Varkon Geometry Tutorial: Conic 2009-03-17


Please refer to CUR_CONIC in Varkon's Programmers Manual

The P-value defines the fullness of the curve. The point is the point furthest away from the chord line.

P-value for the conic

The P-value can also be calculated with triangle areas. The point is any point on the conic.

P-value calculated with triangle areas

In Varkon the P-value is calculated with areas. If a user inputs a mid point the P-value will first be calculated.

If the start and end points, the start and end tangent points and the mid point all are in the same plane
then the mid point will be on the conic.

But the Varkon conic is a Generalized Conic. The cone definition points need not to be in a plane.

Generalized conic

The area method will also for this case be used if the user inputs a mid point.
First a (conic) plane is calculated and the mid point is projected onto this plane.
The input point will therefore normally not be on the curve.

Generalized conic

Interesting is perhaps that if the Generalized Conic is projected onto the conic plane,
this projected segment would be a true conic.