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

2. 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

3. Jaroslav Semančík, 21. 1. 20033 The goal  Flexible and efficient representation   Net of triangular parametric patches  Interpolation 

4. 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.

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

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

7. 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

8. 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 

9. Jaroslav Semančík, 21. 1. 20039 Conclusion and results  Smooth surface interpolating input mesh vertices  Problems  LOD model construction 

10. Jaroslav Semančík, 21. 1. 200310 Results