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Reconstruction of Smooth Surface Suitable for LOD Model Construction Jaroslav Semančík KSVI MFF UK Josefův Důl, 21-22. 1. 2003 MIS 2003

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Jaroslav Semančík, 21. 1. 20032 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, 21. 1. 20033 The goal Flexible and efficient representation Net of triangular parametric patches Interpolation

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Jaroslav Semančík, 21. 1. 20034 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, 21. 1. 20035 1. Boundary curves construction Cubic Hermit curves Determined by endpoints and tangent vectors Tangent vector calculation

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Jaroslav Semančík, 21. 1. 20036 2. Triangular Coons patch Interpolates arbitrary boundary curves Construction by blending of 3 auxiliary patches

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Jaroslav Semančík, 21. 1. 20037 2. 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, 21. 1. 20038 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, 21. 1. 20039 Conclusion and results Smooth surface interpolating input mesh vertices Problems LOD model construction

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Jaroslav Semančík, 21. 1. 200310 Results

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