Mesh Parameterizations Xiao-Ming Fu
Mesh Parameterizations Xiao-Ming Fu
Outline 。Definition Tutte's barycentric mapping Least squares conformal maps(LSCM,ASAP) Angle-Based Flattening (ABF) ·ABF++,LABF As-rigid-as-possible (ARAP) ·Simplex Assembly
Outline • Definition • Tutte’s barycentric mapping • Least squares conformal maps(LSCM, ASAP) • Angle-Based Flattening (ABF) • ABF++, LABF • As-rigid-as-possible (ARAP) • Simplex Assembly
Definition °A function that puts input surface in one-to- one correspondence with a 2D domain. Parameterization of a Triangulated Surface all (ui,vi)coordinates associated with each vertex vi (xi,yi,Zi ) 3D 2D
Definition • A function that puts input surface in one -to - one correspondence with a 2D domain. • Parameterization of a Triangulated Surface • all (𝑢𝑖, 𝑣𝑖) coordinates associated with each vertex 𝒗 𝑖 = 𝑥 𝑖 , 𝑦 𝑖 , 𝑧 𝑖 𝑇 3D 2 D
Goal ·ap attributes 290000 facets 3500 facets 。Color 。Normal map Figure 5.2.Appearance-preserving simplification as another application of pa- rameterization:The initial object (left)is decimated to 1.5%of the original size (center).High-resolution geometric details are encoded in a normal map (right) and mapped to the simplified model,thereby preserving the original appearance. (Model courtesy of Cyberware.Image taken from [Hormann et al.07].C2007 ACM,Inc.Included here by permission.)
Goal • Map attributes • Color • Normal • ……
Constraints ·Bijective The image of the surface in parameter space does not self-intersect. The intersection of any two triangles in parameter space is either a common edge,a common vertex,or empty
Constraints • Bijective • The image of the surface in parameter space does not self-intersect. • The intersection of any two triangles in parameter space is either a common edge, a common vertex, or empty