Trefoil Knot

[Mike Saroch 0]

Topology is the study of shapes and spaces, and their connectedness, continuity, and boundary. These are important topics when creating variable models used for design studies. 

 

This is a model of a mathematical knot known as a trefoil knot.  It's not very practical for engineering but it looks cool, and it's a nice model for illustrating one of curve types in CAESES known as a generic curve as well as the sweep surface.  You can define a curve with a mathematical description in 3D space using the generic curve.

 

The trefoil knot is mathematically defined as follows:

x = sin t + 2 sin 2t

y = cos t - 2 cos 2t

z = -sin 3t

 

In CAESES you can create the pathline for the knot using the generic curve.  So for example, the Z function would like like:  -sin(3*t*2*pi(),true) 

 

Where t is a parameter in CAESES used for all curves, and runs from 0 to 1.  It is multiplied by 2pi to transform it to the correct mathematical range, and "true" is used to indicate that the argument is in radians (and not in degrees).

 

 

trefoilKnot.fdb