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B-spline-based incremental scaling and translation construction method of interpolation curve or curved surface

A technology of interpolation curve and construction method, applied in the field of geometric modeling, can solve the problem of non-interpolating control vertices and so on

Inactive Publication Date: 2017-03-15
SHAANXI UNIV OF TECH
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Problems solved by technology

[0003] The object of the present invention is to provide a kind of incremental stretching and translation construction method based on B-spline interpolation curve or surface, aiming at solving the problem that existing spline curve / surface does not interpolate control vertices

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  • B-spline-based incremental scaling and translation construction method of interpolation curve or curved surface
  • B-spline-based incremental scaling and translation construction method of interpolation curve or curved surface
  • B-spline-based incremental scaling and translation construction method of interpolation curve or curved surface

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[0142] In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

[0143] The application principle of the present invention will be described in detail below in conjunction with the accompanying drawings.

[0144] Such as figure 1 Shown, the interpolation curve of the embodiment of the present invention is based on the spline curve / curve of the de Boor control vertex of the de Boor control vertex of spline curve / curve surface; comprise the following steps:

[0145] S101: first select an appropriate allocation function, and make a straight line connecting the two endpoints of each spline cell and a straight line connecting and corresponding two adjacent de Boor control vertices, and make ...

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Abstract

The present invention discloses a B-spline-based incremental scaling and translation construction method of an interpolation curve or curved surface. The method includes the following steps that: a blending function is selected, a straight line connected with two end points of each spline subinterval and a straight line connected with two adjacent corresponding de Boor control vertexes are constructed, the differences of points on spline curves on spline subintervals and points on the straight line of the two end points of each spline subinterval are obtained, and so that incremental vectors are obtained; the incremental vectors are scaled, and then the scaled incremental vectors are translated onto the straight line connected with the two adjacent de Boor control vertexes, so that an interpolation curve about the interpolation of the spline subintervals into the de Boor control vertexes can be obtained, wherein the constructed curve about the interpolation of the spline subintervals into the de Boor control vertexes is a third-order B-spline curve. As for a four-order quartic B-spline curve, the incremental scaling and translation construction method can be also adopted to generate a corresponding interpolation curve. The method of the invention has the advantages of simplicity and obvious geometric significance, and is of great significance for geometric modeling.

Description

technical field [0001] The invention belongs to the technical field of geometric modeling, and in particular relates to a B-spline-based incremental stretching and translation construction method of interpolation curves or curved surfaces. Background technique [0002] There are many construction methods for interpolation spline curves / surfaces, which play an important role in geometric modeling. At present, the research on rational cubic splines and their application in shape control and interpolation splines of trigonometric polynomials has been carried out in the existing technology, and some useful results have been obtained. However, the current spline curve / surface does not interpolate the control vertices, or does not have the interpolation function, and generates a free curve / surface. Contents of the invention [0003] The purpose of the present invention is to provide a B-spline based interpolation curve or surface incremental stretching and translation construct...

Claims

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Application Information

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IPC IPC(8): G06T11/20G06T17/30
CPCG06T11/203G06T17/30
Inventor 王树勋陈纯
Owner SHAANXI UNIV OF TECH
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