Geometry Utilities (mathutils.geometry)

The Blender geometry module

mathutils.geometry.area_tri(v1, v2, v3)

Returns the area size of the 2D or 3D triangle defined.

Parameters:
Return type:

float

mathutils.geometry.barycentric_transform(point, tri_a1, tri_a2, tri_a3, tri_b1, tri_b2, tri_b3)

Return a transformed point, the transformation is defined by 2 triangles.

Parameters:
Returns:

The transformed point

Return type:

mathutils.Vector’s

mathutils.geometry.box_fit_2d(points)

Returns an angle that best fits the points to an axis aligned rectangle

Parameters:

points (list) – list of 2d points.

Returns:

angle

Return type:

float

mathutils.geometry.box_pack_2d(boxes)

Returns a tuple with the width and height of the packed bounding box.

Parameters:

boxes (list) – list of boxes, each box is a list where the first 4 items are [x, y, width, height, …] other items are ignored.

Returns:

the width and height of the packed bounding box

Return type:

tuple, pair of floats

mathutils.geometry.closest_point_on_tri(pt, tri_p1, tri_p2, tri_p3)

Takes 4 vectors: one is the point and the next 3 define the triangle.

Parameters:
Returns:

The closest point of the triangle.

Return type:

mathutils.Vector

mathutils.geometry.convex_hull_2d(points)

Returns a list of indices into the list given

Parameters:

points (list) – list of 2d points.

Returns:

a list of indices

Return type:

list of ints

mathutils.geometry.delaunay_2d_cdt(vert_coords, edges, faces, output_type, epsilon, need_ids=True)

Computes the Constrained Delaunay Triangulation of a set of vertices, with edges and faces that must appear in the triangulation. Some triangles may be eaten away, or combined with other triangles, according to output type. The returned verts may be in a different order from input verts, may be moved slightly, and may be merged with other nearby verts. The three returned orig lists give, for each of verts, edges, and faces, the list of input element indices corresponding to the positionally same output element. For edges, the orig indices start with the input edges and then continue with the edges implied by each of the faces (n of them for an n-gon). If the need_ids argument is supplied, and False, then the code skips the preparation of the orig arrays, which may save some time. :arg vert_coords: Vertex coordinates (2d) :type vert_coords: list of mathutils.Vector :arg edges: Edges, as pairs of indices in vert_coords :type edges: list of (int, int) :arg faces: Faces, each sublist is a face, as indices in vert_coords (CCW oriented) :type faces: list of list of int :arg output_type: What output looks like. 0 => triangles with convex hull. 1 => triangles inside constraints. 2 => the input constraints, intersected. 3 => like 2 but detect holes and omit them from output. 4 => like 2 but with extra edges to make valid BMesh faces. 5 => like 4 but detect holes and omit them from output. :type output_type: intn :arg epsilon: For nearness tests; should not be zero :type epsilon: float :arg need_ids: are the orig output arrays needed? :type need_args: bool :return: Output tuple, (vert_coords, edges, faces, orig_verts, orig_edges, orig_faces) :rtype: (list of mathutils.Vector, list of (int, int), list of list of int, list of list of int, list of list of int, list of list of int)

mathutils.geometry.distance_point_to_plane(pt, plane_co, plane_no)

Returns the signed distance between a point and a plane (negative when below the normal).

Parameters:
Return type:

float

mathutils.geometry.interpolate_bezier(knot1, handle1, handle2, knot2, resolution)

Interpolate a bezier spline segment.

Parameters:
Returns:

The interpolated points

Return type:

list of mathutils.Vector’s

mathutils.geometry.intersect_line_line(v1, v2, v3, v4)

Returns a tuple with the points on each line respectively closest to the other.

Parameters:
Return type:

tuple of mathutils.Vector’s

mathutils.geometry.intersect_line_line_2d(lineA_p1, lineA_p2, lineB_p1, lineB_p2)

Takes 2 segments (defined by 4 vectors) and returns a vector for their point of intersection or None.

Warning

Despite its name, this function works on segments, and not on lines.

Parameters:
Returns:

The point of intersection or None when not found

Return type:

mathutils.Vector or None

mathutils.geometry.intersect_line_plane(line_a, line_b, plane_co, plane_no, no_flip=False)

Calculate the intersection between a line (as 2 vectors) and a plane. Returns a vector for the intersection or None.

Parameters:
Returns:

The point of intersection or None when not found

Return type:

mathutils.Vector or None

mathutils.geometry.intersect_line_sphere(line_a, line_b, sphere_co, sphere_radius, clip=True)

Takes a line (as 2 points) and a sphere (as a point and a radius) and returns the intersection

Parameters:
Returns:

The intersection points as a pair of vectors or None when there is no intersection

Return type:

A tuple pair containing mathutils.Vector or None

mathutils.geometry.intersect_line_sphere_2d(line_a, line_b, sphere_co, sphere_radius, clip=True)

Takes a line (as 2 points) and a sphere (as a point and a radius) and returns the intersection

Parameters:
Returns:

The intersection points as a pair of vectors or None when there is no intersection

Return type:

A tuple pair containing mathutils.Vector or None

mathutils.geometry.intersect_plane_plane(plane_a_co, plane_a_no, plane_b_co, plane_b_no)

Return the intersection between two planes

Parameters:
Returns:

The line of the intersection represented as a point and a vector

Return type:

tuple pair of mathutils.Vector or None if the intersection can’t be calculated

mathutils.geometry.intersect_point_line(pt, line_p1, line_p2)

Takes a point and a line and returns a tuple with the closest point on the line and its distance from the first point of the line as a percentage of the length of the line.

Parameters:
Return type:

(mathutils.Vector, float)

mathutils.geometry.intersect_point_quad_2d(pt, quad_p1, quad_p2, quad_p3, quad_p4)

Takes 5 vectors (using only the x and y coordinates): one is the point and the next 4 define the quad, only the x and y are used from the vectors. Returns 1 if the point is within the quad, otherwise 0. Works only with convex quads without singular edges.

Parameters:
Return type:

int

mathutils.geometry.intersect_point_tri(pt, tri_p1, tri_p2, tri_p3)

Takes 4 vectors: one is the point and the next 3 define the triangle. Projects the point onto the triangle plane and checks if it is within the triangle.

Parameters:
Returns:

Point on the triangles plane or None if its outside the triangle

Return type:

mathutils.Vector or None

mathutils.geometry.intersect_point_tri_2d(pt, tri_p1, tri_p2, tri_p3)

Takes 4 vectors (using only the x and y coordinates): one is the point and the next 3 define the triangle. Returns 1 if the point is within the triangle, otherwise 0.

Parameters:
Return type:

int

mathutils.geometry.intersect_ray_tri(v1, v2, v3, ray, orig, clip=True)

Returns the intersection between a ray and a triangle, if possible, returns None otherwise.

Parameters:
Returns:

The point of intersection or None if no intersection is found

Return type:

mathutils.Vector or None

mathutils.geometry.intersect_sphere_sphere_2d(p_a, radius_a, p_b, radius_b)

Returns 2 points on between intersecting circles.

Parameters:

  • p_a (mathutils.Vector) – Center of the first circle

  • radius_a (float) – Radius of the first circle

  • p_b (mathutils.Vector) – Center of the second circle

  • radius_b (float) – Radius of the second circle

Return type:

tuple of mathutils.Vector’s or None when there is no intersection

mathutils.geometry.intersect_tri_tri_2d(tri_a1, tri_a2, tri_a3, tri_b1, tri_b2, tri_b3)

Check if two 2D triangles intersect.

Return type:

bool

mathutils.geometry.normal(vectors)

Returns the normal of a 3D polygon.

Parameters:

vectors (sequence of 3 or more 3d vector) – Vectors to calculate normals with

Return type:

mathutils.Vector

mathutils.geometry.points_in_planes(planes)

Returns a list of points inside all planes given and a list of index values for the planes used.

Parameters:

planes (list of mathutils.Vector) – List of planes (4D vectors).

Returns:

two lists, once containing the vertices inside the planes, another containing the plane indices used

Return type:

pair of lists

mathutils.geometry.tessellate_polygon(veclist_list)

Takes a list of polylines (each point a pair or triplet of numbers) and returns the point indices for a polyline filled with triangles. Does not handle degenerate geometry (such as zero-length lines due to consecutive identical points).

Parameters:

veclist_list – list of polylines

Return type:

list

mathutils.geometry.volume_tetrahedron(v1, v2, v3, v4)

Return the volume formed by a tetrahedron (points can be in any order).

Parameters:
Return type:

float