Curved Mesh Generation Based on Limit Subdivision Surface and Gregory Patch Interpolation

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  • 極限細分割曲面に基づく曲線メッシュ生成とGregoryパッチによる内挿
  • キョクゲン サイブンカツ キョクメン ニ モトズク キョクセン メッシュ セイセイ ト Gregory パッチ ニ ヨル ナイソウ

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Abstract

In CG animation, the method for modeling of CG characters such as humans or animals is important. If these shapes are represented by parametric surfaces, such as Bezier, B-spline, or NURBS surfaces, complex procedures are required to make adjacent surfaces connect smoothly. To solve this problem, instead of parametric surfaces, subdivision surfaces are often used to represent shapes. However, how best to fulfill efficient modeling intended by designers is still problematic. On the other hand, smooth surfaces can be generated by interpolating a curved mesh with Gregory Patches. This method has the advantage that the G1 continuity of adjacent surfaces can be maintained even if the curved mesh is modified. Here, we propose a modeling method that involves interpolating a curved mesh with Gregory Patches after generating a curved mesh of a Catmull-Clark subdivision surface. The shape difference between the generated surface and the subdivision surface is very small. One of the characteristics of our method is that if some vertices or edges are modified, only the surfaces connected to them are affected. Also, the surfaces wthin a specified area can be modified freely by keeping the continuity between them and the adjacent surfaces outside the specified area. The cutting and Boolean operations can be executed on the generated surfaces easily and our method can be applied to the polygon meshes generated by Boolean operations and that contain holes or bosses. In the modeling of free-form surfaces, a method that first generates a rough shape with a polygon mesh and then modifies its curved mesh to obtain the final shape is effective.

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