• International Journal of CAD/CAM
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• v.6 no.1
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• pp.139-148
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• 2006

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive tessellation reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this paper, we present a new adaptive tessellation method for general Catmull-Clark subdivision surfaces. Different from previous control mesh refinement based approaches, which generate approximate meshes that usually do not interpolate the limit surface, the new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. With explicit evaluation of general Catmull-Clark subdivision surfaces becoming available, the new adaptive tessellation method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the tessellation result. Cracks are avoided by using a recursive color marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient. The new method is presented for the general Catmull-Clark subdivision scheme. But it can be used for any subdivision scheme that has an explicit evaluation method for its limit surface.

• Proceedings of the Korean Information Science Society Conference
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• 2002.10d
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• pp.439-441
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• 2002

본 논문은 Catmull-Clark 서브디비전 서피스(subdivision surfaces)를 포워드 디퍼렌싱(forward differencing)을 이용하여 효율적으로 evaluation 해서 렌더링하는 알고리즘을 제안하고 있다. 포워드 디퍼렌싱은 순수한 다항식만을 evaluation 할 수 있다. 그러나 Catmull-Clark 서브디비전 서피스는 순수한 다항식이 아니다. 그러므로, Catmull-Clark 서피스를 정규 패치들(regular patches)로 분리하고, 그 패치들에 대한 다항식을 만들고, 포워드 디퍼렌싱을 사용해서 evaluation 하면 된다. 본 알고리즘의 장점은 전통적인 리커시브(recursive) 서브디비전 기법에 비해 메모리의 요구가 적다. 즉, [1]과 마찬가지로 서브디비전 깊이(subdivision depth)에 독립적으로 항상 상수(constant) 메모리 양 만큼만 요구된다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.253-260
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• 2003

In computer-aided geometric modeling(CAGD), subdivision surfaces are frequently employed to construct free-form surfaces. In the present study, Loop scheme and Catmull-Clark scheme are applied to generate smooth surfaces. To be consistent with the limit points of target surface, the initial sampling points are properly rearranged. The pointwise errors of curvature and position in the sequence of subdivision process are evaluated in both Loop scheme & Catmull-Clark subdivision scheme. In partcural, a general subdivision method in order to generate considering extraordinary points are implemented free from surface with arbitrary sampling point information.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.237-243
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• 2002

Recently, in computer-aided geometric modeling(CAGD), subdivision surfaces are frequently employed to construct free-form surface. Subdivision schemes have been very popular in computer graphics and animation community, but the community of CAGD adopts this tool only recently to handle surface geometry. In the present study, Loop scheme and Catmull-Clark scheme are applied to generate smooth surfaces. To be consistent with the limit points of target surface, the initial sampling points are properly rearranged. The pointwise curvature errors and coordinate value errors between the points in the sequence of subdivision process and the points on the target surface are evaluated In the numerical examples in both Loop scheme ＆ Catmull-Clark subdivision scheme.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.91-98
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• 2005

This paper presents a scheme for interpolating intersecting uniform cubic B-spline curves by Catmull-Clark subdivision surfaces. The curves are represented by polygonal complexes and the neighborhoods of intersection points are modeled by X-Configurations. When these structures are embedded within a control polyhedron, the corresponding curves will automatically be interpolated by the surface limit of subdivision of the polyhedron. The paper supplies a construction which clearly shows that interpolation can still be guaranteed even in the absence of symmetry at the X-configurations. In this sense, this scheme generalizes an already existing technique by the same authors, thereby allowing more freedom to designers.

• International Journal of CAD/CAM
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• v.12 no.1
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• pp.29-37
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• 2012

A new algorithm has been developed to construct surface from the contours having branches and the final smooth surface is obtained by the reversible Catmull-Clark subdivision. In branching, a particular layer has more than one contour that correspond with at least one contour at the adjacent layer. In the next step, three-dimensional composite curve is constructed from contours of a layer having correspondence with at least one contour at the adjacent layer by inserting points between them and joining the contours. The points are inserted in such a way that the geometric center of the contours should merge at the center of the contours at the adjacent layer. This process is repeated for all layers having branching problems. Polyhedra are constructed in the next step with the help of composite curves and the contours at adjacent layer. The required smooth surface is obtained in the proposed work by providing the level of smoothness.