compas.geometry

This package defines all functionality for working with geometry in COMPAS. It provides classes representing geometric primitives, transformations, (NURBS) curves and surfaces, shapes, general polygons and polyhedrons, boundary representations (B-reps), and a number of geometry processing algorithms.

Classes

Arc	An arc is a segment of a circle, and is defined by a coordinate system, radius, and start and end angles.
Bezier	A Bezier curve is defined by control points and a degree.
Box	A box is defined by a frame and its dimensions along the frame's x-, y- and z-axes.
Brep	Contains the topological and geometrical information of a Brep shape.
BrepEdge	An interface for a Brep Edge
BrepError	Represents a generic error in the Brep context
BrepFace	An interface for a Brep Face.
BrepFilletError	Raised when a fillet operation has failed or had not result
BrepInvalidError	Raised when the process of re-constructing a Brep has resulted in an invalid Brep
BrepLoop	An interface for a Brep Loop.
BrepOrientation	Possible orientations of a Brep
BrepTrim	An interface for a Brep Trim
BrepTrimIsoStatus	An enumeration of isoparametric curve direction on the surface.
BrepTrimmingError	Raised when a trimming operation has failed or had not result
BrepType	Possible types of a Brep
BrepVertex	An interface for a Brep Vertex
Capsule	A capsule is defined by a frame, radius, and height.
Circle	A circle is a curve defined by a coordinate system and a radius.
Cone	A cone is defined by a frame, radius, and height.
ConicalSurface	A cylindrical surface is defined by a radius and a local coordinate system.
Curve	Class representing a general parametric curve.
CurveType	Enumaration of curve types.
Cylinder	A cylinder is defined by a frame, radius, and height.
CylindricalSurface	A cylindrical surface is defined by a radius and a local coordinate system.
Ellipse	An ellipse is a curve defined by a coordinate system and a major and minor axis.
Frame	A frame is defined by a base point and two orthonormal base vectors.
Geometry	Base class for all geometric objects.
Hyperbola	A hyperbola is defined by a coordinate frame and a major and minor axis.
KDTree	A tree for nearest neighbor search in a k-dimensional space.
Line	A line is a curve defined by two points.
NurbsCurve	A NURBS curve is defined by control points, weights, knots, and a degree.
NurbsSurface	A NURBS surface is defined by control points, weights, knots, and a degree, in two directions U and V.
Parabola	A parabola is defined by a plane and a major and minor axis.
PlanarSurface	A planar surface is defined by a local coordinate system and a size.
Plane	A plane is defined by a base point and a normal vector.
Point	A point is defined by XYZ coordinates.
Pointcloud	Class for working with pointclouds.
Polygon	A polygon is a geometric object defined by a sequence of points forming a closed loop.
Polyhedron	A polyhedron is a geometric object defined by its vertices and faces.
Polyline	A polyline is a curve defined by a sequence of points connected by line segments.
Projection	Class representing a projection transformation.
Quaternion	A quaternion is defined by 4 components, X, Y, Z, and W.
Reflection	Class representing a reflection transformation.
Rotation	Class representing a rotation transformation.
Scale	Class representing a scale transformation.
Shape	Base class for geometric shapes.
Shear	Class representing a shear transformation.
Sphere	A sphere is defined by a point and a radius.
SphericalSurface	A spherical surface is defined by a radius and a frame.
Surface	Class representing a general surface object.
SurfaceType	Enumaration of surface types.
ToroidalSurface	A spherical surface is defined by a radius and a frame.
Torus	A torus is defined by a plane and two radii.
Transformation	Class representing a general 4x4 transformation matrix.
Translation	Class representing a translation transformation.
Vector	A vector is defined by XYZ components and a homogenisation factor.

Functions

add_vectors	Add two vectors.
add_vectors_xy	Add two vectors, assuming they lie in the XY-plane.
angle_planes	Compute the smallest angle between the two normal vectors of two planes.
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_signed	Computes the signed angle between two vectors.
angle_vectors_xy	Compute the smallest angle between the XY components of 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.
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.
argmax	Returns the index of the first maximum value within an array.
argmin	Returns the index of the first minimum value within an array.
axis_and_angle_from_matrix	Returns the axis and the angle of the rotation matrix M.
axis_angle_from_quaternion	Returns an axis and an angle of rotation from the given quaternion.
axis_angle_vector_from_matrix	Returns the axis-angle vector of the rotation matrix M.
barycentric_coordinates	Compute the barycentric coordinates of a point wrt to a triangle.
basis_vectors_from_matrix	Returns the basis vectors from the rotation matrix R.
bestfit_plane	Fit a plane to a list of (more than three) 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.
centroid_points	Compute the centroid of a set of points.
centroid_points_weighted	Compute the weighted centroid of a set of points.
centroid_points_xy	Compute the centroid of a set of points lying in the XY-plane.
centroid_polygon	Compute the centroid of the surface of a polygon.
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_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_xy	Compute the centroid of the surface of a polygon projected to the XY plane.
centroid_polyhedron	Compute the center of mass of a polyhedron.
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_polygon_xy	Compute closest point on a polygon to a given point lying in the XY-plane.
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.
compose_matrix	Calculates a matrix from the components of scale, shear, euler_angles, translation and perspective.
compute_basisfuncs	Compute the nonzero basis functions for a given parameter value.
compute_basisfuncsderivs	Compute the derivatives of the basis functions for a given parameter value.
construct_knotvector	Construct a nonperiodic (clamped), uniform knot vector for a curve with given degree and number of control points.
convex_hull	Construct convex hull for a set of points.
convex_hull_xy	Computes the convex hull of a set of 2D points.
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.
decompose_matrix	Calculates the components of rotation, translation, scale, shear, and perspective of a given transformation matrix M.
dehomogenize_vectors	Dehomogenise a list of vectors.
discrete_coons_patch	Creates a coons patch from a set of four or three boundary polylines (ab, bc, dc, ad).
distance_line_line	Compute the shortest distance between two lines.
distance_point_line	Compute the distance between a point and a line.
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_line_xy	Compute the distance between a point and a line, assuming they lie 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.
distance_point_point	Compute the distance bewteen a and b.
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_point_xy	Compute the distance between points a and b, assuming they lie in the XY plane.
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.
earclip_polygon	Triangulate a polygon using the ear clipping method.
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.
find_span	Find the knot span index for a given knot value.
homogenize_vectors	Homogenise a list of vectors.
identity_matrix	Construct an identity matrix.
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	Computes the intersection of two lines.
intersection_line_line_xy	Compute the intersection of two lines, assuming they lie on the XY plane.
intersection_line_plane	Computes the intersection point of a line and a plane
intersection_line_segment	Compute the intersection of a line and a segment.
intersection_line_segment_xy	Compute the intersection between 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_plane_circle	Computes the intersection of a plane and a circle.
intersection_plane_plane	Computes the intersection of two planes
intersection_plane_plane_plane	Computes the intersection of three planes
intersection_polyline_box_xy	Compute the intersection between a polyline and a box in the XY plane.
intersection_polyline_plane	Calculate the intersection point of a plane with a polyline.
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.
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_matrix_square	Verify that a matrix is square.
is_parallel_line_line	Determine if two lines are parallel.
is_parallel_vector_vector	Determine if two vectors are parallel.
is_point_behind_plane	Determine if a point lies behind 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_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_infrontof_plane	Determine if a point lies in front of a 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.
knots_and_mults_to_knotvector	Convert a list of knots and multiplicities to a knot vector.
knotvector_to_knots_and_mults	Convert a knot vector to a list of knots and multiplicities.
length_vector	Calculate the length of the vector.
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.
length_vector_xy	Compute the length of a vector, assuming it lies in the XY plane.
local_axes
local_to_world_coordinates	Convert local coordinates to global 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.
matrix_minor	Construct the minor corresponding to an element of a matrix.
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.
midpoint_point_point	Compute the midpoint of two points.
midpoint_point_point_xy	Compute the midpoint of two points lying in the XY-plane.
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.
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.
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.
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.
offset_line	Offset a line by a distance.
offset_polygon	Offset a polygon (closed) by a distance.
offset_polyline	Offset a polyline by a distance.
orient_points	Orient points from one plane to another.
orthonormalize_axes	Corrects xaxis and yaxis to be unit vectors and orthonormal.
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.
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.
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.
sort_points	Sorts points of a pointcloud based on their distance from a given point.
sort_points_xy	Sorts points of a pointcloud based on their distance from a given point, assuming all points 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.
tangent_points_to_circle_xy	Calculates the tangent points on a circle in the XY plane.
transform_frames	Transform multiple frames with one transformation matrix.
transform_points	Transform multiple points with one transformation matrix.
transform_vectors	Transform multiple vectors with one transformation matrix.
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.
transpose_matrix	Transpose a matrix.
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.
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.
volume_polyhedron	Compute the volume of a polyhedron represented by a closed mesh.
world_to_local_coordinates	Convert global coordinates to local coordinates.

Functions using Numpy

In environments where numpy is not available, these functions can still be accessed through RPC.

bestfit_circle_numpy	Fit a circle through a set of points.
bestfit_frame_numpy	Fit a frame to a set of points.
bestfit_line_numpy	Fit a line through a set of 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.
closest_points_in_cloud_numpy	Find the closest points in a point cloud to a set of sample points.
convex_hull_numpy	Compute the convex hull of a set of points.
convex_hull_xy_numpy	Compute the convex hull of a set of points in the XY plane.
dehomogenize_and_unflatten_frames_numpy	Dehomogenize a list of vectors and unflatten the 2D list into a 3D list.
dehomogenize_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.
homogenize_numpy	Dehomogenizes points or vectors.
icp_numpy	Align two point clouds using the Iterative Closest Point (ICP) method.
local_to_world_coordinates_numpy	Convert local coordinates to global (world) coordinates.
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.
pca_numpy	Compute the principle components of a set of data points.
transform_points_numpy	Transform multiple points with one Transformation using numpy.
transform_vectors_numpy	Transform multiple vectors with one Transformation using numpy.
trimesh_descent_numpy	Compute the descent directions of a triangular mesh as the gradient of the vertex heights.
trimesh_gradient_numpy	Construct the gradient operator of a trianglular mesh.
world_to_local_coordinates_numpy	Convert global coordinates to local coordinates.

Pluggables

Pluggables are functions that don’t have an actual implementation, but receive an implementation from a plugin.

boolean_difference_mesh_mesh	Compute the boolean difference of two triangle meshes.
boolean_difference_polygon_polygon	Compute the boolean difference of two polygons.
boolean_intersection_mesh_mesh	Compute the boolean intersection of two triangle meshes.
boolean_intersection_polygon_polygon	Compute the boolean intersection of two polygons.
boolean_symmetric_difference_polygon_polygon	Compute the boolean symmetric difference of two polygons.
boolean_union_mesh_mesh	Compute the boolean union of two triangle meshes.
boolean_union_polygon_polygon	Compute the boolean union of two polygons.
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_triangulation	Construct a Delaunay triangulation of set of vertices.
intersection_mesh_mesh	Compute the intersection of two meshes.
intersection_ray_mesh	Compute the intersection(s) between a ray and a mesh.
oriented_bounding_box	Computes the oriented minimum bounding box of a list of points.
quadmesh_planarize	Planarize the faces of a quad mesh.
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_massmatrix	Compute massmatrix on a triangle mesh using a scalarfield of data points assigned to its vertices.
trimesh_mean_curvature	Compute the discrete mean curvature of a triangle mesh.
trimesh_principal_curvature	Compute the principal curvature directions of a triangle mesh.
trimesh_remesh	Remeshing of a triangle mesh.
trimesh_remesh_along_isoline	Remesh a mesh along an isoline of a scalarfield over the vertices.
trimesh_remesh_constrained	Constrained remeshing of a triangle mesh.
trimesh_slice	Slice a mesh by a list of planes.