The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Dinesh Manocha - One of the best experts on this subject based on the ideXlab platform.
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algebraic pruning a fast technique for curve and Surface Intersection
Computer Aided Geometric Design, 1997Co-Authors: Dinesh Manocha, Shankar KrishnanAbstract:Abstract Computing the Intersection of parametric and algebraic curves and Surfaces is a fundamental problem in computer graphics and geometric modeling. This problem has been extensively studied in the literature and different techniques based on subdivision, interval analysis and algebraic formulation are known. For low degree curves and Surfaces algebraic methods are considered to be the fastest, whereas techniques based on subdivision and Bezier clipping perform better for higher degree Intersections. In this paper, we introduce a new technique of algebraic pruning based on the algebraic approaches and eigenvalue formulation of the problem. The resulting algorithm corresponds to computing only selected eigenvalues in the domain of Intersection. This is based on matrix formulation of the Intersection problem, power iterations and geometric properties of Bezier curves and Surfaces. The algorithm prunes the domain and converges to the solutions rapidly. It has been applied to Intersection of parametric and algebraic curves, ray tracing and curve-Surface Intersections. The resulting algorithm compares favorably with earlier methods in terms of performance and accuracy.
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an efficient Surface Intersection algorithm based on lower dimensional formulation
ACM Transactions on Graphics, 1997Co-Authors: Shankar Krishnan, Dinesh ManochaAbstract:We present an efficient algorithm to compute the Intersection of algebraic and NURBS Surfaces. Our approach is based on combining the marching methods with the algbraic formulation. In particular, we propose and matrix computations. We present algorithms to compute a start point on each component of the Intersection curve (both open and closed components), detect the presence of singularities, and find all the curve branches near the singularity. We also suggest methods to compute the step size during tracing to prevent component jumping. The algorithm runs an order of magnitude faster than previously published robust algorithms. The complexity of the algorithm is output sensitive.
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A NEW APPROACH FOR Surface Intersection
International Journal of Computational Geometry and Applications, 1991Co-Authors: Dinesh Manocha, John CannyAbstract:Evaluating the Intersection of two rational parametric Surfaces is a recurring operation in solid modeling. However, Surface Intersection is not an easy problem and continues to be an active topic of research. The main reason lies in the fact that any good Surface Intersection technique has to balance three conflicting goals of accuracy, robustness and efficiency. In this paper, we formulate the problems of curve and Surface Intersections using algebraic sets in a higher dimensional space. Using results from Elimination theory, we project the algebraic set to a lower dimensional space. The projected set can be expressed as a matrix determinant. The matrix itself, rather than its symbolic determinant, is used as the representation for the algebraic set in the lower dimensional space. This is a much more compact and efficient representation. Given such a representation, we perform matrix operations for evaluation and use results from linear algebra for geometric operations on the Intersection curve. Most of the operations involve evaluating numeric determinants and computing the rank, kernel and eigenvalues of matrices. The accuracy of such operations can be improved by pivoting or other numerical techniques. We use this representation for inversion operation, computing the Intersection of curves and Surfaces and tracing the Intersection curve of two Surfaces in lower dimension.
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Symposium on Solid Modeling and Applications - A new approach for Surface Intersection
Proceedings of the first ACM symposium on Solid modeling foundations and CAD CAM applications - SMA '91, 1991Co-Authors: Dinesh Manocha, John CannyAbstract:Evaluating the Intersection of two rational parametric Surfaces is a recurring operation in solid modeling. However, Surface Intersection is not an easy problem and continues to be an active topic of research. The main reason lies in the fact that any good Surface Intersection technique has to balance three con icting goals of accuracy, robustness and e ciency. In this paper, we formulate the problems of curve and Surface Intersections using algebraic sets in a higher dimensional space. Using results from Elimination theory, we project the algebraic set to a lower dimensional space. The projected set can be expressed as a matrix determinant. The matrix itself, rather than its symbolic determinant, is used as the representation for the algebraic set in the lower dimensional space. This is a much more compact and e cient representation. Given such a representation, we perform matrix operations for evaluation and use results from linear algebra for geometric operations on the Intersection curve. Most of the operations involve evaluating numeric determinants and computing the rank, kernel and eigenvalues of matrices. The accuracy of such operations can be improved by pivoting or other numerical techniques. We use this representation for inversion operation, computing the Intersection of curves and Surfaces and tracing the Intersection curve of two Surfaces in lower dimension.
Laurent Busé - One of the best experts on this subject based on the ideXlab platform.
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a line trimmed nurbs Surface Intersection algorithm using matrix representations
Computer Aided Geometric Design, 2016Co-Authors: Jingjing Shen, Laurent Busé, Pierre Alliez, Neil A. DodgsonAbstract:We contribute a reliable line/Surface Intersection method for trimmed NURBS Surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to Intersection points with multiple pre-images. We then apply our Intersection algorithm to mesh NURBS Surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other Intersection approaches as well as a variety of meshing experiments. A reliable line/Surface Intersection method for trimmed NURBS Surfaces is proposed.The method is based on a novel matrix-based implicit representation.A careful treatment is proposed for Intersection points with multiple pre-images.The method is applied to mesh trimmed NURBS Surfaces through Delaunay refinement.
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A line/trimmed NURBS Surface Intersection algorithm using matrix representations
Computer Aided Geometric Design, 2016Co-Authors: Jingjing Shen, Laurent Busé, Pierre Alliez, Neil A. DodgsonAbstract:We contribute a reliable line/Surface Intersection method for trimmed NURBS Surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to Intersection points with multiple pre-images. We then apply our Intersection algorithm to mesh NURBS Surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other Intersection approaches as well as a variety of meshing experiments. A reliable line/Surface Intersection method for trimmed NURBS Surfaces is proposed.The method is based on a novel matrix-based implicit representation.A careful treatment is proposed for Intersection points with multiple pre-images.The method is applied to mesh trimmed NURBS Surfaces through Delaunay refinement.
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A Line/Trimmed NURBS Surface Intersection Algorithm Using Matrix Representations
Computer Aided Geometric Design, 2016Co-Authors: Jingjing Shen, Laurent Busé, Pierre Alliez, Neil DodgsonAbstract:We contribute a reliable line/Surface Intersection method for trimmed NURBS Surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to Intersection points with multiple pre-images. We then apply our Intersection algorithm to mesh NURBS Surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other Intersection approaches as well as a variety of meshing experiments.
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the Surface Surface Intersection problem by means of matrix based representations
Computer Aided Geometric Design, 2012Co-Authors: Laurent BuséAbstract:Evaluating the Intersection of two rational parameterized algebraic Surfaces is an important problem in solid modeling. In this paper, we make use of some generalized matrix based representations of parameterized Surfaces in order to represent the Intersection curve of two such Surfaces as the zero set of a matrix determinant. As a consequence, we extend to a dramatically larger class of rational parameterized Surfaces, the applicability of a general approach to the Surface/Surface Intersection problem due to J. Canny and D. Manocha. In this way, we obtain compact and efficient representations of Intersection curves allowing to reduce some geometric operations on such curves to matrix operations using results from linear algebra.
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The Surface/Surface Intersection problem by means of matrix based representations
Computer Aided Geometric Design, 2012Co-Authors: Laurent Busé, Ba Thang LuuAbstract:Evaluating the Intersection of two rational parameterized algebraic Surfaces is an important problem in solid modeling. In this paper, we make use of some generalized matrix based representations of parameterized Surfaces in order to represent the Intersection curve of two such Surfaces as the zero set of a matrix determinant. As a consequence, we extend to a dramatically larger class of rational parameterized Surfaces, the applicability of a general approach to the Surface/Surface Intersection problem due to J.~Canny and D.~Manocha. In this way, we obtain compact and efficient representations of Intersection curves allowing to reduce some geometric operations on such curves to matrix operations using results from linear algebra.
Andrés Iglesias - One of the best experts on this subject based on the ideXlab platform.
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a differential method for parametric Surface Intersection
International Conference on Computational Science and Its Applications, 2004Co-Authors: Akemi Gálvez, Jaime Puigpey, Andrés IglesiasAbstract:In this paper, a new method for computing the Intersection of parametric Surfaces is proposed. In our approach, this issue is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs), which are to be numerically integrated. In order to determine the initial value for this system, a simple procedure based on the vector field associated with the gradient of the distance function between points lying on each of the parametric Surfaces is described. Such a procedure yields a starting point on the nearest branch of the Intersection curve. The performance of the presented method is analyzed by means of some illustrative examples that contain many of the most common features found in parametric Surface Intersection problems.
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ICCSA (2) - A Differential Method for Parametric Surface Intersection
Computational Science and Its Applications – ICCSA 2004, 2004Co-Authors: Akemi Gálvez, Jaime Puig-pey, Andrés IglesiasAbstract:In this paper, a new method for computing the Intersection of parametric Surfaces is proposed. In our approach, this issue is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs), which are to be numerically integrated. In order to determine the initial value for this system, a simple procedure based on the vector field associated with the gradient of the distance function between points lying on each of the parametric Surfaces is described. Such a procedure yields a starting point on the nearest branch of the Intersection curve. The performance of the presented method is analyzed by means of some illustrative examples that contain many of the most common features found in parametric Surface Intersection problems.
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International Conference on Computational Science - A new differential approach for parametric-implicit Surface Intersection
Lecture Notes in Computer Science, 2003Co-Authors: Jaime Puig-pey, Akemi Gálvez, Andrés IglesiasAbstract:In this paper, we focus on the parametric-implicit Surface Intersection problem. In our approach, this problem is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs). To this end, we take advantage of the orthogonality at any point on the Intersection curve between the tangent vector to that curve and the normal vector to the implicit Surface. This yields an initial value system of ODEs that is numerically integrated through an adaptive Runge-Kutta method. In order to determine the initial value for this system, a simple procedure based on the scalar and vector fields associated with the function defining the implicit Surface and its gradient is described. Such a procedure yields a starting point on the nearest branch of the Intersection curve. The performance of the presented method is analyzed by means of some illustrative examples.
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a new differential approach for parametric implicit Surface Intersection
International Conference on Computational Science, 2003Co-Authors: Jaime Puigpey, Akemi Gálvez, Andrés IglesiasAbstract:In this paper, we focus on the parametric-implicit Surface Intersection problem. In our approach, this problem is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs). To this end, we take advantage of the orthogonality at any point on the Intersection curve between the tangent vector to that curve and the normal vector to the implicit Surface. This yields an initial value system of ODEs that is numerically integrated through an adaptive Runge-Kutta method. In order to determine the initial value for this system, a simple procedure based on the scalar and vector fields associated with the function defining the implicit Surface and its gradient is described. Such a procedure yields a starting point on the nearest branch of the Intersection curve. The performance of the presented method is analyzed by means of some illustrative examples.
Shankar Krishnan - One of the best experts on this subject based on the ideXlab platform.
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algebraic pruning a fast technique for curve and Surface Intersection
Computer Aided Geometric Design, 1997Co-Authors: Dinesh Manocha, Shankar KrishnanAbstract:Abstract Computing the Intersection of parametric and algebraic curves and Surfaces is a fundamental problem in computer graphics and geometric modeling. This problem has been extensively studied in the literature and different techniques based on subdivision, interval analysis and algebraic formulation are known. For low degree curves and Surfaces algebraic methods are considered to be the fastest, whereas techniques based on subdivision and Bezier clipping perform better for higher degree Intersections. In this paper, we introduce a new technique of algebraic pruning based on the algebraic approaches and eigenvalue formulation of the problem. The resulting algorithm corresponds to computing only selected eigenvalues in the domain of Intersection. This is based on matrix formulation of the Intersection problem, power iterations and geometric properties of Bezier curves and Surfaces. The algorithm prunes the domain and converges to the solutions rapidly. It has been applied to Intersection of parametric and algebraic curves, ray tracing and curve-Surface Intersections. The resulting algorithm compares favorably with earlier methods in terms of performance and accuracy.
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an efficient Surface Intersection algorithm based on lower dimensional formulation
ACM Transactions on Graphics, 1997Co-Authors: Shankar Krishnan, Dinesh ManochaAbstract:We present an efficient algorithm to compute the Intersection of algebraic and NURBS Surfaces. Our approach is based on combining the marching methods with the algbraic formulation. In particular, we propose and matrix computations. We present algorithms to compute a start point on each component of the Intersection curve (both open and closed components), detect the presence of singularities, and find all the curve branches near the singularity. We also suggest methods to compute the step size during tracing to prevent component jumping. The algorithm runs an order of magnitude faster than previously published robust algorithms. The complexity of the algorithm is output sensitive.
Neil A. Dodgson - One of the best experts on this subject based on the ideXlab platform.
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a line trimmed nurbs Surface Intersection algorithm using matrix representations
Computer Aided Geometric Design, 2016Co-Authors: Jingjing Shen, Laurent Busé, Pierre Alliez, Neil A. DodgsonAbstract:We contribute a reliable line/Surface Intersection method for trimmed NURBS Surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to Intersection points with multiple pre-images. We then apply our Intersection algorithm to mesh NURBS Surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other Intersection approaches as well as a variety of meshing experiments. A reliable line/Surface Intersection method for trimmed NURBS Surfaces is proposed.The method is based on a novel matrix-based implicit representation.A careful treatment is proposed for Intersection points with multiple pre-images.The method is applied to mesh trimmed NURBS Surfaces through Delaunay refinement.
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A line/trimmed NURBS Surface Intersection algorithm using matrix representations
Computer Aided Geometric Design, 2016Co-Authors: Jingjing Shen, Laurent Busé, Pierre Alliez, Neil A. DodgsonAbstract:We contribute a reliable line/Surface Intersection method for trimmed NURBS Surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to Intersection points with multiple pre-images. We then apply our Intersection algorithm to mesh NURBS Surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other Intersection approaches as well as a variety of meshing experiments. A reliable line/Surface Intersection method for trimmed NURBS Surfaces is proposed.The method is based on a novel matrix-based implicit representation.A careful treatment is proposed for Intersection points with multiple pre-images.The method is applied to mesh trimmed NURBS Surfaces through Delaunay refinement.
