2D vector with the usual linear algebra: dot product, determinant, projection, rotation, angles. More...

#include <MathClasses.h>

Public Member Functions
	Vector2D ()
	Zero vector.
	Vector2D (double x, double y)
	From components.
virtual	~Vector2D ()
double	operator[] (int n) const
	Component access: 0=x, 1=y.
bool	operator== (const Vector2D &v) const
	Component equality.
Vector2D	operator- (const Vector2D &v) const
	Difference.
Vector2D	operator+ (const Vector2D &v) const
	Sum.
double	operator* (const Vector2D &v) const
	Dot product.
Vector2D	operator- (double a) const
	Subtract scalar from each component.
Vector2D	operator+ (double a) const
	Add scalar to each component.
Vector2D	operator* (double a) const
	Scale.
const Vector2D &	operator-= (const Vector2D &v)
	In-place subtract.
const Vector2D &	operator+= (const Vector2D &v)
	In-place add.
const Vector2D &	operator-= (double a)
	In-place scalar subtract.
const Vector2D &	operator+= (double a)
	In-place scalar add.
const Vector2D &	operator*= (double a)
	In-place scale.
double	getX () const
double	getY () const
bool	set (const PointFloat &p1, const PointFloat &p2)
	Set as p2-p1.
bool	set (double x1, double y1, double x2, double y2)
	Set as (x2-x1, y2-y1).
bool	set (double x, double y)
	Set components.
bool	setX (double v)
	Set x.
bool	setY (double v)
	Set y.
bool	setLength (double l)
	Rescale to length `l`, keeping direction.
bool	makeUnitVector ()
	Normalize in place.
double	length () const
double	det (const Vector2D &v) const
	2D cross product / determinant (xv.y - yv.x); sign gives turn direction.
bool	isOrthogonalWith (const Vector2D &v) const
bool	isParallelWith (const Vector2D &v) const
Vector2D	getProjectionOn (const Vector2D &v) const
Vector2D	getUnitVector () const
Vector2D	getOrthogonalVector () const
double	getAngle (const Vector2D &v) const
	Unsigned angle to `v` via acos of the normalized dot product.
double	getArea (const Vector2D &v) const
Vector2D	rotate (double angle)
	Rotated copy; this vector is unchanged.
bool	rotateIt (double angle)
	Rotate in place by `angle` radians (same convention as rotate()).
std::string	print ()
	Human-readable representation for debugging.

Public Attributes
double	x
	X component.
double	y
	Y component.

Detailed Description

2D vector with the usual linear algebra: dot product, determinant, projection, rotation, angles.

operator* between vectors is the dot product; use det() for the 2D cross product. Angles are always radians. Most operations return a new vector; the *It / make* / set* variants modify in place. Note that in the screen coordinate system used by Box/Bitmap (y down), a mathematically counter-clockwise rotation appears clockwise on screen.

using namespace cmlabs;
Vector2D v(3, 4);
double len = v.length();               // 5
Vector2D u = v.getUnitVector();        // (0.6, 0.8); v unchanged
v.rotateIt(M_PI / 2);                  // in place: (3,4) -> (-4,3)
Vector2D w(1, 0);
double dot  = v * w;                   // dot product
double turn = w.det(v);                // sign gives turn direction
double ang  = w.getAngle(v);           // unsigned angle in [0, pi]
Vector2D p  = v.getProjectionOn(w);    // component of v along w

Definition at line 656 of file MathClasses.h.

Constructor & Destructor Documentation

◆ Vector2D() [1/2]

cmlabs::Vector2D::Vector2D ( )

Zero vector.

Definition at line 924 of file MathClasses.cpp.

References x, and y.

Referenced by det(), getAngle(), getArea(), getOrthogonalVector(), getProjectionOn(), getUnitVector(), isOrthogonalWith(), isParallelWith(), operator*(), operator*(), operator*=(), operator+(), operator+(), operator+=(), operator+=(), operator-(), operator-(), operator-=(), operator-=(), operator==(), and rotate().

◆ Vector2D() [2/2]

cmlabs::Vector2D::Vector2D	(	double	x,
		double	y )

From components.

Definition at line 925 of file MathClasses.cpp.

References x, and y.

◆ ~Vector2D()

cmlabs::Vector2D::~Vector2D ( )

virtual

Definition at line 926 of file MathClasses.cpp.

Member Function Documentation

◆ det()

double cmlabs::Vector2D::det ( const Vector2D & v ) const

2D cross product / determinant (x*v.y - y*v.x); sign gives turn direction.

Definition at line 1046 of file MathClasses.cpp.

References Vector2D(), x, and y.

Referenced by getArea(), isParallelWith(), and cmlabs::MathClasses_UnitTest().

◆ getAngle()

double cmlabs::Vector2D::getAngle ( const Vector2D & v ) const

Unsigned angle to v via acos of the normalized dot product.

Returns: Radians in [0, pi]; 0 when either vector is zero.

Note: Sign/turn direction is lost; combine with det() to recover it.

Definition at line 1098 of file MathClasses.cpp.

References length(), and Vector2D().

◆ getArea()

double cmlabs::Vector2D::getArea ( const Vector2D & v ) const

Returns: Area of the parallelogram spanned with v (|det|).

Definition at line 1105 of file MathClasses.cpp.

References det(), and Vector2D().

◆ getOrthogonalVector()

Vector2D cmlabs::Vector2D::getOrthogonalVector ( ) const

Returns: Vector rotated 90 degrees.

Definition at line 1094 of file MathClasses.cpp.

References Vector2D(), x, and y.

Referenced by cmlabs::MathClasses_UnitTest().

◆ getProjectionOn()

Vector2D cmlabs::Vector2D::getProjectionOn ( const Vector2D & v ) const

Returns: Orthogonal projection of this vector onto v.

Definition at line 1058 of file MathClasses.cpp.

References getUnitVector(), and Vector2D().

Referenced by cmlabs::MathClasses_UnitTest().

◆ getUnitVector()

Vector2D cmlabs::Vector2D::getUnitVector ( ) const

Returns: Normalized copy.

Definition at line 1067 of file MathClasses.cpp.

References length(), Vector2D(), x, and y.

Referenced by getProjectionOn(), and cmlabs::MathClasses_UnitTest().

◆ getX()

double cmlabs::Vector2D::getX ( ) const

Returns: x.

Definition at line 1015 of file MathClasses.cpp.

References x.

◆ getY()

double cmlabs::Vector2D::getY ( ) const

Returns: y.

Definition at line 1016 of file MathClasses.cpp.

References y.

◆ isOrthogonalWith()

bool cmlabs::Vector2D::isOrthogonalWith ( const Vector2D & v ) const

Returns: true when the dot product is (approximately) zero.

Definition at line 1050 of file MathClasses.cpp.

References Vector2D().

◆ isParallelWith()

bool cmlabs::Vector2D::isParallelWith ( const Vector2D & v ) const

Returns: true when det() is (approximately) zero.

Definition at line 1054 of file MathClasses.cpp.

References det(), and Vector2D().

◆ length()

double cmlabs::Vector2D::length ( ) const

Returns: Euclidean length.

Definition at line 1042 of file MathClasses.cpp.

References x, and y.

Referenced by getAngle(), getUnitVector(), cmlabs::MathClasses_UnitTest(), and setLength().

◆ makeUnitVector()

bool cmlabs::Vector2D::makeUnitVector ( )

Normalize in place.

Returns: false for the zero vector.

Definition at line 1063 of file MathClasses.cpp.

References setLength().

Referenced by cmlabs::MathClasses_UnitTest().

◆ operator*() [1/2]

double cmlabs::Vector2D::operator* ( const Vector2D & v ) const

Dot product.

Definition at line 958 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator*() [2/2]

Vector2D cmlabs::Vector2D::operator* ( double a ) const

Scale.

Definition at line 976 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator*=()

const Vector2D & cmlabs::Vector2D::operator*= ( double a )

In-place scale.

Definition at line 1007 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator+() [1/2]

Vector2D cmlabs::Vector2D::operator+ ( const Vector2D & v ) const

Sum.

Definition at line 951 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator+() [2/2]

Vector2D cmlabs::Vector2D::operator+ ( double a ) const

Add scalar to each component.

Definition at line 969 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator+=() [1/2]

const Vector2D & cmlabs::Vector2D::operator+= ( const Vector2D & v )

In-place add.

Definition at line 989 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator+=() [2/2]

const Vector2D & cmlabs::Vector2D::operator+= ( double a )

In-place scalar add.

Definition at line 1001 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator-() [1/2]

Vector2D cmlabs::Vector2D::operator- ( const Vector2D & v ) const

Difference.

Definition at line 944 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator-() [2/2]

Vector2D cmlabs::Vector2D::operator- ( double a ) const

Subtract scalar from each component.

Definition at line 962 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator-=() [1/2]

const Vector2D & cmlabs::Vector2D::operator-= ( const Vector2D & v )

In-place subtract.

Definition at line 983 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator-=() [2/2]

const Vector2D & cmlabs::Vector2D::operator-= ( double a )

In-place scalar subtract.

Definition at line 995 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator==()

bool cmlabs::Vector2D::operator== ( const Vector2D & v ) const

Component equality.

Definition at line 938 of file MathClasses.cpp.

References Vector2D(), x, and y.

◆ operator[]()

double cmlabs::Vector2D::operator[] ( int n ) const

Component access: 0=x, 1=y.

Definition at line 928 of file MathClasses.cpp.

References x, and y.

◆ print()

std::string cmlabs::Vector2D::print ( )

Human-readable representation for debugging.

Definition at line 1038 of file MathClasses.cpp.

References cmlabs::utils::StringFormat(), x, and y.

◆ rotate()

Vector2D cmlabs::Vector2D::rotate ( double angle )

Rotated copy; this vector is unchanged.

Parameters

angle Radians, counter-clockwise in a y-up frame (appears clockwise with screen y-down coordinates).

Returns: Rotated copy; the zero vector rotates to the zero vector.

Definition at line 1077 of file MathClasses.cpp.

References Vector2D(), x, and y.

Referenced by cmlabs::MathClasses_UnitTest().

◆ rotateIt()

bool cmlabs::Vector2D::rotateIt ( double angle )

Rotate in place by angle radians (same convention as rotate()).

Returns: false for the zero vector (nothing to rotate), true otherwise.

Definition at line 1085 of file MathClasses.cpp.

References x, and y.

◆ set() [1/3]

bool cmlabs::Vector2D::set	(	const PointFloat &	p1,
		const PointFloat &	p2 )

Set as p2-p1.

Returns: true.

Definition at line 1018 of file MathClasses.cpp.

References set(), cmlabs::PointFloat::x, and cmlabs::PointFloat::y.

Referenced by set(), and set().

◆ set() [2/3]

bool cmlabs::Vector2D::set	(	double	x,
		double	y )

Set components.

Returns: true.

Definition at line 1026 of file MathClasses.cpp.

References x, and y.

◆ set() [3/3]

bool cmlabs::Vector2D::set	(	double	x1,
		double	y1,
		double	x2,
		double	y2 )

Set as (x2-x1, y2-y1).

Returns: true.

Definition at line 1022 of file MathClasses.cpp.

References set().

◆ setLength()

bool cmlabs::Vector2D::setLength ( double l )

Rescale to length l, keeping direction.

Returns: false for the zero vector.

Definition at line 1029 of file MathClasses.cpp.

References length(), x, and y.

Referenced by makeUnitVector(), and cmlabs::MathClasses_UnitTest().

◆ setX()

bool cmlabs::Vector2D::setX ( double v )

Set x.

Returns: true.

Definition at line 1027 of file MathClasses.cpp.

References x.

◆ setY()

bool cmlabs::Vector2D::setY ( double v )

Set y.

Returns: true.

Definition at line 1028 of file MathClasses.cpp.

References y.

Member Data Documentation

◆ x

double cmlabs::Vector2D::x

X component.

Definition at line 663 of file MathClasses.h.

Referenced by det(), getOrthogonalVector(), getUnitVector(), getX(), length(), cmlabs::MathClasses_UnitTest(), cmlabs::Size::operator*(), operator*(), operator*(), operator*=(), cmlabs::Point::operator+(), cmlabs::PointFloat::operator+(), operator+(), operator+(), operator+=(), operator+=(), operator-(), operator-(), operator-=(), operator-=(), operator==(), operator[](), print(), rotate(), rotateIt(), set(), setLength(), setX(), Vector2D(), and Vector2D().

◆ y

double cmlabs::Vector2D::y

Y component.

Definition at line 664 of file MathClasses.h.

Referenced by det(), getOrthogonalVector(), getUnitVector(), getY(), length(), cmlabs::MathClasses_UnitTest(), cmlabs::Size::operator*(), operator*(), operator*(), operator*=(), cmlabs::Point::operator+(), cmlabs::PointFloat::operator+(), operator+(), operator+(), operator+=(), operator+=(), operator-(), operator-(), operator-=(), operator-=(), operator==(), operator[](), print(), rotate(), rotateIt(), set(), setLength(), setY(), Vector2D(), and Vector2D().

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

/home/ubuntu/c/partner/psyclone2/CMSDK/include/MathClasses.h
/home/ubuntu/c/partner/psyclone2/CMSDK/src/MathClasses.cpp

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Vector2D() [1/2]

◆ Vector2D() [2/2]

◆ ~Vector2D()

Member Function Documentation

◆ det()

◆ getAngle()

◆ getArea()

◆ getOrthogonalVector()

◆ getProjectionOn()

◆ getUnitVector()

◆ getX()

◆ getY()

◆ isOrthogonalWith()

◆ isParallelWith()

◆ length()

◆ makeUnitVector()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator==()

◆ operator[]()

◆ print()

◆ rotate()

◆ rotateIt()

◆ set() [1/3]

◆ set() [2/3]

◆ set() [3/3]

◆ setLength()

◆ setX()

◆ setY()

Member Data Documentation

◆ x

◆ y