5 results for Au, Chi Kit

  • A simple algorithm for medial axis transform computation

    Au, Chi Kit (2013)

    Journal article
    University of Waikato

    Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.

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  • Orienting a protein model by crossing number to generate the characteristic views for identification

    Au, Chi Kit; Cai, Yiyu; Zheng, Jianmin; Woo, Tony (2010)

    Journal article
    University of Waikato

    A protein model (such as a ribbon model) can be created from the atomic coordinates in the protein data base files. These coordinates are obtained by X-ray crystallography or NMR spectroscopy with the protein arbitrarily oriented. As such, identifying or comparing a novel structure with a known item using protein model in the protein data base can be a timely process since a large number of transformations may be involved. The identification efficiency will be improved if the protein models are uniformly oriented. This paper presents an approach to orient a protein model to generate the characteristic views with minimum and maximum crossings respectively. The projection directions for these characteristic views are determined by a set of crossing maps (C-maps). Re-orientating the protein models in the protein data base to two characteristic views will facilitate the process of identification.

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  • Garment pattern definition, development and application with associative feature approach

    Au, Chi Kit; Ma, Y.-S. (2010)

    Journal article
    University of Waikato

    Garment virtual design has been evolved significantly with the rapid development of 3D CAD tools, especially with the convenient availability of NURBS surface modeling capability. Parametric development of clothes is demanded in line with the trend of mass customization according to the true measures of customers or regulated sizes of certain markets. Virtual design features with well-defined associations with the parametric mannequins are enablers. To achieve an intelligent mass customization approach, the development of surface patches from 3D clothing designs to 2D flattened patterns become essential. This article addresses the definition, development and application of garment features with an associative feature approach.

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  • Three dimensional extension of Bresenham’s algorithm with Voronoi diagram

    Au, Chi Kit; Woo, Tony (2010)

    Journal article
    University of Waikato

    Bresenham’s algorithm for plotting a two-dimensional line segment is elegant and efficient in its deployment of mid-point comparison and integer arithmetic. It is natural to investigate its three-dimensional extensions. In so doing, this paper uncovers the reason for little prior work. The concept of the mid-point in a unit interval generalizes to that of nearest neighbours involving a Voronoi diagram. Algorithmically, there are challenges. While a unit interval in two-dimension becomes a unit square in three-dimension, “squaring” the number of choices in Bresenham’s algorithm is shown to have difficulties. In this paper, the three-dimensional extension is based on the main idea of Bresenham’s algorithm of minimum distance between the line and the grid points. The structure of the Voronoi diagram is presented for grid points to which the line may be approximated. The deployment of integer arithmetic and symmetry for the three-dimensional extension of the algorithm to raise the computation efficiency are also investigated.

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  • Triangular Bézier sub-surfaces on a triangular Bézier surface

    Chen, Wenyu; Yu, Rongdong; Zheng, Jianmin; Cai, Yiyu; Au, Chi Kit (2011)

    Journal article
    University of Waikato

    This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch.

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