Detailed Description

definitions and functions for optimal numerical precision.

The functions in namespace frechet::numeric are meant to be used transparently with different floating point types.

In particular, the template functions can be used with 'double' precision, with 'long double' precision, and even with 'quad' precision (though quad types are currently not used).

Functions
template<typename Number >
Number	sq (const Number &x)
	square function template for arbitrary number types More...

template<typename Float >
Float	sqrt (const Float &x)
	square-root function template for floating point types More...

template<>
double	sqrt (const double &x)
	default sqrt() specialisation using the run-time libraries More...

template<>
long double	sqrt (const long double &x)
	sqrt() specialisation for "long double" More...

template<typename Number >
Number	abs (const Number &x)
	abs() function template for arbitrary numerical types More...

double	round_up (double x, int ulps=1)
	rounding function with 'units in the last place' Roughly speaking, a ulp is the smallest representable floating point value. More...

template<typename Float >
Float	euclidean_distance_sq (const Float &px, const Float &py, const Float &qx, const Float &qy)
	euclidean distance function template for arbitrary floating point types More...

template<typename Float >
Float	euclidean_distance (const Float &px, const Float &py, const Float &qx, const Float &qy)
	euclidean distance function template for arbitrary floating point types More...

template<typename Float >
Float	euclidean_distance (const Point &p, const Point &q)
	euclidean distance function template for arbitrary floating point types More...

template<typename Float >
Float	euclidean_distance_sq (const Point &p, const Point &q)
	euclidean distance function template for arbitrary floating point types More...

template<typename Float >
Float	euclidean_segment_distance (const Float &ax, const Float &ay, const Float &bx, const Float &by, const Float &px, const Float &py)
	Euclidean Distance between a point and a segment; function template for arbitrary floating point types. More...

template<typename Float >
Float	euclidean_segment_distance (const QLineF &s, const Point &p)
	Euclidean Distance between a point and a segment; function template for arbitrary floating point types. More...

double	min (double a, double b)
	minimum function with checks for NAN More...

double	max (double a, double b)
	maximum function with checks for NAN More...

int	lower_floor (double x, int min=0)
	floor function with lower limit More...

int	compare (double a, double b)
	comparator function More...

Point	normalized (Point p)
	normalize a vector to unit length More...

Point	intersection (Point p1, Point p2, Point p3, Point p4)
	compute the intersection of two lines More...

Point	between (Point p, Point q, double w)
	compute a point on a line segment More...

double	segment_length (const Curve &c, int i)
	compute the length of a polygon segment More...

double	max_euclidean_distance (const Curve &P, const Curve &Q)
	compute the maximum distance between two polygons This value serves as an upper bound for the Frechet Distance between polyongs. More...

Variables
static const constexpr double	double_eps = std::numeric_limits<double>::epsilon()
	smallest double value More...

Function Documentation

◆ abs()

template<typename Number >

Number frechet::numeric::abs ( const Number & x )

inline

abs() function template for arbitrary numerical types

Parameters

x a number

Template Parameters

Number a number type (like int,double,long double,...)

Returns: abs(x)

Definition at line 91 of file numeric.h.

◆ between()

Point frechet::numeric::between	(	Point	p,
		Point	q,
		double	w
	)

inline

compute a point on a line segment

Parameters

p	an endppoint of a line segment
q	the second endppoint of the line segment
w	distance from p (w in [0,1])

Returns: the point on the line segment given by the distance w. Returns p, if w==0. Return q, if w==1. Returns a point between p and q, if 0 < w < 1.

Definition at line 295 of file numeric.h.

◆ compare()

int frechet::numeric::compare	(	double	a,
		double	b
	)

inline

comparator function

Parameters

a	a number
b	a number

Returns: +1 if (a>b); -1 if (a<b); 0 if (a==b)

Definition at line 254 of file numeric.h.

◆ euclidean_distance() [1/2]

template<typename Float >

Float frechet::numeric::euclidean_distance	(	const Float &	px,
		const Float &	py,
		const Float &	qx,
		const Float &	qy
	)

inline

euclidean distance function template for arbitrary floating point types

Parameters

px	x-coordinate of first point
py	y-coordinate of first point
qx	x-coordinate of second point
qy	y-coordinate of second point

Template Parameters

Float a floating point type (float,double,long double,...)

Returns: the euclidean distance between p and q

Definition at line 143 of file numeric.h.

◆ euclidean_distance() [2/2]

template<typename Float >

Float frechet::numeric::euclidean_distance	(	const Point &	p,
		const Point &	q
	)

inline

euclidean distance function template for arbitrary floating point types

Parameters

p	the first point
q	the second point

Template Parameters

Float a floating point type (float,double,long double,...)

Returns: the euclidean distance between p and q

Definition at line 158 of file numeric.h.

◆ euclidean_distance_sq() [1/2]

template<typename Float >

Float frechet::numeric::euclidean_distance_sq	(	const Float &	px,
		const Float &	py,
		const Float &	qx,
		const Float &	qy
	)

inline

euclidean distance function template for arbitrary floating point types

Parameters

px	x-coordinate of first point
py	y-coordinate of first point
qx	x-coordinate of second point
qy	y-coordinate of second point

Template Parameters

Float a floating point type (float,double,long double,...)

Returns: the square of the euclidean distance

Definition at line 126 of file numeric.h.

◆ euclidean_distance_sq() [2/2]

template<typename Float >

Float frechet::numeric::euclidean_distance_sq	(	const Point &	p,
		const Point &	q
	)

inline

euclidean distance function template for arbitrary floating point types

Parameters

p	the first point
q	the second point

Template Parameters

Float a floating point type (float,double,long double,...)

Returns: the squared euclidean distance between p and q

Definition at line 171 of file numeric.h.

◆ euclidean_segment_distance() [1/2]

template<typename Float >

Float frechet::numeric::euclidean_segment_distance	(	const Float &	ax,
		const Float &	ay,
		const Float &	bx,
		const Float &	by,
		const Float &	px,
		const Float &	py
	)

inline

Euclidean Distance between a point and a segment; function template for arbitrary floating point types.

Parameters

ax	an endpoint of a line segment
ay	an endpoint of a line segment
bx	the second endpoint of a line segment
by	the second endpoint of a line segment
px	a point
py	a point

Template Parameters

Float a floating point type (float,double,long double,...)

Returns: the euclidean distance between p and the segment [ab]

Definition at line 189 of file numeric.h.

◆ euclidean_segment_distance() [2/2]

template<typename Float >

Float frechet::numeric::euclidean_segment_distance	(	const QLineF &	s,
		const Point &	p
	)

inline

Euclidean Distance between a point and a segment; function template for arbitrary floating point types.

Parameters

s	a line segment
p	a point

Template Parameters

Float a floating point type (float,double,long double,...)

Returns: the euclidean distance between p and the segment

Definition at line 208 of file numeric.h.

◆ intersection()

Point frechet::numeric::intersection	(	Point	p1,
		Point	p2,
		Point	p3,
		Point	p4
	)

inline

compute the intersection of two lines

Parameters

p1	a point on the first line
p2	another point of the first line
p3	a point on the second line
p4	another point of the second line

Returns: the intersection of both lines, or NAN if they do not intersect

Definition at line 278 of file numeric.h.

◆ lower_floor()

int frechet::numeric::lower_floor	(	double	x,
		int	min = `0`
	)

inline

floor function with lower limit

Parameters

x	a number
min	the minimum return value

Returns: the largest integer properly smaller than x and >= min

Definition at line 243 of file numeric.h.

◆ max()

double frechet::numeric::max	(	double	a,
		double	b
	)

inline

maximum function with checks for NAN

Parameters

a	a floating point value, may be NAN
b	a floating point value, may be NAN

Returns: the maximum of a and b

Definition at line 233 of file numeric.h.

◆ max_euclidean_distance()

double frechet::numeric::max_euclidean_distance	(	const Curve &	P,
		const Curve &	Q
	)

inline

compute the maximum distance between two polygons This value serves as an upper bound for the Frechet Distance between polyongs.

Parameters

P	a polygon
Q	another polygon

Returns: maximum distance between two vertexes of the polygons

Definition at line 318 of file numeric.h.

◆ min()

double frechet::numeric::min	(	double	a,
		double	b
	)

inline

minimum function with checks for NAN

Parameters

a	a floating point value, may be NAN
b	a floating point value, may be NAN

Returns: the minimum of a and b

Definition at line 222 of file numeric.h.

◆ normalized()

Point frechet::numeric::normalized ( Point p )

inline

normalize a vector to unit length

Parameters

p a point

Returns: vector scaled to unit length

Definition at line 265 of file numeric.h.

◆ round_up()

double frechet::numeric::round_up	(	double	x,
		int	ulps = `1`
	)

inline

rounding function with 'units in the last place' Roughly speaking, a ulp is the smallest representable floating point value.

Parameters

x	a value to be rounded
ulps	number of units in the last place to round up

Returns: x rounded upwards by ulps

Definition at line 112 of file numeric.h.

◆ segment_length()

double frechet::numeric::segment_length	(	const Curve &	c,
		int	i
	)

inline

compute the length of a polygon segment

Parameters

c	a polygon
i	index of segment

Returns: euclidean length of the i-th polygon segment

Definition at line 306 of file numeric.h.

◆ sq()

template<typename Number >

Number frechet::numeric::sq ( const Number & x )

inline

square function template for arbitrary number types

Parameters

x a number

Template Parameters

Number a number type (like int,double,long double,...)

Returns: x*x

Definition at line 61 of file numeric.h.

◆ sqrt() [1/3]

template<typename Float >

Float frechet::numeric::sqrt ( const Float & x )

inline

square-root function template for floating point types

Parameters

x a number

Template Parameters

Float a floating point type (like double,long double,...)

Returns: sqrt(x)

◆ sqrt() [2/3]

template<>

double frechet::numeric::sqrt ( const double & x )

inline

default sqrt() specialisation using the run-time libraries

Definition at line 76 of file numeric.h.

◆ sqrt() [3/3]

template<>

long double frechet::numeric::sqrt ( const long double & x )

inline

sqrt() specialisation for "long double"

Definition at line 82 of file numeric.h.

Variable Documentation

◆ double_eps

const constexpr double frechet::numeric::double_eps = std::numeric_limits<double>::epsilon()

static

smallest double value

Definition at line 52 of file numeric.h.

Detailed Description

Functions

Variables

Function Documentation

◆ abs()

◆ between()

◆ compare()

◆ euclidean_distance() [1/2]

◆ euclidean_distance() [2/2]

◆ euclidean_distance_sq() [1/2]

◆ euclidean_distance_sq() [2/2]

◆ euclidean_segment_distance() [1/2]

◆ euclidean_segment_distance() [2/2]

◆ intersection()

◆ lower_floor()

◆ max()

◆ max_euclidean_distance()

◆ min()

◆ normalized()

◆ round_up()

◆ segment_length()

◆ sq()

◆ sqrt() [1/3]

◆ sqrt() [2/3]

◆ sqrt() [3/3]

Variable Documentation

◆ double_eps