Matrix Barycentric Coordinates For Mesh Editing

In recent years, researchers have had deep comprehension on shape manipulation of digital geometries. On the other hand, industry of animations and movies are still striding forward. These make 3-dimensional mesh editing attracting more and more attentions. As it is difficult to directly edit a given 3-dimensional model represented in various forms,3D model editing based on barycentric coordinates is then becoming one of the favorable 3D deformation techniques.This paper proposes a new kind of barycentric coordinate, namely, matrix barycentric coordinate. Its main contribution is to extend a new kind of 2-dimensional barycentric coordinates, the complex barycentric coordinate which is redefined as a 2-dimensional matrix barycentric coordinate, to 3-dimension using a spherical coordinate. The matrix barycentric coordinate is defined for arbitrary polygonal control cages such as triangular, quadrilateral or hybrid meshes. The matrix barycentric coordinates owns many good properties which most other barycentric coordinates have. A detailed experimental study of the matrix barycentric coordinate is carried out, and the analysis of its advantages and disadvantages is also performed.