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
) – Point1v2 (
mathutils.Vector
) – Point2v3 (
mathutils.Vector
) – Point3
 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
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

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
pt (
mathutils.Vector
) – Pointtri_p1 (
mathutils.Vector
) – First point of the triangletri_p2 (
mathutils.Vector
) – Second point of the triangletri_p3 (
mathutils.Vector
) – Third point of the triangle
 Returns
The closest point of the triangle.
 Return type

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).
 Parameters
vert_coords (list of
mathutils.Vector
) – Vertex coordinates (2d)edges (list of (int, int)) – Edges, as pairs of indices in vert_coords
faces (list of list of int) – Faces, each sublist is a face, as indices in vert_coords (CCW oriented)
output_type (intn :arg epsilon: For nearness tests; should not be zero) – 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.
 Returns
Output tuple, (vert_coords, edges, faces, orig_verts, orig_edges, orig_faces)
 Return type
(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
) – Pointplane_co (
mathutils.Vector
) – A point on the planeplane_no (
mathutils.Vector
) – The direction the plane is facing
 Return type
float

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

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 linev2 (
mathutils.Vector
) – Second point of the first linev3 (
mathutils.Vector
) – First point of the second linev4 (
mathutils.Vector
) – Second point of the second line
 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
lineA_p1 (
mathutils.Vector
) – First point of the first linelineA_p2 (
mathutils.Vector
) – Second point of the first linelineB_p1 (
mathutils.Vector
) – First point of the second linelineB_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

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 lineline_b (
mathutils.Vector
) – Second point of the first lineplane_co (
mathutils.Vector
) – A point on the planeplane_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

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 lineline_b (
mathutils.Vector
) – Second point of the linesphere_co (
mathutils.Vector
) – The center of the spheresphere_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

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 lineline_b (
mathutils.Vector
) – Second point of the linesphere_co (
mathutils.Vector
) – The center of the spheresphere_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

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 planeplane_a_no (
mathutils.Vector
) – Normal of the first planeplane_b_co (
mathutils.Vector
) – Point on the second planeplane_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

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
) – Pointline_p1 (
mathutils.Vector
) – First point of the lineline_p1 – Second point of the line
 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
pt (
mathutils.Vector
) – Pointquad_p1 (
mathutils.Vector
) – First point of the quadquad_p2 (
mathutils.Vector
) – Second point of the quadquad_p3 (
mathutils.Vector
) – Third point of the quadquad_p4 (
mathutils.Vector
) – Fourth point of the quad
 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
pt (
mathutils.Vector
) – Pointtri_p1 (
mathutils.Vector
) – First point of the triangletri_p2 (
mathutils.Vector
) – Second point of the triangletri_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

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
) – Pointtri_p1 (
mathutils.Vector
) – First point of the triangletri_p2 (
mathutils.Vector
) – Second point of the triangletri_p3 (
mathutils.Vector
) – Third point of the triangle
 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
v1 (
mathutils.Vector
) – Point1v2 (
mathutils.Vector
) – Point2v3 (
mathutils.Vector
) – Point3ray (
mathutils.Vector
) – Direction of the projectionorig (
mathutils.Vector
) – Originclip (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

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 circleradius_a (float) – Radius of the first circle
p_b (
mathutils.Vector
) – Center of the second circleradius_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.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
) – Point1v2 (
mathutils.Vector
) – Point2v3 (
mathutils.Vector
) – Point3v4 (
mathutils.Vector
) – Point4
 Return type
float