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raymath.go
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raymath.go
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// Package raymath - Some useful functions to work with Vector2, Vector3, Matrix and Quaternions
package raymath
import (
"math"
"github.com/gen2brain/raylib-go/raylib"
)
// Vector2Zero - Vector with components value 0.0
func Vector2Zero() rl.Vector2 {
return rl.NewVector2(0.0, 0.0)
}
// Vector2One - Vector with components value 1.0
func Vector2One() rl.Vector2 {
return rl.NewVector2(1.0, 1.0)
}
// Vector2Add - Add two vectors (v1 + v2)
func Vector2Add(v1, v2 rl.Vector2) rl.Vector2 {
return rl.NewVector2(v1.X+v2.X, v1.Y+v2.Y)
}
// Vector2Subtract - Subtract two vectors (v1 - v2)
func Vector2Subtract(v1, v2 rl.Vector2) rl.Vector2 {
return rl.NewVector2(v1.X-v2.X, v1.Y-v2.Y)
}
// Vector2Length - Calculate vector length
func Vector2Length(v rl.Vector2) float32 {
return float32(math.Sqrt(float64((v.X * v.X) + (v.Y * v.Y))))
}
// Vector2DotProduct - Calculate two vectors dot product
func Vector2DotProduct(v1, v2 rl.Vector2) float32 {
return v1.X*v2.X + v1.Y*v2.Y
}
// Vector2Distance - Calculate distance between two vectors
func Vector2Distance(v1, v2 rl.Vector2) float32 {
return float32(math.Sqrt(float64((v1.X-v2.X)*(v1.X-v2.X) + (v1.Y-v2.Y)*(v1.Y-v2.Y))))
}
// Vector2Angle - Calculate angle between two vectors in X-axis
func Vector2Angle(v1, v2 rl.Vector2) float32 {
angle := float32(math.Atan2(float64(v2.Y-v1.Y), float64(v2.X-v1.X)) * (180.0 / float64(rl.Pi)))
if angle < 0 {
angle += 360.0
}
return angle
}
// Vector2Scale - Scale vector (multiply by value)
func Vector2Scale(v *rl.Vector2, scale float32) {
v.X *= scale
v.Y *= scale
}
// Vector2Multiply - Multiply vector by vector
func Vector2Multiply(v1, v2 *rl.Vector2) rl.Vector2 {
return rl.NewVector2(v1.X*v2.X, v1.Y*v2.Y)
}
// Vector2Negate - Negate vector
func Vector2Negate(v *rl.Vector2) {
v.X = -v.X
v.Y = -v.Y
}
// Vector2Divide - Divide vector by a float value
func Vector2Divide(v *rl.Vector2, div float32) {
v.X = v.X / div
v.Y = v.Y / div
}
// Vector2DivideV - Divide vector by vector
func Vector2DivideV(v1, v2 *rl.Vector2) rl.Vector2 {
return rl.NewVector2(v1.X/v2.X, v1.Y/v2.Y)
}
// Vector2Normalize - Normalize provided vector
func Vector2Normalize(v *rl.Vector2) {
Vector2Divide(v, Vector2Length(*v))
}
// Vector2Lerp - Calculate linear interpolation between two vectors
func Vector2Lerp(v1, v2 *rl.Vector2, amount float32) rl.Vector2 {
return rl.NewVector2(v1.X+amount*(v2.X-v1.X), v1.Y+amount*(v2.Y-v1.Y))
}
// Vector2CrossProduct - Calculate two vectors cross product
func Vector2CrossProduct(v1, v2 rl.Vector2) float32 {
return v1.X*v2.Y - v1.Y*v2.X
}
// Vector2Cross - Calculate the cross product of a vector and a value
func Vector2Cross(value float32, vector rl.Vector2) rl.Vector2 {
return rl.NewVector2(-value*vector.Y, value*vector.X)
}
// Vector2LenSqr - Returns the len square root of a vector
func Vector2LenSqr(vector rl.Vector2) float32 {
return vector.X*vector.X + vector.Y*vector.Y
}
// Mat2Radians - Creates a matrix 2x2 from a given radians value
func Mat2Radians(radians float32) rl.Mat2 {
c := float32(math.Cos(float64(radians)))
s := float32(math.Sin(float64(radians)))
return rl.NewMat2(c, -s, s, c)
}
// Mat2Set - Set values from radians to a created matrix 2x2
func Mat2Set(matrix *rl.Mat2, radians float32) {
cos := float32(math.Cos(float64(radians)))
sin := float32(math.Sin(float64(radians)))
matrix.M00 = cos
matrix.M01 = -sin
matrix.M10 = sin
matrix.M11 = cos
}
// Mat2Transpose - Returns the transpose of a given matrix 2x2
func Mat2Transpose(matrix rl.Mat2) rl.Mat2 {
return rl.NewMat2(matrix.M00, matrix.M10, matrix.M01, matrix.M11)
}
// Mat2MultiplyVector2 - Multiplies a vector by a matrix 2x2
func Mat2MultiplyVector2(matrix rl.Mat2, vector rl.Vector2) rl.Vector2 {
return rl.NewVector2(matrix.M00*vector.X+matrix.M01*vector.Y, matrix.M10*vector.X+matrix.M11*vector.Y)
}
// Vector3Zero - Vector with components value 0.0
func Vector3Zero() rl.Vector3 {
return rl.NewVector3(0.0, 0.0, 0.0)
}
// Vector3One - Vector with components value 1.0
func Vector3One() rl.Vector3 {
return rl.NewVector3(1.0, 1.0, 1.0)
}
// Vector3Add - Add two vectors
func Vector3Add(v1, v2 rl.Vector3) rl.Vector3 {
return rl.NewVector3(v1.X+v2.X, v1.Y+v2.Y, v1.Z+v2.Z)
}
// Vector3Multiply - Multiply vector by scalar
func Vector3Multiply(v rl.Vector3, scalar float32) rl.Vector3 {
result := rl.Vector3{}
result.X = v.X * scalar
result.Y = v.Y * scalar
result.Z = v.Z * scalar
return result
}
// Vector3MultiplyV - Multiply vector by vector
func Vector3MultiplyV(v1, v2 rl.Vector3) rl.Vector3 {
result := rl.Vector3{}
result.X = v1.X * v2.X
result.Y = v1.Y * v2.Y
result.Z = v1.Z * v2.Z
return result
}
// Vector3Subtract - Subtract two vectors
func Vector3Subtract(v1, v2 rl.Vector3) rl.Vector3 {
return rl.NewVector3(v1.X-v2.X, v1.Y-v2.Y, v1.Z-v2.Z)
}
// Vector3CrossProduct - Calculate two vectors cross product
func Vector3CrossProduct(v1, v2 rl.Vector3) rl.Vector3 {
result := rl.Vector3{}
result.X = v1.Y*v2.Z - v1.Z*v2.Y
result.Y = v1.Z*v2.X - v1.X*v2.Z
result.Z = v1.X*v2.Y - v1.Y*v2.X
return result
}
// Vector3Perpendicular - Calculate one vector perpendicular vector
func Vector3Perpendicular(v rl.Vector3) rl.Vector3 {
result := rl.Vector3{}
min := math.Abs(float64(v.X))
cardinalAxis := rl.NewVector3(1.0, 0.0, 0.0)
if math.Abs(float64(v.Y)) < min {
min = math.Abs(float64(v.Y))
cardinalAxis = rl.NewVector3(0.0, 1.0, 0.0)
}
if math.Abs(float64(v.Z)) < min {
cardinalAxis = rl.NewVector3(0.0, 0.0, 1.0)
}
result = Vector3CrossProduct(v, cardinalAxis)
return result
}
// Vector3Length - Calculate vector length
func Vector3Length(v rl.Vector3) float32 {
return float32(math.Sqrt(float64(v.X*v.X + v.Y*v.Y + v.Z*v.Z)))
}
// Vector3DotProduct - Calculate two vectors dot product
func Vector3DotProduct(v1, v2 rl.Vector3) float32 {
return v1.X*v2.X + v1.Y*v2.Y + v1.Z*v2.Z
}
// Vector3Distance - Calculate distance between two vectors
func Vector3Distance(v1, v2 rl.Vector3) float32 {
dx := v2.X - v1.X
dy := v2.Y - v1.Y
dz := v2.Z - v1.Z
return float32(math.Sqrt(float64(dx*dx + dy*dy + dz*dz)))
}
// Vector3Scale - Scale provided vector
func Vector3Scale(v *rl.Vector3, scale float32) {
v.X *= scale
v.Y *= scale
v.Z *= scale
}
// Vector3Negate - Negate provided vector (invert direction)
func Vector3Negate(v *rl.Vector3) {
v.X = -v.X
v.Y = -v.Y
v.Z = -v.Z
}
// Vector3Normalize - Normalize provided vector
func Vector3Normalize(v *rl.Vector3) {
var length, ilength float32
length = Vector3Length(*v)
if length == 0 {
length = 1.0
}
ilength = 1.0 / length
v.X *= ilength
v.Y *= ilength
v.Z *= ilength
}
// Vector3Transform - Transforms a Vector3 by a given Matrix
func Vector3Transform(v *rl.Vector3, mat rl.Matrix) {
x := v.X
y := v.Y
z := v.Z
v.X = mat.M0*x + mat.M4*y + mat.M8*z + mat.M12
v.Y = mat.M1*x + mat.M5*y + mat.M9*z + mat.M13
v.Z = mat.M2*x + mat.M6*y + mat.M10*z + mat.M14
}
// Vector3Lerp - Calculate linear interpolation between two vectors
func Vector3Lerp(v1, v2 rl.Vector3, amount float32) rl.Vector3 {
result := rl.Vector3{}
result.X = v1.X + amount*(v2.X-v1.X)
result.Y = v1.Y + amount*(v2.Y-v1.Y)
result.Z = v1.Z + amount*(v2.Z-v1.Z)
return result
}
// Vector3Reflect - Calculate reflected vector to normal
func Vector3Reflect(vector, normal rl.Vector3) rl.Vector3 {
// I is the original vector
// N is the normal of the incident plane
// R = I - (2*N*( DotProduct[ I,N] ))
result := rl.Vector3{}
dotProduct := Vector3DotProduct(vector, normal)
result.X = vector.X - (2.0*normal.X)*dotProduct
result.Y = vector.Y - (2.0*normal.Y)*dotProduct
result.Z = vector.Z - (2.0*normal.Z)*dotProduct
return result
}
// Vector3Min - Return min value for each pair of components
func Vector3Min(vec1, vec2 rl.Vector3) rl.Vector3 {
result := rl.Vector3{}
result.X = float32(math.Min(float64(vec1.X), float64(vec2.X)))
result.Y = float32(math.Min(float64(vec1.Y), float64(vec2.Y)))
result.Z = float32(math.Min(float64(vec1.Z), float64(vec2.Z)))
return result
}
// Vector3Max - Return max value for each pair of components
func Vector3Max(vec1, vec2 rl.Vector3) rl.Vector3 {
result := rl.Vector3{}
result.X = float32(math.Max(float64(vec1.X), float64(vec2.X)))
result.Y = float32(math.Max(float64(vec1.Y), float64(vec2.Y)))
result.Z = float32(math.Max(float64(vec1.Z), float64(vec2.Z)))
return result
}
// Vector3Barycenter - Barycenter coords for p in triangle abc
func Vector3Barycenter(p, a, b, c rl.Vector3) rl.Vector3 {
v0 := Vector3Subtract(b, a)
v1 := Vector3Subtract(c, a)
v2 := Vector3Subtract(p, a)
d00 := Vector3DotProduct(v0, v0)
d01 := Vector3DotProduct(v0, v1)
d11 := Vector3DotProduct(v1, v1)
d20 := Vector3DotProduct(v2, v0)
d21 := Vector3DotProduct(v2, v1)
denom := d00*d11 - d01*d01
result := rl.Vector3{}
result.Y = (d11*d20 - d01*d21) / denom
result.Z = (d00*d21 - d01*d20) / denom
result.X = 1.0 - (result.Z + result.Y)
return result
}
// MatrixDeterminant - Compute matrix determinant
func MatrixDeterminant(mat rl.Matrix) float32 {
var result float32
a00 := mat.M0
a01 := mat.M1
a02 := mat.M2
a03 := mat.M3
a10 := mat.M4
a11 := mat.M5
a12 := mat.M6
a13 := mat.M7
a20 := mat.M8
a21 := mat.M9
a22 := mat.M10
a23 := mat.M11
a30 := mat.M12
a31 := mat.M13
a32 := mat.M14
a33 := mat.M15
result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 +
a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 +
a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 +
a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 +
a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 +
a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33
return result
}
// MatrixTrace - Returns the trace of the matrix (sum of the values along the diagonal)
func MatrixTrace(mat rl.Matrix) float32 {
return mat.M0 + mat.M5 + mat.M10 + mat.M15
}
// MatrixTranspose - Transposes provided matrix
func MatrixTranspose(mat *rl.Matrix) {
var temp rl.Matrix
temp.M0 = mat.M0
temp.M1 = mat.M4
temp.M2 = mat.M8
temp.M3 = mat.M12
temp.M4 = mat.M1
temp.M5 = mat.M5
temp.M6 = mat.M9
temp.M7 = mat.M13
temp.M8 = mat.M2
temp.M9 = mat.M6
temp.M10 = mat.M10
temp.M11 = mat.M14
temp.M12 = mat.M3
temp.M13 = mat.M7
temp.M14 = mat.M11
temp.M15 = mat.M15
mat = &temp
}
// MatrixInvert - Invert provided matrix
func MatrixInvert(mat *rl.Matrix) {
var temp rl.Matrix
a00 := mat.M0
a01 := mat.M1
a02 := mat.M2
a03 := mat.M3
a10 := mat.M4
a11 := mat.M5
a12 := mat.M6
a13 := mat.M7
a20 := mat.M8
a21 := mat.M9
a22 := mat.M10
a23 := mat.M11
a30 := mat.M12
a31 := mat.M13
a32 := mat.M14
a33 := mat.M15
b00 := a00*a11 - a01*a10
b01 := a00*a12 - a02*a10
b02 := a00*a13 - a03*a10
b03 := a01*a12 - a02*a11
b04 := a01*a13 - a03*a11
b05 := a02*a13 - a03*a12
b06 := a20*a31 - a21*a30
b07 := a20*a32 - a22*a30
b08 := a20*a33 - a23*a30
b09 := a21*a32 - a22*a31
b10 := a21*a33 - a23*a31
b11 := a22*a33 - a23*a32
// Calculate the invert determinant (inlined to avoid double-caching)
invDet := 1.0 / (b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06)
temp.M0 = (a11*b11 - a12*b10 + a13*b09) * invDet
temp.M1 = (-a01*b11 + a02*b10 - a03*b09) * invDet
temp.M2 = (a31*b05 - a32*b04 + a33*b03) * invDet
temp.M3 = (-a21*b05 + a22*b04 - a23*b03) * invDet
temp.M4 = (-a10*b11 + a12*b08 - a13*b07) * invDet
temp.M5 = (a00*b11 - a02*b08 + a03*b07) * invDet
temp.M6 = (-a30*b05 + a32*b02 - a33*b01) * invDet
temp.M7 = (a20*b05 - a22*b02 + a23*b01) * invDet
temp.M8 = (a10*b10 - a11*b08 + a13*b06) * invDet
temp.M9 = (-a00*b10 + a01*b08 - a03*b06) * invDet
temp.M10 = (a30*b04 - a31*b02 + a33*b00) * invDet
temp.M11 = (-a20*b04 + a21*b02 - a23*b00) * invDet
temp.M12 = (-a10*b09 + a11*b07 - a12*b06) * invDet
temp.M13 = (a00*b09 - a01*b07 + a02*b06) * invDet
temp.M14 = (-a30*b03 + a31*b01 - a32*b00) * invDet
temp.M15 = (a20*b03 - a21*b01 + a22*b00) * invDet
mat = &temp
}
// MatrixNormalize - Normalize provided matrix
func MatrixNormalize(mat *rl.Matrix) {
det := MatrixDeterminant(*mat)
mat.M0 /= det
mat.M1 /= det
mat.M2 /= det
mat.M3 /= det
mat.M4 /= det
mat.M5 /= det
mat.M6 /= det
mat.M7 /= det
mat.M8 /= det
mat.M9 /= det
mat.M10 /= det
mat.M11 /= det
mat.M12 /= det
mat.M13 /= det
mat.M14 /= det
mat.M15 /= det
}
// MatrixIdentity - Returns identity matrix
func MatrixIdentity() rl.Matrix {
return rl.NewMatrix(
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0)
}
// MatrixAdd - Add two matrices
func MatrixAdd(left, right rl.Matrix) rl.Matrix {
result := MatrixIdentity()
result.M0 = left.M0 + right.M0
result.M1 = left.M1 + right.M1
result.M2 = left.M2 + right.M2
result.M3 = left.M3 + right.M3
result.M4 = left.M4 + right.M4
result.M5 = left.M5 + right.M5
result.M6 = left.M6 + right.M6
result.M7 = left.M7 + right.M7
result.M8 = left.M8 + right.M8
result.M9 = left.M9 + right.M9
result.M10 = left.M10 + right.M10
result.M11 = left.M11 + right.M11
result.M12 = left.M12 + right.M12
result.M13 = left.M13 + right.M13
result.M14 = left.M14 + right.M14
result.M15 = left.M15 + right.M15
return result
}
// MatrixSubtract - Subtract two matrices (left - right)
func MatrixSubtract(left, right rl.Matrix) rl.Matrix {
result := MatrixIdentity()
result.M0 = left.M0 - right.M0
result.M1 = left.M1 - right.M1
result.M2 = left.M2 - right.M2
result.M3 = left.M3 - right.M3
result.M4 = left.M4 - right.M4
result.M5 = left.M5 - right.M5
result.M6 = left.M6 - right.M6
result.M7 = left.M7 - right.M7
result.M8 = left.M8 - right.M8
result.M9 = left.M9 - right.M9
result.M10 = left.M10 - right.M10
result.M11 = left.M11 - right.M11
result.M12 = left.M12 - right.M12
result.M13 = left.M13 - right.M13
result.M14 = left.M14 - right.M14
result.M15 = left.M15 - right.M15
return result
}
// MatrixTranslate - Returns translation matrix
func MatrixTranslate(x, y, z float32) rl.Matrix {
return rl.NewMatrix(
1.0, 0.0, 0.0, x,
0.0, 1.0, 0.0, y,
0.0, 0.0, 1.0, z,
0, 0, 0, 1.0)
}
// MatrixRotate - Returns rotation matrix for an angle around an specified axis (angle in radians)
func MatrixRotate(axis rl.Vector3, angle float32) rl.Matrix {
var result rl.Matrix
mat := MatrixIdentity()
x := axis.X
y := axis.Y
z := axis.Z
length := float32(math.Sqrt(float64(x*x + y*y + z*z)))
if length != 1.0 && length != 0.0 {
length = 1.0 / length
x *= length
y *= length
z *= length
}
sinres := float32(math.Sin(float64(angle)))
cosres := float32(math.Cos(float64(angle)))
t := 1.0 - cosres
// Cache some matrix values (speed optimization)
a00 := mat.M0
a01 := mat.M1
a02 := mat.M2
a03 := mat.M3
a10 := mat.M4
a11 := mat.M5
a12 := mat.M6
a13 := mat.M7
a20 := mat.M8
a21 := mat.M9
a22 := mat.M10
a23 := mat.M11
// Construct the elements of the rotation matrix
b00 := x*x*t + cosres
b01 := y*x*t + z*sinres
b02 := z*x*t - y*sinres
b10 := x*y*t - z*sinres
b11 := y*y*t + cosres
b12 := z*y*t + x*sinres
b20 := x*z*t + y*sinres
b21 := y*z*t - x*sinres
b22 := z*z*t + cosres
// Perform rotation-specific matrix multiplication
result.M0 = a00*b00 + a10*b01 + a20*b02
result.M1 = a01*b00 + a11*b01 + a21*b02
result.M2 = a02*b00 + a12*b01 + a22*b02
result.M3 = a03*b00 + a13*b01 + a23*b02
result.M4 = a00*b10 + a10*b11 + a20*b12
result.M5 = a01*b10 + a11*b11 + a21*b12
result.M6 = a02*b10 + a12*b11 + a22*b12
result.M7 = a03*b10 + a13*b11 + a23*b12
result.M8 = a00*b20 + a10*b21 + a20*b22
result.M9 = a01*b20 + a11*b21 + a21*b22
result.M10 = a02*b20 + a12*b21 + a22*b22
result.M11 = a03*b20 + a13*b21 + a23*b22
result.M12 = mat.M12
result.M13 = mat.M13
result.M14 = mat.M14
result.M15 = mat.M15
return result
}
// MatrixRotateX - Returns x-rotation matrix (angle in radians)
func MatrixRotateX(angle float32) rl.Matrix {
result := MatrixIdentity()
cosres := float32(math.Cos(float64(angle)))
sinres := float32(math.Sin(float64(angle)))
result.M5 = cosres
result.M6 = -sinres
result.M9 = sinres
result.M10 = cosres
return result
}
// MatrixRotateY - Returns y-rotation matrix (angle in radians)
func MatrixRotateY(angle float32) rl.Matrix {
result := MatrixIdentity()
cosres := float32(math.Cos(float64(angle)))
sinres := float32(math.Sin(float64(angle)))
result.M0 = cosres
result.M2 = sinres
result.M8 = -sinres
result.M10 = cosres
return result
}
// MatrixRotateZ - Returns z-rotation matrix (angle in radians)
func MatrixRotateZ(angle float32) rl.Matrix {
result := MatrixIdentity()
cosres := float32(math.Cos(float64(angle)))
sinres := float32(math.Sin(float64(angle)))
result.M0 = cosres
result.M1 = -sinres
result.M4 = sinres
result.M5 = cosres
return result
}
// MatrixScale - Returns scaling matrix
func MatrixScale(x, y, z float32) rl.Matrix {
result := rl.NewMatrix(
x, 0.0, 0.0, 0.0,
0.0, y, 0.0, 0.0,
0.0, 0.0, z, 0.0,
0.0, 0.0, 0.0, 1.0)
return result
}
// MatrixMultiply - Returns two matrix multiplication
func MatrixMultiply(left, right rl.Matrix) rl.Matrix {
var result rl.Matrix
result.M0 = right.M0*left.M0 + right.M1*left.M4 + right.M2*left.M8 + right.M3*left.M12
result.M1 = right.M0*left.M1 + right.M1*left.M5 + right.M2*left.M9 + right.M3*left.M13
result.M2 = right.M0*left.M2 + right.M1*left.M6 + right.M2*left.M10 + right.M3*left.M14
result.M3 = right.M0*left.M3 + right.M1*left.M7 + right.M2*left.M11 + right.M3*left.M15
result.M4 = right.M4*left.M0 + right.M5*left.M4 + right.M6*left.M8 + right.M7*left.M12
result.M5 = right.M4*left.M1 + right.M5*left.M5 + right.M6*left.M9 + right.M7*left.M13
result.M6 = right.M4*left.M2 + right.M5*left.M6 + right.M6*left.M10 + right.M7*left.M14
result.M7 = right.M4*left.M3 + right.M5*left.M7 + right.M6*left.M11 + right.M7*left.M15
result.M8 = right.M8*left.M0 + right.M9*left.M4 + right.M10*left.M8 + right.M11*left.M12
result.M9 = right.M8*left.M1 + right.M9*left.M5 + right.M10*left.M9 + right.M11*left.M13
result.M10 = right.M8*left.M2 + right.M9*left.M6 + right.M10*left.M10 + right.M11*left.M14
result.M11 = right.M8*left.M3 + right.M9*left.M7 + right.M10*left.M11 + right.M11*left.M15
result.M12 = right.M12*left.M0 + right.M13*left.M4 + right.M14*left.M8 + right.M15*left.M12
result.M13 = right.M12*left.M1 + right.M13*left.M5 + right.M14*left.M9 + right.M15*left.M13
result.M14 = right.M12*left.M2 + right.M13*left.M6 + right.M14*left.M10 + right.M15*left.M14
result.M15 = right.M12*left.M3 + right.M13*left.M7 + right.M14*left.M11 + right.M15*left.M15
return result
}
// MatrixFrustum - Returns perspective projection matrix
func MatrixFrustum(left, right, bottom, top, near, far float32) rl.Matrix {
var result rl.Matrix
rl := right - left
tb := top - bottom
fn := far - near
result.M0 = (near * 2.0) / rl
result.M1 = 0.0
result.M2 = 0.0
result.M3 = 0.0
result.M4 = 0.0
result.M5 = (near * 2.0) / tb
result.M6 = 0.0
result.M7 = 0.0
result.M8 = right + left/rl
result.M9 = top + bottom/tb
result.M10 = -(far + near) / fn
result.M11 = -1.0
result.M12 = 0.0
result.M13 = 0.0
result.M14 = -(far * near * 2.0) / fn
result.M15 = 0.0
return result
}
// MatrixPerspective - Returns perspective projection matrix
func MatrixPerspective(fovy, aspect, near, far float32) rl.Matrix {
top := near * float32(math.Tan(float64(fovy*rl.Pi)/360.0))
right := top * aspect
return MatrixFrustum(-right, right, -top, top, near, far)
}
// MatrixOrtho - Returns orthographic projection matrix
func MatrixOrtho(left, right, bottom, top, near, far float32) rl.Matrix {
var result rl.Matrix
rl := right - left
tb := top - bottom
fn := far - near
result.M0 = 2.0 / rl
result.M1 = 0.0
result.M2 = 0.0
result.M3 = 0.0
result.M4 = 0.0
result.M5 = 2.0 / tb
result.M6 = 0.0
result.M7 = 0.0
result.M8 = 0.0
result.M9 = 0.0
result.M10 = -2.0 / fn
result.M11 = 0.0
result.M12 = -(left + right) / rl
result.M13 = -(top + bottom) / tb
result.M14 = -(far + near) / fn
result.M15 = 1.0
return result
}
// MatrixLookAt - Returns camera look-at matrix (view matrix)
func MatrixLookAt(eye, target, up rl.Vector3) rl.Matrix {
var result rl.Matrix
z := Vector3Subtract(eye, target)
Vector3Normalize(&z)
x := Vector3CrossProduct(up, z)
Vector3Normalize(&x)
y := Vector3CrossProduct(z, x)
Vector3Normalize(&y)
result.M0 = x.X
result.M1 = x.Y
result.M2 = x.Z
result.M3 = -((x.X * eye.X) + (x.Y * eye.Y) + (x.Z * eye.Z))
result.M4 = y.X
result.M5 = y.Y
result.M6 = y.Z
result.M7 = -((y.X * eye.X) + (y.Y * eye.Y) + (y.Z * eye.Z))
result.M8 = z.X
result.M9 = z.Y
result.M10 = z.Z
result.M11 = -((z.X * eye.X) + (z.Y * eye.Y) + (z.Z * eye.Z))
result.M12 = 0.0
result.M13 = 0.0
result.M14 = 0.0
result.M15 = 1.0
return result
}
// QuaternionLength - Compute the length of a quaternion
func QuaternionLength(quat rl.Quaternion) float32 {
return float32(math.Sqrt(float64(quat.X*quat.X + quat.Y*quat.Y + quat.Z*quat.Z + quat.W*quat.W)))
}
// QuaternionNormalize - Normalize provided quaternion
func QuaternionNormalize(q *rl.Quaternion) {
var length, ilength float32
length = QuaternionLength(*q)
if length == 0.0 {
length = 1.0
}
ilength = 1.0 / length
q.X *= ilength
q.Y *= ilength
q.Z *= ilength
q.W *= ilength
}
// QuaternionInvert - Invert provided quaternion
func QuaternionInvert(quat *rl.Quaternion) {
length := QuaternionLength(*quat)
lengthSq := length * length
if lengthSq != 0.0 {
i := 1.0 / lengthSq
quat.X *= -i
quat.Y *= -i
quat.Z *= -i
quat.W *= i
}
}
// QuaternionMultiply - Calculate two quaternion multiplication
func QuaternionMultiply(q1, q2 rl.Quaternion) rl.Quaternion {
var result rl.Quaternion
qax := q1.X
qay := q1.Y
qaz := q1.Z
qaw := q1.W
qbx := q2.X
qby := q2.Y
qbz := q2.Z
qbw := q2.W
result.X = qax*qbw + qaw*qbx + qay*qbz - qaz*qby
result.Y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz
result.Z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx
result.W = qaw*qbw - qax*qbx - qay*qby - qaz*qbz
return result
}
// QuaternionSlerp - Calculates spherical linear interpolation between two quaternions
func QuaternionSlerp(q1, q2 rl.Quaternion, amount float32) rl.Quaternion {
var result rl.Quaternion
cosHalfTheta := q1.X*q2.X + q1.Y*q2.Y + q1.Z*q2.Z + q1.W*q2.W
if math.Abs(float64(cosHalfTheta)) >= 1.0 {
result = q1
} else {
halfTheta := float32(math.Acos(float64(cosHalfTheta)))
sinHalfTheta := float32(math.Sqrt(float64(1.0 - cosHalfTheta*cosHalfTheta)))
if math.Abs(float64(sinHalfTheta)) < 0.001 {
result.X = q1.X*0.5 + q2.X*0.5
result.Y = q1.Y*0.5 + q2.Y*0.5
result.Z = q1.Z*0.5 + q2.Z*0.5
result.W = q1.W*0.5 + q2.W*0.5
} else {
ratioA := float32(math.Sin(float64((1-amount)*halfTheta))) / sinHalfTheta
ratioB := float32(math.Sin(float64(amount*halfTheta))) / sinHalfTheta
result.X = q1.X*ratioA + q2.X*ratioB
result.Y = q1.Y*ratioA + q2.Y*ratioB
result.Z = q1.Z*ratioA + q2.Z*ratioB
result.W = q1.W*ratioA + q2.W*ratioB
}
}
return result
}
// QuaternionFromMatrix - Returns a quaternion for a given rotation matrix
func QuaternionFromMatrix(matrix rl.Matrix) rl.Quaternion {
var result rl.Quaternion
trace := MatrixTrace(matrix)
if trace > 0.0 {
s := float32(math.Sqrt(float64(trace+1)) * 2.0)
invS := 1.0 / s
result.W = s * 0.25
result.X = (matrix.M6 - matrix.M9) * invS
result.Y = (matrix.M8 - matrix.M2) * invS
result.Z = (matrix.M1 - matrix.M4) * invS
} else {
m00 := matrix.M0
m11 := matrix.M5
m22 := matrix.M10
if m00 > m11 && m00 > m22 {
s := float32(math.Sqrt(float64(1.0+m00-m11-m22)) * 2.0)
invS := 1.0 / s
result.W = (matrix.M6 - matrix.M9) * invS
result.X = s * 0.25
result.Y = (matrix.M4 + matrix.M1) * invS
result.Z = (matrix.M8 + matrix.M2) * invS
} else if m11 > m22 {
s := float32(math.Sqrt(float64(1.0+m11-m00-m22)) * 2.0)
invS := 1.0 / s
result.W = (matrix.M8 - matrix.M2) * invS
result.X = (matrix.M4 + matrix.M1) * invS
result.Y = s * 0.25
result.Z = (matrix.M9 + matrix.M6) * invS
} else {
s := float32(math.Sqrt(float64(1.0+m22-m00-m11)) * 2.0)
invS := 1.0 / s
result.W = (matrix.M1 - matrix.M4) * invS
result.X = (matrix.M8 + matrix.M2) * invS
result.Y = (matrix.M9 + matrix.M6) * invS
result.Z = s * 0.25
}
}
return result
}
// QuaternionToMatrix - Returns a matrix for a given quaternion
func QuaternionToMatrix(q rl.Quaternion) rl.Matrix {
var result rl.Matrix
x := q.X
y := q.Y
z := q.Z
w := q.W
x2 := x + x
y2 := y + y
z2 := z + z
xx := x * x2
xy := x * y2
xz := x * z2
yy := y * y2
yz := y * z2
zz := z * z2
wx := w * x2
wy := w * y2
wz := w * z2
result.M0 = 1.0 - (yy + zz)
result.M1 = xy - wz
result.M2 = xz + wy
result.M3 = 0.0
result.M4 = xy + wz
result.M5 = 1.0 - (xx + zz)
result.M6 = yz - wx
result.M7 = 0.0
result.M8 = xz - wy
result.M9 = yz + wx
result.M10 = 1.0 - (xx + yy)
result.M11 = 0.0
result.M12 = 0.0
result.M13 = 0.0
result.M14 = 0.0
result.M15 = 1.0
return result
}
// QuaternionFromAxisAngle - Returns rotation quaternion for an angle and axis
func QuaternionFromAxisAngle(axis rl.Vector3, angle float32) rl.Quaternion {
result := rl.NewQuaternion(0.0, 0.0, 0.0, 1.0)
if Vector3Length(axis) != 0.0 {
angle *= 0.5
}
Vector3Normalize(&axis)
sinres := float32(math.Sin(float64(angle)))
cosres := float32(math.Cos(float64(angle)))
result.X = axis.X * sinres
result.Y = axis.Y * sinres
result.Z = axis.Z * sinres
result.W = cosres
QuaternionNormalize(&result)