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