brlcad Namespace Reference

Data Structures
class	BBNode
class	BRNode
class	CurveTree
class	SurfaceTree

Functions
bool	sortX (const BRNode *first, const BRNode *second)
bool	sortY (const BRNode *first, const BRNode *second)
bool	get_closest_point (ON_2dPoint &outpt, const ON_BrepFace &face, const ON_3dPoint &point, const SurfaceTree *tree=NULL, double tolerance=BREP_FCP_ROOT_EPSILON)
ON_Curve *	pullback_curve (ON_BrepFace *face, const ON_Curve *curve, SurfaceTree *tree=NULL, double tolerance=BREP_FCP_ROOT_EPSILON, double flatness=1.0e-3)

Function Documentation

sortX()

bool brlcad::sortX	(	const BRNode *	first,
		const BRNode *	second
	)

sortY()

bool brlcad::sortY	(	const BRNode *	first,
		const BRNode *	second
	)

get_closest_point()

bool brlcad::get_closest_point	(	ON_2dPoint &	outpt,
		const ON_BrepFace &	face,
		const ON_3dPoint &	point,
		const SurfaceTree *	tree = NULL,
		double	tolerance = BREP_FCP_ROOT_EPSILON
	)

approach:

• get an estimate using the surface tree (if non-null, create one otherwise)

• find a point (u, v) for which S(u, v) is closest to point

  ---

  – minimize the distance function: D(u, v) = sqrt(|S(u, v)-pt|^2)

  ---

  – simplify by minimizing f(u, v) = |S(u, v)-pt|^2

  – minimum occurs when the gradient is zero, i.e.

  \[ \nabla f(u, v) = |\vec{S}(u, v)-\vec{p}|^2 = 0 \]

pullback_curve()

ON_Curve* brlcad::pullback_curve	(	ON_BrepFace *	face,
		const ON_Curve *	curve,
		SurfaceTree *	tree = NULL,
		double	tolerance = BREP_FCP_ROOT_EPSILON,
		double	flatness = 1.0e-3
	)

Pull an arbitrary model-space curve onto the given surface as a curve within the surface's domain when, for each point c = C(t) on the curve and the closest point s = S(u, v) on the surface, we have: distance(c, s) <= tolerance.

The resulting 2-dimensional curve will be approximated using the following process:

1. Adaptively sample the 3d curve in the domain of the surface (ensure tolerance constraint). Sampling terminates when the following flatness criterion is met:

given two parameters on the curve t1 and t2 (which map to points p1 and p2 on the curve) let m be a parameter randomly chosen near the middle of the interval [t1, t2] ____ then the curve between t1 and t2 is flat if distance(C(m), p1p2) < flatness

1. Use the sampled points to perform a global interpolation using universal knot generation to build a B-Spline curve.
2. If the curve is a line or an arc (determined with openNURBS routines), return the appropriate ON_Curve subclass (otherwise, return an ON_NurbsCurve).