Notes on Conic command, rho, ellipses, and eccentricity.







For a given ellipse, there is one value for the eccentricity.

For a given ellipse, there can be many rho values.

The conic involves two tangent lines.
The tangent lines do not need to be symmetric.

The conic is determined by 3 points plus rho, or 4 points. (start, end, apex, through or rho).

rho = vertex distance from chord center / apex distance from chord center.

rho is rounded off, in MoI, to two decimals. (EDIT Incorrect, see next post) :-)

rho can be calculated by using custom distance.

The maximum positive rho value is 1 for a conic.
For a hyperbola, 0.5 < rho <= 1.
For a parabola, rho = 0.5.
For an ellipse, rho < 0.5.

A negative rho has the through point opposite the chord center, from the apex point.
This is a "negative" distance. rho < 0. (examples: rho = -.3, -.6, -1.2, -4.5, -52.0 ...)

When MoI does a conic ellipse, the center point of the ellipse is determined, and can be revealed by drawing a line near to it.
Draw a line from the apex, through the chord center point, to where the center pops up.
Create a line segment from the conic intercept point to the center.
Rotate it 180 degrees, to find the opposite point on the ellipse.
Run conic again, at negative rho, using the opposite point as the through point, to create the whole ellipse.

(rho is also a measure from 0 to 1 of the angle of a plane through a right cone.)

To find the focus, and eccentricity, create a line the length of half the major axis, and rotate it
to the major axis. (from the minor vertex). Eccentricity = f/a.

(So MoI indirectly determines the eccentricity and focus.)