* @file colorspace.c
* @author Pascal Getreuer 2005-2010 <getreuer@gmail.com>
*
* == Summary ==
* This file implements routines for color transformations between the spaces
* sRGB, Y'UV, Y'CbCr, Y'PbPr, Y'DbDr, Y'IQ, HSV, HSL, HSI, CIEXYZ, CIELAB,
* CIELUV, CIELCH, and CIECAT02 LMS.
*
* == Usage ==
* First call GetColorTransform, specifying the source and destination color
* spaces as "dest<-src" or "src->dest". Then call ApplyColorTransform to
* perform the transform:
@code
num S[3] = {173, 0.8, 0.5};
num D[3];
colortransform Trans;
if(!(GetColorTransform(&Trans, "HSI -> Lab")))
{
printf("Invalid syntax or unknown color space\n");
return;
}
ApplyColorTransform(Trans, &D[0], &D[1], &D[2], S[0], S[1], S[2]);
@endcode
* "num" is a typedef defined at the beginning of colorspace.h that may be set
* to either double or float, depending on the application.
*
* Specific transformation routines can also be called directly. The following
* converts an sRGB color to CIELAB and then back to sRGB:
@code
num R = 0.85, G = 0.32, B = 0.5;
num L, a, b;
Rgb2Lab(&L, &a, &b, R, G, B);
Lab2Rgb(&R, &G, &B, L, a, b);
@endcode
* Generally, the calling syntax is
@code
Foo2Bar(&B0, &B1, &B2, F0, F1, F2);
@endcode
* where (F0,F1,F2) are the coordinates of a color in space "Foo" and
* (B0,B1,B2) are the transformed coordinates in space "Bar." For any
* transformation routine, its inverse has the sytax
@code
Bar2Foo(&F0, &F1, &F2, B0, B1, B2);
@endcode
*
* The conversion routines are consistently named with the first letter of a
* color space capitalized with following letters in lower case and omitting
* prime symbols. For example, "Rgb2Ydbdr" converts sRGB to Y'DbDr. For
* any transformation routine Foo2Bar, its inverse is Bar2Foo.
*
* All transformations assume a two degree observer angle and a D65 illuminant.
* The white point can be changed by modifying the WHITEPOINT_X, WHITEPOINT_Y,
* WHITEPOINT_Z definitions at the beginning of colorspace.h.
*
* == List of transformation routines ==
* - Rgb2Yuv(num *Y, num *U, num *V, num R, num G, num B)
* - Rgb2Ycbcr(num *Y, num *Cb, num *Cr, num R, num G, num B)
* - Rgb2Jpegycbcr(num *Y, num *Cb, num *Cr, num R, num G, num B)
* - Rgb2Ypbpr(num *Y, num *Pb, num *Pr, num R, num G, num B)
* - Rgb2Ydbdr(num *Y, num *Db, num *Dr, num R, num G, num B)
* - Rgb2Yiq(num *Y, num *I, num *Q, num R, num G, num B)
* - Rgb2Hsv(num *H, num *S, num *V, num R, num G, num B)
* - Rgb2Hsl(num *H, num *S, num *L, num R, num G, num B)
* - Rgb2Hsi(num *H, num *S, num *I, num R, num G, num B)
* - Rgb2Xyz(num *X, num *Y, num *Z, num R, num G, num B)
* - Xyz2Lab(num *L, num *a, num *b, num X, num Y, num Z)
* - Xyz2Luv(num *L, num *u, num *v, num X, num Y, num Z)
* - Xyz2Lch(num *L, num *C, num *h, num X, num Y, num Z)
* - Xyz2Cat02lms(num *L, num *M, num *S, num X, num Y, num Z)
* - Rgb2Lab(num *L, num *a, num *b, num R, num G, num B)
* - Rgb2Luv(num *L, num *u, num *v, num R, num G, num B)
* - Rgb2Lch(num *L, num *C, num *h, num R, num G, num B)
* - Rgb2Cat02lms(num *L, num *M, num *S, num R, num G, num B)
* (Similarly for the inverse transformations.)
*
* It is possible to transform between two arbitrary color spaces by first
* transforming from the source space to sRGB and then transforming from
* sRGB to the desired destination space. For transformations between CIE
* color spaces, it is convenient to use XYZ as the intermediate space. This
* is the strategy used by GetColorTransform and ApplyColorTransform.
*
* == References ==
* The definitions of these spaces and the many of the transformation formulas
* can be found in
*
* Poynton, "Frequently Asked Questions About Gamma"
* http://www.poynton.com/notes/colour_and_gamma/GammaFAQ.html
*
* Poynton, "Frequently Asked Questions About Color"
* http://www.poynton.com/notes/colour_and_gamma/ColorFAQ.html
*
* and Wikipedia articles
* http://en.wikipedia.org/wiki/SRGB
* http://en.wikipedia.org/wiki/YUV
* http://en.wikipedia.org/wiki/YCbCr
* http://en.wikipedia.org/wiki/YPbPr
* http://en.wikipedia.org/wiki/YDbDr
* http://en.wikipedia.org/wiki/YIQ
* http://en.wikipedia.org/wiki/HSL_and_HSV
* http://en.wikipedia.org/wiki/CIE_1931_color_space
* http://en.wikipedia.org/wiki/Lab_color_space
* http://en.wikipedia.org/wiki/CIELUV_color_space
* http://en.wikipedia.org/wiki/LMS_color_space
*
* == License (BSD) ==
* Copyright (c) 2005-2010, Pascal Getreuer
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include "colorspace.h"
#ifdef MATLAB_MEX_FILE
#include "mex.h"
#endif
#define MIN(A,B) (((A) <= (B)) ? (A) : (B))
#define MAX(A,B) (((A) >= (B)) ? (A) : (B))
#define MIN3(A,B,C) (((A) <= (B)) ? MIN(A,C) : MIN(B,C))
#define MAX3(A,B,C) (((A) >= (B)) ? MAX(A,C) : MAX(B,C))
#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950288
#endif
* @brief sRGB gamma correction, transforms R to R'
* http://en.wikipedia.org/wiki/SRGB
*/
#define GAMMACORRECTION(t) \
(((t) <= 0.0031306684425005883) ? \
(12.92*(t)) : (1.055*pow((t), 0.416666666666666667) - 0.055))
* @brief Inverse sRGB gamma correction, transforms R' to R
*/
#define INVGAMMACORRECTION(t) \
(((t) <= 0.0404482362771076) ? \
((t)/12.92) : pow(((t) + 0.055)/1.055, 2.4))
* @brief CIE L*a*b* f function (used to convert XYZ to L*a*b*)
* http://en.wikipedia.org/wiki/Lab_color_space
*/
#define LABF(t) \
((t >= 8.85645167903563082e-3) ? \
pow(t,0.333333333333333) : (841.0/108.0)*(t) + (4.0/29.0))
* @brief CIE L*a*b* inverse f function
* http://en.wikipedia.org/wiki/Lab_color_space
*/
#define LABINVF(t) \
((t >= 0.206896551724137931) ? \
((t)*(t)*(t)) : (108.0/841.0)*((t) - (4.0/29.0)))
#define WHITEPOINT_U ((4*WHITEPOINT_X) \
/(WHITEPOINT_X + 15*WHITEPOINT_Y + 3*WHITEPOINT_Z))
#define WHITEPOINT_V ((9*WHITEPOINT_Y) \
/(WHITEPOINT_X + 15*WHITEPOINT_Y + 3*WHITEPOINT_Z))
#define UNKNOWN_SPACE 0
#define RGB_SPACE 1
#define YUV_SPACE 2
#define YCBCR_SPACE 3
#define JPEGYCBCR_SPACE 4
#define YPBPR_SPACE 5
#define YDBDR_SPACE 6
#define YIQ_SPACE 7
#define HSV_SPACE 8
#define HSL_SPACE 9
#define HSI_SPACE 10
#define XYZ_SPACE 11
#define LAB_SPACE 12
#define LUV_SPACE 13
#define LCH_SPACE 14
#define CAT02LMS_SPACE 15
#define NUM_TRANSFORM_PAIRS 18
static const struct
{
int Space[2];
void (*Fun[2])(num*, num*, num*, num, num, num);
} TransformPair[NUM_TRANSFORM_PAIRS] = {
{{RGB_SPACE, YUV_SPACE}, {Rgb2Yuv, Yuv2Rgb}},
{{RGB_SPACE, YCBCR_SPACE}, {Rgb2Ycbcr, Ycbcr2Rgb}},
{{RGB_SPACE, JPEGYCBCR_SPACE}, {Rgb2Jpegycbcr, Jpegycbcr2Rgb}},
{{RGB_SPACE, YPBPR_SPACE}, {Rgb2Ypbpr, Ypbpr2Rgb}},
{{RGB_SPACE, YDBDR_SPACE}, {Rgb2Ydbdr, Ydbdr2Rgb}},
{{RGB_SPACE, YIQ_SPACE}, {Rgb2Yiq, Yiq2Rgb}},
{{RGB_SPACE, HSV_SPACE}, {Rgb2Hsv, Hsv2Rgb}},
{{RGB_SPACE, HSL_SPACE}, {Rgb2Hsl, Hsl2Rgb}},
{{RGB_SPACE, HSI_SPACE}, {Rgb2Hsi, Hsi2Rgb}},
{{RGB_SPACE, XYZ_SPACE}, {Rgb2Xyz, Xyz2Rgb}},
{{XYZ_SPACE, LAB_SPACE}, {Xyz2Lab, Lab2Xyz}},
{{XYZ_SPACE, LUV_SPACE}, {Xyz2Luv, Luv2Xyz}},
{{XYZ_SPACE, LCH_SPACE}, {Xyz2Lch, Lch2Xyz}},
{{XYZ_SPACE, CAT02LMS_SPACE}, {Xyz2Cat02lms, Cat02lms2Xyz}},
{{RGB_SPACE, LAB_SPACE}, {Rgb2Lab, Lab2Rgb}},
{{RGB_SPACE, LUV_SPACE}, {Rgb2Luv, Luv2Rgb}},
{{RGB_SPACE, LCH_SPACE}, {Rgb2Lch, Lch2Rgb}},
{{RGB_SPACE, CAT02LMS_SPACE}, {Rgb2Cat02lms, Cat02lms2Rgb}}
};
* == Linear color transformations ==
*
* The following routines implement transformations between sRGB and
* the linearly-related color spaces Y'UV, Y'PbPr, Y'DbDr, and Y'IQ.
*/
* @brief Convert sRGB to NTSC/PAL Y'UV Luma + Chroma
*
* @param Y, U, V pointers to hold the result
* @param R, G, B the input sRGB values
*
* Wikipedia: http://en.wikipedia.org/wiki/YUV
*/
void Rgb2Yuv(num *Y, num *U, num *V, num R, num G, num B)
{
*Y = (num)( 0.299*R + 0.587*G + 0.114*B);
*U = (num)(-0.147*R - 0.289*G + 0.436*B);
*V = (num)( 0.615*R - 0.515*G - 0.100*B);
}
* @brief Convert NTSC/PAL Y'UV to sRGB
*
* @param R, G, B pointers to hold the result
* @param Y, U, V the input YUV values
*/
void Yuv2Rgb(num *R, num *G, num *B, num Y, num U, num V)
{
*R = (num)(Y - 3.945707070708279e-05*U + 1.1398279671717170825*V);
*G = (num)(Y - 0.3946101641414141437*U - 0.5805003156565656797*V);
*B = (num)(Y + 2.0319996843434342537*U - 4.813762626262513e-04*V);
}
void Rgb2Ycbcr(num *Y, num *Cb, num *Cr, num R, num G, num B)
{
*Y = (num)( 65.481*R + 128.553*G + 24.966*B + 16);
*Cb = (num)(-37.797*R - 74.203*G + 112.0 *B + 128);
*Cr = (num)(112.0 *R - 93.786*G - 18.214*B + 128);
}
void Ycbcr2Rgb(num *R, num *G, num *B, num Y, num Cr, num Cb)
{
Y -= 16;
Cb -= 128;
Cr -= 128;
*R = (num)(0.00456621004566210107*Y + 1.1808799897946415e-09*Cr + 0.00625892896994393634*Cb);
*G = (num)(0.00456621004566210107*Y - 0.00153632368604490212*Cr - 0.00318811094965570701*Cb);
*B = (num)(0.00456621004566210107*Y + 0.00791071623355474145*Cr + 1.1977497040190077e-08*Cb);
}
void Rgb2Jpegycbcr(num *Y, num *Cb, num *Cr, num R, num G, num B)
{
Rgb2Ypbpr(Y, Cb, Cr, R, G, B);
*Cb += (num)0.5;
*Cr += (num)0.5;
}
void Jpegycbcr2Rgb(num *R, num *G, num *B, num Y, num Cb, num Cr)
{
Cb -= (num)0.5;
Cr -= (num)0.5;
Ypbpr2Rgb(R, G, B, Y, Cb, Cr);
}
void Rgb2Ypbpr(num *Y, num *Pb, num *Pr, num R, num G, num B)
{
*Y = (num)( 0.299 *R + 0.587 *G + 0.114 *B);
*Pb = (num)(-0.1687367*R - 0.331264*G + 0.5 *B);
*Pr = (num)( 0.5 *R - 0.418688*G - 0.081312*B);
}
void Ypbpr2Rgb(num *R, num *G, num *B, num Y, num Pb, num Pr)
{
*R = (num)(0.99999999999914679361*Y - 1.2188941887145875e-06*Pb + 1.4019995886561440468*Pr);
*G = (num)(0.99999975910502514331*Y - 0.34413567816504303521*Pb - 0.71413649331646789076*Pr);
*B = (num)(1.00000124040004623180*Y + 1.77200006607230409200*Pb + 2.1453384174593273e-06*Pr);
}
void Rgb2Ydbdr(num *Y, num *Db, num *Dr, num R, num G, num B)
{
*Y = (num)( 0.299*R + 0.587*G + 0.114*B);
*Db = (num)(-0.450*R - 0.883*G + 1.333*B);
*Dr = (num)(-1.333*R + 1.116*G + 0.217*B);
}
void Ydbdr2Rgb(num *R, num *G, num *B, num Y, num Db, num Dr)
{
*R = (num)(Y + 9.2303716147657e-05*Db - 0.52591263066186533*Dr);
*G = (num)(Y - 0.12913289889050927*Db + 0.26789932820759876*Dr);
*B = (num)(Y + 0.66467905997895482*Db - 7.9202543533108e-05*Dr);
}
void Rgb2Yiq(num *Y, num *I, num *Q, num R, num G, num B)
{
*Y = (num)(0.299 *R + 0.587 *G + 0.114 *B);
*I = (num)(0.595716*R - 0.274453*G - 0.321263*B);
*Q = (num)(0.211456*R - 0.522591*G + 0.311135*B);
}
void Yiq2Rgb(num *R, num *G, num *B, num Y, num I, num Q)
{
*R = (num)(Y + 0.9562957197589482261*I + 0.6210244164652610754*Q);
*G = (num)(Y - 0.2721220993185104464*I - 0.6473805968256950427*Q);
*B = (num)(Y - 1.1069890167364901945*I + 1.7046149983646481374*Q);
}
* == Hue Saturation Value/Lightness/Intensity color transformations ==
*
* The following routines implement transformations between sRGB and
* color spaces HSV, HSL, and HSI.
*/
* @brief Convert an sRGB color to Hue-Saturation-Value (HSV)
*
* @param H, S, V pointers to hold the result
* @param R, G, B the input sRGB values scaled in [0,1]
*
* This routine transforms from sRGB to the hexcone HSV color space. The
* sRGB values are assumed to be between 0 and 1. The output values are
* H = hexagonal hue angle (0 <= H < 360),
* S = C/V (0 <= S <= 1),
* V = max(R',G',B') (0 <= V <= 1),
* where C = max(R',G',B') - min(R',G',B'). The inverse color transformation
* is given by Hsv2Rgb.
*
* Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV
*/
void Rgb2Hsv(num *H, num *S, num *V, num R, num G, num B)
{
num Max = MAX3(R, G, B);
num Min = MIN3(R, G, B);
num C = Max - Min;
*V = Max;
if(C > 0)
{
if(Max == R)
{
*H = (G - B) / C;
if(G < B)
*H += 6;
}
else if(Max == G)
*H = 2 + (B - R) / C;
else
*H = 4 + (R - G) / C;
*H *= 60;
*S = C / Max;
}
else
*H = *S = 0;
}
* @brief Convert a Hue-Saturation-Value (HSV) color to sRGB
*
* @param R, G, B pointers to hold the result
* @param H, S, V the input HSV values
*
* The input values are assumed to be scaled as
* 0 <= H < 360,
* 0 <= S <= 1,
* 0 <= V <= 1.
* The output sRGB values are scaled between 0 and 1. This is the inverse
* transformation of Rgb2Hsv.
*
* Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV
*/
void Hsv2Rgb(num *R, num *G, num *B, num H, num S, num V)
{
num C = S * V;
num Min = V - C;
num X;
H -= 360*floor(H/360);
H /= 60;
X = C*(1 - fabs(H - 2*floor(H/2) - 1));
switch((int)H)
{
case 0:
*R = Min + C;
*G = Min + X;
*B = Min;
break;
case 1:
*R = Min + X;
*G = Min + C;
*B = Min;
break;
case 2:
*R = Min;
*G = Min + C;
*B = Min + X;
break;
case 3:
*R = Min;
*G = Min + X;
*B = Min + C;
break;
case 4:
*R = Min + X;
*G = Min;
*B = Min + C;
break;
case 5:
*R = Min + C;
*G = Min;
*B = Min + X;
break;
default:
*R = *G = *B = 0;
}
}
* @brief Convert an sRGB color to Hue-Saturation-Lightness (HSL)
*
* @param H, S, L pointers to hold the result
* @param R, G, B the input sRGB values scaled in [0,1]
*
* This routine transforms from sRGB to the double hexcone HSL color space
* The sRGB values are assumed to be between 0 and 1. The outputs are
* H = hexagonal hue angle (0 <= H < 360),
* S = { C/(2L) if L <= 1/2 (0 <= S <= 1),
* { C/(2 - 2L) if L > 1/2
* L = (max(R',G',B') + min(R',G',B'))/2 (0 <= L <= 1),
* where C = max(R',G',B') - min(R',G',B'). The inverse color transformation
* is given by Hsl2Rgb.
*
* Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV
*/
void Rgb2Hsl(num *H, num *S, num *L, num R, num G, num B)
{
num Max = MAX3(R, G, B);
num Min = MIN3(R, G, B);
num C = Max - Min;
*L = (Max + Min)/2;
if(C > 0)
{
if(Max == R)
{
*H = (G - B) / C;
if(G < B)
*H += 6;
}
else if(Max == G)
*H = 2 + (B - R) / C;
else
*H = 4 + (R - G) / C;
*H *= 60;
*S = (*L <= 0.5) ? (C/(2*(*L))) : (C/(2 - 2*(*L)));
}
else
*H = *S = 0;
}
* @brief Convert a Hue-Saturation-Lightness (HSL) color to sRGB
*
* @param R, G, B pointers to hold the result
* @param H, S, L the input HSL values
*
* The input values are assumed to be scaled as
* 0 <= H < 360,
* 0 <= S <= 1,
* 0 <= L <= 1.
* The output sRGB values are scaled between 0 and 1. This is the inverse
* transformation of Rgb2Hsl.
*
* Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV
*/
void Hsl2Rgb(num *R, num *G, num *B, num H, num S, num L)
{
num C = (L <= 0.5) ? (2*L*S) : ((2 - 2*L)*S);
num Min = L - 0.5*C;
num X;
H -= 360*floor(H/360);
H /= 60;
X = C*(1 - fabs(H - 2*floor(H/2) - 1));
switch((int)H)
{
case 0:
*R = Min + C;
*G = Min + X;
*B = Min;
break;
case 1:
*R = Min + X;
*G = Min + C;
*B = Min;
break;
case 2:
*R = Min;
*G = Min + C;
*B = Min + X;
break;
case 3:
*R = Min;
*G = Min + X;
*B = Min + C;
break;
case 4:
*R = Min + X;
*G = Min;
*B = Min + C;
break;
case 5:
*R = Min + C;
*G = Min;
*B = Min + X;
break;
default:
*R = *G = *B = 0;
}
}
* @brief Convert an sRGB color to Hue-Saturation-Intensity (HSI)
*
* @param H, S, I pointers to hold the result
* @param R, G, B the input sRGB values scaled in [0,1]
*
* This routine transforms from sRGB to the cylindrical HSI color space. The
* sRGB values are assumed to be between 0 and 1. The output values are
* H = polar hue angle (0 <= H < 360),
* S = 1 - min(R',G',B')/I (0 <= S <= 1),
* I = (R'+G'+B')/3 (0 <= I <= 1).
* The inverse color transformation is given by Hsi2Rgb.
*
* Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV
*/
void Rgb2Hsi(num *H, num *S, num *I, num R, num G, num B)
{
num alpha = 0.5*(2*R - G - B);
num beta = 0.866025403784439*(G - B);
*I = (R + G + B)/3;
if(*I > 0)
{
*S = 1 - MIN3(R,G,B) / *I;
*H = atan2(beta, alpha)*(180/M_PI);
if(*H < 0)
*H += 360;
}
else
*H = *S = 0;
}
* @brief Convert a Hue-Saturation-Intesity (HSI) color to sRGB
*
* @param R, G, B pointers to hold the result
* @param H, S, I the input HSI values
*
* The input values are assumed to be scaled as
* 0 <= H < 360,
* 0 <= S <= 1,
* 0 <= I <= 1.
* The output sRGB values are scaled between 0 and 1. This is the inverse
* transformation of Rgb2Hsi.
*
* Wikipedia: http://en.wikipedia.org/wiki/HSL_and_HSV
*/
void Hsi2Rgb(num *R, num *G, num *B, num H, num S, num I)
{
H -= 360*floor(H/360);
if(H < 120)
{
*B = I*(1 - S);
*R = I*(1 + S*cos(H*(M_PI/180))/cos((60 - H)*(M_PI/180)));
*G = 3*I - *R - *B;
}
else if(H < 240)
{
H -= 120;
*R = I*(1 - S);
*G = I*(1 + S*cos(H*(M_PI/180))/cos((60 - H)*(M_PI/180)));
*B = 3*I - *R - *G;
}
else
{
H -= 240;
*G = I*(1 - S);
*B = I*(1 + S*cos(H*(M_PI/180))/cos((60 - H)*(M_PI/180)));
*R = 3*I - *G - *B;
}
}
* == CIE color transformations ==
*
* The following routines implement transformations between sRGB and
* the CIE color spaces XYZ, L*a*b, L*u*v*, and L*C*H*. These
* transforms assume a 2 degree observer angle and a D65 illuminant.
*/
* @brief Transform sRGB to CIE XYZ with the D65 white point
*
* @param X, Y, Z pointers to hold the result
* @param R, G, B the input sRGB values
*
* Poynton, "Frequently Asked Questions About Color," page 10
* Wikipedia: http://en.wikipedia.org/wiki/SRGB
* Wikipedia: http://en.wikipedia.org/wiki/CIE_1931_color_space
*/
void Rgb2Xyz(num *X, num *Y, num *Z, num R, num G, num B)
{
R = INVGAMMACORRECTION(R);
G = INVGAMMACORRECTION(G);
B = INVGAMMACORRECTION(B);
*X = (num)(0.4123955889674142161*R + 0.3575834307637148171*G + 0.1804926473817015735*B);
*Y = (num)(0.2125862307855955516*R + 0.7151703037034108499*G + 0.07220049864333622685*B);
*Z = (num)(0.01929721549174694484*R + 0.1191838645808485318*G + 0.9504971251315797660*B);
}
* @brief Transform sRGB to xy
*
* @param X, Y pointers to hold the result
* @param R, G, B the input sRGB values
*/
void Rgb2xy(num *x, num *y, num R, num G, num B)
{
R = INVGAMMACORRECTION(R);
G = INVGAMMACORRECTION(G);
B = INVGAMMACORRECTION(B);
num X = (num)(0.4123955889674142161*R + 0.3575834307637148171*G + 0.1804926473817015735*B);
num Y = (num)(0.2125862307855955516*R + 0.7151703037034108499*G + 0.07220049864333622685*B);
num Z = (num)(0.01929721549174694484*R + 0.1191838645808485318*G + 0.9504971251315797660*B);
*x = X / (X + Y + Z);
*y = Y / (X + Y + Z);
}
* @brief Transform CIE XYZ to sRGB with the D65 white point
*
* @param R, G, B pointers to hold the result
* @param X, Y, Z the input XYZ values
*
* Official sRGB specification (IEC 61966-2-1:1999)
* Poynton, "Frequently Asked Questions About Color," page 10
* Wikipedia: http://en.wikipedia.org/wiki/SRGB
* Wikipedia: http://en.wikipedia.org/wiki/CIE_1931_color_space
*/
void Xyz2Rgb(num *R, num *G, num *B, num X, num Y, num Z)
{
num R1, B1, G1, Min;
R1 = (num)( 3.2406*X - 1.5372*Y - 0.4986*Z);
G1 = (num)(-0.9689*X + 1.8758*Y + 0.0415*Z);
B1 = (num)( 0.0557*X - 0.2040*Y + 1.0570*Z);
Min = MIN3(R1, G1, B1);
if(Min < 0)
{
R1 -= Min;
G1 -= Min;
B1 -= Min;
}
*R = GAMMACORRECTION(R1);
*G = GAMMACORRECTION(G1);
*B = GAMMACORRECTION(B1);
}
* Convert CIE XYZ to CIE L*a*b* (CIELAB) with the D65 white point
*
* @param L, a, b pointers to hold the result
* @param X, Y, Z the input XYZ values
*
* Wikipedia: http://en.wikipedia.org/wiki/Lab_color_space
*/
void Xyz2Lab(num *L, num *a, num *b, num X, num Y, num Z)
{
X /= WHITEPOINT_X;
Y /= WHITEPOINT_Y;
Z /= WHITEPOINT_Z;
X = LABF(X);
Y = LABF(Y);
Z = LABF(Z);
*L = 116*Y - 16;
*a = 500*(X - Y);
*b = 200*(Y - Z);
}
* Convert CIE L*a*b* (CIELAB) to CIE XYZ with the D65 white point
*
* @param X, Y, Z pointers to hold the result
* @param L, a, b the input L*a*b* values
*
* Wikipedia: http://en.wikipedia.org/wiki/Lab_color_space
*/
void Lab2Xyz(num *X, num *Y, num *Z, num L, num a, num b)
{
L = (L + 16)/116;
a = L + a/500;
b = L - b/200;
*X = WHITEPOINT_X*LABINVF(a);
*Y = WHITEPOINT_Y*LABINVF(L);
*Z = WHITEPOINT_Z*LABINVF(b);
}
* Convert CIE XYZ to CIE L*u*v* (CIELUV) with the D65 white point
*
* @param L, u, v pointers to hold the result
* @param X, Y, Z the input XYZ values
*
* Wikipedia: http://en.wikipedia.org/wiki/CIELUV_color_space
*/
void Xyz2Luv(num *L, num *u, num *v, num X, num Y, num Z)
{
num u1, v1, Denom;
if((Denom = X + 15*Y + 3*Z) > 0)
{
u1 = (4*X) / Denom;
v1 = (9*Y) / Denom;
}
else
u1 = v1 = 0;
Y /= WHITEPOINT_Y;
Y = LABF(Y);
*L = 116*Y - 16;
*u = 13*(*L)*(u1 - WHITEPOINT_U);
*v = 13*(*L)*(v1 - WHITEPOINT_V);
}
* Convert CIE L*u*v* (CIELUV) to CIE XYZ with the D65 white point
*
* @param X, Y, Z pointers to hold the result
* @param L, u, v the input L*u*v* values
*
* Wikipedia: http://en.wikipedia.org/wiki/CIELUV_color_space
*/
void Luv2Xyz(num *X, num *Y, num *Z, num L, num u, num v)
{
*Y = (L + 16)/116;
*Y = WHITEPOINT_Y*LABINVF(*Y);
if(L != 0)
{
u /= L;
v /= L;
}
u = u/13 + WHITEPOINT_U;
v = v/13 + WHITEPOINT_V;
*X = (*Y) * ((9*u)/(4*v));
*Z = (*Y) * ((3 - 0.75*u)/v - 5);
}
* Convert CIE XYZ to CIE L*C*H* with the D65 white point
*
* @param L, C, H pointers to hold the result
* @param X, Y, Z the input XYZ values
*
* CIE L*C*H* is related to CIE L*a*b* by
* a* = C* cos(H* pi/180),
* b* = C* sin(H* pi/180).
*/
void Xyz2Lch(num *L, num *C, num *H, num X, num Y, num Z)
{
num a, b;
Xyz2Lab(L, &a, &b, X, Y, Z);
*C = sqrt(a*a + b*b);
*H = atan2(b, a)*180.0/M_PI;
if(*H < 0)
*H += 360;
}
* Convert CIE L*C*H* to CIE XYZ with the D65 white point
*
* @param X, Y, Z pointers to hold the result
* @param L, C, H the input L*C*H* values
*/
void Lch2Xyz(num *X, num *Y, num *Z, num L, num C, num H)
{
num a = C * cos(H*(M_PI/180.0));
num b = C * sin(H*(M_PI/180.0));
Lab2Xyz(X, Y, Z, L, a, b);
}
void Xyz2Cat02lms(num *L, num *M, num *S, num X, num Y, num Z)
{
*L = (num)( 0.7328*X + 0.4296*Y - 0.1624*Z);
*M = (num)(-0.7036*X + 1.6975*Y + 0.0061*Z);
*S = (num)( 0.0030*X + 0.0136*Y + 0.9834*Z);
}
void Cat02lms2Xyz(num *X, num *Y, num *Z, num L, num M, num S)
{
*X = (num)( 1.096123820835514*L - 0.278869000218287*M + 0.182745179382773*S);
*Y = (num)( 0.454369041975359*L + 0.473533154307412*M + 0.072097803717229*S);
*Z = (num)(-0.009627608738429*L - 0.005698031216113*M + 1.015325639954543*S);
}
* == Glue functions for multi-stage transforms ==
*/
void Rgb2Lab(num *L, num *a, num *b, num R, num G, num B)
{
num X, Y, Z;
Rgb2Xyz(&X, &Y, &Z, R, G, B);
Xyz2Lab(L, a, b, X, Y, Z);
}
void Lab2Rgb(num *R, num *G, num *B, num L, num a, num b)
{
num X, Y, Z;
Lab2Xyz(&X, &Y, &Z, L, a, b);
Xyz2Rgb(R, G, B, X, Y, Z);
}
void Rgb2Luv(num *L, num *u, num *v, num R, num G, num B)
{
num X, Y, Z;
Rgb2Xyz(&X, &Y, &Z, R, G, B);
Xyz2Luv(L, u, v, X, Y, Z);
}
void Luv2Rgb(num *R, num *G, num *B, num L, num u, num v)
{
num X, Y, Z;
Luv2Xyz(&X, &Y, &Z, L, u, v);
Xyz2Rgb(R, G, B, X, Y, Z);
}
void Rgb2Lch(num *L, num *C, num *H, num R, num G, num B)
{
num X, Y, Z;
Rgb2Xyz(&X, &Y, &Z, R, G, B);
Xyz2Lch(L, C, H, X, Y, Z);
}
void Lch2Rgb(num *R, num *G, num *B, num L, num C, num H)
{
num X, Y, Z;
Lch2Xyz(&X, &Y, &Z, L, C, H);
Xyz2Rgb(R, G, B, X, Y, Z);
}
void Rgb2Cat02lms(num *L, num *M, num *S, num R, num G, num B)
{
num X, Y, Z;
Rgb2Xyz(&X, &Y, &Z, R, G, B);
Xyz2Cat02lms(L, M, S, X, Y, Z);
}
void Cat02lms2Rgb(num *R, num *G, num *B, num L, num M, num S)
{
num X, Y, Z;
Cat02lms2Xyz(&X, &Y, &Z, L, M, S);
Xyz2Rgb(R, G, B, X, Y, Z);
}
* == Interface Code ==
* The following is to define a function GetColorTransform with a convenient
* string-based interface.
*/
static int IdFromName(const char *Name)
{
if(!strcmp(Name, "rgb") || *Name == 0)
return RGB_SPACE;
else if(!strcmp(Name, "yuv"))
return YUV_SPACE;
else if(!strcmp(Name, "ycbcr"))
return YCBCR_SPACE;
else if(!strcmp(Name, "jpegycbcr"))
return YCBCR_SPACE;
else if(!strcmp(Name, "ypbpr"))
return YPBPR_SPACE;
else if(!strcmp(Name, "ydbdr"))
return YDBDR_SPACE;
else if(!strcmp(Name, "yiq"))
return YIQ_SPACE;
else if(!strcmp(Name, "hsv") || !strcmp(Name, "hsb"))
return HSV_SPACE;
else if(!strcmp(Name, "hsl") || !strcmp(Name, "hls"))
return HSL_SPACE;
else if(!strcmp(Name, "hsi"))
return HSI_SPACE;
else if(!strcmp(Name, "xyz") || !strcmp(Name, "ciexyz"))
return XYZ_SPACE;
else if(!strcmp(Name, "lab") || !strcmp(Name, "cielab"))
return LAB_SPACE;
else if(!strcmp(Name, "luv") || !strcmp(Name, "cieluv"))
return LUV_SPACE;
else if(!strcmp(Name, "lch") || !strcmp(Name, "cielch"))
return LCH_SPACE;
else if(!strcmp(Name, "cat02lms") || !strcmp(Name, "ciecat02lms"))
return CAT02LMS_SPACE;
else
return UNKNOWN_SPACE;
}
* @brief Given a transform string, returns a colortransform struct
*
* @param Trans a colortransform pointer to hold the transform
* @param TransformString string specifying the transformations
* @return 1 on success, 0 on failure
*
* This function provides a convenient interface to the collection of transform
* functions in this file. TransformString specifies the source and
* destination color spaces,
* TransformString = "dest<-src"
* or alternatively,
* TransformString = "src->dest".
*
* Supported color spaces are
* "RGB" sRGB Red Green Blue (ITU-R BT.709 gamma-corrected),
* "YPbPr" Luma (ITU-R BT.601) + Chroma,
* "YCbCr" Luma + Chroma ("digitized" version of Y'PbPr),
* "JPEG-YCbCr" Luma + Chroma space used in JFIF JPEG,
* "YUV" NTSC PAL Y'UV Luma + Chroma,
* "YIQ" NTSC Y'IQ Luma + Chroma,
* "YDbDr" SECAM Y'DbDr Luma + Chroma,
* "HSV" or "HSB" Hue Saturation Value/Brightness,
* "HSL" or "HLS" Hue Saturation Luminance,
* "HSI" Hue Saturation Intensity,
* "XYZ" CIE XYZ,
* "Lab" CIE L*a*b* (CIELAB),
* "Luv" CIE L*u*v* (CIELUV),
* "LCH" CIE L*C*H* (CIELCH),
* "CAT02 LMS" CIE CAT02 LMS.
* Color space names are case-insensitive and spaces are ignored. When sRGB
* is the source or destination, it can be omitted. For example "yuv<-" is
* short for "yuv<-rgb".
*
* The routine returns a colortransform structure representing the transform.
* The transform is performed by calling GetColorTransform. For example,
@code
num S[3] = {173, 0.8, 0.5};
num D[3];
colortransform Trans;
if(!(GetColorTransform(&Trans, "HSI -> Lab")))
{
printf("Invalid syntax or unknown color space\n");
return;
}
ApplyColorTransform(Trans, &D[0], &D[1], &D[2], S[0], S[1], S[2]);
@endcode
*/
int GetColorTransform(colortransform *Trans, const char *TransformString)
{
int LeftNumChars = 0, RightNumChars = 0, LeftSide = 1, LeftToRight = 0;
int i, j, SrcSpaceId, DestSpaceId;
char LeftSpace[16], RightSpace[16], c;
Trans->NumStages = 0;
Trans->Fun[0] = 0;
Trans->Fun[1] = 0;
while(1)
{
c = *(TransformString++);
if(!c)
break;
else if(c == '<')
{
LeftToRight = 0;
LeftSide = 0;
}
else if(c == '>')
{
LeftToRight = 1;
LeftSide = 0;
}
else if(c != ' ' && c != '-' && c != '=')
{
if(LeftSide)
{
if(LeftNumChars < 15)
LeftSpace[LeftNumChars++] = tolower(c);
}
else
{
if(RightNumChars < 15)
RightSpace[RightNumChars++] = tolower(c);
}
}
}
LeftSpace[LeftNumChars] = 0;
RightSpace[RightNumChars] = 0;
if(LeftToRight)
{
SrcSpaceId = IdFromName(LeftSpace);
DestSpaceId = IdFromName(RightSpace);
}
else
{
SrcSpaceId = IdFromName(RightSpace);
DestSpaceId = IdFromName(LeftSpace);
}
if(SrcSpaceId == UNKNOWN_SPACE || DestSpaceId == UNKNOWN_SPACE)
return 0;
if(SrcSpaceId == DestSpaceId)
return 1;
for(i = 0; i < NUM_TRANSFORM_PAIRS; i++)
{
if(SrcSpaceId == TransformPair[i].Space[0]
&& DestSpaceId == TransformPair[i].Space[1])
{
Trans->NumStages = 1;
Trans->Fun[0] = TransformPair[i].Fun[0];
return 1;
}
else if(DestSpaceId == TransformPair[i].Space[0]
&& SrcSpaceId == TransformPair[i].Space[1])
{
Trans->NumStages = 1;
Trans->Fun[0] = TransformPair[i].Fun[1];
return 1;
}
}
for(i = 1; i < NUM_TRANSFORM_PAIRS; i++)
if(SrcSpaceId == TransformPair[i].Space[1])
for(j = 0; j < i; j++)
{
if(DestSpaceId == TransformPair[j].Space[1]
&& TransformPair[i].Space[0] == TransformPair[j].Space[0])
{
Trans->NumStages = 2;
Trans->Fun[0] = TransformPair[i].Fun[1];
Trans->Fun[1] = TransformPair[j].Fun[0];
return 1;
}
}
else if(DestSpaceId == TransformPair[i].Space[1])
for(j = 0; j < i; j++)
{
if(SrcSpaceId == TransformPair[j].Space[1]
&& TransformPair[j].Space[0] == TransformPair[i].Space[0])
{
Trans->NumStages = 2;
Trans->Fun[0] = TransformPair[j].Fun[1];
Trans->Fun[1] = TransformPair[i].Fun[0];
return 1;
}
}
return 0;
}
* @brief Apply a colortransform
*
* @param Trans colortransform struct created by GetColorTransform
* @param D0, D1, D2 pointers to hold the result
* @param S0, S1, S2 the input values
*/
void ApplyColorTransform(colortransform Trans,
num *D0, num *D1, num *D2, num S0, num S1, num S2)
{
switch(Trans.NumStages)
{
case 1:
Trans.Fun[0](D0, D1, D2, S0, S1, S2);
break;
case 2:
{
num T0, T1, T2;
Trans.Fun[0](&T0, &T1, &T2, S0, S1, S2);
Trans.Fun[1](D0, D1, D2, T0, T1, T2);
}
break;
default:
*D0 = S0;
*D1 = S1;
*D2 = S2;
break;
}
}
* From MATLAB, the calling syntax is
* B = colorspace('dest<-src', A);
* See colorspace.m for details.
*/
#ifdef MATLAB_MEX_FILE
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray*prhs[])
{
#define S_IN prhs[0]
#define A_IN prhs[1]
#define B_OUT plhs[0]
#define IS_REAL_FULL_DOUBLE(P) (!mxIsComplex(P) \
&& !mxIsSparse(P) && mxIsDouble(P))
num *A, *B;
char *SBuf;
const int *Size;
colortransform Trans;
int SBufLen, NumPixels, Channel, Channel2;
if(nrhs != 2)
mexErrMsgTxt("Two input arguments required.");
else if(nlhs > 1)
mexErrMsgTxt("Too many output arguments.");
if(!mxIsChar(S_IN))
mexErrMsgTxt("First argument should be a string.");
if(!IS_REAL_FULL_DOUBLE(A_IN))
mexErrMsgTxt("Second argument should be a real full double array.");
Size = mxGetDimensions(A_IN);
if(mxGetNumberOfDimensions(A_IN) > 3
|| Size[mxGetNumberOfDimensions(A_IN) - 1] != 3)
mexErrMsgTxt("Second argument should be an Mx3 or MxNx3 array.");
SBufLen = mxGetNumberOfElements(S_IN)*sizeof(mxChar) + 1;
SBuf = mxMalloc(SBufLen);
mxGetString(S_IN, SBuf, SBufLen);
if(!(GetColorTransform(&Trans, SBuf)))
mexErrMsgTxt("Invalid syntax or unknown color space.");
mxFree(SBuf);
A = (num *)mxGetData(A_IN);
NumPixels = mxGetNumberOfElements(A_IN)/3;
B_OUT = mxCreateDoubleMatrix(0, 0, mxREAL);
mxSetDimensions(B_OUT, Size, mxGetNumberOfDimensions(A_IN));
mxSetData(B_OUT, B = mxMalloc(sizeof(num)*mxGetNumberOfElements(A_IN)));
Channel = NumPixels;
Channel2 = NumPixels*2;
while(NumPixels--)
{
ApplyColorTransform(Trans, B, B + Channel, B + Channel2,
A[0], A[Channel], A[Channel2]);
A++;
B++;
}
return;
}
#endif
#define TEMPERATURE_TO_X_TEMPERATURE_TRESHOLD 4000
#define TEMPERATURE_TO_Y_FIRST_TEMPERATURE_TRESHOLD 2222
#define TEMPERATURE_TO_Y_SECOND_TEMPERATURE_TRESHOLD 4000
#define TEMPERATURE_TO_X_FIRST_FACTOR_FIRST_EQUATION 17440695910400
#define TEMPERATURE_TO_X_SECOND_FACTOR_FIRST_EQUATION 15358885888
#define TEMPERATURE_TO_X_THIRD_FACTOR_FIRST_EQUATION 57520658
#define TEMPERATURE_TO_X_FOURTH_FACTOR_FIRST_EQUATION 11790
#define TEMPERATURE_TO_X_FIRST_FACTOR_SECOND_EQUATION 198301902438400
#define TEMPERATURE_TO_X_SECOND_FACTOR_SECOND_EQUATION 138086835814
#define TEMPERATURE_TO_X_THIRD_FACTOR_SECOND_EQUATION 14590587
#define TEMPERATURE_TO_X_FOURTH_FACTOR_SECOND_EQUATION 15754
#define TEMPERATURE_TO_Y_FIRST_FACTOR_FIRST_EQUATION 18126
#define TEMPERATURE_TO_Y_SECOND_FACTOR_FIRST_EQUATION 22087
#define TEMPERATURE_TO_Y_THIRD_FACTOR_FIRST_EQUATION 35808
#define TEMPERATURE_TO_Y_FOURTH_FACTOR_FIRST_EQUATION 3312
#define TEMPERATURE_TO_Y_FIRST_FACTOR_SECOND_EQUATION 15645
#define TEMPERATURE_TO_Y_SECOND_FACTOR_SECOND_EQUATION 22514
#define TEMPERATURE_TO_Y_THIRD_FACTOR_SECOND_EQUATION 34265
#define TEMPERATURE_TO_Y_FOURTH_FACTOR_SECOND_EQUATION 2744
#define TEMPERATURE_TO_Y_FIRST_FACTOR_THIRD_EQUATION 50491
#define TEMPERATURE_TO_Y_SECOND_FACTOR_THIRD_EQUATION 96229
#define TEMPERATURE_TO_Y_THIRD_FACTOR_THIRD_EQUATION 61458
#define TEMPERATURE_TO_Y_FOURTH_FACTOR_THIRD_EQUATION 6062
#define XY_TO_TEMPERATURE_X_EPICENTER 21757
#define XY_TO_TEMPERATURE_Y_EPICENTER 12176
#define XY_TO_TEMPERATURE_FIRST_FACTOR 44900ull
#define XY_TO_TEMPERATURE_SECOND_FACTOR 352500ull
#define XY_TO_TEMPERATURE_THIRD_FACTOR 682330ull
#define XY_TO_TEMPERATURE_FOURTH_FACTOR 552033ull
\brief Converts color temperature to appropriate XY coordinates
\param[in] temperature - color temperature (attribute value);
\param[out] x - x coordinate (attribute value);
\param[out] y - y coordinate (attribute value)
******************************************************************************/
void MiredColorTemperatureToXY(unsigned short int temperature, unsigned short int *x, unsigned short int *y)
{
if (temperature == 0)
temperature = 153;
unsigned long long localX, localY;
unsigned short int temp = 1000000 / temperature;
if (TEMPERATURE_TO_X_TEMPERATURE_TRESHOLD > temp)
localX = TEMPERATURE_TO_X_THIRD_FACTOR_FIRST_EQUATION / temp +
TEMPERATURE_TO_X_FOURTH_FACTOR_FIRST_EQUATION -
TEMPERATURE_TO_X_SECOND_FACTOR_FIRST_EQUATION / temp / temp -
TEMPERATURE_TO_X_FIRST_FACTOR_FIRST_EQUATION / temp / temp/ temp;
else
localX = TEMPERATURE_TO_X_SECOND_FACTOR_SECOND_EQUATION / temp / temp +
TEMPERATURE_TO_X_THIRD_FACTOR_SECOND_EQUATION / temp +
TEMPERATURE_TO_X_FOURTH_FACTOR_SECOND_EQUATION -
TEMPERATURE_TO_X_FIRST_FACTOR_SECOND_EQUATION / temp / temp / temp;
if (TEMPERATURE_TO_Y_FIRST_TEMPERATURE_TRESHOLD > temp)
localY = TEMPERATURE_TO_Y_THIRD_FACTOR_FIRST_EQUATION * localX / 65536 -
TEMPERATURE_TO_Y_FIRST_FACTOR_FIRST_EQUATION * localX * localX * localX / 281474976710656 -
TEMPERATURE_TO_Y_SECOND_FACTOR_FIRST_EQUATION * localX * localX / 4294967296 -
TEMPERATURE_TO_Y_FOURTH_FACTOR_FIRST_EQUATION;
else if (TEMPERATURE_TO_Y_SECOND_TEMPERATURE_TRESHOLD > temp)
localY = TEMPERATURE_TO_Y_THIRD_FACTOR_SECOND_EQUATION * localX / 65536 -
TEMPERATURE_TO_Y_FIRST_FACTOR_SECOND_EQUATION * localX * localX * localX / 281474976710656 -
TEMPERATURE_TO_Y_SECOND_FACTOR_SECOND_EQUATION * localX * localX / 4294967296 -
TEMPERATURE_TO_Y_FOURTH_FACTOR_SECOND_EQUATION;
else
{
localY = TEMPERATURE_TO_Y_THIRD_FACTOR_THIRD_EQUATION * localX / 65536 +
TEMPERATURE_TO_Y_FIRST_FACTOR_THIRD_EQUATION * localX * localX * localX / 281474976710656 -
TEMPERATURE_TO_Y_SECOND_FACTOR_THIRD_EQUATION * localX * localX / 4294967296 -
TEMPERATURE_TO_Y_FOURTH_FACTOR_THIRD_EQUATION;
}
localY *= 4;
*x = (unsigned)localX;
*y = (unsigned)localY;
}