Slerp

実装リンク集

TypeScript実装

code:ts

export function quatSlerp(a: Quaternion, b: Quaternion, t: number): Quaternion {

// early abort if t is exactly zero or one

if (t === 0.0) { return a; }

if (t === 1.0) { return b; }

let cosHalfTheta = a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w; // dot product

if (cosHalfTheta < 0.0) {

b = new Quaternion(-b.x, -b.y, -b.z, -b.w);

cosHalfTheta = -cosHalfTheta;

}

// I think you two are the same

if (cosHalfTheta >= 1.0) {

return a;

}

const sqrSinHalfTheta = 1.0 - cosHalfTheta * cosHalfTheta;

// very small diff. fallback to simple lerp

if (sqrSinHalfTheta <= Number.EPSILON) {

const s = 1.0 - t;

return new Quaternion(

s * a.x + t * b.x,

s * a.y + t * b.y,

s * a.z + t * b.z,

s * a.w + t * b.w,

).normalized;

}

// welcome

const sinHalfTheta = Math.sqrt(sqrSinHalfTheta);

const halfTheta = Math.atan2(sinHalfTheta, cosHalfTheta);

const ratioA = Math.sin((1.0 - t) * halfTheta) / sinHalfTheta;

const ratioB = Math.sin(t * halfTheta) / sinHalfTheta;

return new Quaternion(

a.x * ratioA + b.x * ratioB,

a.y * ratioA + b.y * ratioB,

a.z * ratioA + b.z * ratioB,

a.w * ratioA + b.w * ratioB,

);

}

GLSL実装

正確にはSlerpではなく三次元方向ベクトル間の補間ですが……

code:glsl

vec3 slerpUniformVec3(vec3 a, vec3 b, float t) {

// early abort if t is exactly zero or one

if (t == 0.0) { return a; }

if (t == 1.0) { return b; }

float ratioA;

float ratioB;

float cosv = dot(a, b);

if (cosv > 1.0 - 1E-4) {

// avoid precision funny, just lerp it

ratioB = t;

ratioA = 1.0 - t;

} else {

// do the proper slerp

float sinv = sqrt(1.0 - cosv * cosv);

float theta = acos(cosv);

ratioA = sin((1.0 - t) * theta) / sinv;

ratioB = sin(t * theta) / sinv;

}

return ratioA * a + ratioB * b;

}