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Constraint-based LN-curves

Published: 22 March 2010 Publication History

Abstract

We consider the design of parametric curves from geometric constraints such as distance from lines or points and tangency to lines or circles. We solve the Hermite problem with such additional geometric constraints. We use a family of curves with linearly varying normals, LN curves, over the parameter interval [0, u]. The nonlinear equations that arise can be of algebraic degree 60. We solve them using the GPU on commodity graphics cards and achieve interactive performance. The family of curves considered has the additional property that the convolution of two curves in the family is again a curve in the family, assuming common Gauss maps, making the class more useful to applications. We also remark on the larger class of LN curves and how it relates to Bézier curves.

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Cited By

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  • (2014)Geometric constraints on quadratic Bézier curves using minimal length and energyJournal of Computational and Applied Mathematics10.5555/2753878.2754090255:C(887-897)Online publication date: 1-Jan-2014
  • (2014)Geometric constraints on quadratic Bézier curves using minimal length and energyJournal of Computational and Applied Mathematics10.1016/j.cam.2013.07.005255(887-897)Online publication date: Jan-2014
  • (2012)Constraint-based LN curvesComputer Aided Geometric Design10.1016/j.cagd.2011.06.00929:1(30-40)Online publication date: Jan-2012
  • Show More Cited By

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  1. Constraint-based LN-curves

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    cover image ACM Conferences
    SAC '10: Proceedings of the 2010 ACM Symposium on Applied Computing
    March 2010
    2712 pages
    ISBN:9781605586397
    DOI:10.1145/1774088
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    Publication History

    Published: 22 March 2010

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    Author Tags

    1. CAGD
    2. GPU programming
    3. LN-curves
    4. MCAD
    5. convolution
    6. geometric constraints

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    March 22 - 26, 2010
    Sierre, Switzerland

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    SAC '10 Paper Acceptance Rate 364 of 1,353 submissions, 27%;
    Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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    Cited By

    View all
    • (2014)Geometric constraints on quadratic Bézier curves using minimal length and energyJournal of Computational and Applied Mathematics10.5555/2753878.2754090255:C(887-897)Online publication date: 1-Jan-2014
    • (2014)Geometric constraints on quadratic Bézier curves using minimal length and energyJournal of Computational and Applied Mathematics10.1016/j.cam.2013.07.005255(887-897)Online publication date: Jan-2014
    • (2012)Constraint-based LN curvesComputer Aided Geometric Design10.1016/j.cagd.2011.06.00929:1(30-40)Online publication date: Jan-2012
    • (2011)Geometric Constraint Solving in Parametric Computer-Aided DesignJournal of Computing and Information Science in Engineering10.1115/1.359340811:2(021001)Online publication date: 2011
    • (2011)Approximate Bézier curves by cubic LN curvesApplied Mathematics and Computation10.1016/j.amc.2011.08.032218:7(3083-3092)Online publication date: Dec-2011

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