`xdesign.geometry`¶

Define geometric objects for compuational geometry operations.

Module author: Doga Gursoy <dgursoy@aps.anl.gov>

Module author: Daniel J Ching <carterbox@users.noreply.github.com>

Zero dimensional entities¶

Define zero dimensional geometric entities.

Classes:

Point(x)

Define a point in ND cartesian space.

class xdesign.geometry.point.Point(x)[source]¶

Bases: xdesign.geometry.entity.Entity

Define a point in ND cartesian space.

Parameters: x (ndarray, list) – ND coordinates of the point.
Raises: TypeError – If x is not a list or ndarray.

collision(other)[source]¶: Return True if this Point collides with another entity.

contains(other)[source]¶

Return wether the other is within the bounds of the Point.

Points can only contain other Points.

distance(other)[source]¶: Return the closest distance this and the other.

property norm¶: Euclidian (L2) norm of the vector to the point.

rotate(theta, point=None, axis=None)[source]¶: Rotates theta radians around an axis.

scale(vector)[source]¶

Scale the ambient space in each dimension according to vector.

Scaling is centered on the origin.

translate(vector)[source]¶: Translate the point along the given vector.

property x¶: Dimension 0 of the point.

property y¶: Dimension 1 of the point.

property z¶: Dimension 2 of the point.

xdesign.geometry.point.calc_standard(A)[source]¶

Return the standard equation for the row-wise points in A.

The coefficents (c_{0}*x + … = c_{1}) describe the hyper-plane defined by the row-wise N-dimensional points A.

Parameters

A (np.array (…, N, N)) – Each row is an N-dimensional point on the plane.

Returns

c0 (np.array (…, N)) – The first N coefficients for the hyper-plane
c1 (np.array (…, 1)) – The last coefficient for the hyper-plane

xdesign.geometry.point.dim(self)[source]¶: Return the dimensionality of the ambient space.

xdesign.geometry.point.distance(self, other)[source]¶: Return the closest distance this and the other.

xdesign.geometry.point.norm(self)[source]¶: Euclidian (L2) norm of the vector.

xdesign.geometry.point.rotated(self, theta, center=None, axis=None)[source]¶: Rotates theta radians around an axis.

One dimensional entities¶

Define one dimensional geometric entities.

Classes:

`Line`(p1, p2)	Line in 2D cartesian space.
`Segment`(p1, p2)	Defines a finite line segment from two unique points.

class xdesign.geometry.line.Line(p1, p2)[source]¶

Bases: xdesign.geometry.line.LinearEntity

Line in 2D cartesian space.

The constructor takes two unique Point.

p1¶

Type: Point

p2¶

Type: Point

distance(other)[source]¶: Returns the closest distance between entities.

intercept(n)[source]¶: Calculates the intercept for the nth dimension.

property standard¶: Returns coeffients for the first N-1 standard equation coefficients. The Nth is returned separately.

property xintercept¶: Return the x-intercept.

property yintercept¶: Return the y-intercept.

class xdesign.geometry.line.Segment(p1, p2)[source]¶

Bases: xdesign.geometry.line.Line

Defines a finite line segment from two unique points.

distance(other)[source]¶: Return the distance to the other.

property midpoint¶: Return the midpoint of the line segment.

Two dimensional entities¶

Define two dimensional geometric entities.

Classes:

`Curve`(center)	The base class for closed manifolds defined by a single equation.
`Circle`(center, radius[, sign])	Circle in 2D cartesian space.
`Polygon`(vertices[, sign])	A convex polygon in 2D cartesian space.
`RegularPolygon`(center, radius, order[, ...])	A regular polygon in 2D cartesian space.
`Triangle`(p1, p2, p3)	Triangle in 2D cartesian space.
`Rectangle`(center, side_lengths)	Rectangle in 2D cartesian space.
`Square`(center[, side_length, radius])	Square in 2D cartesian space.
`Mesh`([obj, faces])	A collection of Entities

class xdesign.geometry.area.Circle(center, radius, sign=1)[source]¶

Bases: xdesign.geometry.area.Curve

Circle in 2D cartesian space.

center¶

The center point of the circle.

Type: Point

radius¶

The radius of the circle.

Type: scalar

sign¶

The sign of the area

Type: int (-1 or 1)

property area¶: Return the area.

property bounding_box¶: Return the axis-aligned bounding box as two numpy vectors.

property circumference¶: Returns the circumference.

contains(other)[source]¶

Return whether other is a proper subset.

Return one boolean for all geometric entities. Return an array of boolean for array input.

property diameter¶: Returns the diameter.

property list¶: Return list representation for saving to files.

property patch¶: Returns a matplotlib patch.

class xdesign.geometry.area.Curve(center)[source]¶

Bases: xdesign.geometry.entity.Entity

The base class for closed manifolds defined by a single equation. e.g. Circle, Sphere, or Torus.

center¶

Type: Point

rotate(theta, point=None, axis=None)[source]¶: Rotates the Curve by theta radians around an axis which passes through a point radians.

translate(vector)[source]¶: Translates the Curve along a vector.

class xdesign.geometry.area.Mesh(obj=None, faces=[])[source]¶

Bases: xdesign.geometry.entity.Entity

A collection of Entities

faces¶

A list of the Entities

Type: list

area¶

The total area of the Entities

Type: float

population¶

The number entities in the Mesh

Type: int

radius¶

The radius of a bounding circle

Type: float

append(t)[source]¶: Add a triangle to the mesh.

property bounding_box¶: Return the axis-aligned bounding box as two numpy vectors.

property center¶

contains(other)[source]¶

Return whether this Mesh contains other.

FOR ALL x, THERE EXISTS a face of the Mesh that contains x AND (ALL cut outs that contain x or THERE DOES NOT EXIST a cut out).

import_triangle(obj)[source]¶: Loads mesh data from a Python Triangle dict.

property patch¶

pop(i=- 1)[source]¶: Pop i-th triangle from the mesh.

rotate(theta, point=None, axis=None)[source]¶: Rotate entity around an axis which passes through a point by theta radians.

scale(vector)[source]¶: Scale entity.

translate(vector)[source]¶: Translate entity.

class xdesign.geometry.area.Polygon(vertices, sign=1)[source]¶

Bases: xdesign.geometry.entity.Entity

A convex polygon in 2D cartesian space.

It is defined by a number of distinct vertices of class Point. Superclasses include Square, Triangle, etc.

vertices¶

Type: List of Points

sign¶

The sign of the area

Type: int (-1 or 1)

:raises ValueError : If the number of vertices is less than three.:

area = <MagicMock name='mock()' id='140346947267856'>¶

property bounding_box¶: Return the axis-aligned bounding box as two numpy vectors.

property bounds¶: Returns a 4-tuple (xmin, ymin, xmax, ymax) representing the bounding rectangle for the Polygon.

center = <MagicMock name='mock()' id='140346947267856'>¶

contains(other)[source]¶: Return whether this Polygon contains the other.

property edges¶: Return a list of lines connecting the points of the Polygon.

half_space = <MagicMock name='mock()' id='140346947267856'>¶

property list¶: Return list representation.

property numpy¶: Return Numpy representation.

property numverts¶

property patch¶: Returns a matplotlib patch.

perimeter = <MagicMock name='mock()' id='140346947267856'>¶

radius = <MagicMock name='mock()' id='140346947267856'>¶

rotate(theta, point=None, axis=None)[source]¶: Rotates the Polygon around an axis which passes through a point by theta radians.

translate(vector)[source]¶: Translates the polygon by a vector.

class xdesign.geometry.area.Rectangle(center, side_lengths)[source]¶

Bases: xdesign.geometry.area.Polygon

Rectangle in 2D cartesian space.

Defined by a point and a vector to enforce perpendicular sides.

Parameters: side_lengths (array) – The lengths of the sides

area = <MagicMock name='mock()' id='140346947267856'>¶

class xdesign.geometry.area.RegularPolygon(center, radius, order, angle=0, sign=1)[source]¶

Bases: xdesign.geometry.area.Polygon

A regular polygon in 2D cartesian space.

It is defined by the polynomial center, order, and radius.

By default (i.e. when the angle parameter is zero), the regular polygon is oriented so that one of the vertices is at coordinates \((x + r, x)\) where \(x\) is the x-coordinate of center and \(r\) = radius. The angle parameter is only meaningful modulo \(2\pi /\) order since rotation by \(2\pi /\) order gives a result equivalent to no rotation.

Parameters

center (Point) – The center of the polygon
radius (float) – Distance from polygon center to vertices
order (int) – Order of the polygon (e.g. order 6 is a hexagon).
angle (float) – Optional rotation angle in radians.
sign (int (-1 or 1)) – Optional sign of the area (see Polygon)

class xdesign.geometry.area.Square(center, side_length=None, radius=None)[source]¶

Bases: xdesign.geometry.area.Rectangle

Square in 2D cartesian space.

Defined by a point and a length to enforce perpendicular sides.

class xdesign.geometry.area.Triangle(p1, p2, p3)[source]¶

Bases: xdesign.geometry.area.Polygon

Triangle in 2D cartesian space.

It is defined by three distinct points.

area = <MagicMock name='mock()' id='140346947267856'>¶

center = <MagicMock name='mock()' id='140346947267856'>¶

Intersect¶

Define algorithms to support intersection calculation.

Functions:

`clip_SH`(clipEdges, polygon)	Clip a polygon using the Sutherland-Hodgeman algorithm.
`halfspacecirc`(d, r)	Return the area of intersection between a circle and half-plane.

xdesign.geometry.intersect.clip_SH(clipEdges, polygon)[source]¶

Clip a polygon using the Sutherland-Hodgeman algorithm.

Parameters

clipEdges [[A, b], …] – half-spaces defined by coefficients
polygon

xdesign.geometry.intersect.halfspacecirc(d, r)[source]¶

Return the area of intersection between a circle and half-plane.

Returns the smaller fraction of a circle split by a line d units away from the center of the circle.

Parameters

d (scalar) – The distance from the line to the center of the circle
r (scalar) – The radius of the circle

Returns

f (scalar) – The proportion of the circle in the smaller half-space

References

Glassner, A. S. (Ed.). (2013). Graphics gems. Elsevier.

xdesign.geometry¶

Zero dimensional entities¶

One dimensional entities¶

Two dimensional entities¶

Intersect¶

`xdesign.geometry`¶