Merge pull request #328 from bjz/move-slerp-to_euler
Move Quaternion::{slerp, to_euler} out of separate impl block
This commit is contained in:
Brendan Zabarauskas
commit
ee5396a64c
1 changed files with 81 additions and 83 deletions
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@ -72,6 +72,87 @@ impl<S: BaseFloat> Quaternion<S> {
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pub fn nlerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S> {
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(self * (S::one() - amount) + other * amount).normalize()
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}
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/// Spherical Linear Intoperlation
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///
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/// Return the spherical linear interpolation between the quaternion and
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/// `other`. Both quaternions should be normalized first.
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///
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/// # Performance notes
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///
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/// The `acos` operation used in `slerp` is an expensive operation, so
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/// unless your quarternions are far away from each other it's generally
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/// more advisable to use `nlerp` when you know your rotations are going
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/// to be small.
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///
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/// - [Understanding Slerp, Then Not Using It]
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/// (http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/)
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/// - [Arcsynthesis OpenGL tutorial]
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/// (http://www.arcsynthesis.org/gltut/Positioning/Tut08%20Interpolation.html)
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pub fn slerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S> {
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let dot = self.dot(other);
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let dot_threshold = cast(0.9995f64).unwrap();
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// if quaternions are close together use `nlerp`
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if dot > dot_threshold {
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self.nlerp(other, amount)
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} else {
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// stay within the domain of acos()
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// TODO REMOVE WHEN https://github.com/mozilla/rust/issues/12068 IS RESOLVED
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let robust_dot = if dot > S::one() {
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S::one()
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} else if dot < -S::one() {
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-S::one()
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} else {
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dot
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};
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let theta = Rad::acos(robust_dot.clone());
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let scale1 = Rad::sin(theta * (S::one() - amount));
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let scale2 = Rad::sin(theta * amount);
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(self * scale1 + other * scale2) * Rad::sin(theta).recip()
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}
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}
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/// Convert a Quaternion to Eular angles
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/// This is a polar singularity aware conversion
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///
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/// Based on:
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/// - [Maths - Conversion Quaternion to Euler]
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/// (http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/)
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pub fn to_euler(self) -> (Rad<S>, Rad<S>, Rad<S>) {
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let sig: S = cast(0.499f64).unwrap();
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let two: S = cast(2f64).unwrap();
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let one: S = cast(1f64).unwrap();
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let (qw, qx, qy, qz) = (self.s, self.v.x, self.v.y, self.v.z);
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let (sqw, sqx, sqy, sqz) = (qw * qw, qx * qx, qy * qy, qz * qz);
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let unit = sqx + sqy + sqz + sqw;
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let test = qx * qy + qz * qw;
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if test > sig * unit {
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(
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Rad::zero(),
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Rad::turn_div_4(),
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Rad::atan2(qx, qw) * two,
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)
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} else if test < -sig * unit {
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(
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Rad::zero(),
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-Rad::turn_div_4(),
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Rad::atan2(qx, qw) * two,
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)
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} else {
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(
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Rad::atan2(two * (qy * qw - qx * qz), one - two * (sqy + sqz)),
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Rad::asin(two * (qx * qy + qz * qw)),
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Rad::atan2(two * (qx * qw - qy * qz), one - two * (sqx + sqz)),
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)
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}
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}
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}
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impl<S: BaseFloat> VectorSpace for Quaternion<S> {
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@ -194,89 +275,6 @@ impl<S: BaseFloat> ApproxEq for Quaternion<S> {
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}
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}
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impl<S: BaseFloat> Quaternion<S> {
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/// Spherical Linear Intoperlation
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///
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/// Return the spherical linear interpolation between the quaternion and
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/// `other`. Both quaternions should be normalized first.
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///
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/// # Performance notes
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///
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/// The `acos` operation used in `slerp` is an expensive operation, so
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/// unless your quarternions are far away from each other it's generally
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/// more advisable to use `nlerp` when you know your rotations are going
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/// to be small.
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///
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/// - [Understanding Slerp, Then Not Using It]
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/// (http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/)
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/// - [Arcsynthesis OpenGL tutorial]
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/// (http://www.arcsynthesis.org/gltut/Positioning/Tut08%20Interpolation.html)
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pub fn slerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S> {
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let dot = self.dot(other);
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let dot_threshold = cast(0.9995f64).unwrap();
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// if quaternions are close together use `nlerp`
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if dot > dot_threshold {
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self.nlerp(other, amount)
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} else {
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// stay within the domain of acos()
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// TODO REMOVE WHEN https://github.com/mozilla/rust/issues/12068 IS RESOLVED
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let robust_dot = if dot > S::one() {
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S::one()
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} else if dot < -S::one() {
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-S::one()
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} else {
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dot
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};
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let theta = Rad::acos(robust_dot.clone());
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let scale1 = Rad::sin(theta * (S::one() - amount));
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let scale2 = Rad::sin(theta * amount);
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(self * scale1 + other * scale2) * Rad::sin(theta).recip()
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}
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}
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/// Convert a Quaternion to Eular angles
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/// This is a polar singularity aware conversion
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///
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/// Based on:
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/// - [Maths - Conversion Quaternion to Euler]
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/// (http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/)
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pub fn to_euler(self) -> (Rad<S>, Rad<S>, Rad<S>) {
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let sig: S = cast(0.499f64).unwrap();
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let two: S = cast(2f64).unwrap();
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let one: S = cast(1f64).unwrap();
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let (qw, qx, qy, qz) = (self.s, self.v.x, self.v.y, self.v.z);
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let (sqw, sqx, sqy, sqz) = (qw * qw, qx * qx, qy * qy, qz * qz);
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let unit = sqx + sqy + sqz + sqw;
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let test = qx * qy + qz * qw;
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if test > sig * unit {
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(
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Rad::zero(),
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Rad::turn_div_4(),
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Rad::atan2(qx, qw) * two,
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)
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} else if test < -sig * unit {
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(
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Rad::zero(),
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-Rad::turn_div_4(),
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Rad::atan2(qx, qw) * two,
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)
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} else {
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(
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Rad::atan2(two * (qy * qw - qx * qz), one - two * (sqy + sqz)),
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Rad::asin(two * (qx * qy + qz * qw)),
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Rad::atan2(two * (qx * qw - qy * qz), one - two * (sqx + sqz)),
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)
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}
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}
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}
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impl<S: BaseFloat> From<Quaternion<S>> for Matrix3<S> {
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/// Convert the quaternion to a 3 x 3 rotation matrix
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fn from(quat: Quaternion<S>) -> Matrix3<S> {
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