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Construction method of barycentric coordinates

A technology of barycentric coordinates and construction methods, which is applied in 3D modeling, image data processing, instruments, etc., can solve the problem that the mean center coordinates do not have non-negativeness, and achieve the effect of speeding up the interpolation algorithm and reducing memory consumption

Active Publication Date: 2015-01-07
UNIV OF SCI & TECH OF CHINA
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Problems solved by technology

But the mean center coordinates are not non-negative

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[0056] In order to make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described below in conjunction with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are only Some, but not all, embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

[0057] The present invention provides a smooth and local barycentric coordinate construction method, according to which, the smooth and local barycentric coordinates of the contained space can be generated from the input plane polygon or three-dimensional triangular grid, such as figure 1 As shown, the method specifically includes the following steps:

[0058] Step A: ...

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Abstract

The invention discloses a construction method of barycentric coordinates. The construction method of the barycentric coordinates comprises the steps that a plane polygonal mesh or a three-dimensional triangular mesh is input; for the plane polygonal mesh, triangularization is carried out on the internal area of a plane polygon to generate a plane triangular mesh inside the polygon; for the three-dimensional triangular mesh, the internal area of the three-dimensional triangular mesh is made to be tetrahedral, so that a three-dimensional tetrahedral mesh inside the triangular mesh is generated; a weighted value of each sampling point to each control point in an area Omega is calculated; according to the input plane polygonal mesh or the three-dimensional triangular mesh and the generated plane triangular mesh or the three-dimensional tetrahedral mesh, an optimization model based on a total variation model is solved, and therefore the barycentric coordinates with local characteristics are obtained. By means of the construction method of the barycentric coordinates, under the restraint of the barycentric coordinates, the weighting total variation of the barycentric coordinates is optimized while serving as an objective function, smooth and local barycentric coordinate values are obtained, memory space for storing the barycentric coordinates is smaller, and the interpolation algorithm of the barycentric coordinates based on the construction method is accelerated.

Description

technical field [0001] The present invention relates to a given plane polygon or a three-dimensional triangular grid, and calculates the barycentric coordinate method of the inner area surrounded by it. Its innovative point is that the barycentric coordinates constructed by the present invention have smoothness and very good local properties at the same time , can be widely used in graphics algorithms, geometric modeling and finite element calculations and other fields. Background technique [0002] As we all know, any point in a triangle can be written as a linear convex combination of its three vertices, where the three coefficients are the barycentric coordinates of the point relative to the triangle. Since three points on the plane that are not collinear are linearly independent, the barycentric coordinates are uniquely defined. The barycentric coordinates of triangles are widely used in graphics algorithms, geometric modeling and other fields. For a point in a plane q...

Claims

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Application Information

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IPC IPC(8): G06T17/00G06T17/30
CPCG06T7/66G06T2207/10012
Inventor 张举勇邓柏林刘子舜刘利刚
Owner UNIV OF SCI & TECH OF CHINA
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