""" The Blender geometry module. """ import typing import collections.abc import typing_extensions import numpy.typing as npt import mathutils def area_tri( v1: collections.abc.Sequence[float] | mathutils.Vector, v2: collections.abc.Sequence[float] | mathutils.Vector, v3: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> float: """Returns the area of the 2D or 3D triangle defined. :param v1: Point1 :param v2: Point2 :param v3: Point3 :return: The area of the triangle. """ def barycentric_transform( point: collections.abc.Sequence[float] | mathutils.Vector, tri_a1: collections.abc.Sequence[float] | mathutils.Vector, tri_a2: collections.abc.Sequence[float] | mathutils.Vector, tri_a3: collections.abc.Sequence[float] | mathutils.Vector, tri_b1: collections.abc.Sequence[float] | mathutils.Vector, tri_b2: collections.abc.Sequence[float] | mathutils.Vector, tri_b3: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> mathutils.Vector: """Return a transformed point, the transformation is defined by 2 triangles. :param point: The point to transform. :param tri_a1: source triangle vertex. :param tri_a2: source triangle vertex. :param tri_a3: source triangle vertex. :param tri_b1: target triangle vertex. :param tri_b2: target triangle vertex. :param tri_b3: target triangle vertex. :return: The transformed point """ def box_fit_2d( points: collections.abc.Sequence[collections.abc.Sequence[float]], /, ) -> float: """Returns an angle that best fits the points to an axis aligned rectangle :param points: Sequence of 2D points. :return: The rotation angle in radians for the best axis-aligned bounding box fit. """ def box_pack_2d( boxes: list[list[float]], /, ) -> tuple[float, float]: """Returns a tuple with the width and height of the packed bounding box. :param boxes: list of boxes, each box is a list where the first 4 items are [X, Y, width, height, ...] other items are ignored. The X & Y values in this list are modified to set the packed positions. :return: The width and height of the packed bounding box. """ def closest_point_on_tri( pt: collections.abc.Sequence[float] | mathutils.Vector, tri_p1: collections.abc.Sequence[float] | mathutils.Vector, tri_p2: collections.abc.Sequence[float] | mathutils.Vector, tri_p3: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> mathutils.Vector: """Takes 4 vectors: one is the point and the next 3 define the triangle. :param pt: Point :param tri_p1: First point of the triangle :param tri_p2: Second point of the triangle :param tri_p3: Third point of the triangle :return: The closest point of the triangle. """ def convex_hull_2d( points: collections.abc.Sequence[collections.abc.Sequence[float]], /, ) -> list[int]: """Returns the indices of the points forming the convex hull, in counter-clockwise order. :param points: Sequence of 2D points. :return: Indices of convex hull vertices in counter-clockwise order. """ def delaunay_2d_cdt( vert_coords: collections.abc.Sequence[ collections.abc.Sequence[float] | mathutils.Vector ], edges: collections.abc.Sequence[tuple[int, int]], faces: collections.abc.Sequence[collections.abc.Sequence[int]], output_type: int, epsilon: float, need_ids: bool = True, /, ) -> tuple[ list[mathutils.Vector], list[tuple[int, int]], list[list[int]], list[list[int]], list[list[int]], list[list[int]], ]: """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. :param vert_coords: Vertex coordinates (2d) :param edges: Edges, as pairs of indices in vert_coords :param faces: Faces, each sublist is a face, as indices in vert_coords (CCW oriented). :param 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. :param epsilon: For nearness tests; should not be zero :param need_ids: are the orig output arrays needed? :return: Output tuple, (vert_coords, edges, faces, orig_verts, orig_edges, orig_faces) """ def distance_point_to_plane( pt: collections.abc.Sequence[float] | mathutils.Vector, plane_co: collections.abc.Sequence[float] | mathutils.Vector, plane_no: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> float: """Returns the signed distance between a point and a plane (negative when below the normal). :param pt: Point :param plane_co: A point on the plane :param plane_no: The direction the plane is facing :return: The signed distance. """ def interpolate_bezier( knot1: collections.abc.Sequence[float] | mathutils.Vector, handle1: collections.abc.Sequence[float] | mathutils.Vector, handle2: collections.abc.Sequence[float] | mathutils.Vector, knot2: collections.abc.Sequence[float] | mathutils.Vector, resolution: int, /, ) -> list[mathutils.Vector]: """Interpolate a bezier spline segment. :param knot1: First bezier spline point. :param handle1: First bezier spline handle. :param handle2: Second bezier spline handle. :param knot2: Second bezier spline point. :param resolution: Number of points to return. :return: The interpolated points. """ def intersect_line_line( v1: collections.abc.Sequence[float] | mathutils.Vector, v2: collections.abc.Sequence[float] | mathutils.Vector, v3: collections.abc.Sequence[float] | mathutils.Vector, v4: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> None | tuple[mathutils.Vector, mathutils.Vector]: """Returns a tuple with the points on each line respectively closest to the other. :param v1: First point of the first line :param v2: Second point of the first line :param v3: First point of the second line :param v4: Second point of the second line :return: The intersection on each line or None when the lines are parallel. """ def intersect_line_line_2d( lineA_p1: collections.abc.Sequence[float] | mathutils.Vector, lineA_p2: collections.abc.Sequence[float] | mathutils.Vector, lineB_p1: collections.abc.Sequence[float] | mathutils.Vector, lineB_p2: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> None | mathutils.Vector: """Takes 2 segments (defined by 4 vectors) and returns a vector for their point of intersection or None. :param lineA_p1: First point of the first segment :param lineA_p2: Second point of the first segment :param lineB_p1: First point of the second segment :param lineB_p2: Second point of the second segment :return: The point of intersection or None when not found """ def intersect_line_plane( line_a: collections.abc.Sequence[float] | mathutils.Vector, line_b: collections.abc.Sequence[float] | mathutils.Vector, plane_co: collections.abc.Sequence[float] | mathutils.Vector, plane_no: collections.abc.Sequence[float] | mathutils.Vector, no_flip: bool = False, /, ) -> None | mathutils.Vector: """Calculate the intersection between a line (as 2 vectors) and a plane. Returns a vector for the intersection or None. :param line_a: First point of the line :param line_b: Second point of the line :param plane_co: A point on the plane :param plane_no: The direction the plane is facing :param no_flip: Currently ignored. :return: The point of intersection or None when not found """ def intersect_line_sphere( line_a: collections.abc.Sequence[float] | mathutils.Vector, line_b: collections.abc.Sequence[float] | mathutils.Vector, sphere_co: collections.abc.Sequence[float] | mathutils.Vector, sphere_radius: float, clip: bool = True, /, ) -> tuple[mathutils.Vector | None, mathutils.Vector | None]: """Takes a line (as 2 points) and a sphere (as a point and a radius) and returns the intersection :param line_a: First point of the line :param line_b: Second point of the line :param sphere_co: The center of the sphere :param sphere_radius: Radius of the sphere :param clip: When False, dont restrict the intersection to the line segment. :return: The intersection points as a pair of vectors (each is None when not found). """ def intersect_line_sphere_2d( line_a: collections.abc.Sequence[float] | mathutils.Vector, line_b: collections.abc.Sequence[float] | mathutils.Vector, sphere_co: collections.abc.Sequence[float] | mathutils.Vector, sphere_radius: float, clip: bool = True, /, ) -> tuple[mathutils.Vector | None, mathutils.Vector | None]: """Takes a line (as 2 points) and a circle (as a point and a radius) and returns the intersection :param line_a: First point of the line :param line_b: Second point of the line :param sphere_co: The center of the circle :param sphere_radius: Radius of the circle :param clip: When False, dont restrict the intersection to the line segment. :return: The intersection points as a pair of vectors (each is None when not found). """ def intersect_plane_plane( plane_a_co: collections.abc.Sequence[float] | mathutils.Vector, plane_a_no: collections.abc.Sequence[float] | mathutils.Vector, plane_b_co: collections.abc.Sequence[float] | mathutils.Vector, plane_b_no: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> tuple[None, None] | tuple[mathutils.Vector, mathutils.Vector]: """Return the intersection between two planes :param plane_a_co: Point on the first plane :param plane_a_no: Normal of the first plane :param plane_b_co: Point on the second plane :param plane_b_no: Normal of the second plane :return: The line of the intersection represented as a point and a vector or None if the intersection cant be calculated """ def intersect_point_line( pt: collections.abc.Sequence[float] | mathutils.Vector, line_p1: collections.abc.Sequence[float] | mathutils.Vector, line_p2: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> tuple[mathutils.Vector, float]: """Takes a point and a line and returns the closest point on the line and its parametric distance from the first point of the line. A value of 0.0 is the first point, 1.0 is the second, values outside [0, 1] are extrapolated. :param pt: Point :param line_p1: First point of the line :param line_p2: Second point of the line :return: The closest point on the line and its parametric distance from the first point. """ def intersect_point_line_segment( pt: collections.abc.Sequence[float] | mathutils.Vector, seg_p1: collections.abc.Sequence[float] | mathutils.Vector, seg_p2: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> tuple[mathutils.Vector, float]: """Takes a point and a segment and returns the closest point on the segment and the distance to the segment. :param pt: Point :param seg_p1: First point of the segment :param seg_p2: Second point of the segment :return: The closest point on the segment and the distance to the segment. """ def intersect_point_quad_2d( pt: collections.abc.Sequence[float] | mathutils.Vector, quad_p1: collections.abc.Sequence[float] | mathutils.Vector, quad_p2: collections.abc.Sequence[float] | mathutils.Vector, quad_p3: collections.abc.Sequence[float] | mathutils.Vector, quad_p4: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> int: """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 a non-zero value if the point is within the quad, otherwise 0. Works only with convex quads without singular edges. :param pt: Point :param quad_p1: First point of the quad :param quad_p2: Second point of the quad :param quad_p3: Third point of the quad :param quad_p4: Fourth point of the quad :return: 1 if inside with CCW winding, -1 if inside with CW winding, otherwise 0. """ def intersect_point_tri( pt: collections.abc.Sequence[float] | mathutils.Vector, tri_p1: collections.abc.Sequence[float] | mathutils.Vector, tri_p2: collections.abc.Sequence[float] | mathutils.Vector, tri_p3: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> None | mathutils.Vector: """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. :param pt: Point :param tri_p1: First point of the triangle :param tri_p2: Second point of the triangle :param tri_p3: Third point of the triangle :return: Point on the triangles plane or None if its outside the triangle """ def intersect_point_tri_2d( pt: collections.abc.Sequence[float] | mathutils.Vector, tri_p1: collections.abc.Sequence[float] | mathutils.Vector, tri_p2: collections.abc.Sequence[float] | mathutils.Vector, tri_p3: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> int: """Takes 4 vectors (using only the x and y coordinates): one is the point and the next 3 define the triangle. Returns a non-zero value if the point is within the triangle, otherwise 0. :param pt: Point :param tri_p1: First point of the triangle :param tri_p2: Second point of the triangle :param tri_p3: Third point of the triangle :return: 1 if inside with CCW winding, -1 if inside with CW winding, otherwise 0. """ def intersect_ray_tri( v1: collections.abc.Sequence[float] | mathutils.Vector, v2: collections.abc.Sequence[float] | mathutils.Vector, v3: collections.abc.Sequence[float] | mathutils.Vector, ray: collections.abc.Sequence[float] | mathutils.Vector, orig: collections.abc.Sequence[float] | mathutils.Vector, clip: bool = True, /, ) -> None | mathutils.Vector: """Returns the intersection between a ray and a triangle, if possible, returns None otherwise. :param v1: Point1 :param v2: Point2 :param v3: Point3 :param ray: Direction of the ray :param orig: Origin :param clip: When False, dont restrict the intersection to the area of the triangle, use the infinite plane defined by the triangle. :return: The point of intersection or None if no intersection is found """ def intersect_sphere_sphere_2d( p_a: collections.abc.Sequence[float] | mathutils.Vector, radius_a: float, p_b: collections.abc.Sequence[float] | mathutils.Vector, radius_b: float, /, ) -> tuple[None, None] | tuple[mathutils.Vector, mathutils.Vector]: """Returns the 2 intersection points of two circles. :param p_a: Center of the first circle :param radius_a: Radius of the first circle :param p_b: Center of the second circle :param radius_b: Radius of the second circle :return: The 2 intersection points or None when there is no intersection. """ def intersect_tri_tri_2d( tri_a1: collections.abc.Sequence[float] | mathutils.Vector, tri_a2: collections.abc.Sequence[float] | mathutils.Vector, tri_a3: collections.abc.Sequence[float] | mathutils.Vector, tri_b1: collections.abc.Sequence[float] | mathutils.Vector, tri_b2: collections.abc.Sequence[float] | mathutils.Vector, tri_b3: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> bool: """Check if two 2D triangles intersect. :param tri_a1: First vertex of the first triangle. :param tri_a2: Second vertex of the first triangle. :param tri_a3: Third vertex of the first triangle. :param tri_b1: First vertex of the second triangle. :param tri_b2: Second vertex of the second triangle. :param tri_b3: Third vertex of the second triangle. :return: True if the triangles intersect. """ def normal( *vectors: collections.abc.Sequence[collections.abc.Sequence[float]], ) -> mathutils.Vector: """Returns the normal of a 3D polygon. :param vectors: 3 or more vectors to calculate normals. :return: The normal vector. """ def points_in_planes( planes: list[collections.abc.Sequence[float] | mathutils.Vector], epsilon_coplanar: float = 0.0001, epsilon_isect: float = 1e-06, /, ) -> tuple[list[mathutils.Vector], list[int]]: """Returns a list of points inside all planes given and a list of index values for the planes used. :param planes: List of planes (4D vectors). :param epsilon_coplanar: Epsilon value for interpreting plane pairs as co-planar. :param epsilon_isect: Epsilon value for intersection. :return: Two lists, one containing the 3D coordinates inside the planes, another containing the plane indices used. """ def tessellate_polygon( polylines: collections.abc.Sequence[ collections.abc.Sequence[collections.abc.Sequence[float]] ], /, ) -> list[tuple[int, int, int]]: """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). :param polylines: Polygons where each polygon is a sequence of 2D or 3D points. :return: A list of triangles. """ def volume_tetrahedron( v1: collections.abc.Sequence[float] | mathutils.Vector, v2: collections.abc.Sequence[float] | mathutils.Vector, v3: collections.abc.Sequence[float] | mathutils.Vector, v4: collections.abc.Sequence[float] | mathutils.Vector, /, ) -> float: """Return the absolute (unsigned) volume formed by a tetrahedron (points can be in any order). :param v1: Point1 :param v2: Point2 :param v3: Point3 :param v4: Point4 :return: The volume of the tetrahedron. """