ddg.math.euclidean2d module

Planar Euclidean geometry utils.

ddg.math.euclidean2d.diagonals_intersection(a, b, c, d)

ddg.math.euclidean2d.intersect_edges(a, b, c, d)

ddg.math.euclidean2d.dual_quadrilateral(a, b, c, d)

ddg.math.euclidean2d.distance_lines(a, v, b, w)

Distance between the lines a + sv and b + tw.

ddg.math.euclidean2d.vertex_angle(x1, x2, x3)

angle of (x1,x2,x3) on the left to the line (not the vector) only reliable for konvex quads!!!

ddg.math.euclidean2d.vertex_angle_with_sign(x1, x2, x3)

like vertex_angle just with sign instead of +pi

ddg.math.euclidean2d.cyclic_order(points, center)

determines the cyclic order of the points beginning with the first wrt the center maybe usefull for angle calculation in non-embedded case???

ddg.math.euclidean2d.circumcircle_center(x, y, z)

ddg.math.euclidean2d.circumcircle_radius(x, y, z)

ddg.math.euclidean2d.coordinates_on_circle_from_cross_ratio(x, x1, x2, q)

get fourth point on a circle from real cross-ratio not exact with fractions right now…!!!

ddg.math.euclidean2d.triangle_area(a, b, c)

Numerically stable version of Heron’s formula for the area of a tringagle with side lengths a,b,c.

ddg.math.euclidean2d.line2D(p1, p2)

Gives the coefficients of the line equation describing the line through given points p1 and p2.

Parameters:

p1np.array([x1, y1])

Point p1 given by its Euclidean 2D coordinates in 2-dim array.

p2np.array([x2, y2])

Point p1 given by its Euclidean 2D coordinates in 2-dim array.

Returns:

[A, B, C]array of three floats

The coefficients of the line equation Ax + By = C describing the line through p1 and p2.

ddg.math.euclidean2d.intersection(l1, l2)

Calculates the intersection of two lines that are given by coefficients of their line equations.

To do so the linear system Ax = b of the line equations is solved via numpy.linalg.solver.

Parameters:

l1, l2[float, float, float]

The two lines whose intersection shall be calculated. Both given by the coefficients of their line equations Ai*x + Bi*y = Ci where i=1,2.

Returns:

[x,y]np.array of two floats

The Euclidean 2D coordinates of the intersection point.

ddg.math.euclidean2d.intersectionCramer(l1, l2)

Calculates the intersection of two lines that are given by coefficients of their line equations via Cramer’s rule.

Parameters:

l1, l2[float, float, float]

The two lines whose intersection shall be calculated. Both given by the coefficients of their line equations Ai*x + Bi*y = Ci where i=1,2.

Returns:

[x,y]array of two floats

The Euclidean 2D coordinates of the intersection point.

Raises:

ValueError

If the given lines do not intersect.

ddg.math.euclidean2d.intersection_in_barycentric_coords(a, b, p, q)

Gives the intersection of two lines in barycentric coordinates relative to the given points which the lines run through.

Parameters:

a, bnp.array([float, float])

The two points the first line for intersecting runs through, given by their Euclidean 2D coordinates.

p, qnp.array([float, float])

The two points the second line for intersecting runs through, given by their Euclidean 2D coordinates.

Returns:

xnp.array[t1, s1, t2, s2] where ti, si float, i=1,2

The intersection of the lines given as the barycentric coordinates corresponding to solving the equation t1*a + s1*b = t2*p + s2*q.

Notes

We establish a homogeneous system and solve it via numpy.