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quat.go
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quat.go
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package gm
import (
"math"
)
// RotationOrder is the order in which rotations will be transformed for the
// purposes of QFromAngles.
type RotationOrder int
// The RotationOrder constants represent a series of rotations along the given
// axes for the use of QFromAngles.
const (
XYX RotationOrder = iota
XYZ
XZX
XZY
YXY
YXZ
YZY
YZX
ZYZ
ZYX
ZXZ
ZXY
)
// Quat short for quaternion:
// https://answers.unity.com/questions/467614/what-is-the-source-code-of-quaternionlookrotation.html
// W is [3]
type Quat [4]Float
// Len computes quaternion length.
func (q Quat) Len() Float {
return Float(math.Sqrt(float64(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3])))
}
// Normalize returns a normalized copy of the quaternion.
func (q Quat) Normalize() Quat {
length := q.Len()
if FloatEqual(1, length) {
return q
}
if length == 0 {
return QIdent()
}
if length == Float(math.Inf(1)) {
length = MaxValue
}
invLen := 1 / length
return Quat{
q[0] * invLen,
q[1] * invLen,
q[2] * invLen,
q[3] * invLen,
}
}
// W returns the W part of the quaternion.
func (q Quat) W() Float {
return q[3]
}
// V returns the Vector (0,1,2) part of the quaternion.
func (q Quat) V() Vec3 {
return Vec3{q[0], q[1], q[2]}
}
// Mul returns a new quaternion based on the multiplication with q2.
func (q Quat) Mul(q2 Quat) Quat {
v1 := q.V()
v2 := q2.V()
qv := v1.Cross(v2).
Add(v2.Mul(q[3])).
Add(v1.Mul(q2[3]))
return Quat{
qv[0],
qv[1],
qv[2],
q[3]*q2[3] - v1.Dot(v2),
}
}
// Add returns a new quaternion based on the sum of q and q2.
func (q Quat) Add(q2 Quat) Quat {
return Quat{
q[0] + q2[0],
q[1] + q2[1],
q[2] + q2[2],
q[3] + q2[3],
}
}
// ToEuler quaternion to euler angles.
func (q Quat) ToEuler() Vec3 {
ret := Vec3{}
q = q.Normalize()
sinRCosP := 2 * (q[3]*q[0] + q[1]*q[2])
cosRCosP := 1 - 2*(q[0]*q[0]+q[1]*q[1])
ret[0] = Atan2(sinRCosP, cosRCosP)
sinP := 2 * (q[3]*q[1] - q[2]*q[0])
if Abs(sinP) >= 1 {
ret[1] = Copysign(math.Pi/2, sinP)
} else {
ret[1] = Asin(sinP)
}
sinYCosP := 2 * (q[3]*q[2] + q[0]*q[1])
cosYCosP := 1 - 2*(q[1]*q[1]+q[2]*q[2])
ret[2] = Atan2(sinYCosP, cosYCosP)
return ret
}
// Mat4 returns a 4x4 matrix from the quaternion.
func (q Quat) Mat4() Mat4 {
x, y, z, w := q[0], q[1], q[2], q[3]
return Mat4{
1 - 2*y*y - 2*z*z, 2*x*y + 2*w*z, 2*x*z - 2*w*y, 0,
2*x*y - 2*w*z, 1 - 2*x*x - 2*z*z, 2*y*z + 2*w*x, 0,
2*x*z + 2*w*y, 2*y*z - 2*w*x, 1 - 2*x*x - 2*y*y, 0,
0, 0, 0, 1,
}
}
// Slerp spherical linear interpolation between two quat
// https://github.com/toji/gl-matrix/blob/6c0268c89f30090b17bcadade9e7feb7205b85c5/src/quat.js#L296
func (q Quat) Slerp(b Quat, t Float) Quat {
ax := q[0]
ay := q[1]
az := q[2]
aw := q[3]
bx := b[0]
by := b[1]
bz := b[2]
bw := b[3]
var omega, cosom, sinom, scale0, scale1 Float
cosom = ax*bx + ay*by + az*bz + aw*bw
if cosom < 0.0 {
cosom = -cosom
bx = -bx
by = -by
bz = -bz
bw = -bw
}
if 1.0-cosom > Epsilon {
omega = Cos(cosom)
sinom = Sin(omega)
scale0 = Sin((1-t)*omega) / sinom
scale1 = Sin(t*omega) / sinom
} else {
scale0 = 1.0 - t
scale1 = t
}
return Quat{
scale0*ax + scale1*bx,
scale0*ay + scale1*by,
scale0*az + scale1*bz,
scale0*aw + scale1*bw,
}
}
// QFromAngles returns a rotation quaternion based on the angles.
func QFromAngles(a1, a2, a3 Float, order RotationOrder) Quat {
var s [3]float64
var c [3]float64
s[0], c[0] = math.Sincos(float64(a1 / 2))
s[1], c[1] = math.Sincos(float64(a2 / 2))
s[2], c[2] = math.Sincos(float64(a3 / 2))
switch order {
case ZYX:
return Quat{
Float(c[0]*c[1]*s[2] - s[0]*s[1]*c[2]),
Float(c[0]*s[1]*c[2] + s[0]*c[1]*s[2]),
Float(s[0]*c[1]*c[2] - c[0]*s[1]*s[2]),
Float(c[0]*c[1]*c[2] + s[0]*s[1]*s[2]),
}
case ZYZ:
return Quat{
Float(c[0]*s[1]*s[2] - s[0]*s[1]*c[2]),
Float(c[0]*s[1]*c[2] + s[0]*s[1]*s[2]),
Float(s[0]*c[1]*c[2] + c[0]*c[1]*s[2]),
Float(c[0]*c[1]*c[2] - s[0]*c[1]*s[2]),
}
case ZXY:
return Quat{
Float(c[0]*s[1]*c[2] - s[0]*c[1]*s[2]),
Float(c[0]*c[1]*s[2] + s[0]*s[1]*c[2]),
Float(c[0]*s[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*c[1]*c[2] - s[0]*s[1]*s[2]),
}
case ZXZ:
return Quat{
Float(c[0]*s[1]*c[2] + s[0]*s[1]*s[2]),
Float(s[0]*s[1]*c[2] - c[0]*s[1]*s[2]),
Float(c[0]*c[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*c[1]*c[2] - s[0]*c[1]*s[2]),
}
case YXZ:
return Quat{
Float(c[0]*s[1]*c[2] + s[0]*c[1]*s[2]),
Float(s[0]*c[1]*c[2] - c[0]*s[1]*s[2]),
Float(c[0]*c[1]*s[2] - s[0]*s[1]*c[2]),
Float(c[0]*c[1]*c[2] + s[0]*s[1]*s[2]),
}
case YXY:
return Quat{
Float(c[0]*s[1]*c[2] + s[0]*s[1]*s[2]),
Float(s[0]*c[1]*c[2] + c[0]*c[1]*s[2]),
Float(c[0]*s[1]*s[2] - s[0]*s[1]*c[2]),
Float(c[0]*c[1]*c[2] - s[0]*c[1]*s[2]),
}
case YZX:
return Quat{
Float(c[0]*c[1]*s[2] + s[0]*s[1]*c[2]),
Float(c[0]*s[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*s[1]*c[2] - s[0]*c[1]*s[2]),
Float(c[0]*c[1]*c[2] - s[0]*s[1]*s[2]),
}
case YZY:
return Quat{
Float(s[0]*s[1]*c[2] - c[0]*s[1]*s[2]),
Float(c[0]*c[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*s[1]*c[2] + s[0]*s[1]*s[2]),
Float(c[0]*c[1]*c[2] - s[0]*c[1]*s[2]),
}
case XYZ:
return Quat{
Float(c[0]*s[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*s[1]*c[2] - s[0]*c[1]*s[2]),
Float(c[0]*c[1]*s[2] + s[0]*s[1]*c[2]),
Float(c[0]*c[1]*c[2] - s[0]*s[1]*s[2]),
}
case XYX:
return Quat{
Float(c[0]*c[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*s[1]*c[2] + s[0]*s[1]*s[2]),
Float(s[0]*s[1]*c[2] - c[0]*s[1]*s[2]),
Float(c[0]*c[1]*c[2] - s[0]*c[1]*s[2]),
}
case XZY:
return Quat{
Float(s[0]*c[1]*c[2] - c[0]*s[1]*s[2]),
Float(c[0]*c[1]*s[2] - s[0]*s[1]*c[2]),
Float(c[0]*s[1]*c[2] + s[0]*c[1]*s[2]),
Float(c[0]*c[1]*c[2] + s[0]*s[1]*s[2]),
}
case XZX:
return Quat{
Float(c[0]*c[1]*s[2] + s[0]*c[1]*c[2]),
Float(c[0]*s[1]*s[2] - s[0]*s[1]*c[2]),
Float(c[0]*s[1]*c[2] + s[0]*s[1]*s[2]),
Float(c[0]*c[1]*c[2] - s[0]*c[1]*s[2]),
}
default:
panic("Unsupported rotation order")
}
}
// QLookAt creates a LookAt Matrix and extract the quaternion
func QLookAt(dir, up Vec3) Quat {
mat := LookAt(dir, Vec3{0, 0, 0}, up)
var (
m00, m01, m02 = mat[0], mat[4], mat[8]
m10, m11, m12 = mat[1], mat[5], mat[9]
m20, m21, m22 = mat[2], mat[6], mat[10]
)
fourXSquaredMinus1 := m00 - m11 - m22
fourYSquaredMinus1 := m11 - m00 - m22
fourZSquaredMinus1 := m22 - m00 - m11
fourWSquaredMinus1 := m00 + m11 + m22
biggestIndex := 0
fourBiggestSquaredMinus1 := fourWSquaredMinus1
if fourXSquaredMinus1 > fourBiggestSquaredMinus1 {
fourBiggestSquaredMinus1 = fourXSquaredMinus1
biggestIndex = 1
}
if fourYSquaredMinus1 > fourBiggestSquaredMinus1 {
fourBiggestSquaredMinus1 = fourYSquaredMinus1
biggestIndex = 2
}
if fourZSquaredMinus1 > fourBiggestSquaredMinus1 {
fourBiggestSquaredMinus1 = fourZSquaredMinus1
biggestIndex = 3
}
biggestVal := Sqrt(fourBiggestSquaredMinus1+1) * 0.5
mult := 0.25 / biggestVal
switch biggestIndex {
case 0:
return Quat{
(m12 - m21) * mult, (m20 - m02) * mult, (m01 - m10) * mult,
biggestVal,
}
case 1:
return Quat{
biggestVal, (m01 + m10) * mult, (m20 + m02) * mult,
(m12 - m21) * mult,
}
case 2:
return Quat{
(m01 + m10) * mult, biggestVal, (m12 + m21) * mult,
(m20 - m02) * mult,
}
case 3:
return Quat{
(m20 + m02) * mult, (m12 + m21) * mult, biggestVal,
(m01 - m10) * mult,
}
}
return QIdent()
}
// QIdent returns a quaternion identity.
func QIdent() Quat {
return Quat{0, 0, 0, 1}
}
// QEuler returns a quaternion based on those euler angles
// https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
func QEuler(x, y, z Float) Quat {
cy, sy := Sincos(z * 0.5)
cp, sp := Sincos(y * 0.5)
cr, sr := Sincos(x * 0.5)
return Quat{
cy*cp*sr - sy*sp*cr,
sy*cp*sr + cy*sp*cr,
sy*cp*cr - cy*sp*sr,
cy*cp*cr + sy*sp*sr,
}
}
// QAxisAngle returns a axis angle quaternion.
func QAxisAngle(v3 Vec3, rad Float) Quat {
s, c := Sincos(rad * 0.5)
return Quat{
v3[0] * s,
v3[1] * s,
v3[2] * s,
c,
}.Normalize()
}
// QBetweenV3 returns a quaternion between two vectors.
func QBetweenV3(v1, v2 Vec3) Quat {
var q Quat
a := v1.Normalize().Cross(v2.Normalize())
q[0] = a[0]
q[1] = a[1]
q[2] = a[2]
q[3] = Sqrt(1 + v1.Dot(v2))
return q.Normalize()
// return QAxisAngle(v1.Cross(v2), v1.Dot(v2))
}