Geom Namespace Reference

Classes
class	Eigen
	Given a matrix (ignoring the translation) this returns the eigen values and vectors. More...
class	Matrix
	The Matrix class. More...
class	Point
	Cartesian point. More...
class	Rotate
	Notionally an Geom::Matrix corresponding to rotation about the origin. More...
class	Scale
class	Translate

Typedefs
typedef double	Coord
	A "real" type with sufficient precision for coordinates. More...

Enumerations
enum	Dim2 { X =0, Y =1 }

Functions
Point	abs (Point const &b)
double	angle_between (Point const a, Point const b)
	compute the angle turning from a to b (signed). More...
void	assert_close (Matrix const &a, Matrix const &b)
double	atan2 (Point const p)
int	bezier_fit_cubic (Point bezier[], Point const data[], int len, double error)
int	bezier_fit_cubic_full (Point bezier[], int split_points[], Point const data[], int len, Point const &tHat1, Point const &tHat2, double error, unsigned max_beziers)
int	bezier_fit_cubic_r (Point bezier[], Point const data[], int len, double error, unsigned max_beziers)
Point	bezier_pt (unsigned degree, Point const V[], double t)
Coord	cross (Point const &a, Point const &b)
	Defined as dot(a, b.cw()). More...
template<typename iterator >
static void	cubic_bezier_poly_coeff (iterator b, Point *pc)
Point	darray_left_tangent (Point const d[], unsigned const len)
Point	darray_left_tangent (Point const d[], unsigned const len, double const tolerance_sq)
Point	darray_right_tangent (Point const d[], unsigned const length, double const tolerance_sq)
Coord	dist_sq (Point const &a, Point const &b)
	compute the square of the distance between points a and b. More...
Coord	distance (Point const &a, Point const &b)
	compute the euclidean distance between points a and b. More...
Coord	dot (Point const &a, Point const &b)
	compute the dot product (inner product) between the vectors a and b. More...
Matrix	elliptic_quadratic_form (Matrix const &m)
	Given a matrix m such that unit_circle = m*x, this returns the quadratic form x*A*x = 1. More...
double	expansion (Matrix const &m)
Matrix	from_basis (const Point x_basis, const Point y_basis, const Point offset=Point(0, 0))
Matrix	identity ()
bool	is_unit_vector (Point const &p)
bool	is_zero (Point const &p)
Coord	L1 (Point const &p)
Coord	L2 (Point const &p)
	Compute the L2, or euclidean, norm of p. More...
Coord	L2sq (Point const &p)
	Compute the square of L2 norm of p. More...
Point	Lerp (double const t, Point const a, Point const b)
	Given two points and a parameter t [0, 1], return a point proportionally from a to b by t. More...
double	LInfty (Point const &p)
bool	matrix_equalp (Matrix const &m0, Matrix const &m1, Geom::Coord const epsilon)
void	matrix_print (const char *say, Matrix const &m)
bool	operator!= (Matrix const &a, Matrix const &b)
bool	operator!= (Point const &a, Point const &b)
Matrix	operator* (Scale const &s, Translate const &t)
Matrix	operator* (Scale const &s, Matrix const &m)
Point	operator* (Point const &v, Translate const &t)
Matrix	operator* (Rotate const &a, Matrix const &b)
Translate	operator* (Translate const &a, Translate const &b)
Matrix	operator* (Translate const &t, Scale const &s)
Matrix	operator* (Translate const &t, Rotate const &r)
Point	operator* (Point const &p, Scale const &s)
Matrix	operator* (Translate const &t, Matrix const &m)
Scale	operator* (Scale const &a, Scale const &b)
Matrix	operator* (Matrix const &m, Translate const &t)
Matrix	operator* (Matrix const &m, Scale const &s)
Matrix	operator* (Matrix const &m, Rotate const &r)
Point	operator* (Point const &v, Rotate const &r)
Rotate	operator* (Rotate const &a, Rotate const &b)
Point	operator* (double const s, Point const &p)
Point	operator* (Point const &p, double const s)
Matrix	operator* (Matrix const &a, Matrix const &b)
Point	operator* (Point const &v, Matrix const &m)
Point	operator+ (Point const &a, Point const &b)
Point	operator- (Point const &a, Point const &b)
Point	operator- (Point const &a)
Point	operator/ (Point const &v, Translate const &t)
Translate	operator/ (Translate const &a, Translate const &b)
Matrix	operator/ (Translate const &t, Scale const &s)
Matrix	operator/ (Translate const &t, Rotate const &r)
Point	operator/ (Point const &p, Scale const &s)
Scale	operator/ (Scale const &a, Scale const &b)
Matrix	operator/ (Matrix const &m, Scale const &s)
Matrix	operator/ (Matrix const &a, Matrix const &b)
Point	operator/ (Point const &v, Rotate const &r)
Rotate	operator/ (Rotate const &a, Rotate const &b)
Point	operator/ (Point const &p, double const s)
Point	operator/ (double const s, Point const &p)
Point	operator/ (Point const &p, Matrix const &m)
std::ostream &	operator<< (std::ostream &out_file, const Geom::Point &in_pnt)
	A function to print out the Point. More...
std::ostream &	operator<< (std::ostream &out_file, const Geom::Matrix &m)
	A function to print out the Matrix (for debugging) More...
bool	operator<= (Point const &a, Point const &b)
	This is a lexicographical ordering for points. More...
bool	operator== (Matrix const &a, Matrix const &b)
bool	operator== (Point const &a, Point const &b)
Point	operator^ (Point const &a, Point const &b)
	This is a rotation (sort of). More...
bool	point_equalp (Point const &a, Point const &b, double const eps)
Point	rot90 (Point const &p)
	Returns p * Geom::rotate_degrees(90), but more efficient. More...
bool	rotate_equalp (Geom::Rotate const &a, Geom::Rotate const &b, double const eps)
Translate	to_translate (Matrix const &m)
bool	transform_equalp (Matrix const &m0, Matrix const &m1, Geom::Coord const epsilon)
bool	translate_equalp (Matrix const &m0, Matrix const &m1, Geom::Coord const epsilon)
Point	unit_vector (Point const &a)
Matrix	without_translation (Matrix const &m)

Typedef Documentation

typedef double Geom::Coord

A "real" type with sufficient precision for coordinates.

You may safely assume that double (or even float) provides enough precision for storing on-canvas points, and hence that double provides enough precision for dot products of differences of on-canvas points.

Enumeration Type Documentation

enum Geom::Dim2

Enumerator
X
Y

Function Documentation

Point Geom::abs

(

Point const &

b

)

double Geom::angle_between	(	Point const	a,
		Point const	b
	)

compute the angle turning from a to b (signed).

void Geom::assert_close	(	Matrix const &	a,
		Matrix const &	b
	)

double Geom::atan2

(

Point const

p

)

int Geom::bezier_fit_cubic	(	Point	bezier[],
		Point const	data[],
		int	len,
		double	error
	)

int Geom::bezier_fit_cubic_full	(	Point	bezier[],
		int	split_points[],
		Point const	data[],
		int	len,
		Point const &	tHat1,
		Point const &	tHat2,
		double	error,
		unsigned	max_beziers
	)

int Geom::bezier_fit_cubic_r	(	Point	bezier[],
		Point const	data[],
		int	len,
		double	error,
		unsigned	max_beziers
	)

Point Geom::bezier_pt	(	unsigned	degree,
		Point const	V[],
		double	t
	)

Coord Geom::cross	(	Point const &	a,
		Point const &	b
	)

Defined as dot(a, b.cw()).

template<typename iterator >

static void Geom::cubic_bezier_poly_coeff ( iterator  b, Point *  pc  )

static

Point Geom::darray_left_tangent	(	Point const	d[],
		unsigned const	len
	)

Point Geom::darray_left_tangent	(	Point const	d[],
		unsigned const	len,
		double const	tolerance_sq
	)

Point Geom::darray_right_tangent	(	Point const	d[],
		unsigned const	length,
		double const	tolerance_sq
	)

Coord Geom::dist_sq	(	Point const &	a,
		Point const &	b
	)

compute the square of the distance between points a and b.

Coord Geom::distance	(	Point const &	a,
		Point const &	b
	)

compute the euclidean distance between points a and b.

XXX: hypot safer/faster?

Coord Geom::dot	(	Point const &	a,
		Point const &	b
	)

compute the dot product (inner product) between the vectors a and b.

Matrix Geom::elliptic_quadratic_form

(

Matrix const &

m

)

Given a matrix m such that unit_circle = m*x, this returns the quadratic form x*A*x = 1.

double Geom::expansion

(

Matrix const &

m

)

Matrix Geom::from_basis	(	const Point	x_basis,
		const Point	y_basis,
		const Point	offset = Point(0, 0)
	)

Matrix Geom::identity

(

)

bool Geom::is_unit_vector

(

Point const &

p

)

bool Geom::is_zero

(

Point const &

p

)

Coord Geom::L1

(

Point const &

p

)

Coord Geom::L2

(

Point const &

p

)

Compute the L2, or euclidean, norm of p.

Coord Geom::L2sq

(

Point const &

p

)

Compute the square of L2 norm of p.

Warning: this can overflow where L2 won't.

Point Geom::Lerp	(	double const	t,
		Point const	a,
		Point const	b
	)

Given two points and a parameter t [0, 1], return a point proportionally from a to b by t.

Akin to 1 degree bezier.

double Geom::LInfty

(

Point const &

p

)

bool Geom::matrix_equalp	(	Matrix const &	m0,
		Matrix const &	m1,
		Geom::Coord const	epsilon
	)

void Geom::matrix_print	(	const char *	say,
		Matrix const &	m
	)

bool Geom::operator!=	(	Matrix const &	a,
		Matrix const &	b
	)

bool Geom::operator!=	(	Point const &	a,
		Point const &	b
	)

Matrix Geom::operator*	(	Scale const &	s,
		Translate const &	t
	)

Matrix Geom::operator*	(	Scale const &	s,
		Matrix const &	m
	)

Point Geom::operator*	(	Point const &	v,
		Translate const &	t
	)

Matrix Geom::operator*	(	Rotate const &	a,
		Matrix const &	b
	)

Translate Geom::operator*	(	Translate const &	a,
		Translate const &	b
	)

Matrix Geom::operator*	(	Translate const &	t,
		Scale const &	s
	)

Matrix Geom::operator*	(	Translate const &	t,
		Rotate const &	r
	)

Point Geom::operator*	(	Point const &	p,
		Scale const &	s
	)

Matrix Geom::operator*	(	Translate const &	t,
		Matrix const &	m
	)

Scale Geom::operator*	(	Scale const &	a,
		Scale const &	b
	)

Matrix Geom::operator*	(	Matrix const &	m,
		Translate const &	t
	)

Matrix Geom::operator*	(	Matrix const &	m,
		Scale const &	s
	)

Matrix Geom::operator*	(	Matrix const &	m,
		Rotate const &	r
	)

Point Geom::operator*	(	Point const &	v,
		Rotate const &	r
	)

Rotate Geom::operator*	(	Rotate const &	a,
		Rotate const &	b
	)

Point Geom::operator*	(	double const	s,
		Point const &	p
	)

Point Geom::operator*	(	Point const &	p,
		double const	s
	)

Matrix Geom::operator*	(	Matrix const &	a,
		Matrix const &	b
	)

Point Geom::operator*	(	Point const &	v,
		Matrix const &	m
	)

Point Geom::operator+	(	Point const &	a,
		Point const &	b
	)

Point Geom::operator-	(	Point const &	a,
		Point const &	b
	)

Point Geom::operator-

(

Point const &

a

)

Point Geom::operator/	(	Point const &	v,
		Translate const &	t
	)

Translate Geom::operator/	(	Translate const &	a,
		Translate const &	b
	)

Matrix Geom::operator/	(	Translate const &	t,
		Scale const &	s
	)

Matrix Geom::operator/	(	Translate const &	t,
		Rotate const &	r
	)

Point Geom::operator/	(	Point const &	p,
		Scale const &	s
	)

Scale Geom::operator/	(	Scale const &	a,
		Scale const &	b
	)

Matrix Geom::operator/	(	Matrix const &	m,
		Scale const &	s
	)

Matrix Geom::operator/	(	Matrix const &	a,
		Matrix const &	b
	)

Point Geom::operator/	(	Point const &	v,
		Rotate const &	r
	)

Rotate Geom::operator/	(	Rotate const &	a,
		Rotate const &	b
	)

Point Geom::operator/	(	Point const &	p,
		double const	s
	)

Point Geom::operator/	(	double const	s,
		Point const &	p
	)

Point Geom::operator/	(	Point const &	p,
		Matrix const &	m
	)

std::ostream& Geom::operator<<	(	std::ostream &	out_file,
		const Geom::Point &	in_pnt
	)

A function to print out the Point.

It just prints out the coords on the given output stream

std::ostream& Geom::operator<<	(	std::ostream &	out_file,
		const Geom::Matrix &	m
	)

A function to print out the Matrix (for debugging)

bool Geom::operator<=	(	Point const &	a,
		Point const &	b
	)

This is a lexicographical ordering for points.

It is remarkably useful for sweepline algorithms

bool Geom::operator==	(	Matrix const &	a,
		Matrix const &	b
	)

bool Geom::operator==	(	Point const &	a,
		Point const &	b
	)

Point Geom::operator^	(	Point const &	a,
		Point const &	b
	)

This is a rotation (sort of).

bool Geom::point_equalp	(	Point const &	a,
		Point const &	b,
		double const	eps
	)

Point Geom::rot90

(

Point const &

p

)

Returns p * Geom::rotate_degrees(90), but more efficient.

Angle direction in Inkscape code: If you use the traditional mathematics convention that y increases upwards, then positive angles are anticlockwise as per the mathematics convention. If you take the common non-mathematical convention that y increases downwards, then positive angles are clockwise, as is common outside of mathematics.

There is no rot_neg90 function: use -rot90(p) instead.

bool Geom::rotate_equalp	(	Geom::Rotate const &	a,
		Geom::Rotate const &	b,
		double const	eps
	)

Translate Geom::to_translate

(

Matrix const &

m

)

bool Geom::transform_equalp	(	Matrix const &	m0,
		Matrix const &	m1,
		Geom::Coord const	epsilon
	)

bool Geom::translate_equalp	(	Matrix const &	m0,
		Matrix const &	m1,
		Geom::Coord const	epsilon
	)

Point Geom::unit_vector

(

Point const &

a

)

Matrix Geom::without_translation

(

Matrix const &

m

)