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, 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:
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 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:
v1 (
mathutils.Vector
) – Point1v2 (
mathutils.Vector
) – Point2v3 (
mathutils.Vector
) – Point3v4 (
mathutils.Vector
) – Point4
- Return type:
float