Math Common Functions

Методы:

Имя	Описание View: Sort by:
abs	Returns the absolute value of the argument.
add3	Returns the result of a componentwise addition of three components of vectors by storing it in the array.
bezier	Calculates the value of a cubic Bezier function for t = time.
blueNoise	Returns a blue noise value for the given pixel coordinates.
ceil	Ceiling function that returns the smallest integer value that is not less than the argument.
ceilInt	Returns the smallest value that's greater than or equal to the argument, stored as an integer.
changeRange	Transforms the value from the source range to the corresponding value within target range.
checkMask	Checks if any of the bits specified in bits are set in mask.
checkRange	Checks if the input value is within the specified range.
clamp	Clamps a value within the specified min and max limits.
compare	Compares two scalars of the int type.
conjugate	Returns the conjugate of a given quaternion.
cross	Cross product of vectors.
cross3	Returns the cross product of three components of vectors by storing it in the array.
distance	Calculates the distance between the two given vectors.
distance2	Calculates the squared distance between the two given vectors.
dot	Dot product of vectors.
dot2	Returns the dot product between a 2-component vector v and another 2-component vector defined by (x, y).
dot3	Dot product of three components of vectors.
dtof	Converts a double value to an integer value.
dtoi	Converts a double value to an integer value.
dtol	Converts a double value to a long value.
floor	Rounds an argument down to the nearest integer.
floorInt	Returns the largest value that is less than or equal to the argument, stored as an integer.
frac	Returns the fractional part of the argument.
ftoc	Converts a float value to a char value.
ftoi	Converts a float value to an integer value.
ftol	Converts a float value to a long value.
getAngle	Returns the angle (in degrees) between the given first and second quaternions.
getBit	Extracts a specific bit from an integer value and returns it as a boolean.
gradient4	Returns a gradient value for the specified argument using four key components.
hashInteger	Computes a hash value from an input value.
hashMixer	Mixes two hash values.
hashCombine	Combines the provided hash with a hash of the specified value.
hashCast64To32	Casts the 64-bit hash value to the 32-bit hash value.
inverse	Returns inverse of the quaternion.
inverseLerp	Returns the value calculated according to the following formula: (v - v0) / (v1 - v0) clamped within 0.
contrastLerp	Performs a smooth interpolation between two vectors (point_a and point_b) using a specified coefficient range to create a smooth transition effect.
isFinite	Returns a value indicating that the given value is a finite number, meaning it is neither NaN nor infinity (positive or negative).
isInf	Returns a value indicating whether the argument evaluates to negative or positive infinity.
isNan	Returns a value that indicates whether the argument is not a number (NaN).
isrgb	Converts sRGB color value to RGB format.
isrgbColor	Converts sRGB color value to RGB format without converting alpha.
itod	Converts an integer value to a double value.
itof	Converts an integer value to a float value.
itos	Converts an integer value to a scalar value (float or double, depending on the precision).
length	Calculates the length of a given vector.
length2	Calculates the squared length of a given vector.
lerp	Returns the interpolated value according to the following formula: v0 + (v 1 - v 0) * k .
lerpOne	Performs the interpolation: v0 * (1.0f - k) + k.
lerpZero	Performs the interpolation: v0 * (1.0f - k).
lerp3	Performs linear interpolation between three vectors.
ltof	Converts a long value to a float value.
ltod	Converts a long value to a double value.
max	Compares the arguments and returns the maximum value.
min	Compares the arguments and returns the minimum value.
mul3	Returns the result of a componentwise multiplication of a 3-component vector with a scalar value.
normalize	Normalizes a quaternion, makes its magnitude equal to 1.
normalizeAngle	Normalizes an input angle to the range (−180, 180).
normalizeValid	Normalizes a quaternion, makes its magnitude equal to 1.
normalize2	Normalizes a 2-component vector, making it a unit vector (a vector with a length of 1) while preserving its direction.
normalize3	Normalizes a 3-component vector, making it a unit vector (a vector with a length of 1) while preserving its direction.
normalizeValid3	Normalizes a vector making its magnitude equal to 1.
npot	Rounds up to the nearest power of two value.
ispot	Checks if the argument value is a power of two by using bitwise operations.
isqrt	Returns the integer square root of the argument value by using bitwise operations.
overlay	Performs overlay A over B with blending coefficient.
rcp	Returns the reciprocal of the specified argument.
rcpFast	Returns the approximated (quicker calculated) reciprocal of the specified argument.
rerange	Returns the value that corresponds to the input value remapped within the limits of the output range.
reverseBits	Returns the value with the reversed order of the bits.
rotate	Returns a resulting matrix for rotation by the specified angle around the axis specified as a quaternion/vector/vector components.
rotate3	Returns a resulting matrix for rotation by the specified angle around the axis specified as a quaternion/vector/vector components.
round	Rounds an argument to the nearest integer value.
roundFast	Rounds an argument to the nearest integer value by adding 0.
saturate	Clamps the value within the range of 0.
sign	Returns the sign of the argument.
signMask	Returns the sign of the argument value.
slerp	Spherical interpolation between two given quaternions.
smoothstep	Returns a smooth Hermite interpolation between 0 and 1, if x is in the range [0, 1].
smootherstep	Returns a smooth interpolation between 0 and 1 using a fifth-order polynomial function, if x is in the range [0, 1].
srgb	Converts RGB color value to sRGB format.
srgbColor	Converts RGB color value to sRGB format without converting alpha.
step	Checks whether the value a is greater than or equal to b.
stoi	Converts a scalar value (float or double, depending on the precision) to an integer value.
sub3	Returns the result of a componentwise subtraction of three components of vectors by storing it in the array.
swap	Swaps two values.
floatToIntBits	Returns an integer corresponding to the bits of the given value.
floatToUIntBits	Returns an unsigned integer corresponding to the bits of the given value.
intBitsToFloat	Returns the float corresponding to the given bits.
floatToLongBits	Returns a long long value corresponding to the given value.
floatToULongBits	Returns a long long value corresponding to the given value.
longBitsToFloat	Returns the double corresponding to the given bits.
doubleIntToLong	Returns a conversion of two unsigned integer values to a unsigned long long value.
toFloat	Converts a double value to a float value.
toHalf	Converts a float value to a half value.
toDouble	Converts a float value to a double value.
toScalar	Converts a double value to a Scalar value.
toInt	Converts a float value to an integer value.
toUInt	Converts a float value to an unsigned int value.
toLong	Converts an integer value to a long value.
toULong	Converts an integer value to an unsigned long value.
toChar	Converts a float value to a character value.
toShort	Converts a float value to a short value.
toUChar	Converts a float value to an unsigned character value.
toUShort	Converts a float value to an unsigned short value.
toBool	Converts a float value to a boolean value.
unsafeToMat2x2	Performs an unsafe conversion of the specified pointer to a source array containing matrix data to the dedicated type used to store elements of a 2x2 matrix.
unsafeToMat3x3	Performs an unsafe conversion of the specified pointer to a source array containing matrix data to the dedicated type used to store elements of a 3x3 matrix.
unsafeToMat4x3	Performs an unsafe conversion of the specified pointer to a source array containing matrix data to the dedicated type used to store elements of a 4x3 matrix.
unsafeToMat4x4	Performs an unsafe conversion of the specified pointer to a source array containing matrix data to the dedicated type used to store elements of a 4x4 matrix.
unsafeToDMat4x3	Performs an unsafe conversion of the specified pointer to a source array containing matrix data to the dedicated type used to store elements of a 4x3 matrix.
unsafeToDMat4x4	Performs an unsafe conversion of the specified pointer to a source array containing matrix data to the dedicated type used to store elements of a 4x4 matrix.
udiv	Performs integer division with rounding up: it adds 1 to the result if there is a remainder from the division.
vogelDisk	Returns a generated set of points with X and Y coordinates in the [-1; 1] range that describe a circle with uniform distribution of samples inside.
operator ==	Checks if two controls are actually the same controls.
operator !=	Checks if two controls are not the same controls.
operator *	Multiplication.
operator +	Addition.
operator -	Subtraction.
operator %	Modulus operation.
operator /	Division.
operator <<	Left bit shift.
operator >>	Right bit shift.
mod	Returns the floating-point remainder of the division operation: first argument / second argument.
mad	Returns the result of multiplication of the first value by the second value and addition of the third value (a * b + c).
select	Returns one of the two argument values (v0 and v1) based on the specified condition (c).
operator <	Less than comparison.
operator >	Greater than comparison.
operator <=	Less than or equal comparison.
operator >=	Greater than or equal comparison.

Variables:

Name	Description
vec4_zero	Vector filled with zeros (0).
vec4_one	Vector filled with ones (1).
vec4_eps	Vector filled with epsilon constant (1e-6f).
vec4_inf	Vector filled with the infinity constant (1e+9f).
vec4_white	White color vector (1, 1, 1, 1).
vec4_black	Black color vector (0, 0, 0, 0).
vec4_red	Red color vector (1, 0, 0, 1).
vec4_green	Green color vector (0, 1, 0, 1).
vec4_blue	Blue color vector (0, 0, 1, 1).

Math Class

Перечисления (Enums)

AXIS#

Имя	Описание
AXIS_X = = 0	Positive X axis.
AXIS_Y = = 1	Positive Y axis.
AXIS_Z = = 2	Positive Z axis.
AXIS_NX = = 3	Negative X axis.
AXIS_NY = = 4	Negative Y axis.
AXIS_NZ = = 5	Negative Z axis.

Members

float abs ( float v ) #

Returns the absolute value of the argument.

Arguments

float v - Float value.

Return value

Absolute value.

double abs ( double v ) #

Returns the absolute value of the argument.

Arguments

double v - Value.

Return value

Absolute value.

int abs ( int v ) #

Returns the absolute value of the argument.

Arguments

int v - Value.

Return value

Absolute value.

long long abs ( long long v ) #

Returns the absolute value of the argument.

Arguments

long long v - Value.

Return value

Absolute value.

vec2 abs ( vec2 v ) #

Returns the absolute values of the vector components.

Arguments

vec2 v - Source vector.

Return value

Vector with absolute values.

vec3 abs ( vec3 v ) #

Returns the absolute values of the vector components.

Arguments

vec3 v - Source vector.

Return value

Vector with absolute values.

vec4 abs ( vec4 v ) #

Returns the absolute values of the vector components.

Arguments

vec4 v - Source vector.

Return value

Vector with absolute values.

dvec2 abs ( dvec2 v ) #

Returns the absolute values of the vector components.

Arguments

dvec2 v - Source vector.

Return value

Vector with absolute values.

dvec3 abs ( dvec3 v ) #

Returns the absolute values of the vector components.

Arguments

dvec3 v - Source vector.

Return value

Vector with absolute values.

dvec4 abs ( dvec4 v ) #

Returns the absolute values of the vector components.

Arguments

dvec4 v - Source vector.

Return value

Vector with absolute values.

ivec2 abs ( ivec2 v ) #

Returns the absolute values of the vector components.

Arguments

ivec2 v - Source vector.

Return value

Vector with absolute values.

ivec3 abs ( ivec3 v ) #

Returns the absolute values of the vector components.

Arguments

ivec3 v - Source vector.

Return value

Vector with absolute values.

ivec4 abs ( ivec4 v ) #

Returns the absolute values of the vector components.

Arguments

ivec4 v - Source vector.

Return value

Vector with absolute values.

float * add3 ( float UNIGINE_RESTRICT ret, const float UNIGINE_RESTRICT v0, const float *UNIGINE_RESTRICT v1 ) #

Returns the result of a componentwise addition of three components of vectors by storing it in the array.

Arguments

float *UNIGINE_RESTRICT ret - Array to store the return value.
const float *UNIGINE_RESTRICT v0 - Pointer to vector.
const float *UNIGINE_RESTRICT v1 - Pointer to vector.

Return value

Pointer to the array that stores the return value.

float bezier ( const float * times, const float * values, float time ) #

Calculates the value of a cubic Bezier function for t = time.

A cubic Bezier curve is represented by 4 points. P_o is the start point, P₁ and P₂ are control points 1 and 2 and P₃ is the end point. The start and end point denote the beginning and end points of the path and the control points determine how the path moves from the start to the finish. As can be seen from the image, the only variable changing is t which determines how far the path has progressed from P0 to P3. Cubic Bezier curves are used as timing functions particularly for keyframe interpolation.

Arguments

const float * times - Coordinates of the four points of the curve along the horizontal T (times) axis in the range [0.0f, 1.0f].
const float * values - Coordinates of the four points of the curve along the vertical V (values) axis in the range [0.0f, 1.0f].
float time - Time in the range [0, 1], for which the value of the Bezier function is to be calculated.

Return value

Value of the Bezier function.

double bezier ( const float * times, const double * values, float time ) #

Calculates the value of a cubic Bezier function for t = time.

Arguments

const float * times - Coordinates of the four points of the curve along the horizontal T (times) axis in the range [0.0f, 1.0f].
const double * values - Coordinates of the four points of the curve along the vertical V (values) axis in the range [0.0f, 1.0f].
float time - Time in the range [0, 1], for which the value of the Bezier function is to be calculated.

Return value

Value of the Bezier function.

vec4 blueNoise ( int x, int y ) #

Returns a blue noise value for the given pixel coordinates.

Arguments

int x - X coordinate of the pixel.
int y - Y coordinate of the pixel.

Return value

Blue noise value.

float ceil ( float v ) #

Ceiling function that returns the smallest integer value that is not less than the argument.

Source code

float a = ceil(3.141593); // a = 4.0

Arguments

float v - Argument.

Return value

Smallest integer value not less than v.

double ceil ( double v ) #

Ceiling function that returns the smallest integer value that is not less than the argument.

Source code

double a = ceil(3.141593); // a = 4.0

Arguments

double v - Argument.

Return value

Smallest integer value not less than v.

const vec2 & ceil ( const vec2 & v ) #

Ceiling function that returns the vector storing the smallest integer values that are not less than the argument.

Arguments

const vec2 & v - Vector storing values.

Return value

Vector storing the smallest integer values not less than v.

const vec3 & ceil ( const vec3 & v ) #

Ceiling function that returns the vector storing the smallest integer values that are not less than the argument.

Arguments

const vec3 & v - Vector storing values.

Return value

Vector storing the smallest integer values not less than v.

const vec4 & ceil ( const vec4 & v ) #

Ceiling function that returns the vector storing the smallest integer values that are not less than the argument.

Arguments

const vec4 & v - Vector storing values.

Return value

Vector storing the smallest integer values not less than v.

const dvec2 & ceil ( const dvec2 & v ) #

Ceiling function that returns the vector storing the smallest integer values that are not less than the argument.

Arguments

const dvec2 & v - Vector storing values.

Return value

Vector storing the smallest integer values not less than v.

const dvec3 & ceil ( const dvec3 & v ) #

Ceiling function that returns the vector storing the smallest integer values that are not less than the argument.

Arguments

const dvec3 & v - Vector storing values.

Return value

Vector storing the smallest integer values not less than v.

const dvec4 & ceil ( const dvec4 & v ) #

Ceiling function that returns the vector storing the smallest integer values that are not less than the argument.

Arguments

const dvec4 & v - Vector storing values.

Return value

Vector storing the smallest integer values not less than v.

int ceilInt ( float v ) #

Returns the smallest value that's greater than or equal to the argument, stored as an integer.

Arguments

float v - Value.

Return value

Resulting int value.

int ceilInt ( double v ) #

Returns the smallest value that's greater than or equal to the argument, stored as an integer.

Arguments

double v - Value.

Return value

Resulting int value.

double changeRange ( double value, const dvec4 & range ) #

Transforms the value from the source range to the corresponding value within target range.

Arguments

double value - The value within the source range.
const dvec4 & range - The vector containing 4 values: values X and Y define the source range, values Z and W define the target range.

Return value

The value within the target range.

bool checkMask ( const int mask, const int bits ) #

Checks if any of the bits specified in bits are set in mask.

Arguments

const int mask - Bit mask to be checked.
const int bits - Bits in the mask to be checked.

Return value

true if there is at least one bit that is specified in both mask and bits, otherwise false.

bool checkMask ( const unsigned int mask, const unsigned int bits ) #

Checks if any of the bits specified in bits are set in mask.

Arguments

const unsigned int mask - Bit mask to be checked.
const unsigned int bits - Bits in the mask to be checked.

Return value

true if there is at least one bit that is specified in both mask and bits, otherwise false.

bool checkMask ( const unsigned int mask, const int bits ) #

Checks if any of the bits specified in bits are set in mask.

Arguments

const unsigned int mask - Bit mask to be checked.
const int bits - Bits in the mask to be checked.

Return value

true if there is at least one bit that is specified in both mask and bits, otherwise false.

bool checkMask ( const int mask, const unsigned int bits ) #

Checks if any of the bits specified in bits are set in mask.

Arguments

const int mask - Bit mask to be checked.
const unsigned int bits - Bits in the mask to be checked.

Return value

true if there is at least one bit that is specified in both mask and bits, otherwise false.

bool checkRange ( float value, float range_min, float range_max ) #

Checks if the input value is within the specified range.

Arguments

float value - Input value.
float range_min - Minimum value of the range.
float range_max - Maximum value of the range.

Return value

true if the value is within the range, otherwise — false.

bool checkRange ( double value, double range_min, double range_max ) #

Checks if the input value is within the specified range.

Arguments

double value - Input value.
double range_min - Minimum value of the range.
double range_max - Maximum value of the range.

Return value

true if the value is within the range, otherwise — false.

bool checkRange ( int value, int range_min, int range_max ) #

Checks if the input value is within the specified range.

Arguments

int value - Input value.
int range_min - Minimum value of the range.
int range_max - Maximum value of the range.

Return value

true if the value is within the range, otherwise — false.

bool checkRange ( long long value, long long range_min, long long range_max ) #

Checks if the input value is within the specified range.

Arguments

long long value - Input value.
long long range_min - Minimum value of the range.
long long range_max - Maximum value of the range.

Return value

true if the value is within the range, otherwise — false.

bool checkRange ( short value, short range_min, short range_max ) #

Checks if the input value is within the specified range.

Arguments

short value - Input value.
short range_min - Minimum value of the range.
short range_max - Maximum value of the range.

Return value

true if the value is within the range, otherwise — false.

bool checkRange ( char value, char range_min, char range_max ) #

Checks if the input value is within the specified range.

Arguments

char value - Input value.
char range_min - Minimum value of the range.
char range_max - Maximum value of the range.