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

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_a1 – target triangle vertex.
• tri_a2 – target triangle vertex.
• tri_a3 – target triangle vertex.

Returns:

The transformed point

Return type:

mathutils.Vector‘s

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.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) – First point of the quad
• plane_no (mathutils.Vector) – Second point of the quad

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 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

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

Takes 2 lines (as 4 vectors) and returns a vector for their point of intersection or None.

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

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
• no_flip (:boolean) – Always return an intersection on the directon defined bt line_a -> line_b

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 lines (as 2 vectors), a sphere as a point and a radius and returns the intersection

Parameters:

• line_a (mathutils.Vector) – First point of the first line
• line_b (mathutils.Vector) – Second point of the first 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

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

Takes a lines (as 2 vectors), a sphere as a point and a radius and returns the intersection

Parameters:

• line_a (mathutils.Vector) – First point of the first line
• line_b (mathutils.Vector) – Second point of the first 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

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

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)

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. :arg pt: Point :type pt: mathutils.Vector :arg quad_p1: First point of the quad :type quad_p1: mathutils.Vector :arg quad_p2: Second point of the quad :type quad_p2: mathutils.Vector :arg quad_p3: Third point of the quad :type quad_p3: mathutils.Vector :arg quad_p4: Forth point of the quad :type quad_p4: mathutils.Vector :rtype: int

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 – 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

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

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(v1, v2, v3, v4=None)

Returns the normal of the 3D tri or quad.

Parameters:

• v1 (mathutils.Vector) – Point1
• v2 (mathutils.Vector) – Point2
• v3 (mathutils.Vector) – Point3
• v4 (mathutils.Vector) – Point4 (optional)

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 indicies 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:

• v1 (mathutils.Vector) – Point1
• v2 (mathutils.Vector) – Point2
• v3 (mathutils.Vector) – Point3
• v4 (mathutils.Vector) – Point4

Return type:

float