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Novel method for modeling B spline surface

A spline surface, a new method of technology, applied in the field of CAD, can solve the problem of surface control vertices more or less control vertex smoothness and so on

Inactive Publication Date: 2010-12-08
SUZHOU UNIV OF SCI & TECH
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Problems solved by technology

[0003] Aiming at the problem that the existing B-spline surface modeling method can only interpolate one-way section line, or can interpolate two-way section line but the surface has too many control vertices, the present invention proposes a new B-spline surface two-way skin modeling method , the skin surface interpolates two families of intersecting section line sampling points, and has fewer control vertices and better smoothness

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  • Novel method for modeling B spline surface
  • Novel method for modeling B spline surface
  • Novel method for modeling B spline surface

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[0011] The input of the algorithm is the sampling point p of m+1 U-direction section line i，j (i=0,1,...,m,j=0,1,...,n i ) and n+1 sampling points q of the V-direction section line k，l (k=0,1,...,n, l=0,1,...,m i ), tolerance ε and B-spline surface degree k u 、k v ; The output is a two-way skinned B-spline interpolation surface S(u, v).

[0012] The main implementation steps of the algorithm are as follows:

[0013] 1. Preprocess the sampling point data to make it meet the compatibility constraints;

[0014] 2. Parameterized sampling points;

[0015] 3. Unify the node vectors U and V of each U and V section B-spline curve;

[0016] 4. Reversely calculate the cross-sectional B-spline curve c with U as the node vector i (u), (i=0, 1, ..., m) and the cross-sectional B-spline curve d with V as the node vector k (v), (k=0,1,...,n);

[0017] 5. Construct U-direction skin surface S with U and V as node vectors 1 (u, v), V-direction skin surface S 2 (u, v) and in parameter...

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Abstract

The invention relates to a novel method for modeling a B spline surface, in particular to a novel method for modeling a free-form surface in the field of CADs (Computer Aided Designs). As long as users interactively design two groups of section line sampling points, a smooth B spline interpolation surface can be automatically generated. The novel method comprises the following steps of: firstly calculating the initial parameter of each section line sampling point with a centripetal parameterization method; then recalculating the parameter of each section line and standardizing the parameters of the sampling points; calculating the node vector of each section line with an averaging method, and then unifying the node vectors of the homodromous section lines according to Schoenberg-Whitney conditions; based on the B spline surface interpolated and calculated with an energy method, respectively lofting the two groups of B spline section lines to obtain two unidirectional skinning surfaces, then constructing a tensor product surface of the common points of the interpolated section lines, wherein the Boolean sum of the three surfaces is bidirectional skinning surface to be solved. The B spline surface constructed in the invention has less control peak quantity, good surface smoothness, can be interpolated with bidirectional sampling points and meet higher surface modeling requirements.

Description

technical field [0001] The invention relates to a new B-spline surface bidirectional skin modeling method for interpolating multiple section line sampling points in two parameter directions in the field of CAD. Background technique [0002] B-spline surface is one of the most commonly used free-form surface expressions. At present, the geometric modeling of B-spline surfaces mostly adopts the one-way skinning method, that is, the section line is designed along a parameter direction, and then the skinned surface is obtained by lofting. Although one-way skinning can meet certain modeling requirements, the obtained surface can only interpolate data in one direction, which cannot meet higher modeling requirements. For example, in the process of polygon mesh hole repair, sometimes it is necessary to construct an interpolation four boundary lines The surface of the sampling point also requires a smooth connection between the interpolation surface and the surrounding grid. 1068~1...

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Application Information

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IPC IPC(8): G06T17/40
Inventor 李涛
Owner SUZHOU UNIV OF SCI & TECH
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