Contents

• 1 Introduction
• 2 Background
• 3 NURBS Geometry
  • 3.1 Curves
  • 3.2 Surfaces
  • 3.3 Properties
• 4 Formulation of D-NURBS
  • 4.1 Curves
  • 4.2 Surfaces
  • 4.3 D-NURBS Equations of Motion
• 5 Forces and Constraints
  • 5.1 Applied Forces
  • 5.2 Linear Constraints
  • 5.3 Nonlinear Constraints
  • 5.4 Constraining the Weights
• 6 Numerical Implementation
  • 6.1 Data Structures for D-NURBS Finite Elements
  • 6.2 Calculation of Element Matrices
  • 6.3 Discrete Dynamics Equations
  • 6.4 Simplifications
• 7 Modeling Environment and Applications
  • 7.1 Interactive Modeling Environment
  • 7.2 Trimming Curves and Surfaces
  • 7.3 Solid Rounding
  • 7.4 Optimal Surface Fitting
  • 7.5 Cross-Sectional Design
  • 7.6 Shape Metamorphosis
  • 7.7 Free-Form Deformation
• 8 Conclusion
• A. Position Equation
• B. Simplification of Motion Equations
• C. Simplification of Motion Equations with Linear Constraints
• D. Explicit Time Integration
• References