TY - GEN
T1 - Parameterization of star-shaped volumes using Green's functions
AU - Xia, Jiazhi
AU - He, Ying
AU - Han, Shuchu
AU - Fu, Chi Wing
AU - Luo, Feng
AU - Gu, Xianfeng
PY - 2010
Y1 - 2010
N2 - Parameterizations have a wide range of applications in computer graphics, geometric design and many other fields of science and engineering. Although surface parameterizations have been widely studied and are well developed, little research exists on the volumetric data due to the intrinsic difficulties in extending surface parameterization algorithms to volumetric domain. In this paper, we present a technique for parameterizing star-shaped volumes using the Green's functions. We first show that the Green's function on the star shape has a unique critical point. Then we prove that the Green's functions can induce a diffeomorphism between two star-shaped volumes. We develop algorithms to parameterize star shapes to simple domains such as balls and star-shaped polycubes, and also demonstrate the volume parameterization applications: volumetric morphing, anisotropic solid texture transfer and GPU-based volumetric computation.
AB - Parameterizations have a wide range of applications in computer graphics, geometric design and many other fields of science and engineering. Although surface parameterizations have been widely studied and are well developed, little research exists on the volumetric data due to the intrinsic difficulties in extending surface parameterization algorithms to volumetric domain. In this paper, we present a technique for parameterizing star-shaped volumes using the Green's functions. We first show that the Green's function on the star shape has a unique critical point. Then we prove that the Green's functions can induce a diffeomorphism between two star-shaped volumes. We develop algorithms to parameterize star shapes to simple domains such as balls and star-shaped polycubes, and also demonstrate the volume parameterization applications: volumetric morphing, anisotropic solid texture transfer and GPU-based volumetric computation.
UR - https://www.scopus.com/pages/publications/77954654116
U2 - 10.1007/978-3-642-13411-1_15
DO - 10.1007/978-3-642-13411-1_15
M3 - Conference contribution
SN - 3642134106
SN - 9783642134104
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 219
EP - 235
BT - Advances in Geometric Modeling and Processing - 6th International Conference, GMP 2010, Proceedings
T2 - 6th International Conference on Advances in Geometric Modeling and Processing, GMP 2010
Y2 - 16 June 2010 through 18 June 2010
ER -