Post on 01-Apr-2015
Reconstruction of Smooth Reconstruction of Smooth Surface Suitable for LOD Model Surface Suitable for LOD Model ConstructionConstruction
Jaroslav Semančík
KSVI MFF UK
Josefův Důl, 21-22. 1. 2003
MIS 2003
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Motivation to use smooth surfaceMotivation to use smooth surface
Accuracy and efficiency
Advancements in theory of geometric modeling
Hardware acceleration
Low-level high-levelanalogy with programming
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The goalThe goal
Flexible and efficient representation Net of triangular parametric patches Interpolation
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Smooth surface reconstructionSmooth surface reconstruction
Two steps1. Construct boundary curves over the mesh edges2. Fill the interiors by triangular patches
(Coons patch) Smoothness on patch boundaries
1.
2.
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1. Boundary curves construction1. Boundary curves construction
Cubic Hermit curves Determined by endpoints and
tangent vectors Tangent vector calculation
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2. Triangular Coons patch2. Triangular Coons patch
Interpolates arbitrary boundary curves Construction by blending of 3 auxiliary patches
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2. Triangular Coons patch – cont.2. Triangular Coons patch – cont.
Convex combination of 3 patches each of them interpolating a pair of curves
. . .+ +
P X = uP1X + vP2X + wP3X
P1X P2X P3X
u v w
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Smoothness on patch boundariesSmoothness on patch boundaries
The same tangent plane G1-smoothness Construct tangent plane fields along
boundaries(tangent plane normal)
Modified patch construction to respect the boundary normals
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Conclusion and resultsConclusion and results
Smooth surface interpolating input mesh vertices
Problems LOD model construction
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ResultsResults