pancake.spiral.PlanarSpiral Class Reference

Inheritance diagram for pancake.spiral.PlanarSpiral:

Collaboration diagram for pancake.spiral.PlanarSpiral:

Public Member Functions
	__init__ (self, sp.Symbol theta, xexpr, yexpr, float pitch, float nturns, float theta0=0.0, int sense=+1, int nodes_per_turn=64)
np.ndarray	derivs_theta (self, float theta)
np.ndarray	base_point (self, float theta)
np.ndarray	outward_normal (self, float theta)
np.ndarray	point_theta (self, float theta)
float	speed_theta (self, float theta)
float	s_of_theta (self, float theta)
float	theta_of_s (self, float s)
float	theta (self, float s)
np.ndarray	r (self, float s)
np.ndarray	v (self, float s)
np.ndarray	a (self, float s)
np.ndarray	b (self, float s)
float	speed (self, float s)
float	segment_length (self, float ta, float tb, int nsub=1)
float	length (self)
np.ndarray	equidistant (self, int n)
	frame (self, float s)
	curvatures (self, float s)
float	signed_curvature (self, float s)
float	turn_gap (self, float theta)
Public Member Functions inherited from pancake.basecurve.Basecurve
	__init__ (self, float tmin=0.0, float tmax=1.0)
np.ndarray	sample (self, int n)
	kappa_tau (self, float t)
	twisted_frame (self, float t, float theta_T=0.0)
np.ndarray	transform (self, float t, float theta_T=0.0)
	strip_curvatures (self, float t, float theta_T=0.0, float dtheta_T_ds=0.0)
np.ndarray	darboux (self, float t)

Public Attributes
	pitch = float(pitch)
	nturns = float(nturns)
	theta0 = float(theta0)
float	theta1 = self.theta0 + 2.0 * math.pi * self.nturns
	sense = int(sense)
Public Attributes inherited from pancake.basecurve.Basecurve
	tmin = float(tmin)
	tmax = float(tmax)
np.ndarray	t = None

Protected Member Functions
float	_gl_length (self, float ta, float tb)
	_eval (self, float s)
Protected Member Functions inherited from pancake.basecurve.Basecurve
int	_nsub_default (self)

Protected Attributes
float	_theta_sym = theta
list	_fun = [sp.lambdify(theta, [ex, ey], modules="numpy", cse=True) for ex, ey in exprs]
	_base_fun = sp.lambdify(theta, [xexpr, yexpr], modules="numpy")
	_normal_fun = sp.lambdify(theta, [dy / nrm, -dx / nrm], modules="numpy")
	_theta_nodes = np.linspace(self.theta0, self.theta1, m + 1)
	_s_nodes = np.zeros(m + 1)
	_cache_s = None
	_cache_val = None

Detailed Description

Offset spiral r = c + delta nu of a symbolic base curve c(theta) = (xexpr, yexpr).

Constructor & Destructor Documentation

__init__()

pancake.spiral.PlanarSpiral.__init__	(		self,
		sp.Symbol	theta,
			xexpr,
			yexpr,
		float	pitch,
		float	nturns,
		float	theta0 = 0.0,
		int	sense = +1,
		int	nodes_per_turn = 64 )

Member Function Documentation

_eval()

pancake.spiral.PlanarSpiral._eval ( self, float s )

protected

(theta, r, T, dT/ds, d2T/ds2) at arc length s (cached for the last s).

_gl_length()

float pancake.spiral.PlanarSpiral._gl_length ( self, float ta, float tb )

protected

a()

np.ndarray pancake.spiral.PlanarSpiral.a	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

b()

np.ndarray pancake.spiral.PlanarSpiral.b	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

base_point()

np.ndarray pancake.spiral.PlanarSpiral.base_point	(		self,
		float	theta )

curvatures()

pancake.spiral.PlanarSpiral.curvatures	(		self,
		float	t )

Curvature parameters (tau, kappa_g, kappa_n) of the frame returned by `frame`.

For the Frenet frame this is (tau, 0, kappa), Eq. (3.30).

Reimplemented from pancake.basecurve.Basecurve.

derivs_theta()

np.ndarray pancake.spiral.PlanarSpiral.derivs_theta	(		self,
		float	theta )

Array (4, 3): position and theta-derivatives 1..3 of the spiral at theta.

equidistant()

np.ndarray pancake.spiral.PlanarSpiral.equidistant	(		self,
		int	n )

Parameters t_0..t_{n-1} such that the arc length between neighbours is constant.

Reimplemented from pancake.basecurve.Basecurve.

frame()

pancake.spiral.PlanarSpiral.frame	(		self,
		float	t )

Strip frame (T, n, b).  Default: Frenet frame (T, N, B), Eq. (3.29).

Reimplemented from pancake.basecurve.Basecurve.

length()

float pancake.spiral.PlanarSpiral.length

(

self

)

Reimplemented from pancake.basecurve.Basecurve.

outward_normal()

np.ndarray pancake.spiral.PlanarSpiral.outward_normal	(		self,
		float	theta )

point_theta()

np.ndarray pancake.spiral.PlanarSpiral.point_theta	(		self,
		float	theta )

r()

np.ndarray pancake.spiral.PlanarSpiral.r	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

s_of_theta()

float pancake.spiral.PlanarSpiral.s_of_theta	(		self,
		float	theta )

Arc length from the start of the spiral to the point at theta.

segment_length()

float pancake.spiral.PlanarSpiral.segment_length	(		self,
		float	ta,
		float	tb,
		int	nsub = 1 )

Arc length between ta and tb by composite 7-point Gauss-Legendre.

Reimplemented from pancake.basecurve.Basecurve.

signed_curvature()

float pancake.spiral.PlanarSpiral.signed_curvature	(		self,
		float	s )

speed()

float pancake.spiral.PlanarSpiral.speed	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

speed_theta()

float pancake.spiral.PlanarSpiral.speed_theta	(		self,
		float	theta )

theta()

float pancake.spiral.PlanarSpiral.theta	(		self,
		float	s )

theta_of_s()

float pancake.spiral.PlanarSpiral.theta_of_s	(		self,
		float	s )

Inverse of s_of_theta by Newton iteration on the arc-length table.

turn_gap()

float pancake.spiral.PlanarSpiral.turn_gap	(		self,
		float	theta )

Normal distance between the turn at theta and the next turn (theta + 2 pi).

Measured along the outward normal of the base curve; equals the pitch up to
second order in pitch / (2 pi R).

v()

np.ndarray pancake.spiral.PlanarSpiral.v	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

Member Data Documentation

_base_fun

pancake.spiral.PlanarSpiral._base_fun = sp.lambdify(theta, [xexpr, yexpr], modules="numpy")

protected

_cache_s

pancake.spiral.PlanarSpiral._cache_s = None

protected

_cache_val

pancake.spiral.PlanarSpiral._cache_val = None

protected

_fun

list pancake.spiral.PlanarSpiral._fun = [sp.lambdify(theta, [ex, ey], modules="numpy", cse=True) for ex, ey in exprs]

protected

_normal_fun

pancake.spiral.PlanarSpiral._normal_fun = sp.lambdify(theta, [dy / nrm, -dx / nrm], modules="numpy")

protected

_s_nodes

pancake.spiral.PlanarSpiral._s_nodes = np.zeros(m + 1)

protected

_theta_nodes

pancake.spiral.PlanarSpiral._theta_nodes = np.linspace(self.theta0, self.theta1, m + 1)

protected

_theta_sym

float pancake.spiral.PlanarSpiral._theta_sym = theta

protected

nturns

pancake.spiral.PlanarSpiral.nturns = float(nturns)

pitch

pancake.spiral.PlanarSpiral.pitch = float(pitch)

sense

pancake.spiral.PlanarSpiral.sense = int(sense)

theta0

pancake.spiral.PlanarSpiral.theta0 = float(theta0)

theta1

pancake.spiral.PlanarSpiral.theta1 = self.theta0 + 2.0 * math.pi * self.nturns

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The documentation for this class was generated from the following file:

• examples/pancake/python/pancake/spiral.py