Static Public Member Functions
static bool	LoS (const Vect3 &so, const Vect3 &si, double D, double H)

static bool	rightOfLine (const Vect2 &so, const Vect2 &vo, const Vect2 &si)

static int	rightOfLinePoints (const Vect2 &a, const Vect2 &b, const Vect2 &p)

static bool	collinear (const Vect3 &p0, const Vect3 &p1, const Vect3 &p2)

static bool	collinear (const Vect2 &p0, const Vect2 &p1, const Vect2 &p2)

static Vect2	midPoint (const Vect2 &p0, const Vect2 &p1)

static Vect3	midPoint (const Vect3 &p0, const Vect3 &p1)

static Vect3	interpolate (const Vect3 &v1, const Vect3 &v2, double f)

static Velocity	interpolateVelocity (const Velocity &v1, const Velocity &v2, double f)

static double	angle_between (const Vect2 &v1, const Vect2 &v2)

static double	angle_between (const Vect2 &v1, const Vect2 &v2, const Vect2 &v3)

static bool	divergentHorizGt (const Vect2 &s, const Vect2 &vo, const Vect2 &vi, double minRelSpeed)

static bool	divergentHorizGt (const Vect3 &s, const Vect3 &vo, const Vect3 &vi, double minRelSpeed)

static bool	divergent (const Vect2 &so, const Vect2 &vo, const Vect2 &si, const Vect2 &vi)

static bool	divergent (const Vect3 &so, const Velocity &vo, const Vect3 &si, const Velocity &vi)

static double	rateOfClosureHorizontal (const Vect3 &so, const Velocity &vo, const Vect3 &si, const Velocity &vi)

static double	rateOfClosureVertical (const Vect3 &so, const Velocity &vo, const Vect3 &si, const Velocity &vi)

static double	tau (const Vect3 &s, const Vect3 &vo, const Vect3 &vi)

static double	distAtTau (const Vect3 &s, const Vect3 &vo, const Vect3 &vi, bool futureOnly)

static std::pair< Vect3, double >	intersection (const Vect3 &so3, const Velocity &vo3, const Vect3 &si3, const Velocity &vi3)

static std::pair< Vect2, double >	intersection2D (const Vect2 &so, const Vect2 &vo, const Vect2 &si, const Vect2 &vi)

static double	distanceH (const Vect3 &soA, const Vect3 &soB)

static std::pair< Vect3, double >	intersectionAvgZ (const Vect3 &so1, const Vect3 &so2, double dto, const Vect3 &si1, const Vect3 &si2)

static std::pair< Vect2, double >	intersection2D (const Vect2 &so1, const Vect2 &so2, double dto, const Vect2 &si1, const Vect2 &si2)

static std::pair< Vect2, double >	intersectSegments (const Vect2 &so, const Vect2 &so2, const Vect2 &si, const Vect2 &si2)

static Vect3	closestPoint3 (const Vect3 &a, const Vect3 &b, const Vect3 &so)

static Vect3	closestPoint (const Vect3 &a, const Vect3 &b, const Vect3 &so)

static Vect2	closestPoint (const Vect2 &a, const Vect2 &b, const Vect2 &so)

static Vect3	closestPointOnSegment (const Vect3 &a, const Vect3 &b, const Vect3 &so)

static Vect2	closestPointOnSegment (const Vect2 &a, const Vect2 &b, const Vect2 &so)

static Vect3	closestPointOnSegment3 (const Vect3 &a, const Vect3 &b, const Vect3 &so)

static std::pair< Vect3, double >	closestPointOnSegment3_extended (const Vect3 &a, const Vect3 &b, const Vect3 &so)

static double	distanceToSegment (const Vect2 &a, const Vect2 &b, const Vect2 &so)

static double	timeOfIntersection (const Vect3 &so3, const Velocity &vo3, const Vect3 &si3, const Velocity &vi3)

static bool	behind (const Vect2 &x, const Vect2 &so, const Vect2 &vo)

static int	passingDirection (const Vect3 &so, const Velocity &vo, const Vect3 &si, const Velocity &vi)

static int	dirForBehind (const Vect2 &so, const Vect2 &vo, const Vect2 &si, const Vect2 &vi)

static int	dirForBehind (const Vect3 &so, const Velocity &vo, const Vect3 &si, const Velocity &vi)

static Vect3	parse (const std::string &s)

Member Function Documentation

◆ behind()

bool larcfm::VectFuns::behind	(	const Vect2 &	x,
		const Vect2 &	so,
		const Vect2 &	vo
	)

static

Returns true if x is "behind" so , that is, x is within the region behind the perpendicular line to vo through so.

Parameters

x	a position
so	aircraft position
vo	aircraft velocity

Returns: true, if x is behind so

Returns true if x is "behind" so , that is, x is within the region behind the perpendicular line to vo through so.

◆ closestPoint()

Vect2 larcfm::VectFuns::closestPoint	(	const Vect2 &	a,
		const Vect2 &	b,
		const Vect2 &	so
	)

static

Return the closest (horizontal) point along line a-b to point so EXPERIMENTAL

Parameters

a	a point to define a line
b	another point to define a line
so	a point

Returns: the closest point

◆ closestPoint3()

Vect3 larcfm::VectFuns::closestPoint3	(	const Vect3 &	a,
		const Vect3 &	b,
		const Vect3 &	so
	)

static

Return the closest point on the line a-b to point so as a 3D norm EXPERIMENTAL

Parameters

a	a point to define a line
b	another point to define a line
so	a point

Returns: the closest point

◆ distanceH()

double larcfm::VectFuns::distanceH	(	const Vect3 &	soA,
		const Vect3 &	soB
	)

static

Calculate the horizontal distance between two points.

Parameters

soA	point A
soB	point B

Returns: horizontal distance between points.

◆ distAtTau()

double larcfm::VectFuns::distAtTau	(	const Vect3 &	s,
		const Vect3 &	vo,
		const Vect3 &	vi,
		bool	futureOnly
	)

static

distance at time of closest approach

Parameters

s	relative position of aircraft
vo	velocity of ownship
vi	velocity of traffic
futureOnly	if true then in divergent cases use distance now

Returns: distance at time of closest approach

◆ divergent() [1/2]

bool larcfm::VectFuns::divergent	(	const Vect2 &	so,
		const Vect2 &	vo,
		const Vect2 &	si,
		const Vect2 &	vi
	)

static

Return if two aircraft in the given state are divergent in the horizontal plane

◆ divergent() [2/2]

bool larcfm::VectFuns::divergent	(	const Vect3 &	so,
		const Velocity &	vo,
		const Vect3 &	si,
		const Velocity &	vi
	)

static

Return if two aircraft in the given state are divergent in a 3D sense

Parameters

so	ownship position
vo	ownship velocity
si	intruder position
vi	intruder velocity

Returns: true, if divergent

◆ divergentHorizGt()

bool larcfm::VectFuns::divergentHorizGt	(	const Vect2 &	s,
		const Vect2 &	vo,
		const Vect2 &	vi,
		double	minRelSpeed
	)

static

determines if divergent and relative speed is greater than a specified minimum relative speed

Parameters

s	relative position of ownship with respect to traffic
vo	initial velocity of ownship
vi	initial velocity of traffic
minRelSpeed	the desired minimum relative speed

Returns: true iff divergent and relative speed is greater than a specified minimum relative speed

◆ intersection()

std::pair< Vect3, double > larcfm::VectFuns::intersection	(	const Vect3 &	so3,
		const Velocity &	vo3,
		const Vect3 &	si3,
		const Velocity &	vi3
	)

static

Computes 2D intersection point of two lines, but also finds z component (projected by time from line 1)

Parameters

s0	starting point of line 1
v0	direction vector for line 1
s1	starting point of line 2
v1	direction vector of line 2

Returns: Pair (2-dimensional point of intersection with 3D projection, relative time of intersection, relative to the so3) If the lines are parallel, this returns the pair (0,NaN).

◆ intersectionAvgZ()

std::pair< Vect3, double > larcfm::VectFuns::intersectionAvgZ	(	const Vect3 &	so1,
		const Vect3 &	so2,
		double	dto,
		const Vect3 &	si1,
		const Vect3 &	si2
	)

static

Computes 2D intersection point of two lines, but also finds z component as average of the closest end point of each line) This z-component is constrained to be within the z components of the defining points.

Parameters

so1	starting point of line o
so2	ending point of line o
si1	starting point of line i
vi2	ending point of line i

Returns: Pair (2-dimensional point of intersection, relative time of intersection, relative to the so1) This includes the average altitude between the endpoints closest to the point of intersection Note the intersection may be in the past (i.e. negative time) If the lines are parallel, this returns the pair (0,NaN).

◆ LoS()

bool larcfm::VectFuns::LoS	(	const Vect3 &	so,
		const Vect3 &	si,
		double	D,
		double	H
	)

static

Returns true if aircraft are in loss of separation at time 0.

Parameters

so	the relative position of the ownship aircraft
si	the relative position of the traffic aircraft
D	the minimum horizontal distance
H	the minimum vertical distance

Returns: true, if aircraft are in loss of separation

◆ passingDirection()

int larcfm::VectFuns::passingDirection	(	const Vect3 &	so,
		const Velocity &	vo,
		const Vect3 &	si,
		const Velocity &	vi
	)

static

Returns values indicating whether the ownship state will pass in front of or behind the intruder (from a horizontal perspective)

Parameters

so	ownship position
vo	ownship velocity
si	intruder position
vi	intruder velocity

Returns: 1 if ownship will pass in front (or collide, from a horizontal sense), -1 if ownship will pass behind, 0 if divergent or parallel

◆ rateOfClosureHorizontal()

double larcfm::VectFuns::rateOfClosureHorizontal	(	const Vect3 &	so,
		const Velocity &	vo,
		const Vect3 &	si,
		const Velocity &	vi
	)

static

Return the horizontal rate of closure of two aircraft in the given state

Parameters

so	position of first aircraft
vo	velocity of first aircraft
si	position of second aircraft
vi	velocity of second aircraft

Returns: rate of closure

◆ rateOfClosureVertical()

double larcfm::VectFuns::rateOfClosureVertical	(	const Vect3 &	so,
		const Velocity &	vo,
		const Vect3 &	si,
		const Velocity &	vi
	)

static

Return the vertical rate of closure of two aircraft in the given state

Parameters

so	position of first aircraft
vo	velocity of first aircraft
si	position of second aircraft
vi	velocity of second aircraft

Returns: rate of closure

◆ rightOfLine()

bool larcfm::VectFuns::rightOfLine	(	const Vect2 &	so,
		const Vect2 &	vo,
		const Vect2 &	si
	)

static

Returns true if si is on the right side of the line (so,vo)

Parameters

so	ownship position
vo	ownship velocity
si	traffic aircraft position

Returns: true if is to the right of line (so,vo)

◆ rightOfLinePoints()

int larcfm::VectFuns::rightOfLinePoints	(	const Vect2 &	a,
		const Vect2 &	b,
		const Vect2 &	p
	)

static

Return if point p is to the right or left of the line from A to B

Parameters

a	point A
b	point B
p	point P

Returns: 1 if to the right or collinear, -1 if to the left.

◆ tau()

double larcfm::VectFuns::tau	(	const Vect3 &	s,
		const Vect3 &	vo,
		const Vect3 &	vi
	)

static

time of closest approach, if parallel return Double.MAX_VALUE

Parameters

s	relative position of aircraft
vo	velocity of ownship
vi	velocity of traffic

Returns: time of closest approach (can be negative)

◆ timeOfIntersection()

double larcfm::VectFuns::timeOfIntersection	(	const Vect3 &	so3,
		const Velocity &	vo3,
		const Vect3 &	si3,
		const Velocity &	vi3
	)

static

Computes 2D intersection point of two infinite lines

Parameters

so3	starting point of line 1
vo3	direction vector for line 1
si3	starting point of line 2
vi3	direction vector of line 2

Returns: time the OWNSHIP (so3) will reach the point. Note that the intruder (si3) may have already passed this point. If the lines are parallel, this returns NaN.

Computes 2D intersection point of two lines, but also finds z component (projected by time from line 1)

Parameters

s0	starting point of line 1
v0	direction vector for line 1
s1	starting point of line 2
v1	direction vector of line 2

Returns: Pair (2-dimensional point of intersection with 3D projection, relative time of intersection, relative to the so3) If the lines are parallel, this returns the pair (0,NaN).

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

Modules/ACCoRD/inc/VectFuns.h
Modules/ACCoRD/src/VectFuns.cpp

Static Public Member Functions

Member Function Documentation

◆ behind()

◆ closestPoint()

◆ closestPoint3()

◆ distanceH()

◆ distAtTau()

◆ divergent() [1/2]

◆ divergent() [2/2]

◆ divergentHorizGt()

◆ intersection()

◆ intersectionAvgZ()

◆ LoS()

◆ passingDirection()

◆ rateOfClosureHorizontal()

◆ rateOfClosureVertical()

◆ rightOfLine()

◆ rightOfLinePoints()

◆ tau()

◆ timeOfIntersection()