shape

shape#

Classes for common shapes and their manipulation.

class Shape#

Bases: object

__init__(shape_func=<function Shape.<lambda>>)#

Base class for all shapes using constructive solid geometry (CSG). This mutable class holds and manipulates a given shape function.

Parameters:: shape_func (Callable[[x,y,z], bool]) – Function returning True if (x,y,z) is within this shape.

transform4(transform_matrix)#: Transform this shape according to a given 4x4 matrix, which can represent any affine transformation (rotate, scale, shear, translate). It is usually of the form [[R, T], [0, 1]], with R a 3x3 rotation matrix and T a 3x1 translation vector. Returns transformed self.

transform3(transform_matrix)#: Transform this shape according to a given 3x3 matrix (rotate, scale, shear). Returns transformed self.

transform(transform_matrix)#: Transform this shape according to a given 3x3 matrix (rotate, scale, shear) or 4x4 matrix (like 3x3 plus translations). It is usually of the form [[R, T], [0, 1]], with R a 3x3 rotation matrix and T a 3x1 translation vector. Returns transformed self.

rotate_x(theta)#: Rotate this shape theta radians counter-clockwise around the x-axis.

rotate_y(theta)#: Rotate this shape theta radians counter-clockwise around the y-axis.

rotate_z(theta)#: Rotate this shape theta radians counter-clockwise around the z-axis.

translate(dx, dy, dz)#: Translate this shape by the vector (dx,dy,dz).

translate_x(dx)#: Translate this shape by dx along the x-axis.

translate_y(dy)#: Translate this shape by dy along the y-axis.

translate_z(dz)#: Translate this shape by dz along the z-axis.

scale(sx, sy=None, sz=1)#

Scale this shape, using (0,0,0) as the origin. Takes 1, 2 or 3 arguments:

(s): scale by s in all directions.
(sx, sy): scale by sx and sy in the xy-plane, but do not scale z.
(sx, sy, sz): scale by sx, sy and sz in the x-, y- and z-direction respectively.

mirror_xy()#: Mirror this shape with respect to the xy-plane.

mirror_yz()#: Mirror this shape with respect to the yz-plane.

mirror_zx()#: Mirror this shape with respect to the zx-plane.

invert()#: Invert this shape (logical NOT).

repeat(min_point, max_point)#

Infinitely repeat everything from this shape enclosed in a bounding box defined by the given minimum and maximum points, while everything outside this box is ignored.

Parameters:

min_point (tuple[float] of size 3) – Smallest x, y and z coordinates of the bounding box (inclusive).
max_point (tuple[float] of size 3) – Largest x, y and z coordinates of the bounding box (exclusive).
direction. (Setting any coordinate to None will not repeat the shape in this)

copy()#: Returns a new shape which is a copy of this shape.

add(other)#

Add given shape to this shape (logical OR). Calling a.add(b), a += b or a |= b is the same.

Parameters:: other (Shape)

sub(other)#

Subtract given shape from this shape (logical AND NOT). Calling a.sub(b) or a -= b is the same.

Parameters:: other (Shape)

intersect(other)#

Intersect given shape with this shape (logical AND). Calling a.intersect(b), a &= b and a /= b are the same.

Parameters:: other (Shape)

xor(other)#

Keep everything from this shape and the given shape, except the intersection (logical XOR). Calling a.xor(b) or a ^= b is the same.

Parameters:: other (Shape)

class Empty#

Bases: Shape

__init__()#: Empty space.

class Universe#

Bases: Shape

__init__()#: All of space.

class Ellipsoid#

Bases: Shape

__init__(diamx, diamy, diamz)#: Ellipsoid with given diameters diamx, diamy, diamz.

class Sphere#

Bases: Ellipsoid

__init__(diam=None, radius=None)#: Sphere with given diameter or radius.

class Ellipse#

Bases: Shape

__init__(diamx, diamy)#: Ellipse in the xy-plane with given diameters diamx and diamy.

class Circle#

Bases: Ellipse

__init__(diam)#: Circle in the xy-plane with given diameter.

class Cone#

Bases: Shape

__init__(diam, height)#: 3D cone with the vertex down. It has a given diameter at a given height.

class Cylinder#

Bases: Shape

__init__(diam, height)#: Cylinder along z with given diameter and height.

class Cuboid#

Bases: Shape

__init__(sidex, sidey, sidez)#: 3D rectangular slab with given sides, including minimum, excluding maximum.

class Cube#

Bases: Cuboid

__init__(side)#: Cube with given side length.

class Rectangle#

Bases: Shape

__init__(sidex, sidey)#: 2D Rectangle in the xy-plane with given sides.

class Square#

Bases: Rectangle

__init__(side)#: Square with given side length.

class XRange#

Bases: Shape

__init__(xmin, xmax)#: Range of x-values: xmin <= x < xmax

class YRange#

Bases: Shape

__init__(ymin, ymax)#: Range of y-values: ymin <= y < ymax

class ZRange#

Bases: Shape

__init__(zmin, zmax)#: Range of z-values: zmin <= z < zmax

class Torus#

Bases: Shape

__init__(major_diam, minor_diam)#

Torus with given major and minor diameters.

Parameters:

major_diam (float) – Distance between opposite centers of the tube.
minor_diam (When major_diam =) – Diameter of the tube.
high. (The torus is major_diam + minor_diam wide and minor_diam)
minor_diam
hole. (there will be no)

class DelaunayHull#

Bases: Shape

__init__(points)#

The Delaunay hull of a list of 3D points. These points can serve as the vertices of a convex polyhedron.

Parameters:: points (ndarray of double, shape (npoints, 3))

class Tetrahedron#

Bases: DelaunayHull

__init__(diam)#: Tetrahedron (4-faced platonic solid) where all vertices lie on a sphere with the given diameter.

class Octahedron#

Bases: Shape

__init__(diam)#: Octahedron (8-faced platonic solid) where all vertices lie on a sphere with the given diameter.

class Dodecahedron#

Bases: DelaunayHull

__init__(diam)#: Dodecahedron (12-faced platonic solid) where all vertices lie on a sphere with the given diameter.

class Icosahedron#

Bases: DelaunayHull

__init__(diam)#: Dodecahedron (20-faced platonic solid) where all vertices lie on a sphere with the given diameter.

class Icosidodecahedron#

Bases: DelaunayHull

__init__(diam)#: Icosidodecahedron where all vertices lie on a sphere with the given diameter.

class Polygon#

Bases: Shape

__init__(vertices)#

A polygon in the xy-plane, with a given list of vertices.

Parameters:: vertices (float ndarray of size (N, 2) or (N, 3)) – If the size is (N, 3), the z-values are simply ignored.

class RegularPolygon#

Bases: Polygon

__init__(N, diam)#: A regular polygon in the xy-plane with N vertices which lie on a circle with given diameter. One point is located at (diam/2, 0).

class ImageShape#

Bases: Shape

__init__(fname, min_point, max_point)#

Use a black and white image as a shape in the xy-plane. The given image file is stretched to the given coordinates. Black is inside the shape (True), white outside (False). Coordinates inside the stretched image assume the value of the nearest pixel. Coordinate outside the edges of the stretched image are treated as outside of the shape (False).

Parameters:

fname (string) – Filename of the image to use.
min_point (tuple of length 2 or 3) – x and y world coordinates to be mapped to the center of the bottom left pixel of the image. z-coordinate can be given but is ignored.
max_point (tuple of length 2 or 3) – x and y world coordinates to be mapped to the center of the top right pixel of the image. z-coordinate can be given but is ignored.

shape

Contents

shape#