pancake.spiral.LameSpiral Class Reference

Inheritance diagram for pancake.spiral.LameSpiral:

Collaboration diagram for pancake.spiral.LameSpiral:

Public Member Functions
	__init__ (self, float a, float b, float n, float pitch, float nturns, float theta0=0.0, int sense=+1, int nodes_per_turn=64)
	__repr__ (self)
Public Member Functions inherited from 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)
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
	a_axis = float(a)
	b_axis = float(b)
	n_exp = float(n)
Public Attributes inherited from pancake.spiral.PlanarSpiral
	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

Additional Inherited Members
Protected Member Functions inherited from pancake.spiral.PlanarSpiral
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 inherited from pancake.spiral.PlanarSpiral
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

Spiral winding on a Lame curve (superellipse)  |x/a|^n + |y/b|^n = 1.

Parameters
----------
a, b : semi-axes of the innermost turn (mandrel) along x and y
n    : Lame exponent (2 = ellipse; 4 ... 6 = rounded rectangle).  Even integers
       give an analytic curve; other exponents are only C^(ceil(n)-1) on the axes.
pitch : radial growth per turn (tape thickness plus insulation)
nturns : number of turns (may be fractional)
theta0 : polar angle where the winding starts
sense : +1 winds counter-clockwise (seen from +z), -1 clockwise

Constructor & Destructor Documentation

__init__()

pancake.spiral.LameSpiral.__init__	(		self,
		float	a,
		float	b,
		float	n,
		float	pitch,
		float	nturns,
		float	theta0 = 0.0,
		int	sense = +1,
		int	nodes_per_turn = 64 )

Member Function Documentation

__repr__()

pancake.spiral.LameSpiral.__repr__

(

self

)

Member Data Documentation

a_axis

pancake.spiral.LameSpiral.a_axis = float(a)

b_axis

pancake.spiral.LameSpiral.b_axis = float(b)

n_exp

pancake.spiral.LameSpiral.n_exp = float(n)

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

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