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Engine directory for ticket #1
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DavidWyand-GG
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329
Engine/source/math/mQuat.cpp
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329
Engine/source/math/mQuat.cpp
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//-----------------------------------------------------------------------------
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// Copyright (c) 2012 GarageGames, LLC
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to
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// deal in the Software without restriction, including without limitation the
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// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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// sell copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in
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// all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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// IN THE SOFTWARE.
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//-----------------------------------------------------------------------------
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#include "platform/platform.h"
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#include "math/mQuat.h"
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#include "math/mAngAxis.h"
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#include "math/mMatrix.h"
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#include "platform/profiler.h"
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const QuatF QuatF::Identity(0.0f,0.0f,0.0f,1.0f);
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QuatF& QuatF::set( const EulerF & e )
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{
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F32 cx, sx;
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F32 cy, sy;
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F32 cz, sz;
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mSinCos( -e.x * 0.5f, sx, cx );
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mSinCos( -e.y * 0.5f, sy, cy );
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mSinCos( -e.z * 0.5f, sz, cz );
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// Qyaw(z) = [ (0, 0, sin z/2), cos z/2 ]
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// Qpitch(x) = [ (sin x/2, 0, 0), cos x/2 ]
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// Qroll(y) = [ (0, sin y/2, 0), cos y/2 ]
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// this = Qresult = Qyaw*Qpitch*Qroll ZXY
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//
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// The code that folows is a simplification of:
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// roll*=pitch;
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// roll*=yaw;
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// *this = roll;
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F32 cycz, sysz, sycz, cysz;
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cycz = cy*cz;
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sysz = sy*sz;
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sycz = sy*cz;
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cysz = cy*sz;
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w = cycz*cx + sysz*sx;
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x = cycz*sx + sysz*cx;
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y = sycz*cx - cysz*sx;
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z = cysz*cx - sycz*sx;
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return *this;
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}
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QuatF& QuatF::operator *=( const QuatF & b )
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{
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QuatF prod;
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prod.w = w * b.w - x * b.x - y * b.y - z * b.z;
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prod.x = w * b.x + x * b.w + y * b.z - z * b.y;
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prod.y = w * b.y + y * b.w + z * b.x - x * b.z;
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prod.z = w * b.z + z * b.w + x * b.y - y * b.x;
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*this = prod;
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return (*this);
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}
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QuatF& QuatF::operator /=( const QuatF & c )
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{
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QuatF temp = c;
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return ( (*this) *= temp.inverse() );
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}
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QuatF& QuatF::square()
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{
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F32 t = w*2.0f;
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w = (w*w) - (x*x + y*y + z*z);
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x *= t;
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y *= t;
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z *= t;
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return *this;
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}
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QuatF& QuatF::inverse()
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{
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F32 magnitude = w*w + x*x + y*y + z*z;
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F32 invMagnitude;
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if( magnitude == 1.0f ) // special case unit quaternion
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{
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x = -x;
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y = -y;
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z = -z;
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}
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else // else scale
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{
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if( magnitude == 0.0f )
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invMagnitude = 1.0f;
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else
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invMagnitude = 1.0f / magnitude;
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w *= invMagnitude;
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x *= -invMagnitude;
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y *= -invMagnitude;
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z *= -invMagnitude;
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}
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return *this;
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}
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QuatF & QuatF::set( const AngAxisF & a )
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{
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return set( a.axis, a.angle );
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}
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QuatF & QuatF::set( const Point3F &axis, F32 angle )
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{
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PROFILE_SCOPE( QuatF_set_AngAxisF );
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F32 sinHalfAngle, cosHalfAngle;
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mSinCos( angle * 0.5f, sinHalfAngle, cosHalfAngle );
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x = axis.x * sinHalfAngle;
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y = axis.y * sinHalfAngle;
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z = axis.z * sinHalfAngle;
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w = cosHalfAngle;
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return *this;
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}
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QuatF & QuatF::normalize()
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{
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PROFILE_SCOPE( QuatF_normalize );
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F32 l = mSqrt( x*x + y*y + z*z + w*w );
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if( l == 0.0f )
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identity();
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else
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{
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x /= l;
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y /= l;
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z /= l;
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w /= l;
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}
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return *this;
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}
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#define idx(r,c) (r*4 + c)
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QuatF & QuatF::set( const MatrixF & mat )
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{
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PROFILE_SCOPE( QuatF_set_MatrixF );
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F32 const *m = mat;
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F32 trace = m[idx(0, 0)] + m[idx(1, 1)] + m[idx(2, 2)];
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if (trace > 0.0f)
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{
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F32 s = mSqrt(trace + F32(1));
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w = s * 0.5f;
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s = 0.5f / s;
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x = (m[idx(1,2)] - m[idx(2,1)]) * s;
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y = (m[idx(2,0)] - m[idx(0,2)]) * s;
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z = (m[idx(0,1)] - m[idx(1,0)]) * s;
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}
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else
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{
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F32* q = &x;
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U32 i = 0;
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if (m[idx(1, 1)] > m[idx(0, 0)]) i = 1;
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if (m[idx(2, 2)] > m[idx(i, i)]) i = 2;
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U32 j = (i + 1) % 3;
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U32 k = (j + 1) % 3;
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F32 s = mSqrt((m[idx(i, i)] - (m[idx(j, j)] + m[idx(k, k)])) + 1.0f);
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q[i] = s * 0.5f;
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s = 0.5f / s;
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q[j] = (m[idx(i,j)] + m[idx(j,i)]) * s;
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q[k] = (m[idx(i,k)] + m[idx(k, i)]) * s;
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w = (m[idx(j,k)] - m[idx(k, j)]) * s;
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}
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// Added to resolve issue #2230
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normalize();
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return *this;
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}
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MatrixF * QuatF::setMatrix( MatrixF * mat ) const
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{
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if( x*x + y*y + z*z < 10E-20f) // isIdentity() -- substituted code a little more stringent but a lot faster
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mat->identity();
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else
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m_quatF_set_matF( x, y, z, w, *mat );
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return mat;
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}
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QuatF & QuatF::slerp( const QuatF & q, F32 t )
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{
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return interpolate( *this, q, t );
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}
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QuatF & QuatF::extrapolate( const QuatF & q1, const QuatF & q2, F32 t )
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{
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// assert t >= 0 && t <= 1
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// q1 is value at time = 0
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// q2 is value at time = t
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// Computes quaternion at time = 1
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F64 flip,cos = q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w;
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if (cos < 0.0)
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{
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cos = -cos;
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flip = -1.0;
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}
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else
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flip = 1.0;
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F64 s1,s2;
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if ((1.0 - cos) > 0.00001)
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{
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F64 om = mAcos(cos) / t;
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F64 sd = 1.0 / mSin(t * om);
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s1 = flip * mSin(om) * sd;
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s2 = mSin((1.0 - t) * om) * sd;
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}
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else
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{
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// If quats are very close, do linear interpolation
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s1 = flip / t;
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s2 = (1.0 - t) / t;
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}
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x = F32(s1 * q2.x - s2 * q1.x);
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y = F32(s1 * q2.y - s2 * q1.y);
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z = F32(s1 * q2.z - s2 * q1.z);
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w = F32(s1 * q2.w - s2 * q1.w);
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return *this;
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}
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QuatF & QuatF::interpolate( const QuatF & q1, const QuatF & q2, F32 t )
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{
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//-----------------------------------
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// Calculate the cosine of the angle:
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double cosOmega = q1.dot( q2 );
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//-----------------------------------
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// adjust signs if necessary:
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F32 sign2;
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if ( cosOmega < 0.0 )
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{
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cosOmega = -cosOmega;
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sign2 = -1.0f;
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}
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else
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sign2 = 1.0f;
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//-----------------------------------
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// calculate interpolating coeffs:
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double scale1, scale2;
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if ( (1.0 - cosOmega) > 0.00001 )
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{
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// standard case
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double omega = mAcos(cosOmega);
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double sinOmega = mSin(omega);
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scale1 = mSin((1.0 - t) * omega) / sinOmega;
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scale2 = sign2 * mSin(t * omega) / sinOmega;
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}
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else
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{
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// if quats are very close, just do linear interpolation
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scale1 = 1.0 - t;
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scale2 = sign2 * t;
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}
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//-----------------------------------
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// actually do the interpolation:
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x = F32(scale1 * q1.x + scale2 * q2.x);
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y = F32(scale1 * q1.y + scale2 * q2.y);
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z = F32(scale1 * q1.z + scale2 * q2.z);
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w = F32(scale1 * q1.w + scale2 * q2.w);
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return *this;
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}
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Point3F & QuatF::mulP(const Point3F& p, Point3F* r)
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{
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QuatF qq;
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QuatF qi = *this;
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QuatF qv( p.x, p.y, p.z, 0.0f);
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qi.inverse();
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qq.mul(qi, qv);
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qv.mul(qq, *this);
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r->set(qv.x, qv.y, qv.z);
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return *r;
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}
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QuatF & QuatF::mul( const QuatF &a, const QuatF &b)
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{
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AssertFatal( &a != this && &b != this, "QuatF::mul: dest should not be same as source" );
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w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z;
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x = a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y;
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y = a.w * b.y + a.y * b.w + a.z * b.x - a.x * b.z;
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z = a.w * b.z + a.z * b.w + a.x * b.y - a.y * b.x;
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return *this;
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}
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QuatF & QuatF::shortestArc( const VectorF &a, const VectorF &b )
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{
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// From Game Programming Gems pg. 217
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VectorF c = mCross( a, b );
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F32 d = mDot( a, b );
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F32 s = mSqrt( ( 1 + d ) * 2 );
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x = c.x / s;
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y = c.y / s;
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z = c.z / s;
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w = s / 2.f;
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return *this;
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}
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