ddg.math.complex module

Utility functions for complex analysis of plane geometry. Uses and generates (numpy) complex numbers.

ddg.math.complex.complex_sample(size=None, seed=None)

Get a sample of random complex numbers (or vectors).

Parameters:

sizeint or tuple of ints (default=None)

size of sample of complex numbers or shape of numpy.ndarray

seedint (default=None)

seed for obtaining a deterministic function

Returns:

complex or numpy.ndarray of numpy.complex128

Notes

Real and imaginary part are standard normally distributed

ddg.math.complex.to_array(z)

Convert complex numbers to 2D arrays of real and imaginary part.

Parameters:

zcomplex

Returns:

numpy.ndarray of shape (2,)

ddg.math.complex.to_complex(x)

Convert 2D array to complex number.

Parameters:

xsequence of length 2

Returns:

complex

ddg.math.complex.homogeneous(z)

Get complex number in homogeneous coordinates.

z is interpreted as the affine coordinate of an element in CP^1.

Parameters:

zcomplex

Returns:

numpy.ndarray of shape (2,)

ddg.math.complex.scalar_product(z1, z2)

For two complex numbers get scalar product of corresponding elements in R^2.

Parameters:

z1,z2complex

Returns:

float

ddg.math.complex.determinant(z1, z2)

For two complex numbers get determinant of matrix of corresponding elements in R^2.

Parameters:

z1,z2complex

Returns:

float

ddg.math.complex.rel_angle(z1, z2)

Get angle in [0,2*pi) between complex numbers z1,z2.

Parameters:

z1,z2complex

Returns:

float

ddg.math.complex.cr(z1, z2, z3, z4)

Compute complex cross ratio.

cr(z1,z2,z3,z4) = (z1 - z2)/(z2 - z3) * (z3 - z4)/(z4 - z1)

Parameters:

z1,z2,z3,z4complex

Returns:

complex

ddg.math.complex.fourth_point_from_cross_ratio(z, z1, z2, q)

Get z12 such that cr(z, z1, z12, z2) = q

For a quadrilateral of the form

z2_____z12
 |     |
 |     |
 z_____z1

with given z,z1,z2 and q, compute z12 .

Parameters:

z,z1,z2,qcomplex

Returns:

complex

ddg.math.complex.circumcenter(z1, z2, z3)

Get center of circle through three complex numbers.

Parameters:

z1,z2,z3complex

Returns:

numpy.complex128

ddg.math.complex.circumradius(z1, z2, z3)

Get radius of circle through three complex numbers.

Parameters:

z1,z2,z3complex

Returns:

float

ddg.math.complex.intersect_diags(z1, z2, z3, z4)

For a complex quadrilateral (z1,z2,z3,z4) get the intersection point of the diagonals.

The four complex points are given as an argument in positive cyclic order.

z4-----z3
 |\   /|
 |  x  |
 |/   \|
z1-----z2

Parameters:

z1,z2,z3,z4complex

Returns:

complex

ddg.math.complex.intersect_edges(z1, z2, z3, z4)

For a complex quadrilateral (z1,z2,z3,z4) get the intersection of the two opposite edges (z1,z2) and (z3,z4).

Will return complex infinity if intersection does not exist.

z4-----z3--
 |     |    \
 |     |     x
 |     |    /
z1-----z2--

Parameters:

z1,z2,z3,z4complex

Returns:

complex