Overview
First Applet
First Application
First Graph
First Project
Models
Loader
Keyframe
Linear Alg
Torus Knot
Picking
Camera Events
Color Selector
Slider
Ruler
Vector Field
Polygon Sets
Scalar Field
ODE
Root Finder
Parm Curve
Parm Surface
L-System
Texture
Refinement
4D Transform
Size Vertex
Size Polygon
Size Edge

## Torus Knots

Periodic curves on rotation torus. A (m,n)-torus-knot is a curve on the torus, which is specified by winding m times around the main axis of the torus and n times around the tube of the torus. In this applet are three geometries displayed: The torus, the torus knot as a polygon and a tube around the torus knot polygon. The tube is generated by carrying a frame parallel along the polygon; this is independent of the surface underlying the polygon, so there may be a distortion between the ends of this tube.

Controls in the project panel:

Slider "U-Windings6quot; Number of windings around the main axis of the torus. Slider "Z-Windings" Number of windings around the tube of the torus. Slider "Knot Discr" Number of Vertices of the torus knot polygon. Slider "Tube Discr" Number of edges along the torus knot tube. Slider "Tube Thick" Radius of torus knot tube. Checkbox "Show Torus" Set torus to be visible or invisible in the display. Checkbox "Show Tube" Set tube around torus knot to be visible or invisible in the display. Button "Reset" Set all sliders back to their default values. Source code:

PaTorusKnot.java of applet

PjTorusKnot.java of project

PjTorusKnot_IP.java of info panel of project.