• International Journal of CAD/CAM
• /
• v.6 no.1
• /
• pp.139-148
• /
• 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 Computational Structural Engineering Institute Conference
• /
• 2003.04a
• /
• pp.253-260
• /
• 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.

• Journal of KIISE:Computer Systems and Theory
• /
• v.26 no.8
• /
• pp.863-874
• /
• 1999

세분화란 초기 원형 모델의 삼각형 메쉬를 여러 개의 작은 메쉬로 변환하는 기법으로, 간략화 된 모델을 다시 원상태로 표현하기 위해 사용된다. 기존의 보간에 의한 세분화는 전체 모델의 에지에 일률적으로 세분화를 적용하기 때문에, 효과가 적은 부분까지도 세분화가 수행하게 되어 효율이 떨어진다. 본 논문에서는 정점 변화율을 기반으로 에지를 선택하여 세분화를 수행한다. 따라서 원형 메쉬를 변환하여 세분화된 메쉬를 생성할 때, 모델의 각 부분들은 정점 변화율의 차이에 의해 서로 다른 세분화 정도를 가지게 된다. 이 과정을 통해 원형 모델의 곡률 특성이 반영된 세분화를 수행할 수 있게 되고, 전체 모델의 세분화 정도를 조정하는 것도 가능해진다. Abstract The subdivision is a mesh transformation, which makes an original triangle mesh to subdivided meshes. This method is used for recovering original model from simplified model. The existing subdivision based on interpolation is inefficient, because it is targeted for whole edges of mesh model. Therefore, this method applies to non-effective parts. In this paper the subdivision is executed by edge selection based on curvature. When original model is transformed to subdivided model by proposed method, the parts of model has different subdivision degrees by means of the averages of vertex curvature.Proposed method makes it enable subdivision, which deploy characteristics of curvatures of original model and adjusting a degree of subdivision in whole model.

• International Journal of CAD/CAM
• /
• v.3 no.1_2
• /
• pp.97-109
• /
• 2003

A large scale polygon models are often used to approximately represent 3D CAD models in Digital Engineering environment such as DMU (Digital Mockups) and network based collaborative design. However, they are not suitable for distribution on the network and for interactive rendering. We introduce a new coding system based on subdivision schemes called S-CODE system. In this system, it is possible to highly compress the model with sufficient accuracy and to view the model efficiently in a level of detail (LOD) fashion. The method is based on subdivision surface fitting by which a subdivision surface and curves which approximate a face of a CAD model are generated. We also apply a subdivision method to analytic surfaces such as conical and cylindrical surfaces. A prototype system is developed and used for evaluation with reasonably complicated data. The results show that the method is useful as a CAD data coding system.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.4
• /
• pp.307-314
• /
• 2009

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.553-562
• /
• 2005

It is well-known that the smoothness of 4-point interpolatory Deslauriers-Dubuc(DD) subdivision scheme is $C^{1}$. N. Dyn[3] proved that 4-point interpolatory subdivision scheme is $C^{1}$ by means of eigenanalysis. In this paper we take advantage of Laurent polynomial method to get the same result, and give new way of strict proof on Laurent polynomial method.

• Korean Journal of Computational Design and Engineering
• /
• v.11 no.3
• /
• pp.205-210
• /
• 2006

Curve tessellation, which generates a sequence of points from a curve, is very important for curves rendering on a computer screen and for NC machining. For the most case the sequence of discrete points is used rather than a continuous curve. This paper deals with a method of tessellation by calculating the maximal deviation of a curve. The maximal deviation condition is introduced to find the point with the maximal chordal deviation on a curve segment. In the previous research a curve tessellation was tried by the subdivision method, that is, a curve is subdivided until the maximal chordal deviation is less than the given tolerance. On the other hand, a curve tessellation by sequential method is tried in this paper, that is, points are generated successively by using the local property of a curve. The sequential method generates relatively much less points than the subdivision method. Besides, the sequential method can generate a sequence of points from a spatial curve by approximation to a planar curve. The proposed method can be applied for high-accuracy curve tessellation and NC tool-path generation.

• International Journal of CAD/CAM
• /
• v.4 no.1
• /
• pp.47-53
• /
• 2004

The subdivision surface is the limit of recursively refined polyhedral mesh. It is quite intuitive that the multi-resolution feature can be utilized to simplify generation of NC (Numerical Control) tool paths for rough machining. In this paper, a new method of parallel NC tool path generation for subdivision surfaces is presented. The basic idea of the method includes two steps: first, extending G-Buffer to a strip buffer (called S-Buffer) by dividing the working area into strips to generate NC tool paths for objects of large size; second, generating NC tool paths by parallel implementation of S-Buffer based on MPI (Message Passing Interface). Moreover, the recursion depth of the surface can be estimated for a user-specified error tolerance, so we substitute the polyhedral mesh for the limit surface during rough machining. Furthermore, we exploit the locality of S-Buffer and develop a dynamic division and load-balanced strategy to effectively parallelize S-Buffer.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2016.10a
• /
• pp.210-212
• /
• 2016

Today, video games created via 3D softwares become a core part of the essential the video game contents field because their properties that can produce more easier than 2D games and can save budget of contents makings. It is very important that reducing polygon counts of 3D characters and environments for Gaming optimization. We can formulate elaborate 3D game models with low polygon counting in virtue of technological advancements, and these technologies continue to evolve. In 2012, Pixar made public Open subdivision which is the new technology to make high quality 3D models with low polygons and distributed that via Open source verification. This paper will compare and analyze the characteristics, and merits and demerits of these various kinds of these skills(Mesh smooth, Turbo Smooth, Open subdivision) and will inquire which method is the most efficient one to make 3D video games.

• Journal of the Korean Society for Precision Engineering
• /
• v.23 no.9 s.186
• /
• pp.190-199
• /
• 2006

A new approach which combines implicit surface scheme and recursive subdivision method is suggested in order to fill the holes with complex shapes in the polygon model. In the method, a base surface is constructed by creating smooth implicit surface from the points selected in the neighborhood of holes. In order to assure C$^1$ continuity between the newly generated surface and the original polygon model, offset points of same number as the selected points are used as the augmented constraint conditions in the calculation of implicit surface. In this paper the well-known recursive subdivision method is used in order to generate the triangular net with good quality using the hole boundary curve and generated base implicit surface. An efficient anisotropic smoothing algorithm is introduced to eliminate the unwanted noise data and improve the quality of polygon model. The effectiveness and validity of the proposed method are demonstrated by performing numerical experiments for the various types of holes and polygon model.