One trimmed boundary curve in a surface's (u, v) domain: a line segment, a circular arc or a clamped (rational) B-spline. More...

#include <BoundedSurface.h>

Public Member Functions
bool	isArc () const

bool	isBSpline () const

double	sweep () const

bool	valid () const

Vec2	pointAtAngle (double angle) const

Vec2	pointAt (double parameter) const
	Point at curve parameter parameter in [0, 1] (0 at the start, 1 at the end).

Vec2	startPoint () const

Vec2	endPoint () const

Vec2	derivativeAt (double parameter) const
	dC/dt at parameter in [0, 1], unnormalised; tangentAt() is it normalised.

Vec2	tangentAt (double parameter) const
	Unit tangent at parameter parameter, pointing in the direction of increasing parameter.

bool	angleInSweep (double angle) const
	True if angle lies within the arc's angular sweep (accounting for direction and wrap).

double	angleParameter (double angle) const
	Map an angle known to lie within the sweep to a clamped parameter in [0, 1].

void	extendBounds (Vec2 &lower, Vec2 &upper) const
	Accumulate this curve's exact extent into a parametric axis-aligned bounding box.

void	extendTightBounds (Vec2 &lower, Vec2 &upper) const
	As extendBounds, measured on the curve: a B-spline contributes its sampled polyline, not its pole hull.

template<typename Include >
void	includeAnalyticExtremes (const Include &include) const
	Endpoints plus an arc's axis-extreme points inside the sweep: the exact extent of a line or an arc.

Vec2	closestPoint (const Vec2 &point, double &parameter) const
	Closest point on the curve to point, returning the clamped parameter in parameter.

double	distanceSq (const Vec2 &point) const
	Squared distance from point to the curve.

double	signedAreaContribution () const

double	representationTolerance () const
	How far this curve's representation can sit from the curve, in parametric units: kBSplineFlatness for a B-spline, else 0.

bool	bsplineBandOrCrossings (const Vec2 &point, double bandSq, int &crossings) const

int	rightwardCrossings (const Vec2 &point, const Vec2 &canonicalStart, const Vec2 &canonicalEnd) const
	Rightward crossings of a horizontal ray from point, with the caller's canonical endpoints so that seams stay consistent.

void	reverseInPlace ()
	Reverse the curve's direction in place (start <-> end), keeping the same geometric image.

B-spline evaluation helpers (kind == BSpline)
double	bsplineT0 () const

double	bsplineT1 () const

bool	bsplineIsClamped () const
	True when the knot vector is clamped, so the curve interpolates its first and last pole.

bool	bsplineRational () const
	True if the curve carries non-unit weights (a rational B-spline).

int	bsplineSpan (double knotValue) const
	Knot span index of parameter knotValue for the clamped knot vector.

void	bsplineBasis (int span, double knotValue, std::vector< double > &basis, std::vector< double > &basisDeriv) const
	Non-zero degree-p basis functions and first derivatives at knotValue in span (The NURBS Book, DersBasisFuns).

void	bsplineEval (double knotValue, Vec2 &pointOut, Vec2 &derivativeOut) const

Vec2	bsplinePointAt (double parameter) const
	B-spline point at curve parameter parameter in [0, 1].

void	bsplineSampleInto (std::vector< Vec2 > &samples, double flatnessSq=kBSplineFlatnessSq, int maxDepth=16) const
	Adaptively sample the B-spline into an on-curve polyline, subdividing until each chord is flat to sqrt(flatnessSq).

bool	spansInteriorKnot (double lowT, double highT) const
	Whether a knot lies strictly inside (lowT, highT); such an interval is never called flat.

void	appendInteriorKnots (double from, double to, std::vector< double > &breakpoints) const
	Append the interior knots in (from, to), in the curve's [0, 1] parameter; none for a line or an arc.

double	uVariation (double from, double to) const
	An upper bound on how far u travels along the curve between from and to.

void	bsplineSampleRecursive (double t0, double t1, const Vec2 &p0, const Vec2 &p1, double flatnessSq, int depth, std::vector< Vec2 > &samples) const

const std::vector< Vec2 > &	bsplineSamples () const
	The flattened polyline in bsplineCache, computed here if the wire has not filled it.

Static Public Member Functions
static Curve2D	makeLine (const Vec2 &start, const Vec2 &end)

static Curve2D	makeArc (const Vec2 &arcCenter, double arcRadius, double arcStartAngle, double arcEndAngle)

static Curve2D	makeCircle (const Vec2 &arcCenter, double arcRadius, bool clockwise=false)
	Full circle as one arc curve (counter-clockwise unless clockwise is set).

static Curve2D	makeBSpline (int splineDegree, std::vector< Vec2 > splinePoles, std::vector< double > splineWeights, std::vector< double > splineKnots)

Public Attributes
CurveKind	kind = CurveKind::Line

Vec2	lineStart
	line: start point (unused for arcs)

Vec2	lineEnd
	line: end point (unused for arcs)

Vec2	center
	arc: circle centre (unused for lines)

double	radius = 0.
	arc: circle radius

double	startAngle = 0.
	arc: start angle [rad]

double	endAngle = 0.
	arc: end angle [rad] (sweep = endAngle - startAngle)

B-spline data (kind == BSpline): poles, optional weights and a clamped knot vector; the curve parameter runs on [0, 1]. @{
int	degree = 0

std::vector< Vec2 >	poles

std::vector< double >	weights

std::vector< double >	knots

std::vector< Vec2 >	bsplineCache
	The flattened on-curve polyline, both ends included; CurveWire::initialize fills it and reversing clears it.

Loop-canonical endpoints: the seam vertices the curve's neighbours agree on, substituted at the polyline's ends
Vec2	canonicalStart

Vec2	canonicalEnd

bool	hasCanonicalEndpoints = false

void	setCanonicalEndpoints (const Vec2 &start, const Vec2 &end)

Vec2	loopStart () const

Vec2	loopEnd () const

Detailed Description

One trimmed boundary curve in a surface's (u, v) domain: a line segment, a circular arc or a clamped (rational) B-spline.

Definition at line 1129 of file BoundedSurface.h.

Member Function Documentation

◆ angleInSweep()

bool o2::cad::surface::Curve2D::angleInSweep ( double angle ) const

inline

True if angle lies within the arc's angular sweep (accounting for direction and wrap).

Definition at line 1604 of file BoundedSurface.h.

◆ angleParameter()

double o2::cad::surface::Curve2D::angleParameter ( double angle ) const

inline

Map an angle known to lie within the sweep to a clamped parameter in [0, 1].

Definition at line 1617 of file BoundedSurface.h.

◆ appendInteriorKnots()

void o2::cad::surface::Curve2D::appendInteriorKnots	(	double	from,
		double	to,
		std::vector< double > &	breakpoints
	)		const

inline

Append the interior knots in (from, to), in the curve's [0, 1] parameter; none for a line or an arc.

Definition at line 1376 of file BoundedSurface.h.

◆ bsplineBandOrCrossings()

bool o2::cad::surface::Curve2D::bsplineBandOrCrossings	(	const Vec2 &	point,
		double	bandSq,
		int &	crossings
	)		const

inline

B-spline only: true if point is within sqrt(bandSq) of the polyline, else adds its rightward crossings. One walk of the polyline with the arithmetic of closestPoint and rightwardCrossings.

Definition at line 1808 of file BoundedSurface.h.

◆ bsplineBasis()

void o2::cad::surface::Curve2D::bsplineBasis	(	int	span,
		double	knotValue,
		std::vector< double > &	basis,
		std::vector< double > &	basisDeriv
	)		const

inline

Non-zero degree-p basis functions and first derivatives at knotValue in span (The NURBS Book, DersBasisFuns).

Definition at line 1266 of file BoundedSurface.h.

◆ bsplineEval()

void o2::cad::surface::Curve2D::bsplineEval	(	double	knotValue,
		Vec2 &	pointOut,
		Vec2 &	derivativeOut
	)		const

inline

Evaluate the (rational) B-spline point pointOut and its knot-parameter derivative derivativeOut at knot parameter knotValue.

Definition at line 1307 of file BoundedSurface.h.

◆ bsplineIsClamped()

bool o2::cad::surface::Curve2D::bsplineIsClamped ( ) const

inline

True when the knot vector is clamped, so the curve interpolates its first and last pole.

Definition at line 1218 of file BoundedSurface.h.

◆ bsplinePointAt()

Vec2 o2::cad::surface::Curve2D::bsplinePointAt ( double parameter ) const

inline

B-spline point at curve parameter parameter in [0, 1].

Definition at line 1335 of file BoundedSurface.h.

◆ bsplineRational()

bool o2::cad::surface::Curve2D::bsplineRational ( ) const

inline

True if the curve carries non-unit weights (a rational B-spline).

Definition at line 1231 of file BoundedSurface.h.

◆ bsplineSampleInto()

void o2::cad::surface::Curve2D::bsplineSampleInto	(	std::vector< Vec2 > &	samples,
		double	flatnessSq = `kBSplineFlatnessSq`,
		int	maxDepth = `16`
	)		const

inline

Adaptively sample the B-spline into an on-curve polyline, subdividing until each chord is flat to sqrt(flatnessSq).

Definition at line 1345 of file BoundedSurface.h.

◆ bsplineSampleRecursive()

void o2::cad::surface::Curve2D::bsplineSampleRecursive	(	double	t0,
		double	t1,
		const Vec2 &	p0,
		const Vec2 &	p1,
		double	flatnessSq,
		int	depth,
		std::vector< Vec2 > &	samples
	)		const

inline

Definition at line 1436 of file BoundedSurface.h.

◆ bsplineSamples()

const std::vector< Vec2 > & o2::cad::surface::Curve2D::bsplineSamples ( ) const

inline

The flattened polyline in bsplineCache, computed here if the wire has not filled it.

Definition at line 1464 of file BoundedSurface.h.

◆ bsplineSpan()

int o2::cad::surface::Curve2D::bsplineSpan ( double knotValue ) const

inline

Knot span index of parameter knotValue for the clamped knot vector.

Definition at line 1242 of file BoundedSurface.h.

◆ bsplineT0()

double o2::cad::surface::Curve2D::bsplineT0 ( ) const

inline

Definition at line 1214 of file BoundedSurface.h.

◆ bsplineT1()

double o2::cad::surface::Curve2D::bsplineT1 ( ) const

inline

Definition at line 1215 of file BoundedSurface.h.

◆ closestPoint()

Vec2 o2::cad::surface::Curve2D::closestPoint	(	const Vec2 &	point,
		double &	parameter
	)		const

inline

Closest point on the curve to point, returning the clamped parameter in parameter.

Definition at line 1684 of file BoundedSurface.h.

◆ derivativeAt()

Vec2 o2::cad::surface::Curve2D::derivativeAt ( double parameter ) const

inline

dC/dt at parameter in [0, 1], unnormalised; tangentAt() is it normalised.

Definition at line 1559 of file BoundedSurface.h.

◆ distanceSq()

double o2::cad::surface::Curve2D::distanceSq ( const Vec2 & point ) const

inline

Squared distance from point to the curve.

Definition at line 1757 of file BoundedSurface.h.

◆ endPoint()

Vec2 o2::cad::surface::Curve2D::endPoint ( ) const

inline

Definition at line 1547 of file BoundedSurface.h.

◆ extendBounds()

void o2::cad::surface::Curve2D::extendBounds	(	Vec2 &	lower,
		Vec2 &	upper
	)		const

inline

Accumulate this curve's exact extent into a parametric axis-aligned bounding box.

Definition at line 1629 of file BoundedSurface.h.

◆ extendTightBounds()

void o2::cad::surface::Curve2D::extendTightBounds	(	Vec2 &	lower,
		Vec2 &	upper
	)		const

inline

As extendBounds, measured on the curve: a B-spline contributes its sampled polyline, not its pole hull.

Definition at line 1649 of file BoundedSurface.h.

◆ includeAnalyticExtremes()

template<typename Include >

void o2::cad::surface::Curve2D::includeAnalyticExtremes ( const Include & include ) const

inline

Endpoints plus an arc's axis-extreme points inside the sweep: the exact extent of a line or an arc.

Definition at line 1668 of file BoundedSurface.h.

◆ isArc()

bool o2::cad::surface::Curve2D::isArc ( ) const

inline

Definition at line 1207 of file BoundedSurface.h.

◆ isBSpline()

bool o2::cad::surface::Curve2D::isBSpline ( ) const

inline

Definition at line 1208 of file BoundedSurface.h.

◆ loopEnd()

Vec2 o2::cad::surface::Curve2D::loopEnd ( ) const

inline

Definition at line 1164 of file BoundedSurface.h.

◆ loopStart()

Vec2 o2::cad::surface::Curve2D::loopStart ( ) const

inline

Where this curve begins and ends as far as the loop is concerned: the canonical seam vertex when a wire has fixed one, and the curve's own endpoint when it stands alone.

Definition at line 1163 of file BoundedSurface.h.

◆ makeArc()

static Curve2D o2::cad::surface::Curve2D::makeArc	(	const Vec2 &	arcCenter,
		double	arcRadius,
		double	arcStartAngle,
		double	arcEndAngle
	)

inlinestatic

Definition at line 1176 of file BoundedSurface.h.

◆ makeBSpline()

static Curve2D o2::cad::surface::Curve2D::makeBSpline	(	int	splineDegree,
		std::vector< Vec2 >	splinePoles,
		std::vector< double >	splineWeights,
		std::vector< double >	splineKnots
	)

inlinestatic

Clamped (rational) B-spline curve of degree splineDegree. splineWeights may be empty for a non-rational curve; splineKnots must be the clamped flat knot vector.

Definition at line 1195 of file BoundedSurface.h.

◆ makeCircle()

static Curve2D o2::cad::surface::Curve2D::makeCircle	(	const Vec2 &	arcCenter,
		double	arcRadius,
		bool	clockwise = `false`
	)

inlinestatic

Full circle as one arc curve (counter-clockwise unless clockwise is set).

Definition at line 1188 of file BoundedSurface.h.

◆ makeLine()

static Curve2D o2::cad::surface::Curve2D::makeLine	(	const Vec2 &	start,
		const Vec2 &	end
	)

inlinestatic

Definition at line 1167 of file BoundedSurface.h.

◆ pointAt()

Vec2 o2::cad::surface::Curve2D::pointAt ( double parameter ) const

inline

Point at curve parameter parameter in [0, 1] (0 at the start, 1 at the end).

Definition at line 1524 of file BoundedSurface.h.

◆ pointAtAngle()

Vec2 o2::cad::surface::Curve2D::pointAtAngle ( double angle ) const

inline

Definition at line 1518 of file BoundedSurface.h.

◆ representationTolerance()

double o2::cad::surface::Curve2D::representationTolerance ( ) const

inline

How far this curve's representation can sit from the curve, in parametric units: kBSplineFlatness for a B-spline, else 0.

Definition at line 1804 of file BoundedSurface.h.

◆ reverseInPlace()

void o2::cad::surface::Curve2D::reverseInPlace ( )

inline

Reverse the curve's direction in place (start <-> end), keeping the same geometric image.

Definition at line 1943 of file BoundedSurface.h.

◆ rightwardCrossings()

int o2::cad::surface::Curve2D::rightwardCrossings	(	const Vec2 &	point,
		const Vec2 &	canonicalStart,
		const Vec2 &	canonicalEnd
	)		const

inline

Rightward crossings of a horizontal ray from point, with the caller's canonical endpoints so that seams stay consistent.

Definition at line 1849 of file BoundedSurface.h.

◆ setCanonicalEndpoints()

void o2::cad::surface::Curve2D::setCanonicalEndpoints	(	const Vec2 &	start,
		const Vec2 &	end
	)

inline

Definition at line 1153 of file BoundedSurface.h.

◆ signedAreaContribution()

double o2::cad::surface::Curve2D::signedAreaContribution ( ) const

inline

Exact contribution of this directed curve to the enclosed signed area, i.e. (1/2) * integral of (u dv - v du) along the curve (Green's theorem).

Definition at line 1765 of file BoundedSurface.h.

◆ spansInteriorKnot()

bool o2::cad::surface::Curve2D::spansInteriorKnot	(	double	lowT,
		double	highT
	)		const

inline

Whether a knot lies strictly inside (lowT, highT); such an interval is never called flat.

Definition at line 1360 of file BoundedSurface.h.

◆ startPoint()

Vec2 o2::cad::surface::Curve2D::startPoint ( ) const

inline

Definition at line 1536 of file BoundedSurface.h.

◆ sweep()

double o2::cad::surface::Curve2D::sweep ( ) const

inline

Definition at line 1210 of file BoundedSurface.h.

◆ tangentAt()

Vec2 o2::cad::surface::Curve2D::tangentAt ( double parameter ) const

inline

Unit tangent at parameter parameter, pointing in the direction of increasing parameter.

Definition at line 1576 of file BoundedSurface.h.

◆ uVariation()

double o2::cad::surface::Curve2D::uVariation	(	double	from,
		double	to
	)		const

inline

An upper bound on how far u travels along the curve between from and to.

Definition at line 1397 of file BoundedSurface.h.

◆ valid()

bool o2::cad::surface::Curve2D::valid ( ) const

inline

Basic structural validity (finite data, positive radius for arcs, well-formed clamped knot vector for B-splines).

Definition at line 1480 of file BoundedSurface.h.

Member Data Documentation

◆ bsplineCache

std::vector<Vec2> o2::cad::surface::Curve2D::bsplineCache

mutable

The flattened on-curve polyline, both ends included; CurveWire::initialize fills it and reversing clears it.

Definition at line 1144 of file BoundedSurface.h.

◆ canonicalEnd

Vec2 o2::cad::surface::Curve2D::canonicalEnd

Definition at line 1150 of file BoundedSurface.h.

◆ canonicalStart

Vec2 o2::cad::surface::Curve2D::canonicalStart

Definition at line 1149 of file BoundedSurface.h.

◆ center

Vec2 o2::cad::surface::Curve2D::center

arc: circle centre (unused for lines)

Definition at line 1133 of file BoundedSurface.h.

◆ degree

int o2::cad::surface::Curve2D::degree = 0

Definition at line 1139 of file BoundedSurface.h.

◆ endAngle

double o2::cad::surface::Curve2D::endAngle = 0.

arc: end angle [rad] (sweep = endAngle - startAngle)

Definition at line 1136 of file BoundedSurface.h.

◆ hasCanonicalEndpoints

bool o2::cad::surface::Curve2D::hasCanonicalEndpoints = false

Definition at line 1151 of file BoundedSurface.h.

◆ kind

CurveKind o2::cad::surface::Curve2D::kind = CurveKind::Line

Definition at line 1130 of file BoundedSurface.h.

◆ knots

std::vector<double> o2::cad::surface::Curve2D::knots

Definition at line 1142 of file BoundedSurface.h.

◆ lineEnd

Vec2 o2::cad::surface::Curve2D::lineEnd

line: end point (unused for arcs)

Definition at line 1132 of file BoundedSurface.h.

◆ lineStart

Vec2 o2::cad::surface::Curve2D::lineStart

line: start point (unused for arcs)

Definition at line 1131 of file BoundedSurface.h.

◆ poles

std::vector<Vec2> o2::cad::surface::Curve2D::poles

Definition at line 1140 of file BoundedSurface.h.

◆ radius

double o2::cad::surface::Curve2D::radius = 0.

arc: circle radius

Definition at line 1134 of file BoundedSurface.h.

◆ startAngle

double o2::cad::surface::Curve2D::startAngle = 0.

arc: start angle [rad]

Definition at line 1135 of file BoundedSurface.h.

◆ weights

std::vector<double> o2::cad::surface::Curve2D::weights

Definition at line 1141 of file BoundedSurface.h.

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

/home/runner/work/AliceO2/AliceO2/Detectors/CADSupport/src/BoundedSurface.h

Public Member Functions

Static Public Member Functions

Public Attributes

Loop-canonical endpoints: the seam vertices the curve's neighbours agree on, substituted at the polyline's ends

Detailed Description

Member Function Documentation

◆ angleInSweep()

◆ angleParameter()

◆ appendInteriorKnots()

◆ bsplineBandOrCrossings()

◆ bsplineBasis()

◆ bsplineEval()

◆ bsplineIsClamped()

◆ bsplinePointAt()

◆ bsplineRational()

◆ bsplineSampleInto()

◆ bsplineSampleRecursive()

◆ bsplineSamples()

◆ bsplineSpan()

◆ bsplineT0()

◆ bsplineT1()

◆ closestPoint()

◆ derivativeAt()

◆ distanceSq()

◆ endPoint()

◆ extendBounds()

◆ extendTightBounds()

◆ includeAnalyticExtremes()

◆ isArc()

◆ isBSpline()

◆ loopEnd()

◆ loopStart()

◆ makeArc()

◆ makeBSpline()

◆ makeCircle()

◆ makeLine()

◆ pointAt()

◆ pointAtAngle()

◆ representationTolerance()

◆ reverseInPlace()

◆ rightwardCrossings()

◆ setCanonicalEndpoints()

◆ signedAreaContribution()

◆ spansInteriorKnot()

◆ startPoint()

◆ sweep()

◆ tangentAt()

◆ uVariation()

◆ valid()

Member Data Documentation

◆ bsplineCache

◆ canonicalEnd

◆ canonicalStart

◆ center

◆ degree

◆ endAngle

◆ hasCanonicalEndpoints

◆ kind

◆ knots

◆ lineEnd

◆ lineStart

◆ poles

◆ radius

◆ startAngle

◆ weights