TY - GEN

T1 - Fundamentals of spherical parameterization for 3D meshes

AU - Gotsman, Craig

AU - Gu, Xianfeng

AU - Sheffer, Alla

PY - 2003/12/1

Y1 - 2003/12/1

N2 - Parameterization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity are not too distorted and do not overlap. Satisfying the non-overlapping requirement is the most difficult and critical component of this process. We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection to spectral graph theory and show how to compute these parameterizations.

AB - Parameterization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity are not too distorted and do not overlap. Satisfying the non-overlapping requirement is the most difficult and critical component of this process. We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection to spectral graph theory and show how to compute these parameterizations.

UR - http://www.scopus.com/inward/record.url?scp=77954025716&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954025716&partnerID=8YFLogxK

U2 - 10.1145/1201775.882276

DO - 10.1145/1201775.882276

M3 - Conference contribution

AN - SCOPUS:77954025716

SN - 1581137095

SN - 9781581137095

T3 - ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

SP - 358

EP - 363

BT - ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

T2 - ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

Y2 - 27 July 2003 through 31 July 2003

ER -