Index of Applets

Each applet corresponds directly to one or more figures from Gerald Farin's book "Curves and Surfaces for CAGD - A Practical Guide", 5th ed., Academic Press, 2002.

In all applets listed below, green points are "draggable", i.e., they can be moved to another location by clicking them with the mouse and moving the mouse while keeping the mouse button pressed. Three-dimensional graphics can also be rotated by clicking anywhere else in the figure and dragging the mouse. Zooming is possible by holding down the SHIFT key and dragging vertically, rotation about an axis perpendicular to the screen is possible by holding down the SHIFT key and dragging horizontally. Other keys include the HOME key for getting back to the original configuration and "s" for stereo display. See the LiveGraphics3D homepage for more information about the employed applet.

The applets are in fact instances of just one applet (called LiveGraphics3D). I (Martin Kraus) produced the (parameterized) graphics for this applet with the help of the computer algebra system Mathematica. If you have any questions about these applets, please send me an e-mail.

• CHAPTER 1: P. BÉZIER: HOW A SIMPLE SYSTEM WAS BORN
  • Figures 1.2 and 1.3 arc in a rectangular frame
  • Figure 1.5 control polygon for an arc of an ellipse
  • Figure 1.10 curve defined inside a parallelepiped
  • Figure 1.13 characteristic net of a surface
  
  
• CHAPTER 2: INTRODUCTORY MATERIAL
  • Figure 2.1 vectors are not affected by translation
  • Figure 2.2 undefined addition of points
  • Figure 2.3 convex hull
  • Figure 2.4 affine maps
  • Figure 2.5 norm ellipses
  • Figure 2.6 hat functions and piecewise linear function f
  
  
• CHAPTER 3: LINEAR INTERPOLATION
  • Figure 3.1 linear interpolation and points
  • Figure 3.2 linear interpolation and vectors
  • Figure 3.3 variation diminishing property
  • Figure 3.4 Menelao's theorem
  • Figure 3.5 barycentric coordinates
  
  
• CHAPTER 4: THE DE CASTELJAU ALGORITHM
  • Figure 4.1 repeated linear interpolation
  • Figure 4.2 de Casteljau algorithm
  • Figure 4.4 Bézier curve, example
  • Figure 4.5 subdivision
  
  
• CHAPTER 5: THE BERNSTEIN FORM OF A BÉZIER CURVE
  • Figure 5.1 Bernstein polynomials
  • Figure 5.2 de Casteljau algorithm: curves of intermediate points
  • Figure 5.3 convex hull property of Bézier curves
  • Figure 5.4 barycentric combination of Bézier curves
  • Figure 5.6 Bézier curve and its first derivative curve (hodograph)
  • Figure 5.7 endpoint derivatives
  • Figure 5.8 subdivision
  • Figure 5.9 minmax box (axis-aligned bounding box)
  • Figures 5.12 and 5.13 composite curves
  • Figures 5.14 first polar
  
  
• CHAPTER 6: BÉZIER CURVE TOPICS
  • Figure 6.1 degree elevation
  • Figure 6.3 functional curves
  • Figure 6.4 cross plot
  
  
• CHAPTER 7: POLYNOMIAL CURVE CONSTRUCTIONS
  • Figure 7.1 polynomial interpolation
  • Figure 7.2 Aitken's algorithm
  • Figure 7.4 cubic Hermite interpolation
  • Figure 7.5 cubic Hermite polynomials
  • Figure 7.7 least squares approximation
  • Figure 7.10 modifying Bézier curves
  
  
• CHAPTER 8: B-SPLINE CURVES
  • Figure 8.1 de Boor algorithm: quadratic case
  • Figure 8.2 de Boor algorithm: cubic case
  • Figure 8.3 (a) B-spline curve: quadratic example
  • Figure 8.3 (b) B-spline curve: cubic example
  • Figure 8.3 (c) same as 8.3 (b) evaluated with common denominators
  • Figure 8.4 conversion to Bézier form
  • Figure 8.5 curve segments
  • Figure 8.6 local convex hull property
  • Figure 8.8 knot insertion: quadratic example
  • Figure 8.9 Chaikin's algorithm
  • Figure 8.10 nonparametric B-spline curves
  • Figure 8.13 smoothness at interior knot
  • Figure 8.15 smoothness of Bézier curves
  • Figure 8.17 B-splines: cubic examples
  • Figure 8.18 B-spline recursion
  
  
• CHAPTER 9: CONSTRUCTING SPLINE CURVES
  (no applets available)
  
  
• CHAPTER 10: DIFFERENTIAL GEOMETRY I
  • Figure 10.1 parametric curve in space (cubic Bézier curve)
  • Figure 10.2 (left) local affine system
  • Figure 10.2 (right) Frenet frame
  • Figure 10.3 Frenet-Serret formulas
  • Figure 10.4 osculating circle, radius of curvature
  
  
• CHAPTERS 11-18
  (no applets available)
  
  
• CHAPTER 19: DIFFERENTIAL GEOMETRY II
  • Figure 19.1 parametric surface (quadratic Bézier patch) (large)
  • Figure 19.2 area element (large)
  • Figure 19.4 osculating circle (of a curve on a quadratic Bézier patch) (large)
  
  
• CHAPTER 20
  (no applets available)
  
  
• CHAPTER 21: SURFACES WITH ARBITRARY TOPOLOGY
  • Figure 21.4 Doo-Sabin algorithm for a cube (and for a tetrahedron)
  • Figure 21.6 Catmull-Clark algorithm for a cube (and for a tetrahedron)
  • Figure 21.6 variant for Loop algorithm for a cube (and for a tetrahedron)
  
  
• CHAPTERS 22-24
  (no applets available)