geometry

Primitives

Inheritance diagram of Circle, Ellipse, Frame, Line, Plane, Point, Polygon, Polyline, Quaternion, Vector

Classes

Circle

A circle is defined by a plane and a radius.

Ellipse

A ellipse is defined by a plane and a major.

Frame

A frame is defined by a base point and two orthonormal base vectors.

Line

A line is defined by two points.

Plane

A plane is defined by a base point and a normal vector.

Point

A point is defined by XYZ coordinates.

Polygon

An object representing an ordered collection of points in space connected by straight line segments forming a closed boundary around the interior space.

Polyline

A polyline is a sequence of points connected by line segments.

Quaternion

Creates a Quaternion object.

Vector

A vector is defined by XYZ components and a homogenisation factor.

Base Classes

Primitive

Base class for geometric primitives.

Shapes

Inheritance diagram of Box, Capsule, Cone, Cylinder, Polyhedron, Torus

Classes

Box

A box is defined by a frame and its dimensions along the frame’s x-, y- and z-axes.

Capsule

A capsule is defined by a line segment and a radius.

Cone

A cone is defined by a circle and a height.

Cylinder

A cylinder is defined by a circle and a height.

Polyhedron

A polyhedron is defined by its vertices and faces.

Sphere

A sphere is defined by a point and a radius.

Torus

A torus is defined by a plane and two radii.

Base Classes

Shape

Base class for geometric shapes.

Transformations

Inheritance diagram of Projection, Reflection, Rotation, Scale, Shear, Transformation, Translation

Classes

Projection

Create a projection transformation.

Reflection

Creates a Reflection that mirrors points at a plane.

Rotation

Create a rotation transformation.

Scale

Creates a scale transformation.

Shear

Create a shear transformation.

Transformation

The Transformation represents a 4x4 transformation matrix.

Translation

Create a translation transformation.

Functions

Predicates 2D

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_xy

Determine if three points are colinear on the XY-plane.

is_polygon_convex_xy

Determine if the polygon is convex on the XY-plane.

is_point_on_line_xy

Determine if a point lies on a line on the XY-plane.

is_point_on_segment_xy

Determine if a point lies on a given line segment on the XY-plane.

is_point_on_polyline_xy

Determine if a point is on a polyline on the XY-plane.

is_point_in_triangle_xy

Determine if a point is in the interior of a triangle 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_convex_polygon_xy

Determine if a point is in the interior of a convex polygon lying on the XY-plane.

is_point_in_circle_xy

Determine if a point lies in a circle lying on the XY-plane.

is_polygon_in_polygon_xy

Determine if a polygon is in the interior of another polygon on the XY-plane.

Predicates 3D

is_colinear

Determine if three points are colinear.

is_coplanar

Determine if the points are coplanar.

is_point_in_halfspace

Determine if a point lies in front of a plane.

is_point_in_polyhedron

Determine if the point lies inside the given polyhedron.

is_point_on_line

Determine if a point lies on a line.

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_segment

Determine if a point lies on a given line segment.

is_polygon_convex

Determine if a polygon is convex.

Transformations

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.

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.

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.

translate_points

Translate points.

translate_points_xy

Translate points and in the XY plane.

Conversions

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.

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.

matrix_from_frame

Computes a change of basis transformation from world XY to the frame.

matrix_from_euler_angles

Calculates a rotation matrix from Euler angles.

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_translation

Returns a 4x4 translation matrix in row-major order.

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_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_perspective_entries

Returns a matrix from perspective entries.

matrix_from_shear_entries

Returns a shear matrix from the 3 factors for x-y, x-z, and y-z axes.

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_scale_factors

Returns a 4x4 scaling transformation.

matrix_from_quaternion

Calculates a rotation matrix from quaternion coefficients.

quaternion_from_matrix

Returns the 4 quaternion coefficients from a rotation matrix.

quaternion_from_euler_angles

Returns a quaternion from Euler angles.

quaternion_from_axis_angle

Returns a quaternion describing a rotation around the given axis by the given angle.

Quaternion math

quaternion_norm

Calculates the length (euclidean norm) of a quaternion.

quaternion_unitize

Makes a quaternion unit-length.

quaternion_is_unit

Checks if a quaternion is unit-length.

quaternion_multiply

Multiplies two quaternions.

quaternion_canonize

Converts a quaternion into a canonic form if needed.

quaternion_conjugate

Conjugate of a quaternion.

Linear algebra

add_vectors

Add two vectors.

add_vectors_xy

Add two vectors, assuming they lie in the XY-plane.

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.

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.

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_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_average

Average of a vector.

vector_variance

Variance of a vector.

vector_standard_deviation

Standard deviation of a vector.

Points, Vectors, Lines, 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_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.

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_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_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.

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.

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

centroid_polygon_edges

Compute the centroid of the edges of a polygon.

centroid_polygon_edges_xy

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

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.

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_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.

Intersections

intersection_circle_circle_xy

Calculates the intersection points of two circles in 2d lying 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_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_plane

Computes the intersection of two planes

intersection_plane_plane_plane

Computes the intersection of three planes

intersection_ray_mesh

Compute the intersection(s) between a ray and a mesh.

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_segment_plane

Computes the intersection point of a line segment and a plane

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.

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.

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.

Fitting

bestfit_circle_numpy

Fit a circle through 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.

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_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_slice

Slice a mesh by a list of planes.

Quad meshes

quadmesh_planarize

Planarize the faces of a quad mesh.

Pointclouds

icp_numpy

Align two point clouds using the Iterative Closest Point (ICP) method.