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Green Coordinates for Triquad Cages in 3D
SessionMaps and Fields
DescriptionWe introduce Green coordinates for triquad cages in 3D.
Based on Green's third identity, they allow defining the harmonic deformation of a 3D point inside a cage as a linear combination of its vertices and face normals.
Using appropriate Neumann boundary conditions, the resulting deformations are quasi-conformal in 3D, and thus best-preserve the local deformed geometry.
Most coordinate systems use cages made of triangles as input, yet quads are in general favored by 3D artists as those align naturally onto important geometric features of the 3D shapes, such as the limbs of a character, without introducing arbitrary asymmetric deformations and representation.
While triangular cages admit per-face constant normals and result in a single Green coordinate per triangle, the case of quad cages is at the same time more involved (as the normal varies along non-planar quads) and more flexible (as many different mathematical models allow defining the smooth geometry of a quad interpolating its four edges).
We consider bilinear quads, and we introduce a new Neumann boundary condition resulting in a simple set of four additional coordinates per quad.
Our coordinates remain quasi-conformal in 3D, and we demonstrate their superior behavior under non-trivial deformations of realistic triquad cages.
Based on Green's third identity, they allow defining the harmonic deformation of a 3D point inside a cage as a linear combination of its vertices and face normals.
Using appropriate Neumann boundary conditions, the resulting deformations are quasi-conformal in 3D, and thus best-preserve the local deformed geometry.
Most coordinate systems use cages made of triangles as input, yet quads are in general favored by 3D artists as those align naturally onto important geometric features of the 3D shapes, such as the limbs of a character, without introducing arbitrary asymmetric deformations and representation.
While triangular cages admit per-face constant normals and result in a single Green coordinate per triangle, the case of quad cages is at the same time more involved (as the normal varies along non-planar quads) and more flexible (as many different mathematical models allow defining the smooth geometry of a quad interpolating its four edges).
We consider bilinear quads, and we introduce a new Neumann boundary condition resulting in a simple set of four additional coordinates per quad.
Our coordinates remain quasi-conformal in 3D, and we demonstrate their superior behavior under non-trivial deformations of realistic triquad cages.
Event Type
Technical Communications
Technical Papers
TimeFriday, 9 December 20229:00am - 10:30am KST
LocationRoom 324, Level 3, West Wing
