119 lines
3.3 KiB
C
119 lines
3.3 KiB
C
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#pragma once
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struct Quaternion4f
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{
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float x, y, z, w;
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};
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static Quaternion4f gQuatRot[4] =
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{ // { x*sin(theta/2), y*sin(theta/2), z*sin(theta/2), cos(theta/2) }
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// => { 0, 0, sin(theta/2), cos(theta/2) } (since <vec> = { 0, 0, +/-1})
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{ 0.f, 0.f, 0.f /*sin(0)*/, 1.f /*cos(0)*/}, // ROTATION_0, theta = 0 rad
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{ 0.f, 0.f, (float)sqrt(2) * 0.5f /*sin(pi/4)*/, -(float)sqrt(2) * 0.5f /*cos(pi/4)*/}, // ROTATION_90, theta = pi/4 rad
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{ 0.f, 0.f, 1.f /*sin(pi/2)*/, 0.f /*cos(pi/2)*/}, // ROTATION_180, theta = pi rad
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{ 0.f, 0.f, -(float)sqrt(2) * 0.5f /*sin(3pi/4)*/, -(float)sqrt(2) * 0.5f /*cos(3pi/4)*/} // ROTATION_270, theta = 3pi/2 rad
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};
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inline void QuatMultiply(Quaternion4f& result, const Quaternion4f& lhs, const Quaternion4f& rhs)
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{
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result.x = lhs.w * rhs.x + lhs.x * rhs.w + lhs.y * rhs.z - lhs.z * rhs.y;
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result.y = lhs.w * rhs.y + lhs.y * rhs.w + lhs.z * rhs.x - lhs.x * rhs.z;
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result.z = lhs.w * rhs.z + lhs.z * rhs.w + lhs.x * rhs.y - lhs.y * rhs.x;
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result.w = lhs.w * rhs.w - lhs.x * rhs.x - lhs.y * rhs.y - lhs.z * rhs.z;
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}
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inline Quaternion4f QuatMultiply(const Quaternion4f& lhs, const Quaternion4f& rhs)
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{
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Quaternion4f output;
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QuatMultiply(output, lhs, rhs);
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return output;
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}
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inline Quaternion4f QuatMake(float x, float y, float z, float w)
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{
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Quaternion4f q = {x, y, z, w};
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return q;
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}
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inline Quaternion4f QuatIdentity()
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{
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return gQuatRot[0];
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}
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inline Quaternion4f QuatScale(const Quaternion4f& q, float s)
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{
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return QuatMake(s * q.x, s * q.y, s * q.z, s * q.w);
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}
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inline float QuatNormSquared(const Quaternion4f& q)
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{
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return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
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}
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inline Quaternion4f QuatConjugate(const Quaternion4f& q)
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{
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return QuatMake(-q.x, -q.y, -q.z, q.w);
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}
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inline Quaternion4f QuatInverse(const Quaternion4f& q)
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{
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return QuatScale(QuatConjugate(q), 1.0f / QuatNormSquared(q));
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}
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inline Vector3f QuatToEuler(const Quaternion4f& q)
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{
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return VecMake(
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atan2f(2.0f * (q.w * q.y + q.x * q.z),
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1.0f - 2.0f * (q.y * q.y + q.x * q.x)),
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asinf(2.0f * (q.w * q.x - q.z * q.y)),
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atan2f(2.0f * (q.w * q.z + q.y * q.x),
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1.0f - 2.0f * (q.x * q.x + q.z * q.z)));
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}
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inline float QuatNorm(const Quaternion4f& q)
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{
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return sqrtf(QuatNormSquared(q));
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}
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inline Quaternion4f QuatNormalize(const Quaternion4f& q)
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{
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return QuatScale(q, 1.0f / QuatNorm(q));
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}
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inline Quaternion4f QuatDifference(const Quaternion4f& a, const Quaternion4f& b)
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{
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return QuatMultiply(QuatInverse(b), a);
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}
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inline Quaternion4f QuatRotationFromTo(const Vector3f& src, const Vector3f& dest)
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{
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// Based on Stan Melax's article in Game Programming Gems
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float mag0 = VecMagnitude(src);
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if (mag0 < FLT_EPSILON)
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return QuatIdentity();
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float mag1 = VecMagnitude(dest);
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if (mag1 < FLT_EPSILON)
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return QuatIdentity();
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Vector3f v0 = VecScale(1.0f / mag0, src);
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Vector3f v1 = VecScale(1.0f / mag1, dest);
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float d = VecDotProduct(v0, v1);
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// If dot == 1, vectors are the same
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if (d >= (1.0f - 1e-6f))
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return QuatIdentity();
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if (d < (1e-6f - 1.0f))
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return gQuatRot[2];
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float s = sqrtf((1.0f + d) * 2.0f);
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float i = 1.0f / s;
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Vector3f c = VecCrossProduct(v0, v1);
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return QuatNormalize(QuatMake(
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c.x * i, c.y * i, c.z * i, s * 0.5f));
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}
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