Finite element mesh generation methods: a review and classification
Computer-Aided Design
ACM Transactions on Graphics (TOG)
Constrained B-spline curve and surface fitting
Computer-Aided Design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Surface modeling with oriented particle systems
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Simulating facial surgery using finite element models
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
An anthropometric face model using variational techniques
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-distorted texture mapping for sheared triangulated meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Graphical Models - Pacific graphics 2001
Pen-based styling design of 3D geometry using concept sketches and template models
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Interactive mesh deformation using equality-constrained least squares
Computers and Graphics
Preserving form features in interactive mesh deformation
Computer-Aided Design
Preserving form-features in interactive mesh deformation
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Computer Aided Geometric Design
Technical Section: Sketch-based surface design using malleable curve networks
Computers and Graphics
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The ability to generate fair curves and surfaces is important in computer graphics (CG), computer-aided design (CAD), and other geometric modeling applications. In this paper, we present an iteration-based algorithm for generating fair polygonal curves and surfaces that is based on a new discrete spring model. In the spring model, a linear spring, whose length approximately represents a curvature radius, is attached along the normal line of each polygon node. Energy is assigned to the difference of the lengths, that is, the difference in curvature radius, of neighboring springs. Our algorithm then minimizes the total energy by an iterative approach. It accepts as inputs (1) an initial polygonal curve (surface), which consists of a set of polygonal segments (faces) and a set of nodes as polygon-vertices, and (2) constraints for controlling the shape. The outputs are polygonal curves (surfaces) with smooth shapes. We also describe a method for improving the performance of our iterative process to obtain a linear execution time. Our algorithm provides a tool for the fair curve and surface design in an interactive environment.