Torque3D/Engine/source/math/mQuat.cpp

//-----------------------------------------------------------------------------
// Copyright (c) 2012 GarageGames, LLC
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
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// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// IN THE SOFTWARE.
//-----------------------------------------------------------------------------

#include "platform/platform.h"
#include "math/mQuat.h"

#include "math/mAngAxis.h"
#include "math/mMatrix.h"
#include "platform/profiler.h"


const QuatF QuatF::Identity(0.0f,0.0f,0.0f,1.0f);

QuatF& QuatF::set( const EulerF & e )
{
	/*
	F32 cx, sx;
	F32 cy, sy;
	F32 cz, sz;
	mSinCos( -e.x * 0.5f, sx, cx );
	mSinCos( -e.y * 0.5f, sy, cy );
	mSinCos( -e.z * 0.5f, sz, cz );

	// Qyaw(z)   = [ (0, 0, sin z/2), cos z/2 ]
	// Qpitch(x) = [ (sin x/2, 0, 0), cos x/2 ]
	// Qroll(y)  = [ (0, sin y/2, 0), cos y/2 ]
	// this = Qresult = Qyaw*Qpitch*Qroll  ZXY
	//
	// The code that folows is a simplification of:
	//    roll*=pitch;
	//    roll*=yaw;
	//    *this = roll;
	F32 cycz, sysz, sycz, cysz;
	cycz = cy*cz;
	sysz = sy*sz;
	sycz = sy*cz;
	cysz = cy*sz;
	w = cycz*cx + sysz*sx;
	x = cycz*sx + sysz*cx;
	y = sycz*cx - cysz*sx;
	z = cysz*cx - sycz*sx;
	*/
	// Assuming the angles are in radians.
	F32 c1 = mCos(e.y * 0.5f);
	F32 s1 = mSin(e.y * 0.5f);
	F32 c2 = mCos(e.z * 0.5f);
	F32 s2 = mSin(e.z * 0.5f);
	F32 c3 = mCos(e.x * 0.5f);
	F32 s3 = mSin(e.x * 0.5f);
	F32 c1c2 = c1*c2;
	F32 s1s2 = s1*s2;
	w =c1c2*c3 - s1s2*s3;
	x =c1c2*s3 + s1s2*c3;
	y =s1*c2*c3 + c1*s2*s3;
	z =c1*s2*c3 - s1*c2*s3;

	return *this;
}

QuatF& QuatF::operator *=( const QuatF & b )
{
   QuatF prod;
   prod.w = w * b.w - x * b.x - y * b.y - z * b.z;
   prod.x = w * b.x + x * b.w + y * b.z - z * b.y;
   prod.y = w * b.y + y * b.w + z * b.x - x * b.z;
   prod.z = w * b.z + z * b.w + x * b.y - y * b.x;
   *this = prod;
   return (*this);
}

QuatF& QuatF::operator /=( const QuatF & c )
{
   QuatF temp = c;
   return ( (*this) *= temp.inverse() );
}

QuatF& QuatF::square()
{
   F32 t = w*2.0f;
   w = (w*w) - (x*x + y*y + z*z);
   x *= t;
   y *= t;
   z *= t;
   return *this;
}

QuatF& QuatF::inverse()
{
   F32 magnitude = w*w + x*x + y*y + z*z;
   F32 invMagnitude;
   if( magnitude == 1.0f )    // special case unit quaternion
   {
      x = -x;
      y = -y;
      z = -z;
   }
   else                       // else scale
   {
      if( magnitude == 0.0f )
         invMagnitude = 1.0f;
      else
         invMagnitude = 1.0f / magnitude;
      w *= invMagnitude;
      x *= -invMagnitude;
      y *= -invMagnitude;
      z *= -invMagnitude;
   }
   return *this;
}

QuatF & QuatF::set( const AngAxisF & a )
{
   return set( a.axis, a.angle );
}

QuatF & QuatF::set( const Point3F &axis, F32 angle )
{
   PROFILE_SCOPE( QuatF_set_AngAxisF );

   F32 sinHalfAngle, cosHalfAngle;
   mSinCos( angle * 0.5f, sinHalfAngle, cosHalfAngle );
   x = axis.x * sinHalfAngle;
   y = axis.y * sinHalfAngle;
   z = axis.z * sinHalfAngle;
   w = cosHalfAngle;
   return *this;
}

QuatF & QuatF::normalize()
{
   PROFILE_SCOPE( QuatF_normalize );

   F32 l = mSqrt( x*x + y*y + z*z + w*w );
   if( l == 0.0f )
      identity();
   else
   {
      x /= l;
      y /= l;
      z /= l;
      w /= l;
   }
   return *this;
}

#define idx(r,c) (r*4 + c)

QuatF & QuatF::set( const MatrixF & mat )
{
   PROFILE_SCOPE( QuatF_set_MatrixF );

   F32 const *m = mat;

   F32 trace = m[idx(0, 0)] + m[idx(1, 1)] + m[idx(2, 2)];
   if (trace > 0.0f) 
   {
      F32 s = mSqrt(trace + F32(1));
      w = s * 0.5f;
      s = 0.5f / s;
      x = (m[idx(1,2)] - m[idx(2,1)]) * s;
      y = (m[idx(2,0)] - m[idx(0,2)]) * s;
      z = (m[idx(0,1)] - m[idx(1,0)]) * s;
   } 
   else 
   {
      F32* q = &x;
      U32 i = 0;
      if (m[idx(1, 1)] > m[idx(0, 0)]) i = 1;
      if (m[idx(2, 2)] > m[idx(i, i)]) i = 2;
      U32 j = (i + 1) % 3;
      U32 k = (j + 1) % 3;

      F32 s = mSqrt((m[idx(i, i)] - (m[idx(j, j)] + m[idx(k, k)])) + 1.0f);
      q[i] = s * 0.5f;
      s = 0.5f / s;
      q[j] = (m[idx(i,j)] + m[idx(j,i)]) * s;
      q[k] = (m[idx(i,k)] + m[idx(k, i)]) * s;
      w = (m[idx(j,k)] - m[idx(k, j)]) * s;
   }

   // Added to resolve issue #2230
   normalize();

   return *this;
}

MatrixF * QuatF::setMatrix( MatrixF * mat ) const
{
   if( x*x + y*y + z*z < 10E-20f) // isIdentity() -- substituted code a little more stringent but a lot faster
      mat->identity();
   else
      m_quatF_set_matF( x, y, z, w, *mat );
   return mat;
}

QuatF & QuatF::slerp( const QuatF & q, F32 t )
{
   return interpolate( *this, q, t );
}

QuatF & QuatF::extrapolate( const QuatF & q1, const QuatF & q2, F32 t )
{
   // assert t >= 0 && t <= 1
   // q1 is value at time = 0
   // q2 is value at time = t
   // Computes quaternion at time = 1
   F64 flip,cos = q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
   if (cos < 0.0)
   {
      cos = -cos;
      flip = -1.0;
   }
   else
      flip = 1.0;

   F64 s1,s2;
   if ((1.0 - cos) > 0.00001)
   {
      F64 om = mAcos(cos) / t;
      F64 sd = 1.0 / mSin(t * om);
      s1 = flip * mSin(om) * sd;
      s2 = mSin((1.0 - t) * om) * sd;
   }
   else
   {
      // If quats are very close, do linear interpolation
      s1 = flip / t;
      s2 = (1.0 - t) / t;
   }

   x = F32(s1 * q2.x - s2 * q1.x);
   y = F32(s1 * q2.y - s2 * q1.y);
   z = F32(s1 * q2.z - s2 * q1.z);
   w = F32(s1 * q2.w - s2 * q1.w);

   return *this;
}

QuatF & QuatF::interpolate( const QuatF & q1, const QuatF & q2, F32 t )
{
   //-----------------------------------
   // Calculate the cosine of the angle:

   double cosOmega = q1.dot( q2 );

   //-----------------------------------
   // adjust signs if necessary:

   F32 sign2;
   if ( cosOmega < 0.0 )
   {
      cosOmega = -cosOmega;
      sign2 = -1.0f;
   }
   else
      sign2 = 1.0f;

   //-----------------------------------
   // calculate interpolating coeffs:

   F64 scale1, scale2;
   if ( (1.0 - cosOmega) > 0.00001 )
   {
      // standard case
      F64 omega = mAcos(cosOmega);
      F64 sinOmega = mSin(omega);
      scale1 = mSin((1.0 - t) * omega) / sinOmega;
      scale2 = sign2 * mSin(t * omega) / sinOmega;
   }
   else
   {
      // if quats are very close, just do linear interpolation
      scale1 = 1.0 - t;
      scale2 = sign2 * t;
   }


   //-----------------------------------
   // actually do the interpolation:

   x = F32(scale1 * q1.x + scale2 * q2.x);
   y = F32(scale1 * q1.y + scale2 * q2.y);
   z = F32(scale1 * q1.z + scale2 * q2.z);
   w = F32(scale1 * q1.w + scale2 * q2.w);
   return *this;
}

Point3F & QuatF::mulP(const Point3F& p, Point3F* r) const
{
   QuatF qq;
   QuatF qi = *this;
   QuatF qv( p.x, p.y, p.z, 0.0f);

   qi.inverse();
   qq.mul(qi, qv);
   qv.mul(qq, *this);
   r->set(qv.x, qv.y, qv.z);
   return *r;
}

QuatF & QuatF::mul( const QuatF &a, const QuatF &b)
{
   AssertFatal( &a != this && &b != this, "QuatF::mul: dest should not be same as source" );
   w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z;
   x = a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y;
   y = a.w * b.y + a.y * b.w + a.z * b.x - a.x * b.z;
   z = a.w * b.z + a.z * b.w + a.x * b.y - a.y * b.x;
   return *this;
}

QuatF & QuatF::shortestArc( const VectorF &a, const VectorF &b )
{
   // From Game Programming Gems pg. 217
   VectorF c = mCross( a, b );
   F32 d = mDot( a, b );
   F32 s = mSqrt( ( 1 + d ) * 2 );

   x = c.x / s;
   y = c.y / s;
   z = c.z / s;
   w = s / 2.f; 

   return *this;
}