pancake.basecurve.Basecurve Class Reference

Inheritance diagram for pancake.basecurve.Basecurve:

Public Member Functions
	__init__ (self, float tmin=0.0, float tmax=1.0)
np.ndarray	r (self, float t)
np.ndarray	v (self, float t)
np.ndarray	a (self, float t)
np.ndarray	b (self, float t)
float	speed (self, float t)
float	segment_length (self, float ta, float tb, int nsub=1)
float	length (self)
np.ndarray	equidistant (self, int n)
np.ndarray	sample (self, int n)
	frame (self, float t)
	curvatures (self, float t)
	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
	tmin = float(tmin)
	tmax = float(tmax)
np.ndarray	t = None

Protected Member Functions
int	_nsub_default (self)

Detailed Description

Regular space curve r(t) on [tmin, tmax] with derivatives v, a, b.

Subclasses implement

    r(t) -> position            (3,)
    v(t) -> dr/dt               (3,)
    a(t) -> d2r/dt2             (3,)
    b(t) -> d3r/dt3 ("jerk")    (3,)

The parameter t need not be the arc length, but all frame quantities are
computed such that they are invariant under reparametrization.

Constructor & Destructor Documentation

__init__()

pancake.basecurve.Basecurve.__init__	(		self,
		float	tmin = 0.0,
		float	tmax = 1.0 )

Member Function Documentation

_nsub_default()

int pancake.basecurve.Basecurve._nsub_default ( self )

protected

a()

np.ndarray pancake.basecurve.Basecurve.a	(		self,
		float	t )

Reimplemented in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

b()

np.ndarray pancake.basecurve.Basecurve.b	(		self,
		float	t )

Reimplemented in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

curvatures()

pancake.basecurve.Basecurve.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 in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

darboux()

np.ndarray pancake.basecurve.Basecurve.darboux	(		self,
		float	t )

Darboux vector of the strip frame in space coordinates: tau T + kappa_g n + kappa_n b.

equidistant()

np.ndarray pancake.basecurve.Basecurve.equidistant	(		self,
		int	n )

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

Reimplemented in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

frame()

pancake.basecurve.Basecurve.frame	(		self,
		float	t )

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

Reimplemented in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

kappa_tau()

pancake.basecurve.Basecurve.kappa_tau	(		self,
		float	t )

Frenet curvature and torsion, Eq. (3.30).

length()

float pancake.basecurve.Basecurve.length

(

self

)

Reimplemented in pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

r()

np.ndarray pancake.basecurve.Basecurve.r	(		self,
		float	t )

Reimplemented in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

sample()

np.ndarray pancake.basecurve.Basecurve.sample	(		self,
		int	n )

Store and return n parameters with equal arc-length spacing.

segment_length()

float pancake.basecurve.Basecurve.segment_length	(		self,
		float	ta,
		float	tb,
		int	nsub = 1 )

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

Reimplemented in pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

speed()

float pancake.basecurve.Basecurve.speed	(		self,
		float	t )

Reimplemented in pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

strip_curvatures()

pancake.basecurve.Basecurve.strip_curvatures	(		self,
		float	t,
		float	theta_T = 0.0,
		float	dtheta_T_ds = 0.0 )

(tau*, kappa_g*, kappa_n*) of the twisted strip, Eqs. (19.30), (19.34), (19.35).

transform()

np.ndarray pancake.basecurve.Basecurve.transform	(		self,
		float	t,
		float	theta_T = 0.0 )

Rotation matrix mapping local cross-section coordinates to space.

Column 0: b*  (tape width direction)
Column 1: -n* (tape thickness direction)
Column 2: T   (tape length direction)

Local coordinates (x0, y0, 0) of a cross section are mapped by
r(t) + R @ (x0, y0, 0).  The triple (b, -n, T) is right handed.

twisted_frame()

pancake.basecurve.Basecurve.twisted_frame	(		self,
		float	t,
		float	theta_T = 0.0 )

Frame (T, n*, b*) after twisting about T by theta_T, Eqs. (19.31)-(19.33).

v()

np.ndarray pancake.basecurve.Basecurve.v	(		self,
		float	t )

Reimplemented in pancake.basecurve.RigidTransform, pancake.pancake.PancakeCurve, and pancake.spiral.PlanarSpiral.

Member Data Documentation

t

np.ndarray pancake.basecurve.Basecurve.t = None

tmax

pancake.basecurve.Basecurve.tmax = float(tmax)

tmin

pancake.basecurve.Basecurve.tmin = float(tmin)

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

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