Approximation and Modeling with B-Splines Klaus Höllig and Jörg Hörner

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Slide Collection

• Polynomials
  • Monomial Form
  • Taylor Approximation
  • Interpolation
  • Bernstein Polynomials
  • Properties of Bernstein Polynomials
  • Hermite Interpolant
  • Approximation of Continuous Functions
• Bézier Curves
  • Control Polygon
  • Properties of Bézier Curves
  • Algorithm of de Casteljau
  • Differentiation
  • Curvature
  • Subdivision
  • Geometric Hermite Interpolation
• Rational Bézier Curves
  • Control Polygon and Weights
  • Basic Properties
  • Algorithms
  • Conic Sections
• B-Splines
  • Recurrence Relation
  • Differentiation
  • Representation of Polynomials
  • Splines
  • Evaluation and Differentiation
  • Periodic Splines
• Approximation
  • Schoenberg's Scheme
  • Quasi-Interpolation
  • Accuracy of Quasi-Interpolation
  • Stability
  • Interpolation
  • Smoothing
• Spline Curves
  • Control Polygon
  • Basic Properties
  • Refinement
  • Algorithms
  • Interpolation
• Multivariate Splines
  • Polynomials
  • Polynomial Approximation
  • Splines
  • Algorithms
  • Approximation Methods
  • Hierarchical Bases
• Surfaces and Solids
  • Bézier Surfaces
  • Spline Surfaces
  • Subdivision Surfaces
  • Blending
  • Solids
• Finite Elements
  • Ritz-Galerkin Approximation
  • Weighted B-Splines
  • Isogeometric Elements
  • Implementation
  • Applications