Wpf: Path surfaces in 3D

Surfaces based on parametric curves: \(x=f(t)\), \(y=g(t)\) \([, z=h(t)]\)

• Introduction to path surfaces
  • Borromean rings, A, B, C
  • Ellipses, A, B, C
  • Trefoil 2
  • Formatting options for path surfaces, Trefoil 5
• Functions with real input and complex results
  • Expj (Cis) function
  • Hankel function of the first kind \(H_{1, \nu}(x)\)
  • Hankel function of the second kind \(H_{2, \nu}(x)\)
  • Kelvin functions ber and bei
  • Kelvin functions ker and kei
• Characteristic functions of statistical distributions
  • Uniform distribution
  • Normal distribution
  • Chi-squared distribution
  • Beta distribution
  • F distribution
  • Non-central Chi-squared distribution
  • Binomial distribution
  • Hypergeometric distribution
  • Distribution of Wilks’ \(\Lambda\)
• Helices and related curves traced on cylinders, cones and spheres
  • Cylindrical helix
  • Conical helix based on Archimedes spiral (spiral of Pappus)
  • Conical helix based on Fermat’s spiral
  • Conical helix based on the logarithmic spiral (Concho-Spiral)
  • Conical helix based on the hyperbolic spiral
  • Rhumb line of the sphere
  • Clelia
  • Spherical helix
  • Satellite curve
  • Seiffert’s spiral
• Coil springs
  • Spring 2
  • Spring 6
  • Spring 7a
  • Spring 7b
  • Spring 7c
  • Spring 7d
  • Spring 8
• General knots
  • Trefoil A
  • Trefoil B
  • Square knot
  • Granny knot
  • Cinquefoil Knot
  • 74 Knot
  • Figure-eight knot
• Torus knots
  • Torus knot 3:2
  • Torus knot 5:2
  • Torus knot 7:2
  • Torus knot 7:3
  • Torus knot 15:2
• Lissajous knots
  • Lissajous knot 1-1-1
  • Lissajous knot 1-2-1
  • Lissajous knot 1-5-3
  • Lissajous knot 3-5-2
  • Lissajous knot 3-5-7
• Polynomial knots
  • Polynomial knot 3-1
  • Polynomial knot 4-1
  • Polynomial knot 5-1
  • Polynomial knot 6-2
  • Polynomial knot 7-4