155 lines
3.1 KiB
Plaintext
155 lines
3.1 KiB
Plaintext
// #include "res://addons/rokojori_action_library/Runtime/Shading/Library/Qauternion.gdshaderinc"
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vec4 quaternionFromMatrix( mat3 m )
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{
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vec4 qa = vec4( 0.0, 0.0, 0.0, 1.0 );
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float trace = m[ 0 ][ 0 ] + m[ 1 ][ 1 ] + m[ 2 ][ 2 ];
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if ( trace > 0.0 )
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{
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float s = 0.5 / sqrt( trace + 1.0 );
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qa.w = 0.25 / s;
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qa.x = ( m[ 1 ][ 2 ] - m[ 2 ][ 1 ] ) * s;
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qa.y = ( m[ 2 ][ 0 ] - m[ 0 ][ 2 ] ) * s;
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qa.z = ( m[ 0 ][ 1 ] - m[ 1 ][ 0 ] ) * s;
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}
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else if ( m[ 0 ][ 0 ] > m[ 1 ][ 1 ] && m[ 0 ][ 0 ] > m[ 2 ][ 2 ] )
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{
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float s = 2.0 * sqrt( 1.0 + m[ 0 ][ 0 ] - m[ 1 ][ 1 ] - m[ 2 ][ 2 ] );
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qa.w = ( m[ 1 ][ 2 ] - m[ 2 ][ 1 ] ) / s;
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qa.x = 0.25 * s;
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qa.y = ( m[ 1 ][ 0 ] + m[ 0 ][ 1 ] ) / s;
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qa.z = ( m[ 2 ][ 0 ] + m[ 0 ][ 2 ] ) / s;
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}
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else if ( m[ 1 ][ 1 ] > m[ 2 ][ 2 ] )
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{
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float s = 2.0 * sqrt( 1.0 + m[ 1 ][ 1 ] - m[ 0 ][ 0 ] - m[ 2 ][ 2 ] );
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qa.w = ( m[ 2 ][ 0 ] - m[ 0 ][ 2 ] ) / s;
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qa.x = ( m[ 1 ][ 0 ] + m[ 0 ][ 1 ] ) / s;
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qa.y = 0.25 * s;
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qa.z = ( m[ 2 ][ 1 ] + m[ 1 ][ 2 ] ) / s;
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}
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else
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{
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float s = 2.0 * sqrt( 1.0 + m[ 2 ][ 2 ] - m[ 0 ][ 0 ] - m[ 1 ][ 1 ] );
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qa.w = ( m[ 0 ][ 1 ] - m[ 1 ][ 0 ] ) / s;
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qa.x = ( m[ 2 ][ 0 ] + m[ 0 ][ 2 ] ) / s;
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qa.y = ( m[ 2 ][ 1 ] + m[ 1 ][ 2 ] ) / s;
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qa.z = 0.25 * s;
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}
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return qa;
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}
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vec4 quaternionMultiply( vec4 a, vec4 b )
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{
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// from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm
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float qax = a.x;
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float qay = a.y;
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float qaz = a.z;
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float qaw = a.w;
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float qbx = b.x;
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float qby = b.y;
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float qbz = b.z;
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float qbw = b.w;
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vec4 q = vec4( 0.0, 0.0, 0.0, 0.0 );
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q.x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
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q.y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
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q.z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
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q.w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
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return q;
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}
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vec4 quaternionSlerp( vec4 qa, vec4 qb, float t )
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{
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if ( t == 0.0 )
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{
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return qa;
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}
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if ( t == 1.0 )
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{
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return qb;
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}
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float x = qa.x;
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float y = qa.y;
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float z = qa.z;
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float w = qa.w;
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float cosHalfTheta = w * qb.w + x * qb.x + y * qb.y + z * qb.z;
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if ( cosHalfTheta < 0.0 )
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{
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qa.w = - qb.w;
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qa.x = - qb.x;
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qa.y = - qb.y;
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qa.z = - qb.z;
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cosHalfTheta = - cosHalfTheta;
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}
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else
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{
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qa = qb;
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}
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if ( cosHalfTheta >= 1.0 )
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{
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qa.w = w;
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qa.x = x;
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qa.y = y;
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qa.z = z;
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return qa;
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}
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float sqrSinHalfTheta = 1.0 - cosHalfTheta * cosHalfTheta;
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if ( sqrSinHalfTheta <= 0.000001 )
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{
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float s = 1.0 - t;
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qa.w = s * w + t * qa.w;
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qa.x = s * x + t * qa.x;
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qa.y = s * y + t * qa.y;
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qa.z = s * z + t * qa.z;
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qa = normalize( qa );
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return qa;
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}
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float sinHalfTheta = sqrt( sqrSinHalfTheta );
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float halfTheta = atan( sinHalfTheta, cosHalfTheta );
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float ratioA = sin( ( 1.0 - t ) * halfTheta ) / sinHalfTheta;
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float ratioB = sin( t * halfTheta ) / sinHalfTheta;
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qa.w = ( w * ratioA + qa.w * ratioB );
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qa.x = ( x * ratioA + qa.x * ratioB );
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qa.y = ( y * ratioA + qa.y * ratioB );
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qa.z = ( z * ratioA + qa.z * ratioB );
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return qa;
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} |