Automatic parametrization of rational curves and surfaces II: cubics and cubicoids
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Cited by (32)
A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points
2013, Journal of Computational and Applied MathematicsCitation Excerpt :Parameterizations allow us to generate points on curves and surfaces, they are also suitable for surface plotting, computing transformations, determining offsets, computing curvatures, e.g. for shading and coloring, for surface–surface intersection problems etc.—see e.g. [1,2]. For algebraic curves and surfaces, various exact parameterization techniques can be found—see e.g. [3–8] for parameterization of curves, and [9–14] for surfaces. However, these techniques are often algorithmically very difficult.
A symbolic-numerical method for computing approximate parameterizations of canal surfaces
2012, CAD Computer Aided DesignCitation Excerpt :Unfortunately, not every geometric object (curve, surfaces, volume) can be described using rational parameterizations–see [3] for more details. We recall that for algebraic curves and surfaces, various symbolic computation based techniques can be found–see e.g. [4–8] for an exact parameterization of curves, and [9–14] for surfaces. However, these techniques are often algorithmically very difficult.
Local parametrization of cubic surfaces
2006, Journal of Symbolic ComputationIsogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
2005, Computer Methods in Applied Mechanics and EngineeringComputing real inflection points of cubic algebraic curves
2003, Computer Aided Geometric DesignComputing quadric surface intersections based on an analysis of plane cubic curves
2002, Graphical Models
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Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA