ddg.math.confocal2d module

Coordinate functions for smooth and discrete confocal conics and quadrics.

ddg.math.confocal2d.confocal_conics_sqrt(u1, u2, a1, a2)

confocal conics – elliptic coordinates (parametrization with square roots)

ddg.math.confocal2d.confocal_conics_trigonometric(u1, u2, a1, a2)

confocal conics – parametrization with trigonometric functions

ddg.math.confocal2d.confocal_conics_concentric(u1, u2, a1, a2)

confocal conics – parametrization with concetric circles on diagonals

ddg.math.confocal2d.confocal_conics_ic(u1, u2, a1, a2, k)

confocal conics – parametrization with elliptic coordinates with diagonals on lines

ddg.math.confocal2d.confocal_conics_ic_hyperbolic(u1, u2, a1, a2, k)

confocal conics – parametrization with elliptic coordinates with diagonals on lines

ddg.math.confocal2d.confocal_conics_hyperbolic_pencil(u1, u2)

confocal conics – parametrization st diagonals are vertical lines and circles

ddg.math.confocal2d.discrete_confocal_conics_gamma(m, n, a1, a2)

discrete confocal conics – parametrization with gamma functions

ddg.math.confocal2d.discrete_confocal_conics_gamma_u1_of_corresponding_continuous(n1)

ddg.math.confocal2d.discrete_confocal_conics_gamma_u2_of_corresponding_continuous(n2)

ddg.math.confocal2d.discrete_confocal_conics_trigonometric(m, n, a1, a2, h1, h2, d1=0.0, d2=0.0)

discrete confocal conics – parametrization with trigonometric functions

ddg.math.confocal2d.discrete_confocal_conics_trigonometric_u1_of_corresponding_continuous(n1, a1, a2, h1, d1=0.0)

Returns u1 of the corresponding continuous conics in the sqrt parametrization.

The continuous conics corresponding to (u1, u2) in the sqrt parametrization establish the polarity relation between points and edges of two dual meshes of the discrete_confocal_conics_trigonometric parametrization.

ddg.math.confocal2d.discrete_confocal_conics_trigonometric_u2_of_corresponding_continuous(n2, a1, a2, h2, d2=0.0)

Returns u1 of the corresponding continuous conics in the sqrt parametrization.

The continuous conics corresponding to (u1, u2) in the sqrt parametrization establish the polarity relation between points and edges of two dual meshes of the discrete_confocal_conics_trigonometric parametrization.

ddg.math.confocal2d.discrete_confocal_conics_concentric(m, n, a1, a2, d, c1=0.0, c2=0.0)

discrete confocal conics – diagonally related to concetric circles

ddg.math.confocal2d.discrete_confocal_conics_concentric_u1_of_corresponding_continuous(n1, a1, a2, d, c1, c2)

ddg.math.confocal2d.discrete_confocal_conics_concentric_u2_of_corresponding_continuous(n2, a1, a2, d, c1, c2)

ddg.math.confocal2d.discrete_confocal_conics_ic(n1, n2, a1, a2, k, h, c1, c2)

discrete confocal conics – parametrization with elliptic coordinates leading to IC-nets

ddg.math.confocal2d.discrete_confocal_conics_ic_u1_of_corresponding_continuous(n1, a1, a2, k, h, c1, c2)

ddg.math.confocal2d.discrete_confocal_conics_ic_u2_of_corresponding_continuous(n2, a1, a2, k, h, c1, c2)

ddg.math.confocal2d.discrete_confocal_conics_ic_hyperbolic(n1, n2, a1, a2, k, h, c1, c2)

discrete confocal conics – parametrization with elliptic coordinates leading to IC-nets

ddg.math.confocal2d.discrete_confocal_conics_hyperbolic_pencil(n1, n2, d, c1, c2)

discrete confocal conics – parametrization st diagonals are vertical lines and dual wrt circles

ddg.math.confocal2d.discrete_confocal_conics_hyperbolic_pencil_u1_of_corresponding_continuous(n1, d, c1)

ddg.math.confocal2d.discrete_confocal_conics_hyperbolic_pencil_u2_of_corresponding_continuous(n2, d, c2)

ddg.math.confocal2d.sampled_confocal_conic(u, a1, a2, samples=10000, end=100, quadrants=None, prefer_ellipse=True)

Coordinates of a sampled version of the conic x^2 / (a1 + u) + y^2 / (a2 + u) = 1.

Returns two arrays. One for x coordinates and one for y coordinates.