pancake.pancake.PancakeCurve Class Reference

Inheritance diagram for pancake.pancake.PancakeCurve:

Collaboration diagram for pancake.pancake.PancakeCurve:

Public Member Functions
	__init__ (self, PlanarSpiral spiral, inner_lead=None, outer_lead=None, float release=0.0)
str	piece (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)
	frame (self, float s)
	curvatures (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)
np.ndarray	sample_spacing (self, float ds, bool include_breakpoints=True)
	connector_states (self)
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
	spiral = spiral
	inner = None
	outer = None
	release = float(release)
float	L_inner = self.inner.length if self.inner is not None else 0.0
	L_spiral = spiral.tmax - spiral.tmin
float	L_outer = self.outer.length if self.outer is not None else 0.0
float	s_spiral0 = self.L_inner
float	s_spiral1 = self.L_inner + self.L_spiral
	breakpoints = np.array(bp)
Public Attributes inherited from pancake.basecurve.Basecurve
	tmin = float(tmin)
	tmax = float(tmax)
np.ndarray	t = None

Protected Member Functions
	_inner (self, float s)
Protected Member Functions inherited from pancake.basecurve.Basecurve
int	_nsub_default (self)

Detailed Description

Parameters
----------
spiral : PlanarSpiral
inner_lead, outer_lead : list of Segment (or a Lead), described in the direction
    that leaves the coil; None for a free end
release : length over which the curvature of the winding is faded to zero
    before the user segments start (0 = tape leaves tangentially with a
    curvature jump; the curve is then only C^1 at the junction)

Constructor & Destructor Documentation

__init__()

pancake.pancake.PancakeCurve.__init__	(		self,
		PlanarSpiral	spiral,
			inner_lead = None,
			outer_lead = None,
		float	release = 0.0 )

Member Function Documentation

_inner()

pancake.pancake.PancakeCurve._inner ( self, float s )

protected

Forward quantities of the reversed inner lead at global s.

With s_L = L_in - s and the leaving-direction lead quantities (r, v_L, a_L, j_L),
frame (T_L, n_L, b_L) and curvatures (tau_L, kg_L, kn_L):
    r = r,  v = -v_L,  a = a_L,  jerk = -j_L
    T = -T_L,  n = -n_L,  b = b_L        (right handed)
    tau = tau_L,  kappa_g = kg_L,  kappa_n = -kn_L

a()

np.ndarray pancake.pancake.PancakeCurve.a	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

b()

np.ndarray pancake.pancake.PancakeCurve.b	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

connector_states()

pancake.pancake.PancakeCurve.connector_states

(

self

)

(r, T, n, b) at the two free ends of the curve (inner first).

curvatures()

pancake.pancake.PancakeCurve.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.

equidistant()

np.ndarray pancake.pancake.PancakeCurve.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.pancake.PancakeCurve.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.pancake.PancakeCurve.length

(

self

)

Reimplemented from pancake.basecurve.Basecurve.

piece()

str pancake.pancake.PancakeCurve.piece	(		self,
		float	s )

r()

np.ndarray pancake.pancake.PancakeCurve.r	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

sample_spacing()

np.ndarray pancake.pancake.PancakeCurve.sample_spacing	(		self,
		float	ds,
		bool	include_breakpoints = True )

Sample parameters with spacing ~ds, snapped so that breakpoints are hit exactly.

segment_length()

float pancake.pancake.PancakeCurve.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.

speed()

float pancake.pancake.PancakeCurve.speed	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

v()

np.ndarray pancake.pancake.PancakeCurve.v	(		self,
		float	s )

Reimplemented from pancake.basecurve.Basecurve.

Member Data Documentation

breakpoints

pancake.pancake.PancakeCurve.breakpoints = np.array(bp)

inner

pancake.pancake.PancakeCurve.inner = None

L_inner

float pancake.pancake.PancakeCurve.L_inner = self.inner.length if self.inner is not None else 0.0

L_outer

float pancake.pancake.PancakeCurve.L_outer = self.outer.length if self.outer is not None else 0.0

L_spiral

pancake.pancake.PancakeCurve.L_spiral = spiral.tmax - spiral.tmin

outer

pancake.pancake.PancakeCurve.outer = None

release

pancake.pancake.PancakeCurve.release = float(release)

s_spiral0

pancake.pancake.PancakeCurve.s_spiral0 = self.L_inner

s_spiral1

pancake.pancake.PancakeCurve.s_spiral1 = self.L_inner + self.L_spiral

spiral

pancake.pancake.PancakeCurve.spiral = spiral

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

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