RTVolumeRendering/Source/MathCommon.h File Reference

Defines useful math functions, constants and types. More...

#include <cmath>
#include <assert.h>
#include "Vector3.h"
#include "Point3.h"
#include "Matrix.h"

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Classes

struct LineSegment

Defines a line segment. More...

struct Ray

Defines a ray. More...

struct Plane

Defines an infinite planes. More...

struct ScreenRect

Defines a 2D rectangular region of screen space. More...

struct Sphere

Defines a sphere. More...

struct CubeDef

Defines a cube. More...

struct CubePlanes

Defines the planes of a cube. More...

struct CubeFrame

Defines the lines that make up a cube. More...

Functions

template<class dataType, class timeType>

dataType Lerp (const dataType &d0, const dataType &d1, const timeType &t)

Linearly interpolates between two data points.

template<class T>

void Swap (T &v1, T &v2)

Swaps the given values.

template<class T>

T Clamp (const T &val, const T &low, const T &high)

Clamps a value to be in a given range.

CubePlanes CreatePlanes (const CubeDef &c)

Creates a CubePlanes structure from a CubeDef.

CubeFrame CreateFrame (const CubeDef &c)

Creates a CubeFrame from a CubeDef.

bool Inside (const Point3f &p, const Sphere &s)

Tests if a point is inside a sphere.

bool Inside (int x, int y, const ScreenRect &rect)

Tests if a point is inside a screen rectangle.

int Intersect (const LineSegment &line, const Plane &plane, float &t)

Finds the intersection point between the a line and a plane.

int Intersect (const Plane &p, const CubeFrame &c, Point3f points[6])

Intersects a Plane with a Cube.

int Intersect (const LineSegment &line, const Sphere &s, Point3f points[2])

Intersects a Line segment with a sphere.

int Intersect (const Ray &r, const Sphere &s, Point3f points[2])

Intersects a Ray with a sphere.

Point3f Average (const Point3f *points, int n)

Computes the average of a set of points.

float ReferanceAngle (const Vector3f &ref, const Vector3f &v1, const Vector3f &v2)

Computes the angle between two vectors and a mutaully perpendicular referance vector.

void SortPoints (Point3f *points, int n, const Vector3f &normal)

Sorts a set of points into cw or ccw order.

Detailed Description

Defines useful math functions, constants and types.

Author:: Joe Forte

Date:: 9/26/2008

Definition in file MathCommon.h.

Function Documentation

Point3f Average	(	const Point3f *	points,
		int	n
	)			`[inline]`

Computes the average of a set of points.

Parameters:

`[in]`	points	the points.
`[in]`	n	the number of points.

Returns:: The average of the given points.

Definition at line 416 of file MathCommon.h.

Referenced by SortPoints().

template<class T>

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

Clamps a value to be in a given range.

Parameters:

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

Returns:: The clamped value in the range [low, high].

Definition at line 154 of file MathCommon.h.

Referenced by TransferFunctionPlot::MouseMove().

CubeFrame CreateFrame ( const CubeDef & c ) [inline]

Creates a CubeFrame from a CubeDef.

Parameters:

[in] c the cube.

Returns:: the equivalent CubeFrame to the given cube.

Definition at line 195 of file MathCommon.h.

References CubeDef::c, CubeDef::dim, CubeFrame::line, LineSegment::p1, and LineSegment::p2.

Referenced by Cube::Init(), and RTVolumeRenderer::RTVolumeRenderer().

CubePlanes CreatePlanes ( const CubeDef & c ) [inline]

Creates a CubePlanes structure from a CubeDef.

Parameters:

[in] c the cube.

Returns:: the equivalent CubePlanes of the given cube.

Definition at line 170 of file MathCommon.h.

References CubeDef::dim, Plane::n, Plane::p, and CubePlanes::plane.

Referenced by Cube::Init().

bool Inside	(	int	x,
		int	y,
		const ScreenRect &	rect
	)			`[inline]`

Tests if a point is inside a screen rectangle.

Parameters:

`[in]`	x	the x coordinate point.
`[in]`	y	the y coordinate point.
`[in]`	rect	the rectangle.

Returns:: true if the point is inside the screen rectangle, false otherwise.

Definition at line 249 of file MathCommon.h.

References ScreenRect::x1, ScreenRect::x2, and ScreenRect::y2.

bool Inside	(	const Point3f &	p,
		const Sphere &	s
	)			`[inline]`

Tests if a point is inside a sphere.

Parameters:

`[in]`	p	the point.
`[in]`	s	the sphere.

Returns:: true if the point is inside the sphere, false otherwise.

Definition at line 234 of file MathCommon.h.

References Sphere::c, Sphere::r, and Vector3< T >::SquaredLength().

Referenced by TransferFunctionPlot::SelectPoint(), and Camera::Zoom().

int Intersect	(	const Ray &	r,
		const Sphere &	s,
		Point3f	points[2]
	)			`[inline]`

Intersects a Ray with a sphere.

Parameters:

`[in]`	r	the ray.
`[in]`	s	the line sphere.
`[out]`	points	the intersection points.

Returns:: the number of intersections: 0, 1 or 2.

Definition at line 369 of file MathCommon.h.

References Sphere::c, Ray::d, Lerp(), Ray::p, and Sphere::r.

int Intersect	(	const LineSegment &	line,
		const Sphere &	s,
		Point3f	points[2]
	)			`[inline]`

Intersects a Line segment with a sphere.

Parameters:

`[in]`	line	the line segment.
`[in]`	s	the line sphere.
`[out]`	points	the intersection points.

Returns:: the number of intersections: 0, 1 or 2.

Definition at line 313 of file MathCommon.h.

References Sphere::c, LineSegment::p1, LineSegment::p2, and Sphere::r.

int Intersect	(	const Plane &	p,
		const CubeFrame &	c,
		Point3f	points[6]
	)			`[inline]`

Intersects a Plane with a Cube.

Parameters:

`[in]`	p	the plane.
`[in]`	c	the cube frame.
`[out]`	points	the intersection points.

Returns:: 0 if the plane doesn't intersect the cube. The number of intersections 3 to 6.

Definition at line 285 of file MathCommon.h.

References Intersect(), CubeFrame::line, LineSegment::p1, and LineSegment::p2.

int Intersect	(	const LineSegment &	line,
		const Plane &	plane,
		float &	t
	)			`[inline]`

Finds the intersection point between the a line and a plane.

Parameters:

`[in]`	line	the line.
`[in]`	plane	the plane.
`[out]`	t	the collision time.

Returns:: 1 if the line intersects the plane. 0 if the line is parallel with the plane (t is not valid).

Definition at line 264 of file MathCommon.h.

References Plane::n, Plane::p, LineSegment::p1, and LineSegment::p2.

Referenced by Intersect(), and Camera::Zoom().

template<class dataType, class timeType>

dataType Lerp	(	const dataType &	d0,
		const dataType &	d1,
		const timeType &	t
	)			`[inline]`

Linearly interpolates between two data points.

Template Parameters:

	dataType	the type of data that is being interpolated.
	timeType	the type of the value that controls the amount of interpolation.

Parameters:

`[in]`	d0	the first data point.
`[in]`	d1	the second data point.
`[in]`	t	the amount to interpolate.

Returns:: the linearly interpolated value between the two data points.

Definition at line 125 of file MathCommon.h.

Referenced by Intersect().

float ReferanceAngle	(	const Vector3f &	ref,
		const Vector3f &	v1,
		const Vector3f &	v2
	)			`[inline]`

Computes the angle between two vectors and a mutaully perpendicular referance vector.

Parameters:

`[in]`	ref	the referance vector.
`[in]`	v1	the first vector.
`[in]`	v2	the second vector.

Returns:: the angle between 'v1' and 'v2' with respect to 'ref'.

Definition at line 436 of file MathCommon.h.

References Vector3< T >::Length().

Referenced by SortPoints().

void SortPoints	(	Point3f *	points,
		int	n,
		const Vector3f &	normal
	)			`[inline]`

Sorts a set of points into cw or ccw order.

Parameters:

`[in,out]`	points	the points to sort.
`[in]`	n	the number of points. Must be in the range [3,6].
`[in]`	normal	the polygon normal that the points lie on.

Definition at line 453 of file MathCommon.h.

References Average(), and ReferanceAngle().

template<class T>

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

Swaps the given values.

Parameters:

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

Definition at line 137 of file MathCommon.h.


Classes
struct	LineSegment
	Defines a line segment. More...
struct	Ray
	Defines a ray. More...
struct	Plane
	Defines an infinite planes. More...
struct	ScreenRect
	Defines a 2D rectangular region of screen space. More...
struct	Sphere
	Defines a sphere. More...
struct	CubeDef
	Defines a cube. More...
struct	CubePlanes
	Defines the planes of a cube. More...
struct	CubeFrame
	Defines the lines that make up a cube. More...
Functions
template<class dataType, class timeType>
dataType	Lerp (const dataType &d0, const dataType &d1, const timeType &t)
	Linearly interpolates between two data points.
template<class T>
void	Swap (T &v1, T &v2)
	Swaps the given values.
template<class T>
T	Clamp (const T &val, const T &low, const T &high)
	Clamps a value to be in a given range.
CubePlanes	CreatePlanes (const CubeDef &c)
	Creates a CubePlanes structure from a CubeDef.
CubeFrame	CreateFrame (const CubeDef &c)
	Creates a CubeFrame from a CubeDef.
bool	Inside (const Point3f &p, const Sphere &s)
	Tests if a point is inside a sphere.
bool	Inside (int x, int y, const ScreenRect &rect)
	Tests if a point is inside a screen rectangle.
int	Intersect (const LineSegment &line, const Plane &plane, float &t)
	Finds the intersection point between the a line and a plane.
int	Intersect (const Plane &p, const CubeFrame &c, Point3f points[6])
	Intersects a Plane with a Cube.
int	Intersect (const LineSegment &line, const Sphere &s, Point3f points[2])
	Intersects a Line segment with a sphere.
int	Intersect (const Ray &r, const Sphere &s, Point3f points[2])
	Intersects a Ray with a sphere.
Point3f	Average (const Point3f *points, int n)
	Computes the average of a set of points.
float	ReferanceAngle (const Vector3f &ref, const Vector3f &v1, const Vector3f &v2)
	Computes the angle between two vectors and a mutaully perpendicular referance vector.
void	SortPoints (Point3f *points, int n, const Vector3f &normal)
	Sorts a set of points into cw or ccw order.