ribbon.spiralarchimedes module

Classes for spirals described by the polar equation r = b * theta^n.

class ribbon.spiralarchimedes.SpiralArchimedesBase(b, n, r0)

Bases: SpiralPolarBase

Base class for archimedean spirals. Polar equation: r = b * theta^n.

The starting point is at r = r0 and theta = t0. The arclength s is measured from (r0, t0) in the direction of increasing radius.

Parameters:

bfloat

Parameter in the polar equation. Must be > 0.

nfloat

Exponent in the polar equation. Must be non-zero. If negative, then r0 must be > 0.

r0float

The spiral curve segment begins at (r = r0). Must be a non-negative value.

Attributes:

tincrbool

Whether radius increases with increasing theta.

r0, t0float

The spiral curve segment begins at (r = r0, theta = t0). r0 may not be negative.

bfloat

Parameter in the polar equation. Must be > 0.

nfloat

Exponent in the polar equation. Must be non-zero. If negative, then r0 must be > 0.

Methods

arclength_to_r(s)	Returns the radial coordinates corresponding to the arclengths.
arclength_to_theta(s[, s0, t0])	Returns the angular coordinates corresponding to the arclengths.
get_arclength(v[, var, v0])	Returns the arclength at the given values of polar coordinates.
get_cart_coords(v[, var])	Returns the cartesian coordinates at the given values of polar coordinates or arclengths.
get_curvature(v[, var])	Returns the curvature at the given values of polar coordinates or arclengths.
get_polar_coords(v[, var])	Returns the polar coordinates at the given values of theta, r, or arclengths.
get_tangent(v[, var])	Returns the unit tangent vector at the given values of polar or arclength coordinates.
r_to_theta(r)	Returns the angular coordinates corresponding to the given radial coordinates.
theta_to_r(theta)	Returns the radial coordinates corresponding to the given angular coordinates.

theta_to_r(theta)

Returns the radial coordinates corresponding to the given angular coordinates.

Parameters:

thetaarray_like

Angular coordinates in radians.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray)

r_to_theta(r)

Returns the angular coordinates corresponding to the given radial coordinates.

Parameters:

rarray_like

Radial coordinates.

Returns:

float or ndarray

Angular coordinates in radians (float if input is scalar, else ndarray).

arclength_to_theta(s, s0=0.0, t0=None)

Returns the angular coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

s0float

Value of the arclength at angle t0.

t0float | None

Measure arclength from this value of the angular coordinate. If None, set to t0, which corresponds to the radial coordinate r0.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_tangent(v, var='s')

Returns the unit tangent vector at the given values of polar or arclength coordinates.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

ndarray

Unit tangent vectors. Shape is (2,) if v is scalar, else (n,2) where n is the length of v.

arclength_to_r(s)

Returns the radial coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_arclength(v, var='theta', v0=None)

Returns the arclength at the given values of polar coordinates.

Parameters:

varray_like

Value of the polar coordinates.

var{‘r’, ‘theta’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta'.

v0float or None

Origin of the arclength. If None, will be set to self.t0 if var = 'theta' or to self.r0 if var = 'r'.

Returns:

float or ndarray

Arclength (float if input is scalar, else ndarray).

get_cart_coords(v, var='s')

Returns the cartesian coordinates at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

x, ytuple

Cartesian coordinates. If v is a scalar, x and y are floats, else they are 1D *ndarray*s.

get_curvature(v, var='s')

Returns the curvature at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

float or ndarray

Curvatures (float if input is scalar, else ndarray).

get_polar_coords(v, var='s')

Returns the polar coordinates at the given values of theta, r, or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

r, thetatuple

Polar coordinates. If v is a scalar, r and theta are floats, else they are 1D *ndarray*s.

class ribbon.spiralarchimedes.SpiralArchimedesGeneral(b, n, r0)

Bases: SpiralArchimedesBase

Class implementing a general archimedean spiral with polar equation r = b * theta^n.

The starting point is at r = r0 and theta = t0. If n > 0, r0 >= 0, otherwise r0 > 0. The arclength s is measured from (r0, t0) in the direction of increasing radius.

For all points on this spiral r must be >= r0 and s must be >= 0. If n > 0, theta must be >= t0, otherwise theta <= t0.

Methods

arclength_to_r(s)	Returns the radial coordinates corresponding to the arclengths.
arclength_to_theta(s[, s0, t0])	Returns the angular coordinates corresponding to the arclengths.
get_arclength(v[, var, v0])	Returns the arclength at the given values of polar coordinates.
get_cart_coords(v[, var])	Returns the cartesian coordinates at the given values of polar coordinates or arclengths.
get_curvature(v[, var])	Returns the curvature at the given values of polar coordinates or arclengths.
get_polar_coords(v[, var])	Returns the polar coordinates at the given values of theta, r, or arclengths.
get_tangent(v[, var])	Returns the unit tangent vector at the given values of polar or arclength coordinates.
r_to_theta(r)	Returns the angular coordinates corresponding to the given radial coordinates.
theta_to_r(theta)	Returns the radial coordinates corresponding to the given angular coordinates.

arclength_to_r(s)

Returns the radial coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

arclength_to_theta(s, s0=0.0, t0=None)

Returns the angular coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

s0float

Value of the arclength at angle t0.

t0float | None

Measure arclength from this value of the angular coordinate. If None, set to t0, which corresponds to the radial coordinate r0.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_arclength(v, var='theta', v0=None)

Returns the arclength at the given values of polar coordinates.

Parameters:

varray_like

Value of the polar coordinates.

var{‘r’, ‘theta’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta'.

v0float or None

Origin of the arclength. If None, will be set to self.t0 if var = 'theta' or to self.r0 if var = 'r'.

Returns:

float or ndarray

Arclength (float if input is scalar, else ndarray).

get_cart_coords(v, var='s')

Returns the cartesian coordinates at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

x, ytuple

Cartesian coordinates. If v is a scalar, x and y are floats, else they are 1D *ndarray*s.

get_curvature(v, var='s')

Returns the curvature at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

float or ndarray

Curvatures (float if input is scalar, else ndarray).

get_polar_coords(v, var='s')

Returns the polar coordinates at the given values of theta, r, or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

r, thetatuple

Polar coordinates. If v is a scalar, r and theta are floats, else they are 1D *ndarray*s.

get_tangent(v, var='s')

Returns the unit tangent vector at the given values of polar or arclength coordinates.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

ndarray

Unit tangent vectors. Shape is (2,) if v is scalar, else (n,2) where n is the length of v.

r_to_theta(r)

Returns the angular coordinates corresponding to the given radial coordinates.

Parameters:

rarray_like

Radial coordinates.

Returns:

float or ndarray

Angular coordinates in radians (float if input is scalar, else ndarray).

theta_to_r(theta)

Returns the radial coordinates corresponding to the given angular coordinates.

Parameters:

thetaarray_like

Angular coordinates in radians.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray)

class ribbon.spiralarchimedes.SpiralArchimedes(b, r0)

Bases: SpiralArchimedesBase

Class implementing an Archimedean spiral with polar equation r = b * theta.

The starting point is at r = r0 and theta = t0, where r0 >= 0. The arclength s is measured from (r0, t0) in the direction of increasing radius.

For all points on this spiral r must be >= r0, s must be >= 0, and theta must be >= t0.

Methods

arclength_to_r(s)	Returns the radial coordinates corresponding to the arclengths.
arclength_to_theta(s[, s0, t0])	Returns the angular coordinates corresponding to the arclengths.
get_arclength(v[, var, v0])	Returns the arclength at the given values of polar coordinates.
get_cart_coords(v[, var])	Returns the cartesian coordinates at the given values of polar coordinates or arclengths.
get_curvature(v[, var])	Returns the curvature at the given values of polar coordinates or arclengths.
get_polar_coords(v[, var])	Returns the polar coordinates at the given values of theta, r, or arclengths.
get_tangent(v[, var])	Returns the unit tangent vector at the given values of polar or arclength coordinates.
r_to_theta(r)	Returns the angular coordinates corresponding to the given radial coordinates.
theta_to_r(theta)	Returns the radial coordinates corresponding to the given angular coordinates.

arclength_to_r(s)

Returns the radial coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

arclength_to_theta(s, s0=0.0, t0=None)

Returns the angular coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

s0float

Value of the arclength at angle t0.

t0float | None

Measure arclength from this value of the angular coordinate. If None, set to t0, which corresponds to the radial coordinate r0.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_arclength(v, var='theta', v0=None)

Returns the arclength at the given values of polar coordinates.

Parameters:

varray_like

Value of the polar coordinates.

var{‘r’, ‘theta’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta'.

v0float or None

Origin of the arclength. If None, will be set to self.t0 if var = 'theta' or to self.r0 if var = 'r'.

Returns:

float or ndarray

Arclength (float if input is scalar, else ndarray).

get_cart_coords(v, var='s')

Returns the cartesian coordinates at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

x, ytuple

Cartesian coordinates. If v is a scalar, x and y are floats, else they are 1D *ndarray*s.

get_curvature(v, var='s')

Returns the curvature at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

float or ndarray

Curvatures (float if input is scalar, else ndarray).

get_polar_coords(v, var='s')

Returns the polar coordinates at the given values of theta, r, or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

r, thetatuple

Polar coordinates. If v is a scalar, r and theta are floats, else they are 1D *ndarray*s.

get_tangent(v, var='s')

Returns the unit tangent vector at the given values of polar or arclength coordinates.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

ndarray

Unit tangent vectors. Shape is (2,) if v is scalar, else (n,2) where n is the length of v.

r_to_theta(r)

Returns the angular coordinates corresponding to the given radial coordinates.

Parameters:

rarray_like

Radial coordinates.

Returns:

float or ndarray

Angular coordinates in radians (float if input is scalar, else ndarray).

theta_to_r(theta)

Returns the radial coordinates corresponding to the given angular coordinates.

Parameters:

thetaarray_like

Angular coordinates in radians.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray)

class ribbon.spiralarchimedes.SpiralFermat(b, r0)

Bases: SpiralArchimedesBase

Class implementing a general archimedean spiral with polar equation r = b * theta^(1/2).

The starting point is at r = r0 and theta = t0, where r0 >= 0. The arclength s is measured from (r0, t0) in the direction of increasing radius.

For all points on this spiral r must be >= r0, s must be >= 0, and theta must be >= t0.

Parameters:

bfloat

Parameter in the polar equation. Must be > 0.

r0float

The spiral curve segment begins at (r = r0). Must be a non-negative value.

Methods

arclength_to_r(s)	Returns the radial coordinates corresponding to the arclengths.
arclength_to_theta(s[, s0, t0])	Returns the angular coordinates corresponding to the arclengths.
get_arclength(v[, var, v0])	Returns the arclength at the given values of polar coordinates.
get_cart_coords(v[, var])	Returns the cartesian coordinates at the given values of polar coordinates or arclengths.
get_curvature(v[, var])	Returns the curvature at the given values of polar coordinates or arclengths.
get_polar_coords(v[, var])	Returns the polar coordinates at the given values of theta, r, or arclengths.
get_tangent(v[, var])	Returns the unit tangent vector at the given values of polar or arclength coordinates.
r_to_theta(r)	Returns the angular coordinates corresponding to the given radial coordinates.
theta_to_r(theta)	Returns the radial coordinates corresponding to the given angular coordinates.

arclength_to_r(s)

Returns the radial coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

arclength_to_theta(s, s0=0.0, t0=None)

Returns the angular coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

s0float

Value of the arclength at angle t0.

t0float | None

Measure arclength from this value of the angular coordinate. If None, set to t0, which corresponds to the radial coordinate r0.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_arclength(v, var='theta', v0=None)

Returns the arclength at the given values of polar coordinates.

Parameters:

varray_like

Value of the polar coordinates.

var{‘r’, ‘theta’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta'.

v0float or None

Origin of the arclength. If None, will be set to self.t0 if var = 'theta' or to self.r0 if var = 'r'.

Returns:

float or ndarray

Arclength (float if input is scalar, else ndarray).

get_cart_coords(v, var='s')

Returns the cartesian coordinates at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

x, ytuple

Cartesian coordinates. If v is a scalar, x and y are floats, else they are 1D *ndarray*s.

get_curvature(v, var='s')

Returns the curvature at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

float or ndarray

Curvatures (float if input is scalar, else ndarray).

get_polar_coords(v, var='s')

Returns the polar coordinates at the given values of theta, r, or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

r, thetatuple

Polar coordinates. If v is a scalar, r and theta are floats, else they are 1D *ndarray*s.

get_tangent(v, var='s')

Returns the unit tangent vector at the given values of polar or arclength coordinates.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

ndarray

Unit tangent vectors. Shape is (2,) if v is scalar, else (n,2) where n is the length of v.

r_to_theta(r)

Returns the angular coordinates corresponding to the given radial coordinates.

Parameters:

rarray_like

Radial coordinates.

Returns:

float or ndarray

Angular coordinates in radians (float if input is scalar, else ndarray).

theta_to_r(theta)

Returns the radial coordinates corresponding to the given angular coordinates.

Parameters:

thetaarray_like

Angular coordinates in radians.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray)

class ribbon.spiralarchimedes.SpiralHyperbolic(b, r0)

Bases: SpiralArchimedesBase

Class implementing a general archimedean spiral with polar equation r = b * theta^(-1).

The starting point is at r = r0 and theta = t0, where r0 > 0. The arclength s is measured from (r0, t0) in the direction of increasing radius.

For all points on this spiral r must be >= r0, s must be >= 0, and theta must be <= t0.

Parameters:

bfloat

Parameter in the polar equation. Must be > 0.

r0float

The spiral curve segment begins at (r = r0). Must be a non-negative value.

Methods

arclength_to_r(s)	Returns the radial coordinates corresponding to the arclengths.
arclength_to_theta(s[, s0, t0])	Returns the angular coordinates corresponding to the arclengths.
get_arclength(v[, var, v0])	Returns the arclength at the given values of polar coordinates.
get_cart_coords(v[, var])	Returns the cartesian coordinates at the given values of polar coordinates or arclengths.
get_curvature(v[, var])	Returns the curvature at the given values of polar coordinates or arclengths.
get_polar_coords(v[, var])	Returns the polar coordinates at the given values of theta, r, or arclengths.
get_tangent(v[, var])	Returns the unit tangent vector at the given values of polar or arclength coordinates.
r_to_theta(r)	Returns the angular coordinates corresponding to the given radial coordinates.
theta_to_r(theta)	Returns the radial coordinates corresponding to the given angular coordinates.

arclength_to_r(s)

Returns the radial coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

arclength_to_theta(s, s0=0.0, t0=None)

Returns the angular coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

s0float

Value of the arclength at angle t0.

t0float | None

Measure arclength from this value of the angular coordinate. If None, set to t0, which corresponds to the radial coordinate r0.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_arclength(v, var='theta', v0=None)

Returns the arclength at the given values of polar coordinates.

Parameters:

varray_like

Value of the polar coordinates.

var{‘r’, ‘theta’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta'.

v0float or None

Origin of the arclength. If None, will be set to self.t0 if var = 'theta' or to self.r0 if var = 'r'.

Returns:

float or ndarray

Arclength (float if input is scalar, else ndarray).

get_cart_coords(v, var='s')

Returns the cartesian coordinates at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

x, ytuple

Cartesian coordinates. If v is a scalar, x and y are floats, else they are 1D *ndarray*s.

get_curvature(v, var='s')

Returns the curvature at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

float or ndarray

Curvatures (float if input is scalar, else ndarray).

get_polar_coords(v, var='s')

Returns the polar coordinates at the given values of theta, r, or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

r, thetatuple

Polar coordinates. If v is a scalar, r and theta are floats, else they are 1D *ndarray*s.

get_tangent(v, var='s')

Returns the unit tangent vector at the given values of polar or arclength coordinates.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

ndarray

Unit tangent vectors. Shape is (2,) if v is scalar, else (n,2) where n is the length of v.

r_to_theta(r)

Returns the angular coordinates corresponding to the given radial coordinates.

Parameters:

rarray_like

Radial coordinates.

Returns:

float or ndarray

Angular coordinates in radians (float if input is scalar, else ndarray).

theta_to_r(theta)

Returns the radial coordinates corresponding to the given angular coordinates.

Parameters:

thetaarray_like

Angular coordinates in radians.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray)

class ribbon.spiralarchimedes.SpiralLituus(b, r0)

Bases: SpiralArchimedesBase

Class implementing a general archimedean spiral with polar equation r = b * theta^(-1/2).

The starting point is at r = r0 and theta = t0, where r0 > 0. The arclength s is measured from (r0, t0) in the direction of increasing radius.

For all points on this spiral r must be >= r0, s must be >= 0, and theta must be <= t0.

Parameters:

bfloat

Parameter in the polar equation. Must be > 0.

r0float

The spiral curve segment begins at (r = r0). Must be a non-negative value.

Methods

arclength_to_r(s)	Returns the radial coordinates corresponding to the arclengths.
arclength_to_theta(s[, s0, t0])	Returns the angular coordinates corresponding to the arclengths.
get_arclength(v[, var, v0])	Returns the arclength at the given values of polar coordinates.
get_cart_coords(v[, var])	Returns the cartesian coordinates at the given values of polar coordinates or arclengths.
get_curvature(v[, var])	Returns the curvature at the given values of polar coordinates or arclengths.
get_polar_coords(v[, var])	Returns the polar coordinates at the given values of theta, r, or arclengths.
get_tangent(v[, var])	Returns the unit tangent vector at the given values of polar or arclength coordinates.
r_to_theta(r)	Returns the angular coordinates corresponding to the given radial coordinates.
theta_to_r(theta)	Returns the radial coordinates corresponding to the given angular coordinates.

arclength_to_r(s)

Returns the radial coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

arclength_to_theta(s, s0=0.0, t0=None)

Returns the angular coordinates corresponding to the arclengths.

Parameters:

sarray_like

Arclengths measured from the starting point (as set by the instance attribute r0) along the direction of increasing radius.

s0float

Value of the arclength at angle t0.

t0float | None

Measure arclength from this value of the angular coordinate. If None, set to t0, which corresponds to the radial coordinate r0.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray).

get_arclength(v, var='theta', v0=None)

Returns the arclength at the given values of polar coordinates.

Parameters:

varray_like

Value of the polar coordinates.

var{‘r’, ‘theta’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta'.

v0float or None

Origin of the arclength. If None, will be set to self.t0 if var = 'theta' or to self.r0 if var = 'r'.

Returns:

float or ndarray

Arclength (float if input is scalar, else ndarray).

get_cart_coords(v, var='s')

Returns the cartesian coordinates at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

x, ytuple

Cartesian coordinates. If v is a scalar, x and y are floats, else they are 1D *ndarray*s.

get_curvature(v, var='s')

Returns the curvature at the given values of polar coordinates or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

float or ndarray

Curvatures (float if input is scalar, else ndarray).

get_polar_coords(v, var='s')

Returns the polar coordinates at the given values of theta, r, or arclengths.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

r, thetatuple

Polar coordinates. If v is a scalar, r and theta are floats, else they are 1D *ndarray*s.

get_tangent(v, var='s')

Returns the unit tangent vector at the given values of polar or arclength coordinates.

Parameters:

varray_like

Value of the polar coordinates or arclengths.

var{‘r’, ‘theta’, ‘s’}

Descriptor for v. Radial coordinates — 'r', angular coordinates — 'theta', and arclengths — 's'.

Returns:

ndarray

Unit tangent vectors. Shape is (2,) if v is scalar, else (n,2) where n is the length of v.

r_to_theta(r)

Returns the angular coordinates corresponding to the given radial coordinates.

Parameters:

rarray_like

Radial coordinates.

Returns:

float or ndarray

Angular coordinates in radians (float if input is scalar, else ndarray).

theta_to_r(theta)

Returns the radial coordinates corresponding to the given angular coordinates.

Parameters:

thetaarray_like

Angular coordinates in radians.

Returns:

float or ndarray

Radial coordinates (float if input is scalar, else ndarray)