• Title, Summary, Keyword: Triangular Net

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A Study of a Surface Modeling Interpolating a Polygonal Curve Net Constructed from Scattered Points (점군으로부터 형성된 다각곡선망을 보간하는 곡면모델링에 관한 연구)

  • Ju, Sang-Yoon;Jun, Cha-Soo
    • Journal of Korean Institute of Industrial Engineers
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    • v.21 no.4
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    • pp.529-540
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    • 1995
  • The paper deals with a procedure for constructing a composite surface interpolating a polygonal curve mesh defined from 3D scattered points. The procedure consists of a poly-angulation, construction of a curve net, and interpolation of the curve net. The poly-angulation contains a stage that changes a triangular edge net obtained from a triangulation into a poly-angular edge net. A curve net is constructed by replacing edges on the edge net with cubic Bezier curves. Finally, inside of an n-sided polygon is interpolated by n subdivided triangular subpatches. The method interpolates given point data with relatively few triangular subpatches. For an n-sided polygon, our method constructs an interpolant with n subdivided triangular subpatches while the existing triangular surface modeling needs 3(n-2) subpatches. The obtained surface is composed of quartic triangular patches which are $G^1$-continuous to adjacent patches.

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Offsetting of Triangular Net using Distance Fields (거리장을 이용한 삼각망의 옵셋팅)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.24 no.9
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    • pp.148-157
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    • 2007
  • A new method which uses distance fields scheme and marching cube algorithm is proposed in order to get an accurate offset model of arbitrary shapes composed of triangular net. In the method, the space bounding the triangular net is divided into smaller cells. For the efficient calculation of distance fields, valid cells which will generate a portion of offset model are selected previously by the suggested detection algorithm. These valid cells are divided again into much smaller voxels which assure required accuracy. At each voxel distance fields are created by calculating the minimum distances between corner points of voxels and triangular net. After generating the whole distance fields, the offset surface were constructed by using the conventional marching cube algorithm together with mesh smoothing scheme. The effectiveness and validity of this new offset method was demonstrated by performing numerical experiments for the various types of triangular net.

Extracting a Regular Triangular Net for Offsetting (옵셋팅을 위한 정규 삼각망 추출)

  • Jung W.H.;Jeong C.S.;Shin H.Y.;Choi B.K.
    • Korean Journal of Computational Design and Engineering
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    • v.9 no.3
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    • pp.203-211
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    • 2004
  • In this paper, we present a method of extracting a regular 2-manifold triangular net from a triangular net including degenerate and self-intersected triangles. This method can be applied to obtaining an offset model without degenerate and self-intersected triangles. Then this offset model can be used to generate CL curves and extract machining features for CAPP The robust and efficient algorithm to detect valid triangles by growing regions from an initial valid triangle is presented. The main advantage of the algorithm is that detection of valid triangles is performed only in valid regions and their adjacent selfintersections, and omitted in the rest regions (invalid regions). This advantage increases robustness of the algorithm. As well as a k-d tree bucketing method is used to detect self-intersections efficiently.

Development of Delaunay Triangulation Algorithm Using Oct-subdivision in Three Dimensions (3차원 8분할 Delaunay 삼각화 알고리즘 개발)

  • Park S.H.;Lee S.S.
    • Korean Journal of Computational Design and Engineering
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    • v.10 no.3
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    • pp.168-178
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    • 2005
  • The Delaunay triangular net is primarily characterized by a balance of the whole by improving divided triangular patches into a regular triangle, which closely resembles an equiangular triangle. A triangular net occurring in certain, point-clustered, data is unique and can always create the same triangular net. Due to such unique characteristics, Delaunay triangulation is used in various fields., such as shape reconstruction, solid modeling and volume rendering. There are many algorithms available for Delaunay triangulation but, efficient sequential algorithms are rare. When these grids involve a set of points whose distribution are not well proportioned, the execution speed becomes slower than in a well-proportioned grid. In order to make up for this weakness, the ids are divided into sub-grids when the sets are integrated inside the grid. A method for finding a mate in an incremental construction algorithm is to first search the area with a higher possibility of forming a regular triangular net, while the existing method is to find a set of points inside the grid that includes the circumscribed sphere, increasing the radius of the circumscribed sphere to a certain extent. Therefore, due to its more efficient searching performance, it takes a shorer time to form a triangular net than general incremental algorithms.

Efficient Calculation of Distance Fields Using Cell Subdivision (셀 분할을 이용한 거리장의 효율적 계산)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.25 no.3
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    • pp.147-156
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    • 2008
  • A new approach based on cone prism intersection method combined with sorting algorithm is proposed for the fast and robust signed distance field computation. In the method, the space bounding the geometric model composed of triangular net is divided into multiple smaller cells. For the efficient calculation of distance fields, valid points among the triangular net which will generate minimum distances with current cell are selected by checking the intersection between current cell and cone prism generated at each point. The method is simple to implement and able to achieve an order of magnitude improvement in the computation time as compared to earlier approaches. Further the method is robust in handling the traditional sign problems. The validity of the suggested method was demonstrated by providing numerous examples including Boolean operation, shape deformation and morphing of complex geometric models.

Shape Deformation of Triangular Net (삼각망의 형상 변형)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.24 no.11
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    • pp.134-143
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    • 2007
  • A new approach based on mean value coordinate combined with Laplacian coordinate is proposed for shape deformation of a large polygon model composed of triangular net. In the method, the spherical mean value coordinates for closed control meshes is introduced to describe a vertex in the triangle meshes to be deformed. Furthermore, the well known quardratic least square method for the Laplacian coordinates is employed in order to deform the control meshes. Because the mean value coordinates are continuous and smooth on the interior of control meshes, deforming operation of control meshes change the shape of polygon model while preserving the intrinsic surface detail. The effectiveness and validity of this novel approach was demonstrated by using it to deform large and complex polygon models with arbitrary topologies.

A Study of Triangular Surface Interpolant for Scattered 3D points (불규칙한 3차원 상의 점군들에 대한 삼각곡면 보간에 관한 연구)

  • Ju, Sang-Yoon
    • Journal of Korean Institute of Industrial Engineers
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    • v.19 no.2
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    • pp.75-82
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    • 1993
  • This paper deals with a systematic procedure for constructing a triangular composite surface which is interpolated from given scattered 3-D points. The procedure consists of a triangulation, construction of curve net, and interpolation of triangular patches. An obtained surface is composed of cubic triangular patches, which are $G^1$ continuous to adjacent other patches.

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Composite $G^{1}$ surface construction from 2D cross-sections (2차원 단면 데이터로부터 복합 $G^{1}$ 자유곡면 생성)

  • Park, Hyung-Jun;Na, Sang-Wook;Bae, Chae-Yeol
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.44-47
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    • 2004
  • This paper proposes an approach for composite surface reconstruction from 2D serial cross-sections, where the number of contours varies from section to section. In a triangular surface-based approach taken in most reconstruction methods, a triangular $G^{1}$ surface is constructed by stitching triangular patches over a triangular net generated from the compiled contours. In the proposed approach, the resulting surface is a composite $G^{1}$ surface consisting of three kinds of surfaces: skinned, surface is first represented by a B-spline surface approximating the serial contours of the skinned region and then serial contours of the skinned region and then transformed into a mesh of rectangular Bezier patches. On branched and capped regions, triangular $G^{1}$ surfaces are constructed so that the connections between the triangular surfaces and their neighboring surfaces are $G^{1}$ continuous. Since each skinned region is represented by an approximated rectangular $G^{2}$ surface instead of an interpolated triangular $G^{1}$ surface, the proposed approach can provide more visually pleasing surfaces and realize more efficient data reduction than the triangular surface-based approach. Some experimental results demonstrate its usefulness and quality.

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Study on Segmentation of Measured Data with Noise in Reverse Engineeing (역공학에서의 노이즈가 포함된 측정데이터의 분할에 관한 연구)

  • Lee, Seok-Hui;Kim, Ho-Chan;Heo, Seong-Min
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.3
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    • pp.560-569
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    • 2002
  • The segmentation has been performed to the data of good quality in most cases, so the adoption of previous segmentation theory to the measured data with a laser scanner does not produce good result because of the characteristics of the data with noise component. A new approach to perform the segmentation on the scanned data is introduced to deal with problems during reverse engineering process. A triangular net is generated from measured point data, and the segmentation on it is classified as plane, smooth and rough segment. The segmentation result in each segment depends on the user-defined criteria. And the difference of the segmentation between the data of good quality and the data with noise is described and analyzed with several real models. The segment boundaries selected are used to maintain the characteristics of the parts during modeling process, thus they contribute to the automation of the reverse engineering.

Three Dimensional Shape Morphing of Triangular Net (삼각망의 3 차원 형상 모핑)

  • Yoo, Dong-Jin
    • Journal of the Korean Society for Precision Engineering
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    • v.25 no.1
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    • pp.160-170
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    • 2008
  • Shape morphing is the process of transforming a source shape, through intermediate shapes, into a target shape. Two main problems to be considered in three dimensional shape morphing are vertex correspondence and path interpolation. In this paper, an approach which uses the linear interpolation of the Laplacian coordinates of the source and target meshes is introduced for the determination of more plausible path when two topologically identical shapes are morphed. When two shapes to be morphed are different in shape and topology, a new method which combines shape deformation theory based on Laplacian coordinate and mean value coordinate with distance field theory is proposed for the efficient treatment of vertex correspondence and path interpolation problems. The validity and effectiveness of the suggested method was demonstrated by using it to morph large and complex polygon models including male and female whole body models.