An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Linear constraints for deformable non-uniform B-spline surfaces
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Haptic sculpting of dynamic surfaces
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Haptic sculpting of multi-resolution B-spline surfaces with shaped tools
Computer-Aided Design
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Merging multiple B-spline surface patches in a virtual reality environment
Computer-Aided Design
A tool for analytical simulation of B-splines surface deformation
Computer-Aided Design
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The construction of the stiffness matrix associated with an Active B-Spline/NURBS surface is one of the most important but time consuming operations performed in CAD/CAM/CAE. This paper aims to address this problem and presents a novel, computationally efficient, generalised mathematical framework and accompanying algorithms based on an analytic solution to the problem. The approach is shown to extend seamlessly to the problem of computing mass, damping and forcing matrices, and importantly, can handle variable mass, damping, and stiffness coefficients. The capabilities of the algorithms are illustrated and their respective performances verified through detailed analysis of the computational efficiency, accuracy and stability in several practical case studies. The main benefit of the proposed approach is a reduction in computation times required for the evaluation of the stiffness matrix by up to a factor of 4, over the standard Gaussian Quadrature approach, for the practical cases considered, while preserving a high degree of accuracy and stability. Additionally, no assumptions regarding the problem complexity, degree, or regularity of the knot vector are imposed upon the solution in order to achieve the computational saving.