“X-splines: a spline model designed for the end-user” by Blanc and Schlick

  • ©Carole Blanc and Christophe Schlick

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Title:

    X-splines: a spline model designed for the end-user

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Abstract:


    This paper presents a new model of spline curves and surfaces. The main characteristic of this model is that it has been created from scratch by using a kind of mathematical engineering process. In a first step, a list of specifications was established. This list groups all the properties that a spline model should contain in order to appear intuitive to a non-mathematician end-user. In a second step, a new family of blending functions was derived, trying to fulfil as many items as possible of the previous list. Finally, the degrees of freedom offered by the model have been reduced to provide only shape parameters that have a visual interpretation on the screen. The resulting model includes many classical properties such as affine and perspective invariance, convex hull, variation diminution, local control and C2 / G2 or C2 / G0 continuity. But it also includes original features such as a continuum between B-splines and Catmull-Rom splines, or the ability to define approximation zones and interpolation zones in the same curve or surface.

References:


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    3. C. Blanc, Techniques de Moddlisation et de Ddformation de Surfaces pour la SynthOse d’Images, PhD Thesis, Universit6 Bordeaux I, 1994 (in french).
    4. C. Blanc, C. Schlick, More Accurate Representation of Conics by NURBS, Technical Report, LaBRI, 1995 (submitted for publication).
    5. C. Blanc, C. Schlick, X-Splines: Some Additional Results, Technical Report, LaBRI, 1995 (available by HTTP at www. labri, u-bordeaux, fr/LaBRl/People/schlick).
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    12. R. Riesenfeld, Applications of B-Spline Approximation to Geometric Problems of Computer Aided Design, PhD Thesis, University Syracuse, 1973.


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