Overview
Animation
Classic Surfaces
Parm Surfaces
Curves on Surfaces
Discrete Geodesics
ODE
Platonic Solids
Cycloid
Root Finder
Harmonic Maps
Rivara Bisection
Scalar Field
Weierstrass
Closed Polygon
Elastic Curve
Billiard in an Ellipse
LIC Visualization
Discrete VF
Hodge Splitting
Textured Surface
Surfaces of Rotation
Mean Curvature Flow
Pythagoraen Tree
Julia Sets

## Curves on Hyper Surfaces

Classic curve on parameterized surfaces. The curves are defined via ordinary differential equations on the surfaces. These equations are numerically integrated in JavaView. Select one of various parameterized hyper surfaces and choose among four types of curves on these surfaces: geodesics, shadow lines, asymptotic lines, and principal curvature lines.

The curve are described by differential equations that are integrated with a fourth-order Runge-Kutta method with constant step size.

#### Usage:

Press key `i`

and pick a point on the surface. The selected
curve is integrated with a step size of length/(discr-1) to a maximum of the
given length, or until the edge of the surface is reached.

Controls in the curve panel:

Choice | Choose curve type. |

Slider "Length" | Analytic length of curve. |

Slider "Polygon Discr" | Number of curve vertices. |

Slider "Direction" | Starting Direction of curve. The direction is given by an angle in the tangent space at the selected point. |

Slider "Thickness" | Radius of tube around curve. |

Slider "Tube Discr" | Number of edges of the tube around the curve. |

Checkbox "Show Tube" | Switch tube around the curve to be visible or invisible in display. |

Checkbox "Show Polygon" | Switch the curve polygon to be visible or invisible in display. |

Checkbox "Show Surface" | Switch the surface underlying the curve to be visible or invisible in display. |

Button "Animate Direction" | Get Animation panel to start animation of the initial curve direction. |