A set of static functions that handle typical math needed for games. More...

#include <MathUtil.h>

Public Types
enum	AABBSplittingAxis { AA_X, AA_Y }
Static Public Member Functions
template<typename T >
static T	Abs (T val)
template<typename T >
static T	Max (T value1, T value2)
template<typename T >
static T	Min (T value1, T value2)
template<typename T >
static T	Distance (T value1, T value2)
template<typename T >
static T	Lerp (T value1, T value2, float amount)
template<typename T >
static T	SmoothStep (T value1, T value2, float amount)
static int	Clamp (int value, int min, int max)
static float	Clamp (float value, float min, float max)
static double	Clamp (double value, double min, double max)
static float	ToDegrees (float radians)
static float	ToRadians (float degrees)
static Vector2	VectorFromAngle (float angle_in_degrees)
static float	AngleFromVector (const Vector2 &v1)
static float	AngleFromVectors (const Vector2 &v1, const Vector2 &v2)
static int	RoundToInt (double x)
static int	RandomInt (int maximum)
static int	RandomIntInRange (int min, int max)
static int	RandomIntWithError (int target, int error)
static float	RandomFloat (float maximum=1.0f)
static float	RandomFloatInRange (float min, float max)
static float	RandomFloatWithError (float target, float error)
static bool	RandomBool ()
static Vector2	RandomVector ()
static Vector2	RandomVector (const Vector2 &maxValues)
static Vector2	RandomVector (const Vector2 &minValues, const Vector2 &maxValues)
static bool	FuzzyEquals (float value1, float value2, float epsilon=Epsilon)
static bool	FuzzyEquals (const Vector2 &v1, const Vector2 &v2, float epsilon=Epsilon)
static Vector2	ScreenToWorld (int x, int y)
static Vector2	ScreenToWorld (const Vec2i &screenCoordinates)
static Vector2	WorldToScreen (float x, float y)
static Vector2	WorldToScreen (const Vector2 &worldCoordinates)
static Vector2	GetWorldDimensions ()
static float	PixelsToWorldUnits (float pixels)
static float	WorldUnitsToPixels (float worldUnits)
static AABBSplittingAxis	GetMajorAxis (const BoundingBox &source)
static void	SplitBoundingBox (const BoundingBox &source, AABBSplittingAxis axis, BoundingBox &LHS, BoundingBox &RHS)
static float	DeltaAngle (float A1, float A2)
static float	VectorDeltaAngle (const Vector2 &v1, const Vector2 &v2)
Static Public Attributes
static const float	E = 2.718282f
static const float	Log10E = 0.4342945f
static const float	Log2E = 1.442695f
static const float	Pi = 3.141593f
static const float	PiOver2 = 1.570796f
static const float	PiOver4 = 0.7853982f
static const float	TwoPi = 6.283185f
static const float	MaxFloat = 3.402823E+38f
static const float	MinFloat = -3.402823E+38f
static const float	Epsilon = 0.000001f

Detailed Description

This class is just a wrapper around a whole bunch of otherwise-loose functions that handle all kinds of math that is typically required in a game.

It also contains a set of constants so you don't have to look them up or declare them yourself.

Definition at line 45 of file MathUtil.h.

Member Function Documentation

template<typename T >

static T MathUtil::Abs ( T val ) [inline, static]

A templated absolute value function that can handle any class where a comparison against 0 makes sense (floats and ints, mostly).

Parameters:

val	The number

Returns:: The absolute value of that number

Definition at line 108 of file MathUtil.h.

template<typename T >

static T MathUtil::Max	(	T	value1,
		T	value2
	)		`[inline, static]`

A templated max function that returns the greater of two values. Works for any class that implements a > operator.

Parameters:

value1	The first value
value2	The second value

Returns:: The greater of the two

Definition at line 122 of file MathUtil.h.

template<typename T >

static T MathUtil::Min	(	T	value1,
		T	value2
	)		`[inline, static]`

A templated min function that returns the lesser of two values. Works for any class that implements a < operator.

Parameters:

value1	The first value
value2	The second value

Returns:: The lesser of the two

Definition at line 136 of file MathUtil.h.

template<typename T >

static T MathUtil::Distance	(	T	value1,
		T	value2
	)		`[inline, static]`

Find the distance between two values. Works for any class that has a subtraction operator and will work with the Abs function.

Parameters:

value1	The first value
value2	The second value

Returns:: The distance between them

Definition at line 150 of file MathUtil.h.

template<typename T >

static T MathUtil::Lerp	(	T	value1,
		T	value2,
		float	amount
	)		`[inline, static]`

Linearly interpolates between two values. Works for any classes that define addition, subtraction, and multiplication (by a float) operators.

http://en.wikipedia.org/wiki/Lerp_(computing)

Parameters:

value1	The starting value
value2	The ending value
amount	The amount to lerp (from 0.0 to 1.0)

Returns:: The interpolated value

Definition at line 168 of file MathUtil.h.

template<typename T >

static T MathUtil::SmoothStep	(	T	value1,
		T	value2,
		float	amount
	)		`[inline, static]`

Smoothly step between two values. Works for any classes that Lerp would work for (and is essentially a drop-in replacement).

http://www.fundza.com/rman_shaders/smoothstep/index.html

Parameters:

value1	The starting value
value2	The ending value
amount	The amount to interpolate (from 0.0 to 1.0)

Returns:: The interpolated value

Definition at line 185 of file MathUtil.h.

static int MathUtil::Clamp	(	int	value,
		int	min,
		int	max
	)		`[inline, static]`

Clamps an integer to a specified range

Parameters:

value	The integer in question
min	The minimum of the range
max	The maximum of the range

Returns:: The clamped value

Definition at line 199 of file MathUtil.h.

static float MathUtil::Clamp	(	float	value,
		float	min,
		float	max
	)		`[inline, static]`

Clamps a float to a specified range

Parameters:

value	The float in question
min	The minimum of the range
max	The maximum of the range

Returns:: The clamped value

Definition at line 212 of file MathUtil.h.

static double MathUtil::Clamp	(	double	value,
		double	min,
		double	max
	)		`[inline, static]`

Clamps a double-precision float to a specified range

Parameters:

value	The double in question
min	The minimum of the range
max	The maximum of the range

Returns:: The clamped value

Definition at line 225 of file MathUtil.h.

float MathUtil::ToDegrees ( float radians ) [static]

Convert radians to degrees

Parameters:

radians The angle in radians

Returns:: The angle in degrees

Definition at line 51 of file MathUtil.cpp.

float MathUtil::ToRadians ( float degrees ) [static]

Convert degrees to radians

Parameters:

degrees The angle in degrees

Returns:: The angle in radians

Definition at line 56 of file MathUtil.cpp.

Vector2 MathUtil::VectorFromAngle ( float angle_in_degrees ) [static]

Get a unit-length vector which indicate a direction along the given angle relative to the screen.

Parameters:

angle_in_degrees The angle, in degrees

Returns:: A vector moving along that angle

Definition at line 61 of file MathUtil.cpp.

float MathUtil::AngleFromVector ( const Vector2 & v1 ) [static]

Get an angle from a vector indicating direction

Parameters:

v1	The vector direction

Returns:: The vector's angle

Definition at line 66 of file MathUtil.cpp.

float MathUtil::AngleFromVectors	(	const Vector2 &	v1,
		const Vector2 &	v2
	)		`[static]`

Get the angle between two vectors

Parameters:

v1	The first vector
v2	The second vector

Returns:: The angle between them in radians

Definition at line 74 of file MathUtil.cpp.

int MathUtil::RoundToInt ( double x ) [static]

Takes a double or float and removes everything after the decimal point, making it into an integer.

Parameters:

x	The double or float to round

Returns:: The rounded integer

Definition at line 80 of file MathUtil.cpp.

int MathUtil::RandomInt ( int maximum ) [static]

Get a random non-negative integer.

Parameters:

maximum The maximum value you want to see

Returns:: A random number between 0 (inclusive) and maximum (exclusive)

Definition at line 85 of file MathUtil.cpp.

int MathUtil::RandomIntInRange	(	int	min,
		int	max
	)		`[static]`

Get a random integer in a specified range.

Parameters:

min	The minimum value you want to see
max	The maximum value you want to see

Returns:: A random number between min (inclusive) and max (exclusive)

Definition at line 100 of file MathUtil.cpp.

int MathUtil::RandomIntWithError	(	int	target,
		int	error
	)		`[static]`

Get a random integer within a specified range of another one.

Parameters:

target	The target integer
error	The maximum amount the returned value can differ from the target (in either direction)

Returns:: A random int from (target - error) to (target + error)

Definition at line 105 of file MathUtil.cpp.

float MathUtil::RandomFloat ( float maximum = 1.0f ) [static]

Get a random non-negative float.

Parameters:

maximum The maximum value you want to see

Returns:: A random number between 0.0 (inclusive) and maximum (exclusive)

Definition at line 110 of file MathUtil.cpp.

float MathUtil::RandomFloatInRange	(	float	min,
		float	max
	)		`[static]`

Get a random float in a specified range.

Parameters:

min	The minimum value you want to see
max	The maximum value you want to see

Returns:: A random number between min (inclusive) and max (exclusive)

Definition at line 118 of file MathUtil.cpp.

float MathUtil::RandomFloatWithError	(	float	target,
		float	error
	)		`[static]`

Get a random float within a specified range of another one.

Parameters:

target	The target float
error	The maximum amount the returned value can differ from the target (in either direction)

Returns:: A random float from (target - error) to (target + error)

Definition at line 123 of file MathUtil.cpp.

bool MathUtil::RandomBool ( ) [static]

Get a random bool.

Returns:: Either true or false, randomly. :-)

Definition at line 128 of file MathUtil.cpp.

Vector2 MathUtil::RandomVector ( ) [static]

Get a random unit-length Vector2

Returns:: A unit-length Vector2 pointing in a random direction

Definition at line 133 of file MathUtil.cpp.

Vector2 MathUtil::RandomVector ( const Vector2 & maxValues ) [static]

Get a random Vector2 with specified maximum values

Parameters:

maxValues The highest values for both axes

Returns:: A random vector ranging from (0, 0) to (maxValues.X, maxValuesY)

Definition at line 138 of file MathUtil.cpp.

Vector2 MathUtil::RandomVector	(	const Vector2 &	minValues,
		const Vector2 &	maxValues
	)		`[static]`

Get a random Vector2 within a specified range

Parameters:

minValues	The lowest values for both axes
maxValues	The highest values for both axes

Returns:: A random vector ranging from (minValues.X, minValues.Y) to (maxValues.X, maxValues.y)

Definition at line 143 of file MathUtil.cpp.

bool MathUtil::FuzzyEquals	(	float	value1,
		float	value2,
		float	epsilon = `Epsilon`
	)		`[static]`

Compare two floating point values for "equality," with a permissible amount of error. Oftentimes you only care if floats are "close enough for government work," and this function lets you make that determination.

(Because of rounding errors inherent in floating point arithmetic, direct comparison of floats is often inadvisable. http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems )

Parameters:

value1	The first value
value2	The second value
epsilon	The maximum allowable difference (defaults to MathUtil::Epsilon)

Returns:: Whether the two values are within epsilon of each other

Definition at line 148 of file MathUtil.cpp.

bool MathUtil::FuzzyEquals	(	const Vector2 &	v1,
		const Vector2 &	v2,
		float	epsilon = `Epsilon`
	)		`[static]`

A Vector2 comparison function using FuzzyEquals on the components.

Parameters:

v1	The first vector
v2	The second vector
epsilon	The maximum allowable difference between them

Returns:: Whether the two vectors have components within epsilon of each other

Definition at line 159 of file MathUtil.cpp.

Vector2 MathUtil::ScreenToWorld	(	int	x,
		int	y
	)		`[static]`

Convert screen (pixel) coordinates to world (GL unit) coordinates. This function is not terribly efficient, so be careful calling it too frequently.

Parameters:

x	The pixel X coordinate
y	The pixel Y coordinate

Returns:: The world space coordinates

Definition at line 173 of file MathUtil.cpp.

Vector2 MathUtil::ScreenToWorld ( const Vec2i & screenCoordinates ) [static]

Convert screen (pixel) coordinates to world (GL unit) coordinates. This function is not terribly efficient, so be careful calling it too frequently.

Parameters:

screenCoordinates The pixel coordinates

Returns:: The world space coordinates

Definition at line 168 of file MathUtil.cpp.

Vector2 MathUtil::WorldToScreen	(	float	x,
		float	y
	)		`[static]`

Convert world (GL unit) coordinates to screen (pixel) coordinates. This function is not terribly efficient, so be careful calling it too frequently.

Parameters:

x	The world X coordinate
y	The world Y coordinate

Returns:: The screen space coordinates

Definition at line 208 of file MathUtil.cpp.

Vector2 MathUtil::WorldToScreen ( const Vector2 & worldCoordinates ) [static]

Convert world (GL unit) coordinates to screen (pixel) coordinates. This function is not terribly efficient, so be careful calling it too frequently.

Parameters:

worldCoordinates The world coordinates

Returns:: The screen space coordinates

Definition at line 192 of file MathUtil.cpp.

Vector2 MathUtil::GetWorldDimensions ( ) [static]

Find out the dimensions of the area currently displayed in the window.

Returns:: The dimensions of the viewport in GL units

Definition at line 213 of file MathUtil.cpp.

float MathUtil::PixelsToWorldUnits ( float pixels ) [static]

Take a number of pixels and find out how many GL units they cover

Parameters:

pixels The number of pixels

Returns:: The number of GL units

Definition at line 240 of file MathUtil.cpp.

float MathUtil::WorldUnitsToPixels ( float worldUnits ) [static]

Take a number of GL units and find out how many pixels stretch across that distance.

Parameters:

worldUnits The number of GL units

Returns:: The number of pixels

Definition at line 247 of file MathUtil.cpp.

MathUtil::AABBSplittingAxis MathUtil::GetMajorAxis ( const BoundingBox & source ) [static]

Used internally by the SpatialGraph when it generates.

Parameters:

source The bounding box to split

Returns:: The appropriate axis on which to split it

Definition at line 254 of file MathUtil.cpp.

void MathUtil::SplitBoundingBox	(	const BoundingBox &	source,
		AABBSplittingAxis	axis,
		BoundingBox &	LHS,
		BoundingBox &	RHS
	)		`[static]`

Used internally by the SpatialGraph when it generates

Parameters:

source	The bounding box to split
axis	The axis on which to split it
LHS	An out parameter that will be set to the left-hand-side bounding box resulting from the split
RHS	An out parameter that will be set to the right-hand-side bounding box resulting from the split

Definition at line 269 of file MathUtil.cpp.

float MathUtil::DeltaAngle	(	float	A1,
		float	A2
	)		`[static]`

Calculates the difference in two angles (in radians) and remaps it to a range from -Pi to Pi.

Parameters:

A1	The first angle (in radians)
A2	The second angle (in radians)

Returns:: The difference, mapped appropriately

Definition at line 287 of file MathUtil.cpp.

float MathUtil::VectorDeltaAngle	(	const Vector2 &	v1,
		const Vector2 &	v2
	)		`[static]`

Calculate the difference in angles between two vectors.

Parameters:

v1	The first vector
v2	The second vector

Returns:: The difference in their angles

Definition at line 309 of file MathUtil.cpp.

Member Data Documentation

const float MathUtil::E = 2.718282f [static]

Euler's number: http://en.wikipedia.org/wiki/E_(mathematical_constant)

Definition at line 51 of file MathUtil.h.

const float MathUtil::Log10E = 0.4342945f [static]

Base-10 logarithm of Euler's number

Definition at line 56 of file MathUtil.h.

const float MathUtil::Log2E = 1.442695f [static]

Base-2 logarithm of Euler's number

Definition at line 61 of file MathUtil.h.

const float MathUtil::Pi = 3.141593f [static]

Pi: http://en.wikipedia.org/wiki/Pi

Definition at line 66 of file MathUtil.h.

const float MathUtil::PiOver2 = 1.570796f [static]

Pi divided by 2

Definition at line 71 of file MathUtil.h.

const float MathUtil::PiOver4 = 0.7853982f [static]

Pi divided by 4

Definition at line 76 of file MathUtil.h.

const float MathUtil::TwoPi = 6.283185f [static]

2 times Pi (Tau)

Definition at line 81 of file MathUtil.h.

const float MathUtil::MaxFloat = 3.402823E+38f [static]

The maximum value that can be represented by a 32-bit floating point number

Definition at line 87 of file MathUtil.h.

const float MathUtil::MinFloat = -3.402823E+38f [static]

The minimum value that can be represented by a 32-bit floating point number

Definition at line 93 of file MathUtil.h.

const float MathUtil::Epsilon = 0.000001f [static]

A very tiny number, useful for floating point comparisons (10e-6)

Definition at line 98 of file MathUtil.h.

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

Util/MathUtil.h
Util/MathUtil.cpp

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

Member Data Documentation