TY - JOUR
T1 - Some applications of scalar and vector fields to geometric processing of surfaces
AU - Puig-Pey, Jaime
AU - Gálvez, Akemi
AU - Iglesias, Andrés
AU - Rodríguez, José
AU - Corcuera, Pedro
AU - Gutiérrez, Flabio
N1 - Funding Information:
This work has been partially supported by the Spanish Ministry of Science and Technology (Ref. DPI2001-1288 project) and the European Union (Ref. IST-2002-35512, GAIA II project).
PY - 2005/10
Y1 - 2005/10
N2 - In this paper, two geometric processing problems are considered: (1) point on a surface nearest to an external point, and (2) silhouette curve of a surface when observed from a given point. Problem (1) is solved by constructing gradient curves on the surface associated with a distance scalar field. Problem (2) appears as the intersection of surfaces (implicit case), or as tracing a plane curve (parametric case). Formulations are geometric-differential, and lead to explicit, first-order systems of ordinary differential equations (ODEs), with initial conditions that can be efficiently integrated by standard numerical methods. The methodology allows us to deal with both implicit and parametric representations, these having any functional structure for which the differential statements are meaningful.
AB - In this paper, two geometric processing problems are considered: (1) point on a surface nearest to an external point, and (2) silhouette curve of a surface when observed from a given point. Problem (1) is solved by constructing gradient curves on the surface associated with a distance scalar field. Problem (2) appears as the intersection of surfaces (implicit case), or as tracing a plane curve (parametric case). Formulations are geometric-differential, and lead to explicit, first-order systems of ordinary differential equations (ODEs), with initial conditions that can be efficiently integrated by standard numerical methods. The methodology allows us to deal with both implicit and parametric representations, these having any functional structure for which the differential statements are meaningful.
KW - Differential geometry
KW - Distance to a surface
KW - Geometric processing
KW - Scalar and vector fields
KW - Silhouette curves
UR - http://www.scopus.com/inward/record.url?scp=27444444432&partnerID=8YFLogxK
U2 - 10.1016/j.cag.2005.08.006
DO - 10.1016/j.cag.2005.08.006
M3 - Article
AN - SCOPUS:27444444432
SN - 0097-8493
VL - 29
SP - 719
EP - 725
JO - Computers and Graphics (Pergamon)
JF - Computers and Graphics (Pergamon)
IS - 5
ER -