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Contains godot api as kotlin classes and jvm cpp interaction code.
@file:Suppress("PackageDirectoryMismatch", "unused")
package godot.core
import godot.EulerOrder
import godot.util.CMP_EPSILON
import godot.util.RealT
import godot.util.cubicInterpolate
import godot.util.cubicInterpolateInTime
import godot.util.isEqualApprox
import godot.util.isZeroApprox
import godot.util.signbit
import godot.util.toRealT
import kotlincompile.definitions.GodotJvmBuildConfig
import kotlin.math.abs
import kotlin.math.acos
import kotlin.math.cos
import kotlin.math.sin
import kotlin.math.sqrt
class Quaternion(
var x: RealT,
var y: RealT,
var z: RealT,
var w: RealT
) : CoreType {
//CONSTANTS
companion object {
val IDENTITY: Quaternion
get() = Quaternion(0.0, 0.0, 0.0, 1.0)
fun fromEuler(euler: Vector3): Quaternion {
val halfA1 = euler.y * 0.5f
val halfA2 = euler.x * 0.5f
val halfA3 = euler.z * 0.5f
// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
// a3 is the angle of the first rotation, following the notation in this reference.
val cosA1 = cos(halfA1)
val sinA1 = sin(halfA1)
val cosA2 = cos(halfA2)
val sinA2 = sin(halfA2)
val cosA3 = cos(halfA3)
val sinA3 = sin(halfA3)
return Quaternion(
sinA1 * cosA2 * sinA3 + cosA1 * sinA2 * cosA3,
sinA1 * cosA2 * cosA3 - cosA1 * sinA2 * sinA3,
-sinA1 * sinA2 * cosA3 + cosA1 * cosA2 * sinA3,
sinA1 * sinA2 * sinA3 + cosA1 * cosA2 * cosA3
)
}
}
//CONSTRUCTOR
constructor() :
this(0.0, 0.0, 0.0, 1.0)
constructor(other: Quaternion) : this(other.x, other.y, other.z, other.w)
constructor(x: Number, y: Number, z: Number, w: Number = 1.0) :
this(x.toRealT(), y.toRealT(), z.toRealT(), w.toRealT())
constructor(axis: Vector3, angle: RealT) : this() {
val d: RealT = axis.length()
if (d == 0.0) {
set(0.0, 0.0, 0.0, 0.0)
} else {
val sinAngle: RealT = sin(angle * 0.5)
val cosAngle: RealT = cos(angle * 0.5)
val s: RealT = sinAngle / d
set(axis.x * s, axis.y * s, axis.z * s, cosAngle)
}
}
constructor(v0: Vector3, v1: Vector3) : this() {
val c = v0.cross(v1)
val d = v0.dot(v1)
if (d < -1.0 + CMP_EPSILON) {
x = 0.0
y = 1.0
z = 0.0
w = 0.0
} else {
val s = sqrt((1.0 + d) * 2.0)
val rs = 1.0 / s
x = c.x * rs
y = c.y * rs
z = c.z * rs
w = s * 0.5
}
}
//API
/**
* Returns the angle between this quaternion and [to]. This is the magnitude of the angle you would need to rotate by
* to get from one to the other.
*
* Note: The magnitude of the floating-point error for this method is abnormally high, so methods such as
* [isZeroApprox] will not work reliably.
*/
fun angleTo(to: Quaternion): Double {
val d = dot(to)
return acos((d * d * 2 - 1).coerceIn(-1.0, 1.0))
}
/**
* Returns the dot product of two quaternions.5
*/
fun dot(q: Quaternion): RealT {
return x * q.x + y * q.y + z * q.z + w * q.w
}
fun exp(): Quaternion {
var srcV = Vector3(x, y, z)
val theta = srcV.length()
srcV = srcV.normalized()
if (theta < CMP_EPSILON || !srcV.isNormalized()) {
return Quaternion(0, 0, 0, 1)
}
return Quaternion(srcV, theta)
}
fun getAngle() = 2 * acos(w)
fun getAxis(): Vector3 {
if (abs(w) > 1 - CMP_EPSILON) {
return Vector3(x, y, z)
}
val r = 1 / sqrt(1 - w * w)
return Vector3(x * r, y * r, z * r)
}
/**
* Returns Euler angles (in the YXZ convention: first Z, then X, and Y last) corresponding to the rotation
* represented by the unit quaternion. Returned vector contains the rotation angles in the format (X angle, Y angle,
* Z angle).
*/
fun getEuler(order: EulerOrder = EulerOrder.EULER_ORDER_YXZ): Vector3 {
if (GodotJvmBuildConfig.DEBUG) {
require(isNormalized()) {
"The quaternion must be normalized."
}
}
return Basis(this).getEuler(order)
}
/**
* Returns the inverse of the quaternion.
*/
fun inverse(): Quaternion {
return Quaternion(-x, -y, -z, -w)
}
/**
* Returns true if this quaterion and quat are approximately equal, by running isEqualApprox on each component.
*/
fun isEqualApprox(other: Quaternion): Boolean {
return other.x.isEqualApprox(x)
&& other.y.isEqualApprox(y)
&& other.z.isEqualApprox(z)
&& other.w.isEqualApprox(w)
}
/**
* Returns `true` if this quaternion is finite, by calling [Float.isFinite] on each component.
*/
fun isFinite() = x.isFinite() && y.isFinite() && z.isFinite() && w.isFinite()
/**
* Returns whether the quaternion is normalized or not.
*/
fun isNormalized(): Boolean {
return abs(lengthSquared() - 1.0) < CMP_EPSILON
}
/**
* Returns the length of the quaternion.
*/
fun length(): RealT {
return sqrt(this.lengthSquared())
}
/**
* Returns the length of the quaternion, squared.
*/
fun lengthSquared(): RealT {
return dot(this)
}
fun log(): Quaternion {
val srcV = getAxis() * getAngle()
return Quaternion(srcV.x, srcV.y, srcV.z, 0)
}
/**
* Returns a copy of the quaternion, normalized to unit length.
*/
fun normalized(): Quaternion {
return this / this.length()
}
internal fun normalize() {
val l = this.length()
x /= l
y /= l
z /= l
w /= l
}
/**
* Returns the result of rotating toward [to] by [delta] (in radians). Passing a negative [delta] will rotate toward the inverse of [to].
*
* **Note:** Both quaternions must be normalized.
*/
fun rotateToward(to: Quaternion, delta: Double): Quaternion {
val unsignedDelta: RealT
val unsignedTo: Quaternion
if (delta < 0.0) {
unsignedDelta = -delta
unsignedTo = to.inverse()
} else {
unsignedDelta = delta
unsignedTo = to
}
val angle = angleTo(unsignedTo)
return if (angle < unsignedDelta) {
unsignedTo
} else {
slerp(unsignedTo, unsignedDelta / angle)
}
}
/**
* Sets the quaternion to a rotation which rotates around axis by the specified angle, in radians. The axis must be a normalized vector.
*/
fun setAxisAndAngle(axis: Vector3, angle: RealT) {
if (GodotJvmBuildConfig.DEBUG) {
require(axis.isNormalized()) { "Axis must be normalized!" }
}
val d = axis.length()
if (d.isEqualApprox(0.0)) {
set(0.0, 0.0, 0.0, 0.0)
} else {
val sin = sin(angle * 0.5)
val cos = cos(angle * 0.5)
val s = sin / d
set(axis.x * s, axis.y * s, axis.z * s, cos)
}
}
/**
* Performs a spherical-linear interpolation with another quaternion.
*/
fun slerp(q: Quaternion, t: RealT): Quaternion {
val to1 = Quaternion()
val omega: RealT
var cosom: RealT
val sinom: RealT
val scale0: RealT
val scale1: RealT
cosom = dot(q)
if (cosom < 0) {
cosom = -cosom
to1.x = -q.x
to1.y = -q.y
to1.z = -q.z
to1.w = -q.w
} else {
to1.x = q.x
to1.y = q.y
to1.z = q.z
to1.w = q.w
}
if ((1.0 - cosom) > CMP_EPSILON) {
// standard case (slerp)
omega = acos(cosom)
sinom = sin(omega)
scale0 = sin((1.0 - t) * omega) / sinom
scale1 = sin(t * omega) / sinom
} else {
// "from" and "to" quaternions are very close
// ... so we can do a linear interpolation
scale0 = 1.0 - t
scale1 = t
}
// calculate final values
return Quaternion(
scale0 * x + scale1 * to1.x,
scale0 * y + scale1 * to1.y,
scale0 * z + scale1 * to1.z,
scale0 * w + scale1 * to1.w
)
}
/**
* Performs a spherical-linear interpolation with another quaterion without checking if the rotation path is not bigger than 90°.
*/
fun slerpni(q: Quaternion, t: RealT): Quaternion {
val from = this
val dot: RealT = from.dot(q)
if (abs(dot) > 0.9999) return from
val theta = acos(dot)
val sinT = 1.0 / sin(theta)
val newFactor: RealT = sin(t * theta) * sinT
val invFactor: RealT = sin((1.0 - t) * theta) * sinT
return Quaternion(
invFactor * from.x + newFactor * q.x,
invFactor * from.y + newFactor * q.y,
invFactor * from.z + newFactor * q.z,
invFactor * from.w + newFactor * q.w
)
}
/**
* Performs a spherical cubic interpolation between quaternions [preA], this vector, [b], and [postB], by the given
* amount [weight].
*/
fun sphericalCubicInterpolate(b: Quaternion, preA: Quaternion, postB: Quaternion, weight: RealT): Quaternion {
if (GodotJvmBuildConfig.DEBUG) {
require(isNormalized()) {
"The start quaternion must be normalized."
}
require(b.isNormalized()) {
"The end quaternion must be normalized."
}
}
var fromQ = this
var preQ = preA
var toQ = b
var postQ = postB
// Align flip phases.
fromQ = Basis(fromQ).getRotationQuaternion()
preQ = Basis(preQ).getRotationQuaternion()
toQ = Basis(toQ).getRotationQuaternion()
postQ = Basis(postQ).getRotationQuaternion()
// Flip quaternions to shortest path if necessary.
val flip1 = fromQ.dot(preQ).signbit
preQ = if (flip1) -preQ else preQ
val flip2 = fromQ.dot(toQ).signbit
toQ = if (flip2) -toQ else toQ
val flip3 = if (flip2) toQ.dot(postQ) <= 0 else toQ.dot(postQ).signbit
postQ = if (flip3) -postQ else postQ
// Calc by Expmap in from_q space.
var lnFrom = Quaternion(0, 0, 0, 0)
var lnTo = (fromQ.inverse() * toQ).log()
var lnPre = (fromQ.inverse() * preQ).log()
var lnPost = (fromQ.inverse() * postQ).log()
var ln = Quaternion(0, 0, 0, 0)
ln.x = cubicInterpolate(lnFrom.x, lnTo.x, lnPre.x, lnPost.x, weight)
ln.y = cubicInterpolate(lnFrom.y, lnTo.y, lnPre.y, lnPost.y, weight)
ln.z = cubicInterpolate(lnFrom.z, lnTo.z, lnPre.z, lnPost.z, weight)
val q1 = fromQ * ln.exp()
// Calc by Expmap in to_q space.
lnFrom = (toQ.inverse() * fromQ).log()
lnTo = Quaternion(0, 0, 0, 0)
lnPre = (toQ.inverse() * preQ).log()
lnPost = (toQ.inverse() * postQ).log()
ln = Quaternion(0, 0, 0, 0)
ln.x = cubicInterpolate(lnFrom.x, lnTo.x, lnPre.x, lnPost.x, weight)
ln.y = cubicInterpolate(lnFrom.y, lnTo.y, lnPre.y, lnPost.y, weight)
ln.z = cubicInterpolate(lnFrom.z, lnTo.z, lnPre.z, lnPost.z, weight)
val q2 = toQ * ln.exp()
// To cancel error made by Expmap ambiguity, do blending.
return q1.slerp(q2, weight)
}
/**
* Performs a spherical cubic interpolation between quaternions pre_a, this vector, b, and post_b, by the given
* amount weight.
*
* It can perform smoother interpolation than spherical_cubic_interpolate() by the time values.
*/
fun sphericalCubicInterpolateInTime(
p_b: Quaternion,
p_pre_a: Quaternion,
p_post_b: Quaternion,
p_weight: RealT,
p_b_t: RealT,
p_pre_a_t: RealT,
p_post_b_t: RealT
): Quaternion {
if (GodotJvmBuildConfig.DEBUG) {
require(isNormalized()) {
"The start quaternion must be normalized."
}
require(p_b.isNormalized()) {
"The end quaternion must be normalized."
}
}
var from_q = this
var pre_q = p_pre_a
var to_q = p_b
var post_q = p_post_b
// Align flip phases.
from_q = Basis(from_q).getRotationQuaternion()
pre_q = Basis(pre_q).getRotationQuaternion()
to_q = Basis(to_q).getRotationQuaternion()
post_q = Basis(post_q).getRotationQuaternion()
// Flip quaternions to shortest path if necessary.
val flip1 = from_q.dot(pre_q).signbit
pre_q = if (flip1) -pre_q else pre_q
val flip2 = from_q.dot(to_q).signbit
to_q = if (flip2) -to_q else to_q
val flip3 = if (flip2) to_q.dot(post_q) <= 0 else to_q.dot(post_q).signbit
post_q = if (flip3) -post_q else post_q
// Calc by Expmap in from_q space.
var ln_from = Quaternion(0, 0, 0, 0)
var ln_to = (from_q.inverse() * to_q).log()
var ln_pre = (from_q.inverse() * pre_q).log()
var ln_post = (from_q.inverse() * post_q).log()
var ln = Quaternion(0, 0, 0, 0)
ln.x = cubicInterpolateInTime(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t)
ln.y = cubicInterpolateInTime(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t)
ln.z = cubicInterpolateInTime(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t)
val q1 = from_q * ln.exp()
// Calc by Expmap in to_q space.
ln_from = (to_q.inverse() * from_q).log()
ln_to = Quaternion(0, 0, 0, 0)
ln_pre = (to_q.inverse() * pre_q).log()
ln_post = (to_q.inverse() * post_q).log()
ln = Quaternion(0, 0, 0, 0)
ln.x = cubicInterpolateInTime(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t)
ln.y = cubicInterpolateInTime(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t)
ln.z = cubicInterpolateInTime(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t)
val q2 = to_q * ln.exp()
// To cancel error made by Expmap ambiguity, do blending.
return q1.slerp(q2, p_weight);
}
fun set(px: RealT, py: RealT, pz: RealT, pw: RealT) {
x = px
y = py
z = pz
w = pw
}
internal fun xform(v: Vector3): Vector3 {
if (GodotJvmBuildConfig.DEBUG) {
require(isNormalized()) {
"The quaternion must be normalized."
}
}
val u = Vector3(x, y, z)
val uv = u.cross(v)
return v + (uv * w + u.cross(uv)) * 2.0f
}
internal fun xformInv(v: Vector3): Vector3 {
return inverse().xform(v)
}
operator fun plus(q2: Quaternion) = Quaternion(this.x + q2.x, this.y + q2.y, this.z + q2.z, this.w + q2.w)
operator fun minus(q2: Quaternion) = Quaternion(this.x - q2.x, this.y - q2.y, this.z - q2.z, this.w - q2.w)
operator fun times(v: Vector3) = xform(v)
operator fun times(q2: Quaternion): Quaternion {
val xx = w * q2.x + x * q2.w + y * q2.z - z * q2.y
val yy = w * q2.y + y * q2.w + z * q2.x - x * q2.z
val zz = w * q2.z + z * q2.w + x * q2.y - y * q2.x
val ww = w * q2.w - x * q2.x - y * q2.y - z * q2.z
return Quaternion(xx, yy, zz, ww)
}
operator fun times(scalar: Int) = Quaternion(x * scalar, y * scalar, z * scalar, w * scalar)
operator fun times(scalar: Long) = Quaternion(x * scalar, y * scalar, z * scalar, w * scalar)
operator fun times(scalar: Float) = Quaternion(x * scalar, y * scalar, z * scalar, w * scalar)
operator fun times(scalar: Double) = Quaternion(x * scalar, y * scalar, z * scalar, w * scalar)
operator fun div(f: RealT) = Quaternion(x / f, y / f, z / f, w / f)
operator fun unaryMinus() = Quaternion(-this.x, -this.y, -this.z, -this.w)
override fun equals(other: Any?): Boolean = when (other) {
is Quaternion -> (x == other.x && y == other.y && z == other.z && w == other.w)
else -> false
}
override fun toString(): String {
return "($x, $y, $z, $w)"
}
override fun hashCode(): Int {
var result = x.hashCode()
result = 31 * result + y.hashCode()
result = 31 * result + z.hashCode()
result = 31 * result + w.hashCode()
return result
}
/*
* GDScript related members
*/
constructor(from: Basis) : this() {
from.getQuaternion().also {
set(it.x, it.y, it.z, it.w)
}
}
}
operator fun Int.times(quaternion: Quaternion) = quaternion * this
operator fun Long.times(quaternion: Quaternion) = quaternion * this
operator fun Float.times(quaternion: Quaternion) = quaternion * this
operator fun Double.times(quaternion: Quaternion) = quaternion * this
operator fun Vector3.times(quaternion: Quaternion) = quaternion.xformInv(this)
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