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OGRE-Next 3.0.0
Object-Oriented Graphics Rendering Engine
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Class to provide access to common mathematical functions. More...
#include <OgreMath.h>
Classes | |
| class | RandomValueProvider |
| This class is used to provide an external random value provider. More... | |
Public Types | |
| enum | AngleUnit { AU_DEGREE , AU_RADIAN } |
| The angular units used by the API. More... | |
Public Member Functions | |
| Math (unsigned int trigTableSize=4096) | |
| Default constructor. | |
| ~Math () | |
| Default destructor. | |
Static Public Member Functions | |
| static Degree | Abs (const Degree &dValue) |
| Absolute value function. | |
| static Radian | Abs (const Radian &rValue) |
| Absolute value function. | |
| static Real | Abs (Real fValue) |
| Absolute value function. | |
| static Radian | ACos (Real fValue) |
| Arc cosine function. | |
| static Real | AngleUnitsToDegrees (Real units) |
| Convert from the current AngleUnit to degrees. | |
| static Real | AngleUnitsToRadians (Real units) |
| Convert from the current AngleUnit to radians. | |
| static Radian | ASin (Real fValue) |
| Arc sine function. | |
| static Radian | ATan (Real fValue) |
| Arc tangent function. | |
| static Radian | ATan2 (Real fY, Real fX) |
| Arc tangent between two values function. | |
| static Real | boundingRadiusFromAABB (const AxisAlignedBox &aabb) |
| Get a bounding radius value from a bounding box. | |
| static Matrix4 | buildReflectionMatrix (const Plane &p) |
| Build a reflection matrix for the passed in plane. | |
| static Vector3 | calculateBasicFaceNormal (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3) |
| Calculate a face normal, no w-information. | |
| static Vector3 | calculateBasicFaceNormalWithoutNormalize (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3) |
| Calculate a face normal without normalize, no w-information. | |
| static Vector4 | calculateFaceNormal (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3) |
| Calculate a face normal, including the w component which is the offset from the origin. | |
| static Vector4 | calculateFaceNormalWithoutNormalize (const Vector3 &v1, const Vector3 &v2, const Vector3 &v3) |
| Calculate a face normal without normalize, including the w component which is the offset from the origin. | |
| static Vector3 | calculateTangentSpaceVector (const Vector3 &position1, const Vector3 &position2, const Vector3 &position3, Real u1, Real v1, Real u2, Real v2, Real u3, Real v3) |
| Calculates the tangent space vector for a given set of positions / texture coords. | |
| static Real | Ceil (Real fValue) |
| Ceiling function Returns the smallest following integer. | |
| template<typename T> | |
| static T | Clamp (T val, T minval, T maxval) |
| Clamp a value within an inclusive range. | |
| static uint32 | ClosestPow2 (uint32 x) |
| Return closest power of two not smaller than given number. | |
| static Real | Cos (const Radian &fValue, bool useTables=false) |
| Cosine function. | |
| static Real | Cos (Real fValue, bool useTables=false) |
| Cosine function. | |
| static Real | DegreesToAngleUnits (Real degrees) |
| Convert from degrees to the current AngleUnit. | |
| static Real | DegreesToRadians (Real degrees) |
| static Real | Exp (Real fValue) |
| static Real | Floor (Real fValue) |
| Floor function Returns the largest previous integer. | |
| static Real | gaussianDistribution (Real x, Real offset=0.0f, Real scale=1.0f) |
| Generates a value based on the Gaussian (normal) distribution function with the given offset and scale parameters. | |
| static size_t | gcd (size_t a, size_t b) |
| Returns Greatest Common Denominator. | |
| static AngleUnit | getAngleUnit () |
| Get the unit being used for angles. | |
| static int | IAbs (int iValue) |
| static int | ICeil (float fValue) |
| static int | IFloor (float fValue) |
| static bool | intersects (const Plane &plane, const AxisAlignedBox &box) |
| Plane / box intersection test. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const AxisAlignedBox &box) |
| Ray / box intersection, returns boolean result and distance. | |
| static bool | intersects (const Ray &ray, const AxisAlignedBox &box, Real *d1, Real *d2) |
| Ray / box intersection, returns boolean result and two intersection distance. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const Plane &plane) |
| Ray / plane intersection, returns boolean result and distance. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const Sphere &sphere, bool discardInside=true) |
| Ray / sphere intersection, returns boolean result and distance. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const StdList< Plane > &planeList, bool normalIsOutside) |
| Ray / convex plane list intersection test. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const StdVector< Plane > &planeList, bool normalIsOutside) |
| Ray / convex plane list intersection test. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const Vector3 &a, const Vector3 &b, const Vector3 &c, bool positiveSide=true, bool negativeSide=true) |
| Ray / triangle intersection, returns boolean result and distance. | |
| static std::pair< bool, Real > | intersects (const Ray &ray, const Vector3 &a, const Vector3 &b, const Vector3 &c, const Vector3 &normal, bool positiveSide=true, bool negativeSide=true) |
| Ray / triangle intersection, returns boolean result and distance. | |
| static bool | intersects (const Sphere &sphere, const AxisAlignedBox &box) |
| Sphere / box intersection test. | |
| static bool | intersects (const Sphere &sphere, const Plane &plane) |
| Sphere / plane intersection test. | |
| static Real | InvSqrt (Real fValue) |
| Inverse square root i.e. | |
| static int | ISign (int iValue) |
| static bool | isNaN (Real f) |
| static size_t | lcm (size_t a, size_t b) |
| Returns Least Common Multiple. | |
| template<typename T, typename S> | |
| static FORCEINLINE T | lerp (const T &a, const T &b, const S &w) |
| Linear interpolation. | |
| static Real | Log (Real fValue) |
| static Real | Log2 (Real fValue) |
| static Real | LogN (Real base, Real fValue) |
| static Matrix4 | makeViewMatrix (const Vector3 &position, const Quaternion &orientation, const Matrix4 *reflectMatrix=0) |
| static Vector3 | octahedronMappingDecode (Vector2 f) |
| Takes a 2D value in range [0; 1] and returns a unit-length 3D vector. | |
| static Vector2 | octahedronMappingEncode (Vector3 n) |
| Takes a directional 3D vector n and returns a 2D value in range [0; 1] Vector 'n' doesn't have to be normalized. | |
| static bool | pointInTri2D (const Vector2 &p, const Vector2 &a, const Vector2 &b, const Vector2 &c) |
| Checks whether a given point is inside a triangle, in a 2-dimensional (Cartesian) space. | |
| static bool | pointInTri3D (const Vector3 &p, const Vector3 &a, const Vector3 &b, const Vector3 &c, const Vector3 &normal) |
| Checks whether a given 3D point is inside a triangle. | |
| static Real | Pow (Real fBase, Real fExponent) |
| static Real | RadiansToAngleUnits (Real radians) |
| Convert from radians to the current AngleUnit . | |
| static Real | RadiansToDegrees (Real radians) |
| static Real | RangeRandom (Real fLow, Real fHigh) |
| Generate a random number within the range provided. | |
| static bool | RealEqual (Real a, Real b, Real tolerance=std::numeric_limits< Real >::epsilon()) |
| Compare 2 reals, using tolerance for inaccuracies. | |
| static double | saturate (double t) |
| static float | saturate (float t) |
| static void | setAngleUnit (AngleUnit unit) |
| These functions used to set the assumed angle units (radians or degrees) expected when using the Angle type. | |
| static void | SetRandomValueProvider (RandomValueProvider *provider) |
| static Degree | Sign (const Degree &dValue) |
| static Radian | Sign (const Radian &rValue) |
| static Real | Sign (Real fValue) |
| static Real | Sin (const Radian &fValue, bool useTables=false) |
| Sine function. | |
| static Real | Sin (Real fValue, bool useTables=false) |
| Sine function. | |
| template<typename T, typename S> | |
| static FORCEINLINE T | smoothstep (const T &edge0, const T &edge1, const S &x) |
| Performs smooth Hermite interpolation between 0 and 1 when edge0 < x < edge1. | |
| static Real | Sqr (Real fValue) |
| Squared function. | |
| static Degree | Sqrt (const Degree &fValue) |
| Square root function. | |
| static Radian | Sqrt (const Radian &fValue) |
| Square root function. | |
| static Real | Sqrt (Real fValue) |
| Square root function. | |
| static Real | SymmetricRandom () |
| Generate a random number in the range [-1,1]. | |
| static Real | Tan (const Radian &fValue, bool useTables=false) |
| Tangent function. | |
| static Real | Tan (Real fValue, bool useTables=false) |
| Tangent function. | |
| static Real | UnitRandom () |
| Generate a random number of unit length. | |
| static Real | Wrap (Real v) |
| Wraps the value 'v' into the range [0; 1) | |
Static Public Attributes | |
| static const Real | fDeg2Rad |
| static const Real | fRad2Deg |
| static const Real | HALF_PI |
| static const Real | LOG2 |
| Stored value of log(2) for frequent use. | |
| static const Real | NEG_INFINITY |
| static const Real | PI |
| static const Real | POS_INFINITY |
| static const Real | TWO_PI |
Class to provide access to common mathematical functions.
The angular units used by the API.
This functionality is now deprecated in favor of discreet angular unit types ( see Degree and Radian above ). The only place this functionality is actually still used is when parsing files. Search for usage of the Angle class for those instances
| Enumerator | |
|---|---|
| AU_DEGREE | |
| AU_RADIAN | |
| Ogre::Math::Math | ( | unsigned int | trigTableSize = 4096 | ) |
Default constructor.
| trigTableSize | Optional parameter to set the size of the tables used to implement Sin, Cos, Tan |
| Ogre::Math::~Math | ( | ) |
Default destructor.
Absolute value function.
| dValue | The value, in degrees, whose absolute value will be returned. |
References Ogre::Degree::valueDegrees().
Absolute value function.
| rValue | The value, in radians, whose absolute value will be returned. |
References Ogre::Radian::valueRadians().
Absolute value function.
| fValue | The value whose absolute value will be returned. |
Referenced by Ogre::MathlibC::Abs4(), Ogre::Vector3::absDotProduct(), Ogre::Vector3::directionEquals(), Ogre::Volume::OctreeNode::isIsoSurfaceNear(), Ogre::Vector3::makeAbs(), Ogre::Vector3::primaryAxis(), and Ogre::AxisAlignedBox::transformAffine().
Arc cosine function.
| fValue | The value whose arc cosine will be returned. |
Referenced by Ogre::Vector2::angleBetween(), Ogre::Vector3::angleBetween(), and Ogre::Vector3::directionEquals().
Convert from the current AngleUnit to degrees.
Referenced by Ogre::Angle::operator Degree().
Convert from the current AngleUnit to radians.
Referenced by Ogre::Angle::operator Radian().
Arc sine function.
| fValue | The value whose arc sine will be returned. |
Arc tangent function.
| fValue | The value whose arc tangent will be returned. |
Arc tangent between two values function.
| fY | The first value to calculate the arc tangent with. |
| fX | The second value to calculate the arc tangent with. |
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Get a bounding radius value from a bounding box.
Build a reflection matrix for the passed in plane.
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Calculate a face normal, no w-information.
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Calculate a face normal without normalize, no w-information.
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Calculate a face normal, including the w component which is the offset from the origin.
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Calculate a face normal without normalize, including the w component which is the offset from the origin.
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Calculates the tangent space vector for a given set of positions / texture coords.
Ceiling function Returns the smallest following integer.
(example: Ceil(1.1) = 2)
| fValue | The value to round up to the nearest integer. |
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Clamp a value within an inclusive range.
Referenced by Ogre::Vector2::angleBetween(), Ogre::Vector3::angleBetween(), Ogre::Bitwise::floatToSnorm16(), and Ogre::Bitwise::floatToSnorm8().
Return closest power of two not smaller than given number.
Cosine function.
| fValue | Angle in radians |
| useTables | If true, uses lookup tables rather than calculation - faster but less accurate. |
References HALF_PI, and Ogre::Radian::valueRadians().
Referenced by Ogre::Vector2::randomDeviant().
Convert from degrees to the current AngleUnit.
Referenced by Ogre::Degree::valueAngleUnits().
References fDeg2Rad, and OGRE_ASSERT_HIGH.
Referenced by Ogre::Degree::valueRadians().
Floor function Returns the largest previous integer.
(example: Floor(1.9) = 1)
| fValue | The value to round down to the nearest integer. |
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Generates a value based on the Gaussian (normal) distribution function with the given offset and scale parameters.
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Get the unit being used for angles.
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Plane / box intersection test.
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Ray / box intersection, returns boolean result and distance.
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Ray / box intersection, returns boolean result and two intersection distance.
| ray | The ray. |
| box | The box. |
| d1 | A real pointer to retrieve the near intersection distance from the ray origin, maybe null which means don't care about the near intersection distance. |
| d2 | A real pointer to retrieve the far intersection distance from the ray origin, maybe null which means don't care about the far intersection distance. |
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Ray / plane intersection, returns boolean result and distance.
Referenced by Ogre::AxisAlignedBox::intersects(), Ogre::AxisAlignedBox::intersects(), Ogre::PlaneBoundedVolume::intersects(), Ogre::Ray::intersects(), Ogre::Ray::intersects(), Ogre::Ray::intersects(), Ogre::Ray::intersects(), Ogre::Sphere::intersects(), and Ogre::Sphere::intersects().
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Ray / sphere intersection, returns boolean result and distance.
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Ray / convex plane list intersection test.
| ray | The ray to test with |
| planeList | List of planes which form a convex volume |
| normalIsOutside | Does the normal point outside the volume |
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Ray / convex plane list intersection test.
| ray | The ray to test with |
| planeList | List of planes which form a convex volume |
| normalIsOutside | Does the normal point outside the volume |
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Ray / triangle intersection, returns boolean result and distance.
| ray | The ray. |
| a | The triangle's first vertex. |
| b | The triangle's second vertex. |
| c | The triangle's third vertex. |
| positiveSide | Intersect with "positive side" of the triangle |
| negativeSide | Intersect with "negative side" of the triangle |
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Ray / triangle intersection, returns boolean result and distance.
| ray | The ray. |
| a | The triangle's first vertex. |
| b | The triangle's second vertex. |
| c | The triangle's third vertex. |
| normal | The triangle plane's normal (passed in rather than calculated on demand since the caller may already have it), doesn't need normalised since we don't care. |
| positiveSide | Intersect with "positive side" of the triangle |
| negativeSide | Intersect with "negative side" of the triangle |
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Sphere / plane intersection test.
Inverse square root i.e.
1 / Sqrt(x), good for vector normalisation.
| fValue | The value whose inverse square root will be calculated. |
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Returns Least Common Multiple.
References gcd().
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Linear interpolation.
Given 3 parameters a, b and w the function returns the value of (1 – w)* a + w * b. Where a and b are matching vector or scalar types and w can be either a scalar or a vector of the same type as a and b.
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Takes a 2D value in range [0; 1] and returns a unit-length 3D vector.
Takes a directional 3D vector n and returns a 2D value in range [0; 1] Vector 'n' doesn't have to be normalized.
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Checks whether a given point is inside a triangle, in a 2-dimensional (Cartesian) space.
| p | The point. |
| a | The triangle's first vertex. |
| b | The triangle's second vertex. |
| c | The triangle's third vertex. |
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Checks whether a given 3D point is inside a triangle.
| p | p The point. |
| a | The triangle's first vertex. |
| b | The triangle's second vertex. |
| c | The triangle's third vertex. |
| normal | The triangle plane's normal (passed in rather than calculated on demand since the caller may already have it) |
Convert from radians to the current AngleUnit .
Referenced by Ogre::Radian::valueAngleUnits().
References fRad2Deg, and OGRE_ASSERT_HIGH.
Referenced by Ogre::Radian::valueDegrees().
Generate a random number within the range provided.
| fLow | The lower bound of the range. |
| fHigh | The upper bound of the range. |
Referenced by Ogre::Vector2::randomDeviant().
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Compare 2 reals, using tolerance for inaccuracies.
Referenced by Ogre::Matrix3::hasScale(), Ogre::Matrix4::hasScale(), and Ogre::Vector3::positionEquals().
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Referenced by smoothstep().
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References Sign(), and Ogre::Degree::valueDegrees().
References Sign(), and Ogre::Radian::valueRadians().
Sine function.
| fValue | Angle in radians |
| useTables | If true, uses lookup tables rather than calculation - faster but less accurate. |
References Ogre::Radian::valueRadians().
Referenced by Ogre::Vector2::randomDeviant().
Sine function.
| fValue | Angle in radians |
| useTables | If true, uses lookup tables rather than calculation - faster but less accurate. |
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inlinestatic |
Performs smooth Hermite interpolation between 0 and 1 when edge0 < x < edge1.
This is useful in cases where a threshold function with a smooth transition is desired.
References saturate().
Squared function.
| fValue | The value to be squared (fValue^2) |
Referenced by Ogre::Sphere::intersects(), Ogre::Sphere::intersects(), and Ogre::Sphere::merge().
Square root function.
| fValue | The value, in degrees, whose square root will be calculated. |
References Ogre::Degree::valueDegrees().
Square root function.
| fValue | The value, in radians, whose square root will be calculated. |
References Ogre::Radian::valueRadians().
Square root function.
| fValue | The value whose square root will be calculated. |
Referenced by Ogre::AxisAlignedBox::distance(), Ogre::Vector3::getRotationTo(), Ogre::Vector2::length(), Ogre::Vector3::length(), Ogre::Sphere::merge(), Ogre::Vector2::normalise(), and Ogre::Vector3::normalise().
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Generate a random number in the range [-1,1].
Tangent function.
| fValue | Angle in radians |
| useTables | If true, uses lookup tables rather than calculation - faster but less accurate. |
References Ogre::Radian::valueRadians().
Tangent function.
| fValue | Angle in radians |
| useTables | If true, uses lookup tables rather than calculation - faster but less accurate. |
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Generate a random number of unit length.
Referenced by Ogre::Vector3::randomDeviant().
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Referenced by DegreesToRadians().
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Referenced by RadiansToDegrees().
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Stored value of log(2) for frequent use.
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Referenced by Ogre::Vector3::getRotationTo().
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Referenced by Ogre::Vector2::angleTo(), and Ogre::Vector3::randomDeviant().