// Some useful functions to work with Vector3, Matrix and Quaternions package raymath import ( "math" "github.com/gen2brain/raylib-go/raylib" ) // Add two vectors func VectorAdd(v1, v2 raylib.Vector3) raylib.Vector3 { result := raylib.Vector3{} result.X = v1.X + v2.X result.Y = v1.Y + v2.Y result.Z = v1.Z + v2.Z return result } // Subtract two vectors func VectorSubtract(v1, v2 raylib.Vector3) raylib.Vector3 { result := raylib.Vector3{} result.X = v1.X - v2.X result.Y = v1.Y - v2.Y result.Z = v1.Z - v2.Z return result } // Calculate two vectors cross product func VectorCrossProduct(v1, v2 raylib.Vector3) raylib.Vector3 { result := raylib.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 } // Calculate one vector perpendicular vector func VectorPerpendicular(v raylib.Vector3) raylib.Vector3 { result := raylib.Vector3{} min := math.Abs(float64(v.X)) cardinalAxis := raylib.NewVector3(1.0, 0.0, 0.0) if math.Abs(float64(v.Y)) < min { min = math.Abs(float64(v.Y)) cardinalAxis = raylib.NewVector3(0.0, 1.0, 0.0) } if math.Abs(float64(v.Z)) < min { cardinalAxis = raylib.NewVector3(0.0, 0.0, 1.0) } result = VectorCrossProduct(v, cardinalAxis) return result } // Calculate two vectors dot product func VectorDotProduct(v1, v2 raylib.Vector3) float32 { return v1.X*v2.X + v1.Y*v2.Y + v1.Z*v2.Z } // Calculate vector length func VectorLength(v raylib.Vector3) float32 { return float32(math.Sqrt(float64(v.X*v.X + v.Y*v.Y + v.Z*v.Z))) } // Scale provided vector func VectorScale(v *raylib.Vector3, scale float32) { v.X *= scale v.Y *= scale v.Z *= scale } // Negate provided vector (invert direction) func VectorNegate(v *raylib.Vector3) { v.X = -v.X v.Y = -v.Y v.Z = -v.Z } // Normalize provided vector func VectorNormalize(v *raylib.Vector3) { var length, ilength float32 length = VectorLength(*v) if length == 0 { length = 1.0 } ilength = 1.0 / length v.X *= ilength v.Y *= ilength v.Z *= ilength } // Calculate distance between two points func VectorDistance(v1, v2 raylib.Vector3) float32 { var result float32 dx := v2.X - v1.X dy := v2.Y - v1.Y dz := v2.Z - v1.Z result = float32(math.Sqrt(float64(dx*dx + dy*dy + dz*dz))) return result } // Calculate linear interpolation between two vectors func VectorLerp(v1, v2 raylib.Vector3, amount float32) raylib.Vector3 { result := raylib.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 } // Calculate reflected vector to normal func VectorReflect(vector, normal raylib.Vector3) raylib.Vector3 { // I is the original vector // N is the normal of the incident plane // R = I - (2*N*( DotProduct[ I,N] )) result := raylib.Vector3{} dotProduct := VectorDotProduct(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 } // Transforms a Vector3 by a given Matrix func VectorTransform(v *raylib.Vector3, mat raylib.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 } // Return a Vector3 init to zero func VectorZero() raylib.Vector3 { return raylib.NewVector3(0.0, 0.0, 0.0) } // Return min value for each pair of components func VectorMin(vec1, vec2 raylib.Vector3) raylib.Vector3 { result := raylib.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 } // Return max value for each pair of components func VectorMax(vec1, vec2 raylib.Vector3) raylib.Vector3 { result := raylib.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 } // Compute matrix determinant func MatrixDeterminant(mat raylib.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 } // Returns the trace of the matrix (sum of the values along the diagonal) func MatrixTrace(mat raylib.Matrix) float32 { return mat.M0 + mat.M5 + mat.M10 + mat.M15 } // Transposes provided matrix func MatrixTranspose(mat *raylib.Matrix) { var temp raylib.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 } // Invert provided matrix func MatrixInvert(mat *raylib.Matrix) { var temp raylib.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 } // Normalize provided matrix func MatrixNormalize(mat *raylib.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 } // Returns identity matrix func MatrixIdentity() raylib.Matrix { return raylib.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) } // Add two matrices func MatrixAdd(left, right raylib.Matrix) raylib.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 } // Subtract two matrices (left - right) func MatrixSubtract(left, right raylib.Matrix) raylib.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 } // Returns translation matrix func MatrixTranslate(x, y, z float32) raylib.Matrix { return raylib.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, x, y, z, 1.0) } // Returns rotation matrix for an angle around an specified axis (angle in radians) func MatrixRotate(axis raylib.Vector3, angle float32) raylib.Matrix { var result raylib.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 } // Returns x-rotation matrix (angle in radians) func MatrixRotateX(angle float32) raylib.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 } // Returns y-rotation matrix (angle in radians) func MatrixRotateY(angle float32) raylib.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 } // Returns z-rotation matrix (angle in radians) func MatrixRotateZ(angle float32) raylib.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 } // Returns scaling matrix func MatrixScale(x, y, z float32) raylib.Matrix { result := raylib.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 } // Returns two matrix multiplication func MatrixMultiply(left, right raylib.Matrix) raylib.Matrix { var result raylib.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 } // Returns perspective projection matrix func MatrixFrustum(left, right, bottom, top, near, far float32) raylib.Matrix { var result raylib.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 } // Returns perspective projection matrix func MatrixPerspective(fovy, aspect, near, far float32) raylib.Matrix { top := near * float32(math.Tan(float64(fovy*raylib.Pi)/360.0)) right := top * aspect return MatrixFrustum(-right, right, -top, top, near, far) } // Returns orthographic projection matrix func MatrixOrtho(left, right, bottom, top, near, far float32) raylib.Matrix { var result raylib.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 } // Returns camera look-at matrix (view matrix) func MatrixLookAt(eye, target, up raylib.Vector3) raylib.Matrix { var result raylib.Matrix z := VectorSubtract(eye, target) VectorNormalize(&z) x := VectorCrossProduct(up, z) VectorNormalize(&x) y := VectorCrossProduct(z, x) VectorNormalize(&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 } // Compute the length of a quaternion func QuaternionLength(quat raylib.Quaternion) float32 { return float32(math.Sqrt(float64(quat.X*quat.X + quat.Y*quat.Y + quat.Z*quat.Z + quat.W*quat.W))) } // Normalize provided quaternion func QuaternionNormalize(q *raylib.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 } // Invert provided quaternion func QuaternionInvert(quat *raylib.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 } } // Calculate two quaternion multiplication func QuaternionMultiply(q1, q2 raylib.Quaternion) raylib.Quaternion { var result raylib.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 } // Calculates spherical linear interpolation between two quaternions func QuaternionSlerp(q1, q2 raylib.Quaternion, amount float32) raylib.Quaternion { var result raylib.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 } // Returns a quaternion for a given rotation matrix func QuaternionFromMatrix(matrix raylib.Matrix) raylib.Quaternion { var result raylib.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 } // Returns a matrix for a given quaternion func QuaternionToMatrix(q raylib.Quaternion) raylib.Matrix { var result raylib.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 } // Returns rotation quaternion for an angle and axis func QuaternionFromAxisAngle(axis raylib.Vector3, angle float32) raylib.Quaternion { result := raylib.NewQuaternion(0.0, 0.0, 0.0, 1.0) if VectorLength(axis) != 0.0 { angle *= 0.5 } VectorNormalize(&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) return result } // Returns the rotation angle and axis for a given quaternion func QuaternionToAxisAngle(q raylib.Quaternion, outAxis *raylib.Vector3, outAngle *float32) { if math.Abs(float64(q.W)) > 1.0 { QuaternionNormalize(&q) } resAxis := raylib.NewVector3(0.0, 0.0, 0.0) resAngle := 2.0 * float32(math.Acos(float64(q.W))) den := float32(math.Sqrt(float64(1.0 - q.W*q.W))) if den > 0.0001 { resAxis.X = q.X / den resAxis.Y = q.Y / den resAxis.Z = q.Z / den } else { // This occurs when the angle is zero. // Not a problem: just set an arbitrary normalized axis. resAxis.X = 1.0 } *outAxis = resAxis *outAngle = resAngle } // Transform a quaternion given a transformation matrix func QuaternionTransform(q *raylib.Quaternion, mat raylib.Matrix) { x := q.X y := q.Y z := q.Z w := q.W q.X = mat.M0*x + mat.M4*y + mat.M8*z + mat.M12*w q.Y = mat.M1*x + mat.M5*y + mat.M9*z + mat.M13*w q.Z = mat.M2*x + mat.M6*y + mat.M10*z + mat.M14*w q.W = mat.M3*x + mat.M7*y + mat.M11*z + mat.M15*w }