| Construction Principle (2008) | |||||||||||||||
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| Abstract. We present a gallery of simple curvature continuous surfaces that possess the topological structure of the Platonic solids. These spherelike surfaces consist of one cubic triangular or biquadratic quadrilateral patch per vertex of the solid and interpolate the vertices of the dual solid. x1. Polynomial curvature continuous surfaces Constructing low degree polynomial curvature continuous surfaces is a difficult problem. Existing parametric solutions [3, 6, 5] require both a large number of patches and high degree. A recent implicit curvature continuous construction requires only algebraic degree 4, but consists of many pieces [4]. On the other hand the existence of low degree (rational) curvature continues representations of shapes such as the sphere hints at the existence of elegant solutions for restricted geometric shapes. | |||||||||||||||
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