Modeling with Triangular B-Splines

Authors:
Gunther. Greiner;Hans-Peter Seidel
Affiliations:
-;-
Venue:
IEEE Computer Graphics and Applications
Year:
1994

Citing 2
Cited 14

Representing piecewise polynomials as linear combinations of multivariate &Bgr;-splines

Mathematical methods in computer aided geometric design II
An implementation of triangular B-spline surfaces over arbitrary triangulations

Selected papers of the international symposium on Free-form curves and free-form surfaces

Dynamic manipulation of triangular B-splines

SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A signal processing approach to fair surface design

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fast dynamic simulation of flexible and rigid bodies with kinematic constraints

VRST '97 Proceedings of the ACM symposium on Virtual reality software and technology
What is the natural generalization of univariate splines to higher dimensions?

Mathematical Methods for Curves and Surfaces
Manifold splines

Proceedings of the 2005 ACM symposium on Solid and physical modeling
Manifold splines

Graphical Models - Special issue on SPM 05
Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines

SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
A coarse-to-fine method for shape recognition

Journal of Computer Science and Technology
Dynamic spherical volumetric simplex splins with application in biomedical simulation

Proceedings of the 2008 ACM symposium on Solid and physical modeling
Technical Section: A new construction of smooth surfaces from triangle meshes using parametric pseudo-manifolds

Computers and Graphics
Technical Section: Surface reconstruction using bivariate simplex splines on Delaunay configurations

Computers and Graphics
Physically based modeling and simulation with dynamic spherical volumetric simplex splines

Computer-Aided Design
Shape recognition with coarse-to-fine point correspondence under image deformations

Proceedings of the 2005 joint Chinese-German conference on Cognitive systems
A surface modeling method based on the envelope template

Computer Aided Geometric Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

B-splines are a new tool for modeling complex objects with nonrectangular topology. The scheme is based on blending functions and control points, and lets us model piecewise polynomial surfaces of degree n that are C/sup n-1/-continuous throughout. Triangular B-splines permit the construction of smooth surfaces with the lowest degree possible. Because they can represent any piecewise polynomial surface, they provide a unified data format. The new B-spline scheme for modeling complex irregular objects over arbitrary triangulations has many desirable features. Applications like filling polygonal holes or constructing smooth blends demonstrate its potential for dealing with concrete design problems. The method permits real-time editing and rendering. Currently, we are improving the editor to accept simpler user input, optimizing intersection computations and developing new applications.