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 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.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.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.

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.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 vector) and returns the point indices for a polyline filled with triangles.

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