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/* ========================================================================
* PROJECT: ARToolKitPlus
* ========================================================================
* This work is based on the original ARToolKit developed by
* Hirokazu Kato
* Mark Billinghurst
* HITLab, University of Washington, Seattle
* http://www.hitl.washington.edu/artoolkit/
*
* Copyright of the derived and new portions of this work
* (C) 2006 Graz University of Technology
*
* This framework is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This framework is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this framework; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* For further information please contact
* Dieter Schmalstieg
* <schmalstieg@icg.tu-graz.ac.at>
* Graz University of Technology,
* Institut for Computer Graphics and Vision,
* Inffeldgasse 16a, 8010 Graz, Austria.
* ========================================================================
** @author Daniel Wagner
*
* $Id$
* @file
* ======================================================================== */
#include <math.h>
#include <assert.h>
#include <stdio.h>
#include "FixedPoint.h"
namespace ARToolKitPlus {
#ifdef _USE_GENERIC_TRIGONOMETRIC_
// Select LUT size wisely: the number of bits chosen
// for SIN_LUT_SIZEBITS will quite closely resemble
// the number of correct bits look-ups will have...
// Memory footprint: 4*(2<<SIN_LUT_SIZEBITS) bytes
//
#define SIN_LUT_SIZEBITS 12 // maximum error for sin/cos for SIN_LUT_SIZEBITS=12: 0.000383
#define SIN_LUT_SIZE (1<<SIN_LUT_SIZEBITS)
#define SIN_LUT_BITS 28
#define DOUBLE_PI 3.1415926535897932384626433832795
#define DOUBLE_PI_OVER_2 (DOUBLE_PI/2.0)
#define DOUBLE_3_PI_OVER_2 (3.0*DOUBLE_PI/2.0)
#define DOUBLE_2_PI (2.0*DOUBLE_PI)
#define DOUBLE_2_OVER_PI (2.0/DOUBLE_PI)
#define FIXED28_PI FIXED_Float_To_Fixed_n(DOUBLE_PI, 28)
#define FIXED28_PI_OVER_2 FIXED_Float_To_Fixed_n(DOUBLE_PI_OVER_2, 28)
#define FIXED28_3_PI_OVER_2 FIXED_Float_To_Fixed_n(DOUBLE_3_PI_OVER_2, 28)
#define FIXED28_2_PI FIXED_Float_To_Fixed_n(DOUBLE_2_PI, 28)
#define FIXED28_2_OVER_PI FIXED_Float_To_Fixed_n(DOUBLE_2_OVER_PI, 28)
static I32 *sinLUT_28 = 0;
static I32*
createSinLUT(int nSize, int nBits)
{
I32* lut = new I32[nSize];
for(int i=0; i<nSize; i++)
{
double phi = i*DOUBLE_PI_OVER_2/nSize;
double sinPhi = sin(phi);
I32 sinPhiFixed = FIXED_Float_To_Fixed_n(sinPhi, nBits);
lut[i] = sinPhiFixed;
}
return lut;
}
inline void
Fixed28_SinCos(I32 phi, I32 &sin, I32 &cos)
{
I32 quadrant, i;
bool negative = false;
if(phi < 0)
{
negative = true;
phi = -phi;
}
phi %= FIXED28_2_PI; // modulo clamps to range 0 to 2*Pi
if(phi<FIXED28_PI_OVER_2)
quadrant = 0;
else if(phi<FIXED28_PI)
{
quadrant = 1;
phi=FIXED28_PI-phi;
}
else if(phi<FIXED28_3_PI_OVER_2)
{
quadrant = 2;
phi=phi-FIXED28_PI;
}
else
{
quadrant = 3;
phi=FIXED28_2_PI-phi;
}
// scale from [0..1<<28] to [0..SIN_LUT_SIZE-1]
FIXED_MUL2(phi, FIXED28_2_OVER_PI, i, SIN_LUT_BITS);
i>>=(SIN_LUT_BITS-SIN_LUT_SIZEBITS);
assert(i<SIN_LUT_SIZE);
sin = sinLUT_28[i];
cos = sinLUT_28[SIN_LUT_SIZE-1-i];
switch(quadrant)
{
case 0:
break;
case 1:
cos=-cos;
break;
case 2:
sin=-sin;
cos=-cos;
break;
case 3:
sin=-sin;
break;
}
if(negative)
sin = -sin;
}
void
checkPrecisionSinCos()
{
double maxErrorSin=0.0, maxErrorCos=0.0;
for(double phi=-5.0; phi<5.0; phi+=0.0001)
{
I32 fixedPhi = FIXED_Float_To_Fixed_n(phi, SIN_LUT_BITS);
I32 fixedSin,fixedCos;
Fixed28_SinCos(fixedPhi, fixedSin,fixedCos);
double doubleSin=sin(phi),doubleCos=cos(phi);
double doubleSinF=FIXED_Fixed_n_To_Float(fixedSin, SIN_LUT_BITS),
doubleCosF=FIXED_Fixed_n_To_Float(fixedCos, SIN_LUT_BITS);
double diffSin = fabs(doubleSin-doubleSinF),
diffCos = fabs(doubleCos-doubleCosF);
if(diffSin>maxErrorSin)
maxErrorSin=diffSin;
if(diffCos>maxErrorCos)
maxErrorCos=diffCos;
}
printf("Maximum error for sin() and cos(): %f %f\n", (float)maxErrorSin, (float)maxErrorCos);
}
void
Fixed28_Init()
{
if(!sinLUT_28)
sinLUT_28 = createSinLUT(SIN_LUT_SIZE, SIN_LUT_BITS);
}
void
Fixed28_Deinit()
{
delete sinLUT_28;
}
#endif //_USE_GENERIC_TRIGONOMETRIC_
} // namespace ARToolKitPlus
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