intersectConicMatrices¶

Overview¶

Handles intersections of conic sections (based on their matrix representations).

Modelled off of https://math.stackexchange.com/questions/425366/finding-intersection-of-an-ellipse-with-another-ellipse-when-both-are-rotated/425412#425412

Should be in the form specified by https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections, i.e. given

Q(x,y) = Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

The matrix should be in the form:

[ A, B/2, D/2 ] [ B/2, C, E/2 ] [ D/2, E/2, F ]

In this file, we often handle matrices of complex values. They are typically 3x3 and stored in row-major order, thus:

[ A, B, C ] [ D, E, F ] [ G, H, I ]

will be stored as [ A, B, C, D, E, F, G, H, I ].

If something is noted as a "line", it is a homogeneous-coordinate form in complex numbers, e.g. an array [ a, b, c ] represents the line ax + by + c = 0.

@author Jonathan Olson <jonathan.olson@colorado.edu>

Source Code¶

See the source for intersectConicMatrices.ts in the kite repository.