wehub-resource-sync
304 lines
7.4 KiB
HLSL
304 lines
7.4 KiB
HLSL
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#define QUATERNION_IDENTITY float4(0, 0, 0, 1)
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#ifndef PI
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#define PI 3.14159265359f
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#endif
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#ifndef TAU
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#define TAU (3.14159265359f / 180)
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#endif
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#pragma warning(disable : 4118)
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const static float NAN = sqrt(-1);
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#ifndef mod
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#define mod(x, y) ((x) - (y) * floor((x) / (y)))
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#endif
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inline float q_separate_v(float4 q, out float4 normalized)
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{
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float l = length(q);
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normalized = q / l;
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return l - 1;
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}
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inline float4 q_encode_v(float4 q, float v)
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{
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return q * (v + 1);
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}
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float4 qMul(float4 q1, float4 q2)
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{
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return float4(
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q2.xyz * q1.w + q1.xyz * q2.w + cross(q1.xyz, q2.xyz),
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q1.w * q2.w - dot(q1.xyz, q2.xyz));
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}
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// Vector rotation with a quaternion
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// http://mathworld.wolfram.com/Quaternion.html
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// inline float3 qRotateVec3(float3 v, float4 quat)
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// {
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// float4 r_c = quat * float4(-1, -1, -1, 1);
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// return qMul(quat, qMul(float4(v, 0), r_c)).xyz;
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// }
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// https://blog.molecular-matters.com/2013/05/24/a-faster-quaternion-vector-multiplication/
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inline float3 qRotateVec3(float3 v, float4 q)
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{
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float3 t = 2 * cross(q.xyz, v);
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return v + q.w * t + cross(q.xyz, t);
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}
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float4 qConjugate(float4 q)
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{
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return float4(-q.x, -q.y, -q.z, q.w);
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}
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// https://jp.mathworks.com/help/aeroblks/quaternioninverse.html
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float4 qInverse(float4 q)
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{
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float4 conj = qConjugate(q);
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return conj / (q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
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}
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// A given angle of rotation about a given axis
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float4 qFromAngleAxis(float angle, float3 axis)
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{
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float sn = sin(angle * 0.5);
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float cs = cos(angle * 0.5);
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return float4(axis * sn, cs);
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}
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// https://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another
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float4 qFromVectors(float3 v1, float3 v2)
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{
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float4 q;
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float d = dot(v1, v2);
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if (d < -0.999999)
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{
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float3 right = float3(1, 0, 0);
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float3 up = float3(0, 1, 0);
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float3 tmp = cross(right, v1);
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if (length(tmp) < 0.000001)
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{
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tmp = cross(up, v1);
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}
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tmp = normalize(tmp);
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q = qFromAngleAxis(PI, tmp);
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}
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else if (d > 0.999999)
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{
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q = QUATERNION_IDENTITY;
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}
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else
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{
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q.xyz = cross(v1, v2);
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q.w = 1 + d;
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q = normalize(q);
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}
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return q;
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}
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float4 qLookAt(float3 forward, float3 up)
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{
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float3 right = normalize(cross(forward, up));
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up = normalize(cross(forward, right));
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float m00 = right.x;
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float m01 = right.y;
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float m02 = right.z;
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float m10 = up.x;
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float m11 = up.y;
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float m12 = up.z;
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float m20 = forward.x;
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float m21 = forward.y;
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float m22 = forward.z;
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float num8 = (m00 + m11) + m22;
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float4 q = QUATERNION_IDENTITY;
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if (num8 > 0.0)
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{
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float num = sqrt(num8 + 1.0);
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q.w = num * 0.5;
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num = 0.5 / num;
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q.x = (m12 - m21) * num;
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q.y = (m20 - m02) * num;
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q.z = (m01 - m10) * num;
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return q;
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}
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if ((m00 >= m11) && (m00 >= m22))
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{
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float num7 = sqrt(((1.0 + m00) - m11) - m22);
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float num4 = 0.5 / num7;
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q.x = 0.5 * num7;
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q.y = (m01 + m10) * num4;
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q.z = (m02 + m20) * num4;
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q.w = (m12 - m21) * num4;
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return q;
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}
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if (m11 > m22)
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{
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float num6 = sqrt(((1.0 + m11) - m00) - m22);
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float num3 = 0.5 / num6;
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q.x = (m10 + m01) * num3;
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q.y = 0.5 * num6;
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q.z = (m21 + m12) * num3;
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q.w = (m20 - m02) * num3;
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return q;
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}
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float num5 = sqrt(((1.0 + m22) - m00) - m11);
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float num2 = 0.5 / num5;
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q.x = (m20 + m02) * num2;
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q.y = (m21 + m12) * num2;
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q.z = 0.5 * num5;
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q.w = (m01 - m10) * num2;
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return q;
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}
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float4 qSlerp(in float4 a, in float4 b, float t)
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{
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// if either input is zero, return the other.
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if (length(a) == 0.0)
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{
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if (length(b) == 0.0)
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{
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return QUATERNION_IDENTITY;
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}
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return b;
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}
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else if (length(b) == 0.0)
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{
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return a;
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}
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float cosHalfAngle = a.w * b.w + dot(a.xyz, b.xyz);
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if (cosHalfAngle >= 1.0 || cosHalfAngle <= -1.0)
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{
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return a;
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}
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else if (cosHalfAngle < 0.0)
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{
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b.xyz = -b.xyz;
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b.w = -b.w;
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cosHalfAngle = -cosHalfAngle;
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}
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float blendA;
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float blendB;
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if (cosHalfAngle < 0.99)
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{
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// do proper slerp for big angles
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float halfAngle = acos(cosHalfAngle);
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float sinHalfAngle = sin(halfAngle);
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float oneOverSinHalfAngle = 1.0 / sinHalfAngle;
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blendA = sin(halfAngle * (1.0 - t)) * oneOverSinHalfAngle;
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blendB = sin(halfAngle * t) * oneOverSinHalfAngle;
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}
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else
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{
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// do lerp if angle is really small.
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blendA = 1.0 - t;
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blendB = t;
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}
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float4 result = float4(blendA * a.xyz + blendB * b.xyz, blendA * a.w + blendB * b.w);
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if (length(result) > 0.0)
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{
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return normalize(result);
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}
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return QUATERNION_IDENTITY;
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}
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float4 qFromEuler(float yaw, float pitch, float roll)
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{
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return float4(
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sin(roll / 2) * cos(pitch / 2) * cos(yaw / 2) - cos(roll / 2) * sin(pitch / 2) * sin(yaw / 2),
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cos(roll / 2) * sin(pitch / 2) * cos(yaw / 2) + sin(roll / 2) * cos(pitch / 2) * sin(yaw / 2),
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cos(roll / 2) * cos(pitch / 2) * sin(yaw / 2) - sin(roll / 2) * sin(pitch / 2) * cos(yaw / 2),
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cos(roll / 2) * cos(pitch / 2) * cos(yaw / 2) + sin(roll / 2) * sin(pitch / 2) * sin(yaw / 2));
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}
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float4x4 qToMatrix(float4 quat)
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{
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float4x4 m = 0; // float4x4(float4(0, 0, 0, 0), float4(0, 0, 0, 0), float4(0, 0, 0, 0), float4(0, 0, 0, 0));
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float x = quat.x, y = quat.y, z = quat.z, w = quat.w;
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float x2 = x + x, y2 = y + y, z2 = z + z;
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float xx = x * x2, xy = x * y2, xz = x * z2;
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float yy = y * y2, yz = y * z2, zz = z * z2;
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float wx = w * x2, wy = w * y2, wz = w * z2;
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m[0][0] = 1.0 - (yy + zz);
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m[0][1] = xy - wz;
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m[0][2] = xz + wy;
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m[1][0] = xy + wz;
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m[1][1] = 1.0 - (xx + zz);
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m[1][2] = yz - wx;
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m[2][0] = xz - wy;
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m[2][1] = yz + wx;
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m[2][2] = 1.0 - (xx + yy);
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m[3][3] = 1.0;
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return m;
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}
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float4 qFromMatrix3(float3x3 m)
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{
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float w = sqrt(1.0 + m._m00 + m._m11 + m._m22) / 2.0;
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float w4 = (4.0 * w);
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float x = (m._m21 - m._m12) / w4;
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float y = (m._m02 - m._m20) / w4;
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float z = (m._m10 - m._m01) / w4;
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return float4(x, y, z, w);
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}
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float4 qFromMatrix3Precise(float3x3 m)
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{
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float tr = m._m00 + m._m11 + m._m22;
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if (tr > 0)
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{
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float S = sqrt(tr + 1.0) * 2; // S=4*qw
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return float4(
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(m._m21 - m._m12) / S,
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(m._m02 - m._m20) / S,
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(m._m10 - m._m01) / S,
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0.25 * S);
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}
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else if ((m._m00 > m._m11) & (m._m00 > m._m22))
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{
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float S = sqrt(1.0 + m._m00 - m._m11 - m._m22) * 2; // S=4*qx
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return float4(
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0.25 * S,
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(m._m01 + m._m10) / S,
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(m._m02 + m._m20) / S,
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(m._m21 - m._m12) / S);
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}
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else if (m._m11 > m._m22)
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{
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float S = sqrt(1.0 + m._m11 - m._m00 - m._m22) * 2; // S=4*qy
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return float4(
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(m._m01 + m._m10) / S,
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0.25 * S,
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(m._m12 + m._m21) / S,
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(m._m02 - m._m20) / S);
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}
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else
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{
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float S = sqrt(1.0 + m._m22 - m._m00 - m._m11) * 2; // S=4*qz
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return float4(
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(m._m02 + m._m20) / S,
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(m._m12 + m._m21) / S,
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0.25 * S,
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(m._m10 - m._m01) / S);
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}
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}
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