geometry

Primitives

Bases

`Geometry`	Base class for all geometric objects.
`Primitive`	Base class for geometric primitives.
`Shape`	Base class for geometric shapes.
`Curve`	Class representing a general curve object.
`Surface`	Class representing a general surface object.

0-dimensional

`Vector`	A vector is defined by XYZ components and a homogenisation factor.
`Quaternion`	A quaternion is defined by 4 components, X, Y, Z, and W.
`Point`	A point is defined by XYZ coordinates.
`Pointcloud`	Class for working with pointclouds.
`Plane`	A plane is defined by a base point and a normal vector.
`Frame`	A frame is defined by a base point and two orthonormal base vectors.

1-dimensional

`Line`	A line is defined by two points.
`Polyline`	A polyline is defined by a sequence of points connected by line segments.
`Bezier`	A Bezier curve is defined by control points and a degree.
`NurbsCurve`	A NURBS curve is defined by control points, weights, knots, and a degree.

2-dimensional

`Circle`	A circle is defined by a plane and a radius.
`Ellipse`	A ellipse is defined by a plane and a major and minor axis.
`Polygon`	A polygon is defined by a sequence of points forming a closed loop.
`NurbsSurface`	A NURBS surface is defined by control points, weights, knots, and a degree, in two directions U and V.

3-dimensional

`Box`	A box is defined by a frame and its dimensions along the frame's x-, y- and z-axes.
`Sphere`	A sphere is defined by a point and a radius.
`Cylinder`	A cylinder is defined by a circle and a height.
`Cone`	A cone is defined by a circle and a height.
`Capsule`	A capsule is defined by a line segment and a radius.
`Torus`	A torus is defined by a plane and two radii.
`Polyhedron`	A polyhedron is defined by its vertices and faces.

Transformations

`Projection`	Class representing a projection transformation.
`Reflection`	Class representing a reflection transformation.
`Rotation`	Class representing a rotation transformation.
`Scale`	Class representing a scale transformation.
`Shear`	Class representing a shear transformation.
`Transformation`	Class representing a general 4x4 transformation matrix.
`Translation`	Class representing a translation transformation.

Functions

Points, Vectors, Lines, Planes, Circles

`angle_points`	Compute the smallest angle between the vectors defined by three points.
`angle_points_xy`	Compute the smallest angle between the vectors defined by the XY components of three points.
`angle_vectors`	Compute the smallest angle between two vectors.
`angle_vectors_xy`	Compute the smallest angle between the XY components of two vectors.
`angle_vectors_signed`	Computes the signed angle between two vectors.
`angles_points`	Compute the two angles between two vectors defined by three points.
`angles_points_xy`	Compute the two angles between the two vectors defined by the XY components of three points.
`angles_vectors`	Compute the the 2 angles formed by a pair of vectors.
`angles_vectors_xy`	Compute the angles between the XY components of two vectors.
`angle_planes`	Compute the smallest angle between the two normal vectors of two planes.
`centroid_points`	Compute the centroid of a set of points.
`centroid_points_xy`	Compute the centroid of a set of points lying in the XY-plane.
`centroid_points_weighted`	Compute the weighted centroid of a set of points.
`circle_from_points`	Construct a circle from three points.
`circle_from_points_xy`	Create a circle from three points lying in the XY-plane
`midpoint_point_point`	Compute the midpoint of two points.
`midpoint_point_point_xy`	Compute the midpoint of two points lying in the XY-plane.
`midpoint_line`	Compute the midpoint of a line defined by two points.
`midpoint_line_xy`	Compute the midpoint of a line defined by two points.
`tangent_points_to_circle_xy`	Calculates the tangent points on a circle in the XY plane.

Polygons & Polyhedrons

`area_polygon`	Compute the area of a polygon.
`area_polygon_xy`	Compute the area of a polygon lying in the XY-plane.
`area_triangle`	Compute the area of a triangle defined by three points.
`area_triangle_xy`	Compute the area of a triangle defined by three points lying in the XY-plane.
`centroid_polygon`	Compute the centroid of the surface of a polygon.
`centroid_polygon_xy`	Compute the centroid of the surface of a polygon projected to the XY plane.
`centroid_polygon_vertices`	Compute the centroid of the vertices of a polygon.
`centroid_polygon_vertices_xy`	Compute the centroid of the vertices of a polygon projected to the XY plane.
`centroid_polygon_edges`	Compute the centroid of the edges of a polygon.
`centroid_polygon_edges_xy`	Compute the centroid of the edges of a polygon prohected to the XY plane.
`centroid_polyhedron`	Compute the center of mass of a polyhedron.
`normal_polygon`	Compute the normal of a polygon defined by a sequence of points.
`normal_triangle`	Compute the normal vector of a triangle.
`normal_triangle_xy`	Compute the normal vector of a triangle assumed to lie in the XY plane.
`volume_polyhedron`	Compute the volume of a polyhedron represented by a closed mesh.

Point Sets

`bestfit_circle_numpy`	Fit a circle through a set of points.
`bestfit_frame_numpy`	Fit a frame to a set of points.
`bestfit_plane`	Fit a plane to a list of (more than three) points.
`bestfit_plane_numpy`	Fit a plane through more than three (non-coplanar) points.
`bestfit_sphere_numpy`	Returns the sphere's center and radius that fits best through a set of points.
`bounding_box`	Computes the axis-aligned minimum bounding box of a list of points.
`bounding_box_xy`	Compute the axis-aligned minimum bounding box of a list of points in the XY-plane.
`convex_hull`	Construct convex hull for a set of points.
`convex_hull_numpy`	Compute the convex hull of a set of points.
`convex_hull_xy`	Computes the convex hull of a set of 2D points.
`convex_hull_xy_numpy`	Compute the convex hull of a set of points in the XY plane.
`icp_numpy`	Align two point clouds using the Iterative Closest Point (ICP) method.
`oabb_numpy`	Oriented bounding box of a set of points.
`oriented_bounding_box_numpy`	Compute the oriented minimum bounding box of a set of points in 3D space.
`oriented_bounding_box_xy_numpy`	Compute the oriented minimum bounding box of set of points in the XY plane.

Distance

`closest_line_to_point`	Compute closest line to a point from a list of lines.
`closest_point_in_cloud`	Calculates the closest point in a pointcloud.
`closest_point_in_cloud_xy`	Calculates the closest point in a list of points in the XY-plane.
`closest_point_on_line`	Computes closest point on line to a given point.
`closest_point_on_line_xy`	Compute closest point on line (continuous) to a given point lying in the XY-plane.
`closest_point_on_plane`	Compute closest point on a plane to a given point.
`closest_point_on_polyline`	Find the closest point on a polyline to a given point.
`closest_point_on_polyline_xy`	Compute closest point on a polyline to a given point, assuming they both lie in the XY-plane.
`closest_point_on_segment`	Computes closest point on line segment (p1, p2) to test point.
`closest_point_on_segment_xy`	Compute closest point on a line segment to a given point lying in the XY-plane.
`distance_line_line`	Compute the shortest distance between two lines.
`distance_point_point`	Compute the distance bewteen a and b.
`distance_point_point_xy`	Compute the distance between points a and b, assuming they lie in the XY plane.
`distance_point_point_sqrd`	Compute the squared distance bewteen points a and b.
`distance_point_point_sqrd_xy`	Compute the squared distance between points a and b lying in the XY plane.
`distance_point_line`	Compute the distance between a point and a line.
`distance_point_line_xy`	Compute the distance between a point and a line, assuming they lie in the XY-plane.
`distance_point_line_sqrd`	Compute the squared distance between a point and a line.
`distance_point_line_sqrd_xy`	Compute the squared distance between a point and a line lying in the XY-plane.
`distance_point_plane`	Compute the distance from a point to a plane defined by origin point and normal.
`distance_point_plane_signed`	Compute the signed distance from a point to a plane defined by origin point and normal.

Intersections

`intersection_circle_circle_xy`	Calculates the intersection points of two circles in 2d lying in the XY plane.
`intersection_ellipse_line_xy`	Computes the intersection of an ellipse and a line in the XY plane.
`intersection_line_box_xy`	Compute the intersection between a line and a box in the XY plane.
`intersection_line_line_xy`	Compute the intersection of two lines, assuming they lie on the XY plane.
`intersection_line_line`	Computes the intersection of two lines.
`intersection_line_plane`	Computes the intersection point of a line and a plane
`intersection_line_segment_xy`	Compute the intersection between a line and a segment.
`intersection_line_segment`	Compute the intersection of a line and a segment.
`intersection_line_triangle`	Computes the intersection point of a line (ray) and a triangle based on the Moeller Trumbore intersection algorithm
`intersection_mesh_mesh`	Compute the intersection of tow meshes.
`intersection_plane_circle`	Computes the intersection of a plane and a circle.
`intersection_plane_plane_plane`	Computes the intersection of three planes
`intersection_plane_plane`	Computes the intersection of two planes
`intersection_polyline_plane`	Calculate the intersection point of a plane with a polyline.
`intersection_ray_mesh`	Compute the intersection(s) between a ray and a mesh.
`intersection_segment_plane`	Computes the intersection point of a line segment and a plane
`intersection_segment_polyline`	Calculate the intersection point of a segment and a polyline.
`intersection_segment_polyline_xy`	Calculate the intersection point of a segment and a polyline on the XY-plane.
`intersection_segment_segment`	Compute the intersection of two lines segments.
`intersection_segment_segment_xy`	Compute the intersection of two lines segments, assuming they lie in the XY plane.
`intersection_sphere_line`	Computes the intersection of a sphere and a line.
`intersection_sphere_sphere`	Computes the intersection of 2 spheres.

Interpolation

`barycentric_coordinates`	Compute the barycentric coordinates of a point wrt to a triangle.
`discrete_coons_patch`	Creates a coons patch from a set of four or three boundary polylines (ab, bc, dc, ad).
`tween_points`	Compute the interpolated points between two sets of points.
`tween_points_distance`	Compute an interpolated set of points between two sets of points, at a given distance.

Offsets

`offset_line`	Offset a line by a distance.
`offset_polyline`	Offset a polyline by a distance.
`offset_polygon`	Offset a polygon (closed) by a distance.

Boolean operations

`boolean_union_mesh_mesh`	Compute the boolean union of two triangle meshes.
`boolean_difference_mesh_mesh`	Compute the boolean difference of two triangle meshes.
`boolean_intersection_mesh_mesh`	Compute the boolean intersection of two triangle meshes.

Triangulation

`conforming_delaunay_triangulation`	Construct a Conforming Delaunay triangulation of set of vertices, constrained to the specified segments.
`constrained_delaunay_triangulation`	Construct a Delaunay triangulation of set of vertices, constrained to the specified segments.
`delaunay_from_points`	Computes the delaunay triangulation for a list of points.
`delaunay_from_points_numpy`	Computes the delaunay triangulation for a list of points using Numpy.
`delaunay_triangulation`	Construct a Delaunay triangulation of set of vertices.
`voronoi_from_points_numpy`	Generate a voronoi diagram from a set of points.

Triangle meshes

`trimesh_gaussian_curvature`	Compute the discrete gaussian curvature of a triangle mesh.
`trimesh_geodistance`	Compute the geodesic distance from every vertex of the mesh to a source vertex.
`trimesh_harmonic`	Compute the harmonic parametrisation of a triangle mesh within a fixed circular boundary.
`trimesh_isolines`	Compute isolines on a triangle mesh using a scalarfield of data points assigned to its vertices.
`trimesh_lscm`	Compute the least squares conformal map of a triangle mesh.
`trimesh_mean_curvature`	Compute the discrete mean curvature of a triangle mesh.
`trimesh_massmatrix`	Compute massmatrix on a triangle mesh using a scalarfield of data points assigned to its vertices.
`trimesh_principal_curvature`	Compute the principal curvature directions of a triangle mesh.
`trimesh_remesh`	Remeshing of a triangle mesh.
`trimesh_remesh_constrained`	Constrained remeshing of a triangle mesh.
`trimesh_remesh_along_isoline`	Remesh a mesh along an isoline of a scalarfield over the vertices.
`trimesh_slice`	Slice a mesh by a list of planes.

Quad meshes

quadmesh_planarize

Planarize the faces of a quad mesh.

Predicates

`is_ccw_xy`	Determine if c is on the left of ab when looking from a to b, and assuming that all points lie in the XY plane.
`is_colinear`	Determine if three points are colinear.
`is_colinear_line_line`	Determine if two lines are colinear.
`is_colinear_xy`	Determine if three points are colinear on the XY-plane.
`is_coplanar`	Determine if the points are coplanar.
`is_intersection_line_line`	Verifies if two lines intersect.
`is_intersection_line_line_xy`	Verifies if two lines intersect on the XY-plane.
`is_intersection_line_plane`	Determine if a line (ray) intersects with a plane.
`is_intersection_line_triangle`	Verifies if a line (ray) intersects with a triangle.
`is_intersection_plane_plane`	Verifies if two planes intersect.
`is_intersection_segment_plane`	Determine if a line segment intersects with a plane.
`is_intersection_segment_segment`	Verifies if two segments intersect.
`is_intersection_segment_segment_xy`	Determines if two segments, ab and cd, intersect.
`is_point_behind_plane`	Determine if a point lies behind a plane.
`is_point_infront_plane`	Determine if a point lies in front of a plane.
`is_point_in_circle`	Determine if a point lies in a circle.
`is_point_in_circle_xy`	Determine if a point lies in a circle lying on the XY-plane.
`is_point_in_convex_polygon_xy`	Determine if a point is in the interior of a convex polygon lying on the XY-plane.
`is_point_in_halfspace`	Determine if a point lies in front of a plane.
`is_point_in_polygon_xy`	Determine if a point is in the interior of a polygon lying on the XY-plane.
`is_point_in_polyhedron`	Determine if the point lies inside the given polyhedron.
`is_point_in_triangle`	Determine if a point is in the interior of a triangle.
`is_point_in_triangle_xy`	Determine if a point is in the interior of a triangle lying on the XY-plane.
`is_point_on_line`	Determine if a point lies on a line.
`is_point_on_line_xy`	Determine if a point lies on a line on the XY-plane.
`is_point_on_plane`	Determine if a point lies on a plane.
`is_point_on_polyline`	Determine if a point is on a polyline.
`is_point_on_polyline_xy`	Determine if a point is on a polyline on the XY-plane.
`is_point_on_segment`	Determine if a point lies on a given line segment.
`is_point_on_segment_xy`	Determine if a point lies on a given line segment on the XY-plane.
`is_polygon_convex`	Determine if a polygon is convex.
`is_polygon_convex_xy`	Determine if the polygon is convex on the XY-plane.
`is_polygon_in_polygon_xy`	Determine if a polygon is in the interior of another polygon on the XY-plane.

Transformations

`axis_and_angle_from_matrix`	Returns the axis and the angle of the rotation matrix M.
`axis_angle_vector_from_matrix`	Returns the axis-angle vector of the rotation matrix M.
`axis_angle_from_quaternion`	Returns an axis and an angle of rotation from the given quaternion.
`basis_vectors_from_matrix`	Returns the basis vectors from the rotation matrix R.
`compose_matrix`	Calculates a matrix from the components of scale, shear, euler_angles, translation and perspective.
`decompose_matrix`	Calculates the components of rotation, translation, scale, shear, and perspective of a given transformation matrix M.
`dehomogenize_numpy`	Dehomogenizes points or vectors.
`dehomogenize_and_unflatten_frames_numpy`	Dehomogenize a list of vectors and unflatten the 2D list into a 3D list.
`euler_angles_from_matrix`	Returns Euler angles from the rotation matrix M according to specified axis sequence and type of rotation.
`euler_angles_from_quaternion`	Returns Euler angles from a quaternion.
`homogenize_numpy`	Dehomogenizes points or vectors.
`homogenize_and_flatten_frames_numpy`	Homogenize a list of frames and flatten the 3D list into a 2D list using numpy.
`identity_matrix`	Construct an identity matrix.
`local_axes`
`local_to_world_coordinates`	Convert local coordinates to global coordinates.
`local_to_world_coordinates_numpy`	Convert local coordinates to global (world) coordinates.
`matrix_determinant`	Calculates the determinant of a square matrix M.
`matrix_from_axis_and_angle`	Calculates a rotation matrix from an rotation axis, an angle and an optional point of rotation.
`matrix_from_axis_angle_vector`	Calculates a rotation matrix from an axis-angle vector.
`matrix_from_basis_vectors`	Creates a rotation matrix from basis vectors (= orthonormal vectors).
`matrix_from_change_of_basis`	Computes a change of basis transformation between two frames.
`matrix_from_euler_angles`	Calculates a rotation matrix from Euler angles.
`matrix_from_frame`	Computes a change of basis transformation from world XY to the frame.
`matrix_from_frame_to_frame`	Computes a transformation between two frames.
`matrix_from_orthogonal_projection`	Returns an orthogonal projection matrix to project onto a plane.
`matrix_from_parallel_projection`	Returns an parallel projection matrix to project onto a plane.
`matrix_from_perspective_entries`	Returns a matrix from perspective entries.
`matrix_from_perspective_projection`	Returns a perspective projection matrix to project onto a plane along lines that emanate from a single point, called the center of projection.
`matrix_from_quaternion`	Calculates a rotation matrix from quaternion coefficients.
`matrix_from_scale_factors`	Returns a 4x4 scaling transformation.
`matrix_from_shear`	Constructs a shear matrix by an angle along the direction vector on the shear plane (defined by point and normal).
`matrix_from_shear_entries`	Returns a shear matrix from the 3 factors for x-y, x-z, and y-z axes.
`matrix_from_translation`	Returns a 4x4 translation matrix in row-major order.
`matrix_inverse`	Calculates the inverse of a square matrix M.
`mirror_point_plane`	Mirror a point about a plane.
`mirror_points_line`	Mirror a point about a line.
`mirror_points_line_xy`	Mirror a point about a line.
`mirror_points_plane`	Mirror a point about a plane.
`mirror_points_point`	Mirror multiple points about a point.
`mirror_points_point_xy`	Mirror multiple points about a point.
`mirror_vector_vector`	Mirrors vector about vector.
`orient_points`	Orient points from one plane to another.
`orthonormalize_axes`	Corrects xaxis and yaxis to be unit vectors and orthonormal.
`project_point_line`	Project a point onto a line.
`project_point_line_xy`	Project a point onto a line in the XY plane.
`project_point_plane`	Project a point onto a plane.
`project_points_line`	Project points onto a line.
`project_points_line_xy`	Project points onto a line in the XY plane.
`project_points_plane`	Project multiple points onto a plane.
`quaternion_canonize`	Converts a quaternion into a canonic form if needed.
`quaternion_conjugate`	Conjugate of a quaternion.
`quaternion_from_axis_angle`	Returns a quaternion describing a rotation around the given axis by the given angle.
`quaternion_from_euler_angles`	Returns a quaternion from Euler angles.
`quaternion_from_matrix`	Returns the 4 quaternion coefficients from a rotation matrix.
`quaternion_is_unit`	Checks if a quaternion is unit-length.
`quaternion_multiply`	Multiplies two quaternions.
`quaternion_norm`	Calculates the length (euclidean norm) of a quaternion.
`quaternion_unitize`	Makes a quaternion unit-length.
`reflect_line_plane`	Bounce a line of a reflection plane.
`reflect_line_triangle`	Bounce a line of a reflection triangle.
`rotate_points`	Rotates points around an arbitrary axis in 3D.
`rotate_points_xy`	Rotates points in the XY plane around the Z axis at a specific origin.
`scale_points`	Scale points.
`scale_points_xy`	Scale points in the XY plane.
`transform_frames`	Transform multiple frames with one transformation matrix.
`transform_points`	Transform multiple points with one transformation matrix.
`transform_points_numpy`	Transform multiple points with one Transformation using numpy.
`transform_vectors`	Transform multiple vectors with one transformation matrix.
`transform_vectors_numpy`	Transform multiple vectors with one Transformation using numpy.
`translate_points`	Translate points.
`translate_points_xy`	Translate points and in the XY plane.
`translation_from_matrix`	Returns the 3 values of translation from the matrix M.
`world_to_local_coordinates`	Convert global coordinates to local coordinates.
`world_to_local_coordinates_numpy`	Convert global coordinates to local coordinates.

Linear algebra

`add_vectors`	Add two vectors.
`add_vectors_xy`	Add two vectors, assuming they lie in the XY-plane.
`allclose`	Returns True if two lists are element-wise equal within a tolerance.
`argmax`	Returns the index of the first maximum value within an array.
`argmin`	Returns the index of the first minimum value within an array.
`close`	Returns True if two values are equal within a tolerance.
`cross_vectors`	Compute the cross product of two vectors.
`cross_vectors_xy`	Compute the cross product of two vectors, assuming they lie in the XY-plane.
`dehomogenize_vectors`	Dehomogenise a list of vectors.
`divide_vectors`	Element-wise division of two vectors.
`divide_vectors_xy`	Element-wise division of two vectors assumed to lie in the XY plane.
`dot_vectors`	Compute the dot product of two vectors.
`dot_vectors_xy`	Compute the dot product of two vectors, assuming they lie in the XY-plane.
`homogenize_vectors`	Homogenise a list of vectors.
`length_vector`	Calculate the length of the vector.
`length_vector_xy`	Compute the length of a vector, assuming it lies in the XY plane.
`length_vector_sqrd`	Compute the squared length of a vector.
`length_vector_sqrd_xy`	Compute the squared length of a vector, assuming it lies in the XY plane.
`multiply_matrices`	Mutliply a matrix with a matrix.
`multiply_matrix_vector`	Multiply a matrix with a vector.
`multiply_vectors`	Element-wise multiplication of two vectors.
`multiply_vectors_xy`	Element-wise multiplication of two vectors assumed to lie in the XY plane.
`norm_vector`	Calculate the length of a vector.
`norm_vectors`	Calculate the norm of each vector in a list of vectors.
`normalize_vector`	Normalise a given vector.
`normalize_vector_xy`	Normalize a vector, assuming it lies in the XY-plane.
`normalize_vectors`	Normalise multiple vectors.
`normalize_vectors_xy`	Normalise multiple vectors, assuming they lie in the XY plane.
`orthonormalize_vectors`	Orthonormalize a set of vectors.
`power_vector`	Raise a vector to the given power.
`power_vectors`	Raise a list of vectors to the given power.
`scale_vector`	Scale a vector by a given factor.
`scale_vector_xy`	Scale a vector by a given factor, assuming it lies in the XY plane.
`scale_vectors`	Scale multiple vectors by a given factor.
`scale_vectors_xy`	Scale multiple vectors by a given factor, assuming they lie in the XY plane.
`square_vector`	Raise a vector to the power 2.
`square_vectors`	Raise a multiple vectors to the power 2.
`subtract_vectors`	Subtract one vector from another.
`subtract_vectors_xy`	Subtract one vector from another, assuming they lie in the XY plane.
`sum_vectors`	Calculate the sum of a series of vectors along the specified axis.
`transpose_matrix`	Transpose a matrix.
`vector_average`	Average of a vector.
`vector_component`	Compute the component of u in the direction of v.
`vector_component_xy`	Compute the component of u in the direction of v, assuming they lie in the XY-plane.
`vector_standard_deviation`	Standard deviation of a vector.
`vector_variance`	Variance of a vector.

Misc

KDTree

A tree for nearest neighbor search in a k-dimensional space.

`archimedean_spiral_evaluate`	Evalutes a spiral at a parameter.
`circle_evaluate`	Evalutes a circle at a parameter.
`helix_evaluate`	Evalutes an helix at a parameter.
`logarithmic_spiral_evaluate`	Evalutes a logarithmic spiral at a parameter.

geometry

Primitives

Bases

0-dimensional

1-dimensional

2-dimensional

3-dimensional

Transformations

Functions

Points, Vectors, Lines, Planes, Circles

Polygons & Polyhedrons

Point Sets

Distance

Intersections

Interpolation

Offsets

Boolean operations

Triangulation

Triangle meshes

Quad meshes

Predicates

Transformations

Linear algebra

Misc

COMPAS