ddg.math.grids module

This module provides functions to create quad and triangle grids.

ddg.math.grids.quad_grid(shape)[source]

Create a rectangular grid of the input shape.

Returns the quad faces and points of a box grid in Z^2 or Z^3.

Parameters:

shapetuple of length 2 or 3: Shape of the grid. The first entry defines the number of vertices in the first coordinate axis, the second the number of vertices in the second coordinate axid and the third (if given) the number of vertices in the third coordinate axis.

Returns:

facesnp.ndarray of shape (k, 4)

The quad faces of the grid, where k is the number of faces.

coordinatesnp.ndarray

Default coordinates which start at (0,0) (or (0,0,0)) and expand to the specified values of shape.

The shape of the array is (n, 2) if the input shape has length 2, otherwise it is (n, 3).

Raises:

ValueError: If the given shape does not have .ndim 2 or 3.

Examples

>>> from ddg.math.grids import quad_grid
>>> faces, coords = quad_grid((2, 3))
>>> faces
array([[0, 1, 3, 2],
       [2, 3, 5, 4]])
>>> coords
array([[0, 0],
       [1, 0],
       [0, 1],
       [1, 1],
       [0, 2],
       [1, 2]])

In the 3D case we get

>>> from ddg.math.grids import quad_grid
>>> faces, coords = quad_grid((2, 2, 2))
>>> faces
array([[0, 1, 3, 2],
       [4, 5, 7, 6],
       [0, 1, 5, 4],
       [2, 3, 7, 6],
       [0, 2, 6, 4],
       [1, 3, 7, 5]])
>>> coords
array([[0, 0, 0],
       [1, 0, 0],
       [0, 1, 0],
       [1, 1, 0],
       [0, 0, 1],
       [1, 0, 1],
       [0, 1, 1],
       [1, 1, 1]])

ddg.math.grids.triangulate_quads(quads)[source]

Subdivide quads into lower left and upper right triangles.

Parameters:

quadsnp.ndarray of shape (n, 4): The quad faces of the grid, where n is the number of faces.

Returns:

np.ndarray of shape (n*2, 3): The triangle faces of the given quad faces, where n*2 is the number of triangle faces.

Examples

>>> import numpy as np
>>> from ddg.math.grids import triangulate_quads
>>> quad_faces = np.array([[0, 1, 4, 3], [1, 2, 5, 4]])
>>> triangulate_quads(quad_faces)
array([[0, 1, 4],
       [1, 2, 5],
       [0, 4, 3],
       [1, 5, 4]])

ddg.math.grids.triangle_grid(shape)[source]

Create a triangle grid of the input shape.

The input shape defines the amount of vertices in each direction. Both 2D and 3D are supported. Returns the faces and default coordinates. Currently, the 3D version only supports (m, n, 1) for the shape.

A shape of (2, 3) will return the following combinatorics

      o-----o
     / \   /
    /   \ /
   o-----o
  / \   /
 /   \ /
o-----o

Parameters:

shapetuple of length 2 or 3: Shape of the grid. The first entry defines the number of vertices in the first coordinate axis, the second the number of vertices in the second coordinate axid and the third (if given) the number of vertices in the third coordinate axis.

Returns:

facesnp.ndarray of shape (k, 3)

The faces of the triangle grid, where k is the number of faces.

coordinatesnp.ndarray

The default coordinates which start at (0,0) (or (0,0,0)) and expand to the specified values of shape.

The shape of the array is (n, 2) if the input shape has length 2, otherwise it is (n, 3).

The coordinates get spanned by the basis vectors

\[b_1 = (2, 0), \quad b_2 = (1, 2)\]

See examples for more detail.

Raises:

ValueError: If the given shape has .ndim 3 and shape[2] != 1.
ValueError: If the given shape does not have .ndim 2 or 3.

Notes

Currently supports planar 3D grids only. Meaning you can only put in a shape of (m, n, 1) or use (m, n) for 2D grids.

Examples

>>> from ddg.math.grids import triangle_grid
>>> faces, coords = triangle_grid((2, 3))
>>> faces
array([[0, 1, 2],
       [2, 3, 4],
       [1, 3, 2],
       [3, 5, 4]])
>>> coords
array([[0, 0],
       [2, 0],
       [1, 2],
       [3, 2],
       [2, 4],
       [4, 4]])

In the 3D case we get

>>> faces, coords = triangle_grid((2, 3, 1))
>>> faces
array([[0, 1, 2],
       [2, 3, 4],
       [1, 3, 2],
       [3, 5, 4]])
>>> coords
array([[0, 0, 0],
       [2, 0, 0],
       [1, 2, 0],
       [3, 2, 0],
       [2, 4, 0],
       [4, 4, 0]])

ddg.math.grids.triangulated_quad_grid(shape)[source]

Create a triangled quad grid of the input shape.

The input shape defines the number of vertices in each direction. Both 2D and 3D are supported. Returns the faces and default coordinates.

A shape of (2, 3) will return the following combinatorics

o-----o
|   / |
| /   |
o-----o
|   / |
| /   |
o-----o

Parameters:

shapetuple of length 2 or 3: Shape of the grid. The first entry defines the number of vertices in the first coordinate axis, the second the number of vertices in the second coordinate axid and the third (if given) the number of vertices in the third coordinate axis.

Returns:

facesnp.ndarray of shape (k, 3)

The faces of the triangle grid, where k is the number of faces.

coordinatesnp.ndarray

The default coordinates which start at (0,0) (or (0,0,0)) and expand to the specified values of shape.

The shape of the array is (n, 2) if the input shape has length 2, otherwise it is (n, 3).

Examples

>>> from ddg.math.grids import triangulated_quad_grid
>>> faces, coords = triangulated_quad_grid((2, 3))
>>> faces
array([[0, 1, 3],
       [2, 3, 5],
       [0, 3, 2],
       [2, 5, 4]])
>>> coords
array([[0, 0],
       [1, 0],
       [0, 1],
       [1, 1],
       [0, 2],
       [1, 2]])

In the 3D case we get

>>> faces, coords = triangulated_quad_grid((2, 2, 2))
>>> faces
array([[0, 1, 3],
       [4, 5, 7],
       [0, 1, 5],
       [2, 3, 7],
       [0, 2, 6],
       [1, 3, 7],
       [0, 3, 2],
       [4, 7, 6],
       [0, 5, 4],
       [2, 7, 6],
       [0, 6, 4],
       [1, 7, 5]])
>>> coords
array([[0, 0, 0],
       [1, 0, 0],
       [0, 1, 0],
       [1, 1, 0],
       [0, 0, 1],
       [1, 0, 1],
       [0, 1, 1],
       [1, 1, 1]])