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Reconstruction of Smooth Surface Suitable for LOD Model Construction Jaroslav Semančík KSVI MFF UK Josefův Důl, MIS 2003

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Jaroslav Semančík, Motivation to use smooth surface Accuracy and efficiency Advancements in theory of geometric modeling Hardware acceleration Low-level high-level analogy with programming

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Jaroslav Semančík, The goal Flexible and efficient representation Net of triangular parametric patches Interpolation

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Jaroslav Semančík, Smooth surface reconstruction Two steps 1.Construct boundary curves over the mesh edges 2.Fill the interiors by triangular patches (Coons patch) Smoothness on patch boundaries 1. 2.

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Jaroslav Semančík, Boundary curves construction Cubic Hermit curves Determined by endpoints and tangent vectors Tangent vector calculation

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Jaroslav Semančík, Triangular Coons patch Interpolates arbitrary boundary curves Construction by blending of 3 auxiliary patches

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Jaroslav Semančík, Triangular Coons patch – cont. Convex combination of 3 patches each of them interpolating a pair of curves P X = u P 1 X + v P 2 X + w P 3 X P1XP1X P2XP2X P3XP3X uvw

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Jaroslav Semančík, Smoothness on patch boundaries The same tangent plane G 1 -smoothness Construct tangent plane fields along boundaries (tangent plane normal) Modified patch construction to respect the boundary normals

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Jaroslav Semančík, Conclusion and results Smooth surface interpolating input mesh vertices Problems LOD model construction

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Jaroslav Semančík, Results

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