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Mesh Parameterization: Theory and Practice
Comparisons and Applications of Planar Methods
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Overview texture mapping detail mapping
Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Overview remeshing surface reconstruction
Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Texture Mapping Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Detail Mapping general idea types of detail low resolution geometry
high resolution details types of detail shading information normals or normal variation geometric displacements Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Bump Mapping basic geometric shape height variation
low resolution triangle mesh height variation grey level image variation in surface normal direction new surface normal per pixel nice shading effect same geometry & silhouette Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Normal Mapping store full 3D normal field as RGB texture
still same geometry & silhouette Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Displacement Mapping store geometric variation real 3D effect
base surface bump mapping store geometric variation real 3D effect Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Regular Meshes successive refinement of a base mesh
built-in hierarchy useful for progressive transmission wavelet representation and compression hierarchical modeling Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Remeshing replace arbitrary mesh with a regular one
parameterization (3D 2D) remeshing in 2D lift the regular mesh (2D 3D) Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Examples Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Interpolation of Regular Grids
regularity allows for simple interpolation bicubic tensor-product B-spline surfaces problem reduces to curve interpolation tri-diagonal linear systems Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Approximation of Scattered Data
z (xi, yi, zi) v (ui, vi) F y u x bicubic tensor-product B-spline surfaces numerically stable and efficient standard surfaces in CAGD Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Approximation Methods
classical approach: least squares approximation solving a linear system stabilization by smoothing functionals Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Approximation of Triangle Meshes
effect of the parameterization uniform chordal discrete harmonic MIPS Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Surface Reconstruction
construct connectivity graph compute spring model parameterization triangulate parameter and surface points optimize triangulation Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Goals minimal distortion global optimization bijectivity fast
as close to isometry as possible global optimization boundary develops naturally bijectivity no fold-overs of parameter triangles fast linear methods are preferred Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Hierarchical Parameterization
acceleration by using hierarchies Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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huge distortion no bijectivity no bijectivity
Linear Methods uniform harmonic mean value conformal huge distortion no bijectivity no bijectivity Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Linear Methods mean value conformal
Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Non-Linear Methods ABF++ circle patterns MIPS stretch
Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Non-Linear Methods ABF++ circle patterns MIPS stretch
Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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Synopsis linear methods are fast non-linear methods slower
mean value weights to be preferred good results for disk-like patches non-linear methods slower less distortion for complex shapes ABF++ or stretch to be preferred general problems discontinuities at patch boundaries Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods
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