• 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.

• ETRI Journal
• /
• v.35 no.6
• /
• pp.1115-1125
• /
• 2013

This paper presents a scheme for geometric correction of projected content for planar and quadratic projection surfaces. The scheme does not require the projection surface to be perfectly quadratic or planar and is therefore suitable for uneven low-cost commercial and home projection surfaces. An approach based on the recursive subdivision of second-order B$\acute{e}$zier patches is proposed for the estimation of projection distortion owing to surface imperfections. Unlike existing schemes, the proposed scheme is completely automatic, requires no prior knowledge of the projection surface, and uses a single uncalibrated camera without requiring any physical markers on the projection surface. Furthermore, the scheme is scalable for geometric calibration of multi-projector setups. The efficacy of the proposed scheme is demonstrated using simulations and via practical experiments on various surfaces. A relative distortion error metric is also introduced that provides a quantitative measure of the suppression of geometric distortions, which occurs as the result of an imperfect projection surface.

• 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 Korean Society of Precision Engineering Conference
• /
• 2003.06a
• /
• pp.873-876
• /
• 2003

Z-map model is the most widely used model for NC simulation and verification. But it has several limitations to get a high precision, to apply 5 axis machining simulation. In this paper, we tried to use quadtree for searching cutting region. Quadtree representation of two dimensional objects is performed with a tree that describes the recursive subdivision. By using these quadtree model. storage requirements were reduced. And also, recursive subdivision was processed in the boundries, so, useless computation could be reduced, too. To get more high Accuracy, we applied the supersampling method in the boundaries. The Supersampling method is the most common form of the antialiasing and usually used with polygon mesh rendering in computer graphics To verify quadtree model we compared simulated results with z-map model and enhanced z-map model

• International Journal of CAD/CAM
• /
• v.4 no.1
• /
• pp.11-17
• /
• 2004

In this paper, an exponential bound of the distance between a Loop subdivision surface and its control mesh is derived based on the topological structure of the control mesh. The exponential bound is independent of the process of recursive subdivisions and can be evaluated without subdividing the control mesh actually. Using the exponential bound, we can predict the depth of recursion within a user-specified tolerance as well as the error bound after n steps of subdivision. The error-estimating approach can be used in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and the like.

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

• Proceedings of the Korean Information Science Society Conference
• /
• 2002.10d
• /
• pp.439-441
• /
• 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 Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.422-425
• /
• 2004

This paper develops an octree-based algorithm for machining simulation. Most commercial machining simulators are based on the Z map model, which has several limitations in terms of achieving a high level of precision in five-axis machining simulation. Octree representation being a three-dimensional (3D) decomposition method, an octree-based algorithm is expected to be able to overcome such limitations. With the octree model, storage requirement is reduced. Moreover, recursive subdivision is processed in the boundaries, which reduces useless computations. The supersampling method is the most common form of antialiasing and is typically used with polygon mesh rendering in computer graphics. The supersampling technique is being used to advance the efficiency of the octree algorithm..

• Korean Journal of Computational Design and Engineering
• /
• v.10 no.2
• /
• pp.107-113
• /
• 2005

Octree-based algorithm is developed for machining simulation. Most of commercial machining simulators are based on Z map model, which have several limitations to get a high precision in 5 axis machining simulation. Octree representation is three dimensional decomposition method. So it is expected that these limitations be overcome by using octree based algorithm. By using the octree model, storage requirement is reduced. And also recursive subdivision was processed in the boundaries, which reduces useless computation. The supersampling method is the most common form of the anti-aliasing and usually used with polygon mesh rendering in computer graphics. Supersampling technique is applied for advancing its efficiency of the octree algorithm.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2005.06a
• /
• pp.956-959
• /
• 2005

The overall goal of this thesis is to develop a new algorithm based on the octree model for geometric and mechanistic milling operation at the same time. Most commercial machining simulators are based on the Z map model, which has several limitations in terms of achieving a high level of precision in five-axis machining simulation. Octree representation being a three-dimensional (3D) decomposition method, an octree-based algorithm is expected to be able to overcome such limitations. With the octree model, storage requirement is reduced. Moreover, recursive subdivision is processed in the boundaries, which reduces useless computations. To achieve a high level of accuracy, fast computation time and less memory consumption, the advanced octree model is suggested. By adopting the supersampling technique of computer graphics, the accuracy can be significantly improved at approximately equal computation time. The proposed algorithm can verify the NC machining process and estimate the material removal volume at the same time.