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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Copyright 2021 Leszek Koltunski //
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// //
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// This file is part of Magic Cube. //
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// //
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// Magic Cube is free software: you can redistribute it and/or modify //
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// it under the terms of the GNU General Public License as published by //
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// the Free Software Foundation, either version 2 of the License, or //
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// (at your option) any later version. //
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// //
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// Magic Cube is distributed in the hope that it will be useful, //
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// but WITHOUT ANY WARRANTY; without even the implied warranty of //
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
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// GNU General Public License for more details. //
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// //
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// You should have received a copy of the GNU General Public License //
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// along with Magic Cube. If not, see <http://www.gnu.org/licenses/>. //
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///////////////////////////////////////////////////////////////////////////////////////////////////
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package org.distorted.library.main;
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import org.distorted.library.type.Static4D;
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///////////////////////////////////////////////////////////////////////////////////////////////////
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public class QuatHelper
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{
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// return quat1*quat2
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public static Static4D quatMultiply( Static4D quat1, Static4D quat2 )
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{
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float qx = quat1.get0();
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float qy = quat1.get1();
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float qz = quat1.get2();
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float qw = quat1.get3();
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float rx = quat2.get0();
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float ry = quat2.get1();
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float rz = quat2.get2();
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float rw = quat2.get3();
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float tx = rw*qx - rz*qy + ry*qz + rx*qw;
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float ty = rw*qy + rz*qx + ry*qw - rx*qz;
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float tz = rw*qz + rz*qw - ry*qx + rx*qy;
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float tw = rw*qw - rz*qz - ry*qy - rx*qx;
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return new Static4D(tx,ty,tz,tw);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// return quat1*(rx,ry,rz,rw)
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public static Static4D quatMultiply( Static4D quat1, float rx, float ry, float rz, float rw )
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{
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float qx = quat1.get0();
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float qy = quat1.get1();
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float qz = quat1.get2();
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float qw = quat1.get3();
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float tx = rw*qx - rz*qy + ry*qz + rx*qw;
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float ty = rw*qy + rz*qx + ry*qw - rx*qz;
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float tz = rw*qz + rz*qw - ry*qx + rx*qy;
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float tw = rw*qw - rz*qz - ry*qy - rx*qx;
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return new Static4D(tx,ty,tz,tw);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// return (qx,qy,qz,qw)*quat2
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public static Static4D quatMultiply( float qx, float qy, float qz, float qw, Static4D quat2 )
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{
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float rx = quat2.get0();
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float ry = quat2.get1();
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float rz = quat2.get2();
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float rw = quat2.get3();
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float tx = rw*qx - rz*qy + ry*qz + rx*qw;
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float ty = rw*qy + rz*qx + ry*qw - rx*qz;
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float tz = rw*qz + rz*qw - ry*qx + rx*qy;
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float tw = rw*qw - rz*qz - ry*qy - rx*qx;
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return new Static4D(tx,ty,tz,tw);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// return (qx,qy,qz,qw)*(rx,ry,rz,rw)
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public static Static4D quatMultiply( float qx, float qy, float qz, float qw, float rx, float ry, float rz, float rw )
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{
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float tx = rw*qx - rz*qy + ry*qz + rx*qw;
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float ty = rw*qy + rz*qx + ry*qw - rx*qz;
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float tz = rw*qz + rz*qw - ry*qx + rx*qy;
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float tw = rw*qw - rz*qz - ry*qy - rx*qx;
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return new Static4D(tx,ty,tz,tw);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// ret = (qx,qy,qz,qw)*(rx,ry,rz,rw)
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public static void quatMultiply( float[] ret, float[] q, float[] r )
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{
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ret[0] = r[3]*q[0] - r[2]*q[1] + r[1]*q[2] + r[0]*q[3];
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ret[1] = r[3]*q[1] + r[2]*q[0] + r[1]*q[3] - r[0]*q[2];
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ret[2] = r[3]*q[2] + r[2]*q[3] - r[1]*q[0] + r[0]*q[1];
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ret[3] = r[3]*q[3] - r[2]*q[2] - r[1]*q[1] - r[0]*q[0];
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// rotate 'vector' by quat ( i.e. return quat*vector*(quat^-1) )
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public static Static4D rotateVectorByQuat(Static4D vector, Static4D quat)
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{
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float qx = quat.get0();
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float qy = quat.get1();
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float qz = quat.get2();
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float qw = quat.get3();
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Static4D tmp = quatMultiply(qx,qy,qz,qw,vector);
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return quatMultiply(tmp,-qx,-qy,-qz,qw);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// rotate (x1,x2,x3,x4) by quat ( i.e. return quat*vector*(quat^-1) )
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public static Static4D rotateVectorByQuat(float x, float y, float z, float w, Static4D quat)
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{
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float qx = quat.get0();
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float qy = quat.get1();
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float qz = quat.get2();
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float qw = quat.get3();
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Static4D tmp = quatMultiply(qx,qy,qz,qw,x,y,z,w);
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return quatMultiply(tmp,-qx,-qy,-qz,qw);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// rotate vec by quat ( i.e. return quat*vector*(quat^-1) )
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public static void rotateVectorByQuat(float[] output, float[] vec, float[] quat)
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{
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float[] tmp = new float[4];
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quatMultiply(tmp,quat,vec);
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quat[0] = -quat[0];
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quat[1] = -quat[1];
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quat[2] = -quat[2];
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quatMultiply(output,tmp,quat);
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quat[0] = -quat[0];
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quat[1] = -quat[1];
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quat[2] = -quat[2];
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// rotate 'vector' by quat^(-1) ( i.e. return (quat^-1)*vector*quat )
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public static Static4D rotateVectorByInvertedQuat(Static4D vector, Static4D quat)
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{
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float qx = quat.get0();
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float qy = quat.get1();
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float qz = quat.get2();
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float qw = quat.get3();
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Static4D tmp = quatMultiply(-qx,-qy,-qz,qw,vector);
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return quatMultiply(tmp,quat);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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public static Static4D quatFromDrag(float dragX, float dragY)
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{
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float axisX = dragY; // inverted X and Y - rotation axis is perpendicular to (dragX,dragY)
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float axisY = dragX; // Why not (-dragY, dragX) ? because Y axis is also inverted!
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float axisZ = 0;
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float axisL = (float)Math.sqrt(axisX*axisX + axisY*axisY + axisZ*axisZ);
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if( axisL>0 )
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{
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axisX /= axisL;
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axisY /= axisL;
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axisZ /= axisL;
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float ratio = axisL;
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ratio = ratio - (int)ratio; // the cos() is only valid in (0,Pi)
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float cosA = (float)Math.cos(Math.PI*ratio);
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float sinA = (float)Math.sqrt(1-cosA*cosA);
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return new Static4D(axisX*sinA, axisY*sinA, axisZ*sinA, cosA);
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}
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return new Static4D(0f, 0f, 0f, 1f);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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public static double computeCos(double oldX, double oldY, double newX, double newY, double len1, double len2)
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{
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double ret= (oldX*newX+oldY*newY) / (len1*len2);
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if( ret<-1.0 ) return -1.0;
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if( ret> 1.0 ) return 1.0;
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return ret;
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// sin of (signed!) angle between vectors 'old' and 'new', counterclockwise!
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public static double computeSin(double oldX, double oldY, double newX, double newY, double len1, double len2)
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{
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double ret= (newX*oldY-oldX*newY) / (len1*len2);
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if( ret<-1.0 ) return -1.0;
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if( ret> 1.0 ) return 1.0;
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return ret;
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// return quat Q that turns 3D vector A=(ax,ay,az) to another 3D vector B=(bx,by,bz)
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// take care of double-cover by ensuring that always Q.get3() >=0
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public static Static4D retRotationQuat(float ax, float ay, float az, float bx, float by, float bz)
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{
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float nx = ay*bz - az*by;
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float ny = az*bx - ax*bz;
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float nz = ax*by - ay*bx;
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float sin = (float)Math.sqrt(nx*nx + ny*ny + nz*nz);
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float cos = ax*bx + ay*by + az*bz;
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if( sin!=0 )
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{
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nx /= sin;
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ny /= sin;
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nz /= sin;
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}
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// Why sin<=0 and cos>=0 ?
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// 0<angle<180 -> 0<halfAngle<90 -> both sin and cos are positive.
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// But1: quats work counterclockwise -> negate cos.
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// But2: double-cover, we prefer to have the cos positive (so that unit=(0,0,0,1))
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// so negate again both cos and sin.
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float sinHalf =-(float)Math.sqrt((1-cos)/2);
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float cosHalf = (float)Math.sqrt((1+cos)/2);
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return new Static4D(nx*sinHalf,ny*sinHalf,nz*sinHalf,cosHalf);
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}
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}
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