Contents
How are large deformations performed on 3D meshes?
We present a novel technique for large deformations on 3D meshes using the volumetric graph Laplacian. We first construct a graph representing the volume inside the input mesh. The graph need not form a solid meshing of the input mesh’s interior; its edges sim- ply connect nearby points in the volume.
How does the Laplacian relate to the mesh?
The graph need not form a solid meshing of the input mesh’s interior; its edges sim- ply connect nearby points in the volume. This graph’s Laplacian encodes volumetric details as the difference between each point in the graph and the average of its neighbors.
How is freeform deformation used in 3D Studio?
Freeform deformation (FFD) is used in commercial software such as 3D Studio and Maya. A general treatment can be found in [Mil- liron et al. 2002].
How are differential domain methods used in deformation?
Differential domain methods, including ours, minimize an energy function rep- resenting how well the details are preserved after a deformation and can be solved as a sparse linear system.
How is volume preserving mesh parameterization based on optimal?
This work introduces a novel volumetric parameterization method, which guarantees to be free of volume distortion.
How is volume preserving free form deformation useful?
Volume-preserving free-form deformation is not only a useful tool for modeling, but can also be a powerful visual aid in engineering animation and virtual prototyping as well. This technique can also be used to automatically create the standard squash and stretch effects in computer animation and help bring life to the animated characters.
How is volumetric angle preserving parameterization approximated?
Volumetric angle-preserving parameterization can be approximated by volumetric harmonic mapping. Intuitively, the harmonic energy of a map between two Riemannian manifolds measures the elastic deformation energy induced by the map, a harmonic map minimizes the harmonic energy.
How are displacement volumes related to volumetric details?
Displacement volumes [Botsch and Kobbelt 2003] extend the multi-resolution approach from surfaces to volumes, and coin the term “volumetric details” which we borrow here.
How is the volumetric graph Laplacian used in geometry?
To apply the volumetric graph Laplacian to a triangular mesh, we construct a volumetric graph which includes the original mesh points as well as points derived from a simple lattice lying inside the mesh. These points are connected by graph edges which are a superset of the edges of the original mesh.
How to create a texture coordinate for a vertex?
Texture coordinate generation allows an application to map a vertex position or vector to a texture coordinate. For linear transforms, the transformation is texcoord = f ( x, y, z, w ), where texcoord can be any one of s, t, r, or q, and f ( x, y, z, w) = Ax + By + Cz + Dw, where the coefficients are set by the application.