aim2dat.utils.maths¶

Module that contains custom mathematical functions.

Module Contents¶

Functions¶

aim2dat.utils.maths.calc_angle(vector1, vector2)[source]¶

Calculate the angle between two vectors.

Parameters:¶

• vector1 (list) – List containing three numbers.

• vector2 (list) – List containing three numbers.

Returns:¶

angle (float) – Angle in radian.

aim2dat.utils.maths.calc_circular_segment_area(radius, distance)[source]¶

Calculate the circular segment.

See: https://en.wikipedia.org/wiki/Circular_segment.

Parameters:¶

• radius (float) – Radius of the circle.

• distance (float) – Distance of the segment from the circle center.

Returns:¶

segment_area (float) – Area of the segment.

aim2dat.utils.maths.calc_plane_equation(point1, point2, point3)[source]¶

Calculate the plane from 3 given points in the form a*x + b*y + c*z = d.

Parameters:¶

• point1 (list or np.array) – Point in 3-dimensional space.

• point2 (list or np.array) – Point in 3-dimensional space.

• point3 (list or np.array) – Point in 3-dimensional space.

Returns:¶

• a (float) – plane parameter.

• b (float) – plane parameter.

• c (float) – plane parameter.

• d (float) – plane parameter.

aim2dat.utils.maths.calc_polygon_area(vertices)[source]¶

Calculate the area of a polygon.

Parameters:¶

vertices (list or np.array) – (n x 3) list of the vertices.

Returns:¶

area (float) – Area of the polygon.

aim2dat.utils.maths.calc_reflection_matrix(n_vector)[source]¶

Calculate the 3d reflection matrix normal to the input vector.

Parameters:¶

n_vector (list or np.array) – Normal vector of the reflection plane.

Returns:¶

np.array – Reflection matrix.

aim2dat.utils.maths.calc_solid_angle(center, points)[source]¶

Calculate the solid angle between a center point and points that span a polyhedron.

Parameters:¶

• center (list) – Center point.

• points (list) – Nested list of points.

Returns:¶

solid_angle (float) – Solid angle of the polyhedron.

aim2dat.utils.maths.create_lin_ind_vector(vector)[source]¶

Create linearly independent vector with reference to the input vector. The method adds one to the first element of the vector which is zero. In case all elements are non-zero, one is added to the first element of the vector.

Parameters:¶

vector (list, tuple or np.array) – Input vector

Returns:¶

np.array – Linearly independent vector.

aim2dat.utils.maths.gaussian_function(x, mu, sigma)[source]¶

Calculate the Gaussian function with a certain sigma-value.

Parameters:¶

• x (float) – x value for which the y value is calculated.

• mu (float) – Expected value.

• sigma (float) – Variance.

Returns:¶

y (float) – y value.