col(x,index)
Extract a column from the specified matrix.
x: The matrix to extract a column from.index: The index of the column (zero based).A vector extracted from the matrix.
>>> col(float4x4(1..16), 2)
# col(float4x4(1..16), 2)
out = float4(3, 7, 11, 15)
cross(x,y)
Returns the cross product of two floating-point, 3D vectors.
x: The first floating-point, 3D vector.y: The second floating-point, 3D vector.The cross product of the x parameter and the y parameter.
>>> cross(float3(1,2,3), float3(4,5,6))
# cross(float3(1, 2, 3), float3(4, 5, 6))
out = float3(-3, 6, -3)
>>> cross(float3(1,0,0), float3(0,1,0))
# cross(float3(1, 0, 0), float3(0, 1, 0))
out = float3(0, 0, 1)
>>> cross(float3(0,0,1), float3(0,1,0))
# cross(float3(0, 0, 1), float3(0, 1, 0))
out = float3(-1, 0, 0)
determinant(m)
Calculates the determinant of the specified matrix.
m: The matrix to calculate the determinant for.A scalar representing the determinant of the matrix.
>>> float4x4(4,3,2,2,0,1,-3,3,0,-1,3,3,0,3,1,1)
# float4x4(4, 3, 2, 2, 0, 1, -3, 3, 0, -1, 3, 3, 0, 3, 1, 1)
out = float4x4(4, 3, 2, 2, 0, 1, -3, 3, 0, -1, 3, 3, 0, 3, 1, 1)
# col 0 1 2 3 / row
float4(4 , 3 , 2 , 2 ) # 0
float4(0 , 1 , -3 , 3 ) # 1
float4(0 , -1 , 3 , 3 ) # 2
float4(0 , 3 , 1 , 1 ) # 3
>>> determinant out
# determinant(out)
out = -240
diag(x)
Returns the diagonal vector of a squared matrix or a diagonal matrix from the specified vector.
x: A vector or matrix to return the associated diagonal for.A diagonal vector of a matrix or a diagonal matrix of a vector.
>>> diag(float4x4(1..16))
# diag(float4x4(1..16))
out = float4(1, 6, 11, 16)
>>> diag(float4(1,2,3,4))
# diag(float4(1, 2, 3, 4))
out = float4x4(1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4)
# col 0 1 2 3 / row
float4(1 , 0 , 0 , 0 ) # 0
float4(0 , 2 , 0 , 0 ) # 1
float4(0 , 0 , 3 , 0 ) # 2
float4(0 , 0 , 0 , 4 ) # 3
dot(x,y)
Returns the dot product of two vectors.
x: The first vector.y: The second vector.The dot product of the x parameter and the y parameter.
>>> dot(float3(1,2,3), float3(4,5,6))
# dot(float3(1, 2, 3), float3(4, 5, 6))
out = 32
>>> dot(float3(1,2,3), 4)
# dot(float3(1, 2, 3), 4)
out = 24
>>> dot(4, float3(1,2,3))
# dot(4, float3(1, 2, 3))
out = 24
>>> dot(5,6)
# dot(5, 6)
out = 30
identity(m)
Creates an identity of a squared matrix.
m: The type of the squared matrix.The identity matrix of the squared matrix type.
>>> identity(float4x4)
# identity(float4x4)
out = float4x4(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)
# col 0 1 2 3 / row
float4(1 , 0 , 0 , 0 ) # 0
float4(0 , 1 , 0 , 0 ) # 1
float4(0 , 0 , 1 , 0 ) # 2
float4(0 , 0 , 0 , 1 ) # 3
inverse(m)
Calculates the inverse of the specified matrix.
m: The matrix to calculate the inverse for.The inverse matrix of the specified matrix.
>>> inverse(float3x3(10,20,10,4,5,6,2,3,5))
# inverse(float3x3(10, 20, 10, 4, 5, 6, 2, 3, 5))
out = float3x3(-0.1, 1, -1, 0.11428571, -0.42857143, 0.28571427, -0.028571427, -0.14285715, 0.42857143)
# col 0 1 2 / row
float3(-0.1 , 1 , -1 ) # 0
float3( 0.11428571 , -0.42857143, 0.28571427) # 1
float3(-0.028571427, -0.14285715, 0.42857143) # 2
length(x)
Returns the length of the specified floating-point vector.
x: The specified floating-point vector.A floating-point scalar that represents the length of the x parameter.
>>> length float2(1, 2)
# length(float2(1, 2))
out = 2.23606797749979
>>> length(-5)
# length(-5)
out = 5
mul(x,y)
Multiplies a vector x vector (dot product), or a vector x matrix, or a matrix x vector or a matrix x matrix.
x: A left vector or a matrix.y: A right vector or matrix.The result of the multiplication.
>>> mul(float4(1,2,3,4), float4(5,6,7,8))
# mul(float4(1, 2, 3, 4), float4(5, 6, 7, 8))
out = 70
>>> mul(float3(3,7,5), float3x3(2,3,-4,11,8,7,2,5,3))
# mul(float3(3, 7, 5), float3x3(2, 3, -4, 11, 8, 7, 2, 5, 3))
out = float3(7, 124, 56)
>>> mul(float3x3(2,3,-4,11,8,7,2,5,3), float3(3,7,5))
# mul(float3x3(2, 3, -4, 11, 8, 7, 2, 5, 3), float3(3, 7, 5))
out = float3(93, 90, 52)
>>> mul(float3x3(2,7,4,3,2,1,9,-1,2), float3x3(1,4,6,-1,-2,5,8,7,6))
# mul(float3x3(2, 7, 4, 3, 2, 1, 9, -1, 2), float3x3(1, 4, 6, -1, -2, 5, 8, 7, 6))
out = float3x3(68, 9, 20, 37, -16, 4, 91, 64, 51)
# col 0 1 2 / row
float3(68 , 9 , 20 ) # 0
float3(37 , -16 , 4 ) # 1
float3(91 , 64 , 51 ) # 2
normalize(x)
Normalizes the specified floating-point vector according to x / length(x).
x: he specified floating-point vector.The normalized x parameter. If the length of the x parameter is 0, the result is indefinite.
>>> normalize float2(1,2)
# normalize(float2(1, 2))
out = float2(0.4472136, 0.8944272)
row(x,index)
Extract a row from the specified matrix.
x: The matrix to extract a row from.index: The index of the row (zero based).A vector extracted from the matrix.
>>> row(float4x4(1..16), 2)
# row(float4x4(1..16), 2)
out = float4(9, 10, 11, 12)
transpose(m)
Transposes the specified matrix.
m: The matrix to transpose.The transposed matrix.
>>> transpose float3x4(1..12)
# transpose(float3x4(1..12))
out = float4x3(1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12)
# col 0 1 2 / row
float3(1 , 5 , 9 ) # 0
float3(2 , 6 , 10 ) # 1
float3(3 , 7 , 11 ) # 2
float3(4 , 8 , 12 ) # 3
>>> transpose(out)
# transpose(out)
out = float3x4(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
# col 0 1 2 3 / row
float4(1 , 2 , 3 , 4 ) # 0
float4(5 , 6 , 7 , 8 ) # 1
float4(9 , 10 , 11 , 12 ) # 2