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:  v1 (
mathutils.Vector
) – Point1  v2 (
mathutils.Vector
) – Point2  v3 (
mathutils.Vector
) – Point3
Return type: float
 v1 (

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:  point (
mathutils.Vector
) – The point to transform.  tri_a1 (
mathutils.Vector
) – source triangle vertex.  tri_a2 (
mathutils.Vector
) – source triangle vertex.  tri_a3 (
mathutils.Vector
) – source triangle vertex.  tri_b1 (
mathutils.Vector
) – target triangle vertex.  tri_b2 (
mathutils.Vector
) – target triangle vertex.  tri_b3 (
mathutils.Vector
) – target triangle vertex.
Returns: The transformed point
Return type:  point (

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 the normal of the 3D tri or quad.
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:  pt (
mathutils.Vector
) – Point  tri_p1 (
mathutils.Vector
) – First point of the triangle  tri_p2 (
mathutils.Vector
) – Second point of the triangle  tri_p3 (
mathutils.Vector
) – Third point of the triangle
Returns: The closest point of the triangle.
Return type:  pt (

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)¶
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 ngon).
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 with extra edges to make valid BMesh faces. type output_type: intn :arg epsilon: For nearness tests; should not be zero type epsilon: float 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:  pt (
mathutils.Vector
) – Point  plane_co (
mathutils.Vector
) – A point on the plane  plane_no (
mathutils.Vector
) – The direction the plane is facing
Return type: float
 pt (

mathutils.geometry.
interpolate_bezier
(knot1, handle1, handle2, knot2, resolution)¶ Interpolate a bezier spline segment.
Parameters:  knot1 (
mathutils.Vector
) – First bezier spline point.  handle1 (
mathutils.Vector
) – First bezier spline handle.  handle2 (
mathutils.Vector
) – Second bezier spline handle.  knot2 (
mathutils.Vector
) – Second bezier spline point.  resolution (int) – Number of points to return.
Returns: The interpolated points
Return type: list of
mathutils.Vector
’s knot1 (

mathutils.geometry.
intersect_line_line
(v1, v2, v3, v4)¶ Returns a tuple with the points on each line respectively closest to the other.
Parameters:  v1 (
mathutils.Vector
) – First point of the first line  v2 (
mathutils.Vector
) – Second point of the first line  v3 (
mathutils.Vector
) – First point of the second line  v4 (
mathutils.Vector
) – Second point of the second line
Return type: tuple of
mathutils.Vector
’s v1 (

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:  lineA_p1 (
mathutils.Vector
) – First point of the first line  lineA_p2 (
mathutils.Vector
) – Second point of the first line  lineB_p1 (
mathutils.Vector
) – First point of the second line  lineB_p2 (
mathutils.Vector
) – Second point of the second line
Returns: The point of intersection or None when not found
Return type: mathutils.Vector
or None lineA_p1 (

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:  line_a (
mathutils.Vector
) – First point of the first line  line_b (
mathutils.Vector
) – Second point of the first line  plane_co (
mathutils.Vector
) – A point on the plane  plane_no (
mathutils.Vector
) – The direction the plane is facing
Returns: The point of intersection or None when not found
Return type: mathutils.Vector
or None line_a (

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:  line_a (
mathutils.Vector
) – First point of the line  line_b (
mathutils.Vector
) – Second point of the line  sphere_co (
mathutils.Vector
) – The center of the sphere  sphere_radius (sphere_radius) – Radius of the sphere
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 line_a (

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:  line_a (
mathutils.Vector
) – First point of the line  line_b (
mathutils.Vector
) – Second point of the line  sphere_co (
mathutils.Vector
) – The center of the sphere  sphere_radius (sphere_radius) – Radius of the sphere
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 line_a (

mathutils.geometry.
intersect_plane_plane
(plane_a_co, plane_a_no, plane_b_co, plane_b_no)¶ Return the intersection between two planes
Parameters:  plane_a_co (
mathutils.Vector
) – Point on the first plane  plane_a_no (
mathutils.Vector
) – Normal of the first plane  plane_b_co (
mathutils.Vector
) – Point on the second plane  plane_b_no (
mathutils.Vector
) – Normal of the second plane
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 plane_a_co (

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:  pt (
mathutils.Vector
) – Point  line_p1 (
mathutils.Vector
) – First point of the line  line_p1 – Second point of the line
Return type: (
mathutils.Vector
, float) pt (

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:  pt (
mathutils.Vector
) – Point  quad_p1 (
mathutils.Vector
) – First point of the quad  quad_p2 (
mathutils.Vector
) – Second point of the quad  quad_p3 (
mathutils.Vector
) – Third point of the quad  quad_p4 (
mathutils.Vector
) – Fourth point of the quad
Return type: int
 pt (

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:  pt (
mathutils.Vector
) – Point  tri_p1 (
mathutils.Vector
) – First point of the triangle  tri_p2 (
mathutils.Vector
) – Second point of the triangle  tri_p3 (
mathutils.Vector
) – Third point of the triangle
Returns: Point on the triangles plane or None if its outside the triangle
Return type: mathutils.Vector
or None pt (

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:  pt (
mathutils.Vector
) – Point  tri_p1 (
mathutils.Vector
) – First point of the triangle  tri_p2 (
mathutils.Vector
) – Second point of the triangle  tri_p3 (
mathutils.Vector
) – Third point of the triangle
Return type: int
 pt (

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:  v1 (
mathutils.Vector
) – Point1  v2 (
mathutils.Vector
) – Point2  v3 (
mathutils.Vector
) – Point3  ray (
mathutils.Vector
) – Direction of the projection  orig (
mathutils.Vector
) – Origin  clip (boolean) – When False, don’t restrict the intersection to the area of the triangle, use the infinite plane defined by the triangle.
Returns: The point of intersection or None if no intersection is found
Return type: mathutils.Vector
or None v1 (

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 p_a (

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 zerolength 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:  v1 (
mathutils.Vector
) – Point1  v2 (
mathutils.Vector
) – Point2  v3 (
mathutils.Vector
) – Point3  v4 (
mathutils.Vector
) – Point4
Return type: float
 v1 (