pylinkage.geometry package

Submodules

pylinkage.geometry.core module

Basic geometry features with numba optimization.

pylinkage.geometry.core.cyl_to_cart(radius: float, theta: float, ori_x: float = 0.0, ori_y: float = 0.0) → tuple[float, float]

Convert polar coordinates into cartesian.

Parameters:

  • radius – Distance from origin.

  • theta – Angle starting from abscissa axis.

  • ori_x – Origin X coordinate (Default value = 0.0).

  • ori_y – Origin Y coordinate (Default value = 0.0).

Returns:

Cartesian coordinates (x, y).

pylinkage.geometry.core.dist(x1: float, y1: float, x2: float, y2: float) → float

Distance between two points.

Parameters:

  • x1 – X coordinate of first point.

  • y1 – Y coordinate of first point.

  • x2 – X coordinate of second point.

  • y2 – Y coordinate of second point.

Returns:

Euclidean distance.

pylinkage.geometry.core.get_nearest_point(ref_x: float, ref_y: float, p1_x: float, p1_y: float, p2_x: float, p2_y: float) → tuple[float, float]

Return the point closer to the reference.

Parameters:

  • ref_x – X coordinate of reference point.

  • ref_y – Y coordinate of reference point.

  • p1_x – X coordinate of first candidate.

  • p1_y – Y coordinate of first candidate.

  • p2_x – X coordinate of second candidate.

  • p2_y – Y coordinate of second candidate.

Returns:

Coordinates of the nearest point.

pylinkage.geometry.core.line_from_points(first_x: float, first_y: float, second_x: float, second_y: float) → tuple[float, float, float]

A cartesian equation of the line joining two points.

Parameters:

  • first_x – X coordinate of first point.

  • first_y – Y coordinate of first point.

  • second_x – X coordinate of second point.

  • second_y – Y coordinate of second point.

Returns:

A cartesian equation of this line (a, b, c) where ax + by + c = 0.

pylinkage.geometry.core.norm(x: float, y: float) → float

Return the norm of a 2-dimensional vector.

Parameters:

  • x – X component.

  • y – Y component.

Returns:

Vector magnitude.

pylinkage.geometry.core.sqr_dist(x1: float, y1: float, x2: float, y2: float) → float

Square of the distance between two points.

Faster than dist when only comparing distances.

Parameters:

  • x1 – X coordinate of first point.

  • y1 – Y coordinate of first point.

  • x2 – X coordinate of second point.

  • y2 – Y coordinate of second point.

Returns:

Squared distance.

pylinkage.geometry.secants module

The geometry module provides general geometry functions.

It is used extensively, so each function is optimized with numba.

pylinkage.geometry.secants.bounding_box(locus: list[tuple[float, float]]) → tuple[float, float, float, float]

Compute the bounding box of a locus.

Parameters:

locus – A list of points or any iterable with the same structure.

Returns:

Bounding box as (y_min, x_max, y_max, x_min).

pylinkage.geometry.secants.circle_intersect(x1: float, y1: float, r1: float, x2: float, y2: float, r2: float, tol: float = 0.0) → tuple[int, float, float, float, float]

Get the intersections of two circles.

Transcription of a Matt Woodhead program, method provided by Paul Bourke, 1997. http://paulbourke.net/geometry/circlesphere/.

Parameters:

  • x1 – X coordinate of first circle center.

  • y1 – Y coordinate of first circle center.

  • r1 – Radius of first circle.

  • x2 – X coordinate of second circle center.

  • y2 – Y coordinate of second circle center.

  • r2 – Radius of second circle.

  • tol – Distance under which two points are considered equal.

Returns:

Tuple of (n_intersections, x1, y1, x2, y2) where: - n=0: No intersection (other values undefined) - n=1: One intersection at (x1, y1) - n=2: Two intersections at (x1, y1) and (x2, y2) - n=3: Same circle (x1, y1, x2 are center and radius)

pylinkage.geometry.secants.circle_line_from_points_intersection(cx: float, cy: float, r: float, p1_x: float, p1_y: float, p2_x: float, p2_y: float) → tuple[int, float, float, float, float]

Intersection(s) of a circle and a line defined by two points.

Parameters:

  • cx – X coordinate of circle center.

  • cy – Y coordinate of circle center.

  • r – Circle radius.

  • p1_x – X coordinate of first point on line.

  • p1_y – Y coordinate of first point on line.

  • p2_x – X coordinate of second point on line.

  • p2_y – Y coordinate of second point on line.

Returns:

Tuple of (n_intersections, x1, y1, x2, y2) where: - n=0: No intersection - n=1: One intersection (tangent) at (x1, y1) - n=2: Two intersections at (x1, y1) and (x2, y2)

pylinkage.geometry.secants.circle_line_intersection(cx: float, cy: float, r: float, a: float, b: float, c: float) → tuple[int, float, float, float, float]

Return the intersection between a line and a circle.

From https://mathworld.wolfram.com/Circle-LineIntersection.html

Parameters:

  • cx – X coordinate of circle center.

  • cy – Y coordinate of circle center.

  • r – Circle radius.

  • a – Line equation coefficient a (ax + by + c = 0).

  • b – Line equation coefficient b.

  • c – Line equation coefficient c.

Returns:

Tuple of (n_intersections, x1, y1, x2, y2).

pylinkage.geometry.secants.intersection(obj_1: tuple[float, float] | tuple[float, float, float], obj_2: tuple[float, float] | tuple[float, float, float], tol: float = 0.0) → tuple[float, float] | tuple[tuple[float, float], ...] | tuple[float, float, float] | None

Intersection of two arbitrary objects.

The input objects should be points or circles.

Parameters:

  • obj_1 – First point or circle (as tuple).

  • obj_2 – Second point or circle (as tuple).

  • tol – Absolute tolerance to use if provided.

Returns:

The intersection found, if any.

Module contents

Basic geometry package.

pylinkage.geometry.circle_intersect(x1: float, y1: float, r1: float, x2: float, y2: float, r2: float, tol: float = 0.0) → tuple[int, float, float, float, float]

Get the intersections of two circles.

Transcription of a Matt Woodhead program, method provided by Paul Bourke, 1997. http://paulbourke.net/geometry/circlesphere/.

Parameters:

  • x1 – X coordinate of first circle center.

  • y1 – Y coordinate of first circle center.

  • r1 – Radius of first circle.

  • x2 – X coordinate of second circle center.

  • y2 – Y coordinate of second circle center.

  • r2 – Radius of second circle.

  • tol – Distance under which two points are considered equal.

Returns:

Tuple of (n_intersections, x1, y1, x2, y2) where: - n=0: No intersection (other values undefined) - n=1: One intersection at (x1, y1) - n=2: Two intersections at (x1, y1) and (x2, y2) - n=3: Same circle (x1, y1, x2 are center and radius)

pylinkage.geometry.circle_line_from_points_intersection(cx: float, cy: float, r: float, p1_x: float, p1_y: float, p2_x: float, p2_y: float) → tuple[int, float, float, float, float]

Intersection(s) of a circle and a line defined by two points.

Parameters:

  • cx – X coordinate of circle center.

  • cy – Y coordinate of circle center.

  • r – Circle radius.

  • p1_x – X coordinate of first point on line.

  • p1_y – Y coordinate of first point on line.

  • p2_x – X coordinate of second point on line.

  • p2_y – Y coordinate of second point on line.

Returns:

Tuple of (n_intersections, x1, y1, x2, y2) where: - n=0: No intersection - n=1: One intersection (tangent) at (x1, y1) - n=2: Two intersections at (x1, y1) and (x2, y2)

pylinkage.geometry.circle_line_intersection(cx: float, cy: float, r: float, a: float, b: float, c: float) → tuple[int, float, float, float, float]

Return the intersection between a line and a circle.

From https://mathworld.wolfram.com/Circle-LineIntersection.html

Parameters:

  • cx – X coordinate of circle center.

  • cy – Y coordinate of circle center.

  • r – Circle radius.

  • a – Line equation coefficient a (ax + by + c = 0).

  • b – Line equation coefficient b.

  • c – Line equation coefficient c.

Returns:

Tuple of (n_intersections, x1, y1, x2, y2).

pylinkage.geometry.cyl_to_cart(radius: float, theta: float, ori_x: float = 0.0, ori_y: float = 0.0) → tuple[float, float]

Convert polar coordinates into cartesian.

Parameters:

  • radius – Distance from origin.

  • theta – Angle starting from abscissa axis.

  • ori_x – Origin X coordinate (Default value = 0.0).

  • ori_y – Origin Y coordinate (Default value = 0.0).

Returns:

Cartesian coordinates (x, y).

pylinkage.geometry.get_nearest_point(ref_x: float, ref_y: float, p1_x: float, p1_y: float, p2_x: float, p2_y: float) → tuple[float, float]

Return the point closer to the reference.

Parameters:

  • ref_x – X coordinate of reference point.

  • ref_y – Y coordinate of reference point.

  • p1_x – X coordinate of first candidate.

  • p1_y – Y coordinate of first candidate.

  • p2_x – X coordinate of second candidate.

  • p2_y – Y coordinate of second candidate.

Returns:

Coordinates of the nearest point.

pylinkage.geometry.intersection(obj_1: tuple[float, float] | tuple[float, float, float], obj_2: tuple[float, float] | tuple[float, float, float], tol: float = 0.0) → tuple[float, float] | tuple[tuple[float, float], ...] | tuple[float, float, float] | None

Intersection of two arbitrary objects.

The input objects should be points or circles.

Parameters:

  • obj_1 – First point or circle (as tuple).

  • obj_2 – Second point or circle (as tuple).

  • tol – Absolute tolerance to use if provided.

Returns:

The intersection found, if any.

pylinkage.geometry.norm(x: float, y: float) → float

Return the norm of a 2-dimensional vector.

Parameters:

  • x – X component.

  • y – Y component.

Returns:

Vector magnitude.

pylinkage.geometry.sqr_dist(x1: float, y1: float, x2: float, y2: float) → float

Square of the distance between two points.

Faster than dist when only comparing distances.

Parameters:

  • x1 – X coordinate of first point.

  • y1 – Y coordinate of first point.

  • x2 – X coordinate of second point.

  • y2 – Y coordinate of second point.

Returns:

Squared distance.