping, mesh restoration, 3D modeling, mesh segmentation, and data fitting. At present, geometric surfaces are generally represented by two kinds of meshes: triangular meshes and quadrilateral meshes. Existing parameterization techniques mainly focus on the parameterization of triangular mesh surfaces. Representative works include: [0003] 1) Based on the discretization method of the Cauchy-Riemann equation, the Cauchy-Riemann equation is used to judge whether a mapping is a conformal mapping. The focus of such methods is how to discretize the Cauchy-Riemann equa...

AI Technical Summary

Problems solved by technology

However, for the parameterization of quadrilateral mesh surfaces, the current practice is to further divide each quadrilateral into two triangles, and then use the parameterization method based on triangular meshes to parameterize the surface, without directly analyzing the quadrilateral mesh. Parametric technology for lattice surfaces

This scheme does not take into account the nature of the quadrilateral itself, and the parameterization of the quadrilateral mesh is separated into two different processes, which is not an optimal method for quadrilateral parameterization

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