Manuals/calci/TORUS

TORUS (Radius,TubeRadius,w1)

• $Radius$ and $TubeRadius$ are radius value of the circle.

Description

• This function shows the Torus for the given value.
• In $TORUS(Radius,TubeRadius,w1)$, $Radius$ is the radius value of the bigger circle.
• $TubeRadius$ is the radius value of the smaller circle.
• A torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis co planar with the circle. *If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution.
• For example of TORUS are rings, doughnuts, and bagels.
• A torus can be defined parametrically by:

$x(\theta ,\phi )=(R+rCos\theta )Cos\phi$ $y(\theta ,\phi )=(R+rCos\theta )Sin\phi$ $z(\theta ,\phi )=rSin\theta$ where $\theta$,$\phi$ are angles which make a full circle, so that their values start and end at the same point.

• $R$ is the distance from the center of the tube to the center of the torus.
• $r$ is the radius of the tube.
• $R$ is known as the "major radius" and $r$ is known as the "minor radius".
• The ratio R divided by r is known as the aspect ratio.
• The typical doughnut confectionery has an aspect ratio of about 3 to 2.

See Also

• FRACTAL
• LISSAJOUS
• SURFACEGRAPH

References

• Torus

• List of Main Z Functions
• Z3 home