geometry

Function summary

eqn_of_plane(pts)	Equation of plane defined by polygon points
integrate_f_over_polygon_code(f)	Generate code that will integrate a function over a polygon
integrate_f_over_polyhedra_code(f)	Generate code that will integrate a function over a polyhedra
make_hexahedron(coords)	Assemble the face vertices of a hexahedron
polygon_2nd_moment_of_area(pts)	2nd moment of area of polygon defined by points
polygon_area(pts)	Area of polygon defined by points
polygon_centroid(pts)	Centroid of polygon defined by points
polyhedron_volume(faces)	Volume of polyhedron defined by faces defined py pts
replace_x0_and_x1_with_vect(s[, xyz])	Replaces strings x0 with x[:-1], x1 with x[1:], y0 with y[:-1] ...
xyz_from_pts(pts[, close_polygon])	Extract x, y and z values from an (n, 3) or (n, 2) shaped array

Module listing

Some routines loosely related to geometry.

geotecha.mathematics.geometry.eqn_of_plane(pts)

Equation of plane defined by polygon points

a, b, c, d from a*x+b*y+c*z+d = 0 Looking at the plane, counter-clockwise (CCW) points the positive normal is towards you. For clockwise points (CW) the positive normal is away from you.

Parameters:

pts : array_like

aAray of x, y or x, y, z points.

Returns:

[a, b, c] : ndarray with 3 elements

Direction cosines of normal to plane.

d : float

Constant in plane equation.

geotecha.mathematics.geometry.integrate_f_over_polygon_code(f)

Generate code that will integrate a function over a polygon

Parameters:

f : sympy expression

Expression to be integrated over the polygon.

Returns:

out : str

Multiline string of function code

geotecha.mathematics.geometry.integrate_f_over_polyhedra_code(f)

Generate code that will integrate a function over a polyhedra

Parameters:

f : sympy expression

Expression to be integrated over the polyhedron.

Returns:

out : str

Multiline string of funciton code.

geotecha.mathematics.geometry.make_hexahedron(coords)

Assemble the face vertices of a hexahedron

Parameters:

coords : 8 by 3 ndarray

x, y, z coords of 8 corner nodes of hexahedron. node numbering is as per Smith and Grifiths.

Returns:

faces : list of pts arrays

List of pts arrays. Each list defines vertices of a face.

Notes

Node numbering:

                        x
    (6)-------(7)       ^
    /         /|        |  y
   /         / |        | /
  /         /  |        |/
(2)-------(3) (8)       |-------->x
 |         |   /
 |         |  /
 |         | /
(1)-------(4)

geotecha.mathematics.geometry.polygon_2nd_moment_of_area(pts)

2nd moment of area of polygon defined by points

Parameters:

pts : array_like

Array of x, y or x, y, z points.

Returns:

[Ixx, Iyy, Izz] : ndarray of float

2nd moment of area about centroidal x, y, and z axes.

geotecha.mathematics.geometry.polygon_area(pts)

Area of polygon defined by points

Parameters:

pts : array_like

Array of x, y or x, y, z points.

Returns:

a : float

Area of polygon.

geotecha.mathematics.geometry.polygon_centroid(pts)

Centroid of polygon defined by points

Parameters:

pts : array_like

Array of x, y or x, y, z points.

Returns:

[xc, yc, zc] : ndarray of float

Coordinates of centroid.

geotecha.mathematics.geometry.polyhedron_volume(faces)

Volume of polyhedron defined by faces defined py pts

Parameters:

faces : list

A list of pts arrays defining x,y,z coords of face vertices.

Returns:

v : float

Volume of polyhedron.

Notes

I think points on a face have to be defined in anti clockwise (CCW) order to give a positive volume. No checks are done to check the order.

geotecha.mathematics.geometry.replace_x0_and_x1_with_vect(s, xyz=['x', 'y', 'z'])

Replaces strings x0 with x[:-1], x1 with x[1:], y0 with y[:-1] ...

Parameters:

s : string, or sympy_expression

Expression to make replacements on

xyz : list of strings

Replacements will be made for each element of xyz. default xyz=[‘x’,’y’,’z’].

Returns:

out : string

string with all replacements made

geotecha.mathematics.geometry.xyz_from_pts(pts, close_polygon=False)

Extract x, y and z values from an (n, 3) or (n, 2) shaped array

Parameters:

pts : array_like

Array of x, y or x, y, z points.

close_polygon : boolean, optional

If True then 1st point will be repeated i.e. to close the polygon. Default close_polygon=False.

Returns:

x, y, z : 1d ndarrays

1d array of x coords, y coords, z coords.