MathCommon.h File Reference

Defines and includes common Math data types and functions. More...

#include <cmath>
#include <algorithm>
#include <vector>
#include <limits>
#include <float.h>
#include "Math/Point.h"
#include "Math/Vector.h"
#include "Math/Matrix.h"

Classes
struct	Rect_t< T >
	A 2D rectangle. More...
struct	Line
	A 2D Line segment. More...
class	Ray
	A 2D Ray. More...
class	AABB
	2D Axis Aligned Bounding Box. More...
Defines
#define	BIT(x) (1 << (x))
	Constructs an integer with one bit set.
Typedefs
typedef Rect_t< float >	Rectf
	A Template instantiation of the Rect_t template using the `float` data type.
typedef Rect_t< double >	Rectd
	A Template instantiation of the Rect_t template using the `double` data type.
typedef Rect_t< int >	Recti
	A Template instantiation of the Rect_t template using the `int` data type.
Functions
float	ClosestPoints (const Line &l1, const Line &l2, Point2f &out1, Point2f &out2)
	Computes the closest points between the two given lines.
int	Intersect (const Ray &r, const Circle &c, float &t1, float &t2)
	Intersects a Ray with a Circle and finds the enter and exit time.
int	Intersect (const Line &l, const Circle &c, float &t1, float &t2)
	Intersects a Line with a Circle and finds the enter and exit time.
template<class T , class U >
T	lerp (const T &t1, const T &t2, U t)
	Linear interpolates between two objects of type T.
template<class T >
AABB	RectToAABB (const Rect_t< T > &r)
	Converts a Rect to an AABB.
template<class T >
Rect_t< T >	AABBToRect (const AABB &aabb)
	Converts an AABB to a Rect.
template<class T >
Rect_t< T >	ExpandRect (const Rect_t< T > &r, float dx, float dy)
	Expands (or contracts) the size of the given rectangle about the center.
template<class T >
bool	InsideRect (const Rect_t< T > &r, const Point2< T > &p)
	Tests if the given point is inside the given rect.
template<class T >
void	ClampInPlace (T &val, const T &low, const T &high)
	Clamps a given value into a given range.
template<class T >
T	Clamp (const T &val, const T &low, const T &high)
	Clamps a given value into a given range.
template<class T >
void	ClampLow (T &val, const T &low)
	Clamps a given value into a given range.
template<class T >
void	ClampHigh (T &val, const T &high)
	Clamps a given value into a given range.
template<class T >
T	Sign (const T &val)
	Determines the sign of the given value.
template<class T >
T	SignZero (const T &val)
	Determines the sign of the given value.
template<class T >
T	Minimum (const T &v1, const T &v2)
	Determines the minimum of two elements.
template<class T >
T	Maximum (const T &v1, const T &v2)
	Determines the maximum of two elements.
template<class T >
void	Swap (T &v1, T &v2)
	Swaps the given two values.
float	RadToDeg (float a)
	Converts an angle in Radians to Degrees.
float	DegToRad (float a)
	Converts an angle in Degrees to Radians.
bool	Close (float a, float b, float tol=0.00001f)
	Tests if two floating point values are within a given tolerance.
float	RandomFloat (float min, float max)
	Computes a random float in a given range.
uint	TimeSeed ()
	Computes a pretty good seed for a random number generator using the system time.
void	Transform (Poly &p, const Matrixf &m)
	Transforms the given polygon.
void	Transform (Point2f *p, uint n, const Matrixf &m)
	Transforms the given points.
Point2f	ScreenToNormCoords (const Point2f &p)
	Converts a point in absolute Screen coordinates to normalized device coordinates.
Point2f	NormToScreenCoords (const Point2f &p)
	Converts a point in normalized device coordinates to absolute Screen coordinates.
AABB	ScreenToNormCoords (const AABB &a)
	Converts an AABB in normalized device coordinates to absolute Screen coordinates.
AABB	NormToScreenCoords (const AABB &a)
	Converts an AABB in normalized device coordinates to absolute Screen coordinates.
Variables
const float	PI = 3.141592653589793f
const float	PI_2 = PI / 2.0f
const float	PI_4 = PI / 4.0f
const float	_2PI = 2.0f * PI
const float	INV_PI = 1.0f / PI
const float	E = 2.718281828459045f
const float	SQRT2 = 1.414213562373095f
const float	INV_SQRT2 = 1.0f / SQRT2
const float	SQRT2_2 = 0.707106781186547f
const float	RAD_TO_DEG = 180.0f / PI
const float	DEG_TO_RAD = PI / 180.0f
const float	EPSILON = 0.0001f

Detailed Description

Defines and includes common Math data types and functions.

Author:: Joe Forte

Date:: 3/27/2008

Define Documentation

#define BIT ( x ) (1 << (x))

Constructs an integer with one bit set.

Parameters:

[in] x the xth bit in the integer to set.

Function Documentation

template<class T >

Rect_t<T> AABBToRect ( const AABB & aabb ) [inline]

Converts an AABB to a Rect.

Template Parameters:

T the data type of the Rect. If T is not float data may be truncated.

Parameters:

[in] aabb The AABB to convert.

See also:: RectToAABB

Returns:: A Rect equivalent to aabb.

template<class T >

T Clamp	(	const T &	val,
		const T &	low,
		const T &	high
	)			`[inline]`

Clamps a given value into a given range.

Template Parameters:

T

the data type of used.

Parameters:

`[in]`	val	the value to clamp.
`[in]`	low	the low end of the range.
`[in]`	high	the hight end of the range.

See also:: ClampLow; ClampHigh

Returns:: The result of clamping val into the range [low,high]

template<class T >

void ClampHigh	(	T &	val,
		const T &	high
	)			`[inline]`

Clamps a given value into a given range.

Template Parameters:

T

the data type of used.

Parameters:

`[in,out]`	val	the value to clamp. Will be set to be in the range (infinity,high]
`[in]`	high	the hight end of the range.

See also:: Clamp; ClampLow

template<class T >

void ClampInPlace	(	T &	val,
		const T &	low,
		const T &	high
	)			`[inline]`

Clamps a given value into a given range.

Template Parameters:

T

the data type of used.

Parameters:

`[in,out]`	val	the value to clamp. Will be set to be in the range [low,high]
`[in]`	low	the low end of the range.
`[in]`	high	the hight end of the range.

See also:: ClampLow; ClampHigh

template<class T >

void ClampLow	(	T &	val,
		const T &	low
	)			`[inline]`

Clamps a given value into a given range.

Template Parameters:

T

the data type of used.

Parameters:

`[in,out]`	val	the value to clamp. Will be set to be in the range [low,infinity)
`[in]`	low	the low end of the range.

See also:: Clamp; ClampHigh

bool Close	(	float	a,
		float	b,
		float	tol = `0.00001f`
	)			`[inline]`

Tests if two floating point values are within a given tolerance.

Parameters:

`[in]`	a	the first value.
`[in]`	b	the second value.
`[in]`	tol	the tolerance. Defaults to 0.00001f.

Returns:: true if the given values are within the given tolerance from each other.

float ClosestPoints	(	const Line &	l1,
		const Line &	l2,
		Point2f &	out1,
		Point2f &	out2
	)

Computes the closest points between the two given lines.

Parameters:

`[in]`	l1	the first line.
`[in]`	l2	the second line.
`[out]`	out1	the closest point on the first line.
`[out]`	out2	the closest point on the second line.

Returns:: The distance between out1 and out2.

pg 149

float DegToRad ( float a ) [inline]

Converts an angle in Degrees to Radians.

Parameters:

[in] a the angle in Degrees to convert.

See also:: RadToDeg

Returns:: The angle a in Radians.

template<class T >

Rect_t<T> ExpandRect	(	const Rect_t< T > &	r,
		float	dx,
		float	dy
	)			`[inline]`

Expands (or contracts) the size of the given rectangle about the center.

Template Parameters:

T the data type of the Rect. If T is not float data may be truncated.

Parameters:

`[in]`	r	the Rect to expand.
`[in]`	dx	the amount to expand in the x direction.
`[in]`	dy	the amount to expand in the y direction.

Returns:: The expanded Rect.

template<class T >

bool InsideRect	(	const Rect_t< T > &	r,
		const Point2< T > &	p
	)			`[inline]`

Tests if the given point is inside the given rect.

Template Parameters:

T

the data type of the Rect and the Point2

Parameters:

`[in]`	r	the Rect to check against.
`[in]`	p	the point to test.

Returns:: True if the point p is inside Rect r.

int Intersect	(	const Line &	l,
		const Circle &	c,
		float &	t1,
		float &	t2
	)

Intersects a Line with a Circle and finds the enter and exit time.

Parameters:

`[in]`	l	the Line.
`[in]`	c	the circle.
`[out]`	t1	the time the Line l enters the Circle c.
`[out]`	t2	the time the Line l exits the Circle c.

Returns:: The number of intersections the Line l has with the Circle c. If 0 is returned there where was no intersection. If 1 is returned then there was one intersection and t1 holds the time. If 2 is returned then there were two intersections and the times are in t1 and t2 where t1 < t2.

int Intersect	(	const Ray &	r,
		const Circle &	c,
		float &	t1,
		float &	t2
	)

Intersects a Ray with a Circle and finds the enter and exit time.

Parameters:

`[in]`	r	the Ray.
`[in]`	c	the circle.
`[out]`	t1	the time the Ray r enters the Circle c.
`[out]`	t2	the time the Ray r exits the Circle c.

Returns:: The number of intersections the Ray r has with the Circle c. If 0 is returned there where was no intersection. If 1 is returned then there was one intersection and t1 holds the time. If 2 is returned then there were two intersections and the times are in t1 and t2 where t1 < t2.

pg 178

template<class T , class U >

T lerp	(	const T &	t1,
		const T &	t2,
		U	t
	)			`[inline]`

Linear interpolates between two objects of type T.

Template Parameters:

T

the data type to linearly interpolate between. The type must support the following operators:

T operator+(const &T) const
T operator-(const &T) const
T operator*(const &U) const

U the data type time takes. Usually float or double.

Parameters:

`[in]`	t1	the starting point to interpolate from.
`[in]`	t2	the ending point to interpolate to.
`[in]`	t	the time to interpolate to.

Returns:: The interpolated position between t1 and t2 such that t1 is returned when t = 0 and t2 is returned when t = 1.

template<class T >

T Maximum	(	const T &	v1,
		const T &	v2
	)			`[inline]`

Determines the maximum of two elements.

Template Parameters:

T

the data type of used.

Parameters:

`[in]`	v1	the first value.
`[in]`	v2	the second value.

Returns:: v1 if v1 >= v2, or v2 if v1 < v2.

template<class T >

T Minimum	(	const T &	v1,
		const T &	v2
	)			`[inline]`

Determines the minimum of two elements.

Template Parameters:

T

the data type of used.

Parameters:

`[in]`	v1	the first value.
`[in]`	v2	the second value.

Returns:: v1 if v1 <= v2, or v2 if v1 > v2.

AABB NormToScreenCoords ( const AABB & a ) [inline]

Converts an AABB in normalized device coordinates to absolute Screen coordinates.

Parameters:

[in] a the AABB to convert.

Returns:: The AABB a in absolute Screen coordinates.

Point2f NormToScreenCoords ( const Point2f & p )

Converts a point in normalized device coordinates to absolute Screen coordinates.

Parameters:

[in] p the point to convert.

See also:: ScreenToNormCoords

Returns:: The point p in absolute Screen coordinates.

float RadToDeg ( float a ) [inline]

Converts an angle in Radians to Degrees.

Parameters:

[in] a the angle in Radians to convert.

See also:: DegToRad

Returns:: The angle a in Degrees.

float RandomFloat	(	float	min,
		float	max
	)			`[inline]`

Computes a random float in a given range.

Parameters:

`[in]`	min	the minimum end of the range.
`[in]`	max	the maximum end of the range.

Returns:: A random float in the range [min,max]

template<class T >

AABB RectToAABB ( const Rect_t< T > & r ) [inline]

Converts a Rect to an AABB.

Template Parameters:

T the data type of the Rect. If T is not float data may be truncated.

Parameters:

[in] r The Rect to convert.

See also:: AABBToRect

Returns:: An AABB equivalent to r.

AABB ScreenToNormCoords ( const AABB & a ) [inline]

Converts an AABB in normalized device coordinates to absolute Screen coordinates.

Parameters:

[in] a the AABB to convert.

Returns:: The AABB a in absolute Screen coordinates.

Point2f ScreenToNormCoords ( const Point2f & p )

Converts a point in absolute Screen coordinates to normalized device coordinates.

Parameters:

[in] p the point to convert.

See also:: NormToScreenCoords

Returns:: The point p in normalized device coordinates.

template<class T >

T Sign ( const T & val ) [inline]

Determines the sign of the given value.

Template Parameters:

T

the data type of used.

Parameters:

[in] val the value to determine the sign of.

See also:: SignZero

Returns:: -1 if val < 0 or 1 if val >= 0.

template<class T >

T SignZero ( const T & val ) [inline]

Determines the sign of the given value.

Template Parameters:

T

the data type of used.

Parameters:

[in] val the value to determine the sign of.

See also:: Sign

Returns:: -1 if val < 0, 0 if val == 0 or 1 if val > 0.

template<class T >

void Swap	(	T &	v1,
		T &	v2
	)			`[inline]`

Swaps the given two values.

Template Parameters:

T

the data type of the values to Swap.

Parameters:

`[in,out]`	v1	will be set to v2.
`[in,out]`	v2	will be set to v1.

uint TimeSeed ( )

Computes a pretty good seed for a random number generator using the system time.

Returns:: A seed value.

void Transform	(	Point2f *	p,
		uint	n,
		const Matrixf &	m
	)			`[inline]`

Transforms the given points.

Parameters:

`[in,out]`	p	the points to be transformed.
`[in]`	n	the number of points.
`[in]`	m	the transformation matrix.

void Transform	(	Poly &	p,
		const Matrixf &	m
	)			`[inline]`

Transforms the given polygon.

Parameters:

`[in,out]`	p	the polygon to be transformed.
`[in]`	m	the transformation matrix.

Variable Documentation

const float _2PI = 2.0f * PI

$2\pi$

const float DEG_TO_RAD = PI / 180.0f

Degrees to Radians constant $\frac{\pi}{180}$

const float E = 2.718281828459045f

$e$

const float EPSILON = 0.0001f

Small floating point value.

const float INV_PI = 1.0f / PI

$\frac{1}{\pi}$

const float INV_SQRT2 = 1.0f / SQRT2

$\frac{1}\sqrt{2}$

const float PI = 3.141592653589793f

$\pi$

const float PI_2 = PI / 2.0f

$\frac{\pi}{2}$

const float PI_4 = PI / 4.0f

$\frac{\pi}{4}$

const float RAD_TO_DEG = 180.0f / PI

Radians to Degrees constant $\frac{180}{\pi}$

const float SQRT2 = 1.414213562373095f

$\sqrt{2}$

const float SQRT2_2 = 0.707106781186547f

$\frac{\sqrt{2}}{2}$

MathCommon.h File Reference

Classes

Defines

Typedefs

Functions

Variables

Detailed Description

Define Documentation

Function Documentation

Variable Documentation