Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

Overview texture mapping detail mapping Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

Overview remeshing surface reconstruction Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

Texture Mapping Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

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

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

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

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

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

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

Examples Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

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

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

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

Approximation of Triangle Meshes effect of the parameterization uniform chordal discrete harmonic MIPS Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

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

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

Hierarchical Parameterization acceleration by using hierarchies Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

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

Linear Methods mean value conformal Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

Non-Linear Methods ABF++ circle patterns MIPS stretch Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

Non-Linear Methods ABF++ circle patterns MIPS stretch Mesh Parameterization: Theory and Practice Comparisons and Applications of Planar Methods

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