gvf_adapted_step.h File Reference

Dynamic parametric step adaptation for the GVF algorithm. More...

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Functions
float	step_adaptation (float ds, float f1d, float f2d, float f3d, float f1dd, float f2dd, float f3dd)
	Compute the adapted parametric step given the wanted geometric distance.

Detailed Description

Dynamic parametric step adaptation for the GVF algorithm.

Contains two macro-defined parameters:

• ADAPTED_STEP_NULL_TOLERANCE: Numbers with absolute values smaller than ADAPTED_STEP_NULL_TOLERANCE will be considered equal to 0. Default to 1e-6
• ADAPTED_STEP_MAX_ROOTFINDING_STEPS: Maximum number of steps used in the root finding algorithm. Default to 1e6

Definition in file gvf_adapted_step.h.

Function Documentation

step_adaptation()

float step_adaptation	(	float	ds,
		float	f1d,
		float	f2d,
		float	f3d,
		float	f1dd,
		float	f2dd,
		float	f3dd
	)

Compute the adapted parametric step given the wanted geometric distance.

Given the 3D parametric curve described by f at p and a wanted geometric distance ds, computes the parametric step dp such that: |ds| = || f(p+dp) - f(p) || and (ds)(dp) > 0

To do so, it uses second order Taylor approximation around p to reduce the problem to finding a root of a degree 4 polynomial. This root is found using Halley's method.

We assume the curve non 2-singular (that is both f' and f'' does not vanish). (If it is the case, then the method falls back to returning dp = ds, and print an error to stderr).

Parameters

ds	Wanted geometric distance
f1d	x value of f'(p)
f2d	y value of f'(p)
f3d	z value of f'(p)
f1dd	x value of f''(p)
f2dd	y value of f''(p)
f3dd	z value of f''(p)

Returns

float The corresponding parametric step to take

Definition at line 108 of file gvf_adapted_step.c.

References ADAPTED_STEP_MAX_ROOTFINDING_STEPS, ADAPTED_STEP_NULL_TOLERANCE, foo, init, and p4_halley().

Referenced by gvf_parametric_control_2D().

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