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fix(math): Fix slerpQuaternions results being wrong at certain angles #961

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Nov 14, 2024
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fix(math): Fix slerpQuaternions results being wrong at certain angles #961

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24 changes: 15 additions & 9 deletions src/math/Quat.js
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Original file line number Diff line number Diff line change
Expand Up @@ -285,31 +285,37 @@ export class Quat {
* @param {number} t
*/
static slerpQuaternions(quatA, quatB, t) {
quatA = quatA.clone();
quatB = quatB.clone();
// https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
if (t == 0) {
return quatA.clone();
}
if (t == 1) {
return quatB.clone();
}
if (t == 0) return quatA;
if (t == 1) return quatB;

let cosHalfTheta = new Vec4(quatA).dot(quatB);
if (cosHalfTheta < 0) {
quatB.x = -quatB.x;
quatB.y = -quatB.y;
quatB.z = -quatB.z;
quatB.w = -quatB.w;
cosHalfTheta = -cosHalfTheta;
}

// If quatA = quatB or quatA = -quatB then theta = 0 and we can return quatA
if (Math.abs(cosHalfTheta) >= 1) {
if (cosHalfTheta >= 1) {
return quatA.clone();
}

// Calculate temporary values.
const halfTheta = Math.acos(cosHalfTheta);
const sinHalfTheta = Math.sqrt(1 - cosHalfTheta * cosHalfTheta);
const sqrSinHalfTheta = 1 - cosHalfTheta * cosHalfTheta;

// When sinHalfTheta is very small, we run into precision errors.
// It's best to just linearly interpolate the two quaternions in that case
if (sqrSinHalfTheta <= Number.EPSILON) {
const vec = Vec4.lerp(quatA, quatB, t);
return new Quat(vec);
}

const sinHalfTheta = Math.sqrt(sqrSinHalfTheta);
const ratioA = Math.sin((1 - t) * halfTheta) / sinHalfTheta;
const ratioB = Math.sin(t * halfTheta) / sinHalfTheta;

Expand Down
39 changes: 36 additions & 3 deletions test/unit/src/math/Quat.test.js
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Original file line number Diff line number Diff line change
Expand Up @@ -33,9 +33,9 @@ Deno.test({
* @param {number} t
* @param {Quat} expected
*/
function basicSlerpTest(a, b, t, expected) {
function basicSlerpTest(a, b, t, expected, tolerance = 0.00001) {
const result = Quat.slerpQuaternions(a, b, t);
assertQuatAlmostEquals(result, expected);
assertQuatAlmostEquals(result, expected, tolerance);
}

Deno.test({
Expand Down Expand Up @@ -64,6 +64,21 @@ Deno.test({
},
});

Deno.test({
name: "two quaternions that are very close to each other",
fn() {
const a = new Quat();
const b = Quat.fromAxisAngle(0, 1, 0, 0.00000003);
basicSlerpTest(a, b, 0, a, 0);
basicSlerpTest(a, b, 0.1, new Quat(0, 1.5e-9, 0, 1), 0);
basicSlerpTest(a, b, 0.25, new Quat(0, 3.75e-9, 0, 1), 0);
basicSlerpTest(a, b, 0.5, new Quat(0, 7.5e-9, 0, 1), 0);
basicSlerpTest(a, b, 0.75, new Quat(0, 1.1249999999999998e-8, 0, 0.9999999999999999), 0);
basicSlerpTest(a, b, 0.9, new Quat(0, 1.3499999999999998e-8, 0, 0.9999999999999999), 0);
basicSlerpTest(a, b, 1, b, 0);
},
});

Deno.test({
name: "slerp that results in a negative cosHalfTheta",
fn() {
Expand All @@ -74,12 +89,30 @@ Deno.test({
},
});

Deno.test({
name: "another slerp that results in a negative cosHalfTheta",
fn() {
const a = new Quat();
const b = Quat.fromAxisAngle(1, 1, 1, 4);
basicSlerpTest(a, b, 0.219, Quat.fromAxisAngle(1, 1, 1, -0.5));
basicSlerpTest(a, b, 0.5, Quat.fromAxisAngle(1, 1, 1, -1.14157));
},
});

Deno.test({
name: "slerp two quaternions that are the same",
fn() {
const a = new Quat(0, 0.2, 20, 1);
basicSlerpTest(a, a, 0.5, a);
const b = new Quat(12, 34, 56, 78);
basicSlerpTest(a, a, 0.01, a);
basicSlerpTest(b, b, 0.01, b);
basicSlerpTest(a, a, 0.1, a);
basicSlerpTest(b, b, 0.1, b);
basicSlerpTest(a, a, 0.5, a);
basicSlerpTest(b, b, 0.5, b);
basicSlerpTest(a, a, 0.9, a);
basicSlerpTest(b, b, 0.9, b);
basicSlerpTest(a, a, 0.99, a);
basicSlerpTest(b, b, 0.99, b);
},
});
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