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-/*
- Colour Rendering of Spectra
-
- by John Walker
- http://www.fourmilab.ch/
-
- Last updated: March 9, 2003
-
- This program is in the public domain.
-
- For complete information about the techniques employed in
- this program, see the World-Wide Web document:
-
- http://www.fourmilab.ch/documents/specrend/
-
- The xyz_to_rgb() function, which was wrong in the original
- version of this program, was corrected by:
-
- Andrew J. S. Hamilton 21 May 1999
- Andrew.Hamilton@Colorado.EDU
- http://casa.colorado.edu/~ajsh/
-
- who also added the gamma correction facilities and
- modified constrain_rgb() to work by desaturating the
- colour by adding white.
-
- A program which uses these functions to plot CIE
- "tongue" diagrams called "ppmcie" is included in
- the Netpbm graphics toolkit:
- http://netpbm.sourceforge.net/
- (The program was called cietoppm in earlier
- versions of Netpbm.)
-
-*/
-
-#include <stdio.h>
-#include <math.h>
-#include "spectrum.h"
-
-/* A colour system is defined by the CIE x and y coordinates of
- its three primary illuminants and the x and y coordinates of
- the white point. */
-
-struct colourSystem {
- const char *name; /* Colour system name */
- double xRed, yRed, /* Red x, y */
- xGreen, yGreen, /* Green x, y */
- xBlue, yBlue, /* Blue x, y */
- xWhite, yWhite, /* White point x, y */
- gamma; /* Gamma correction for system */
-};
-
-/* White point chromaticities. */
-
-#if 0
-#define IlluminantC 0.3101, 0.3162 /* For NTSC television */
-#define IlluminantD65 0.3127, 0.3291 /* For EBU and SMPTE */
-#endif
-#define IlluminantE 0.33333333, 0.33333333 /* CIE equal-energy illuminant */
-
-/* Gamma of nonlinear correction.
-
- See Charles Poynton's ColorFAQ Item 45 and GammaFAQ Item 6 at:
-
- http://www.poynton.com/ColorFAQ.html
- http://www.poynton.com/GammaFAQ.html
-
-*/
-
-#define GAMMA_REC709 0 /* Rec. 709 */
-
-static struct colourSystem
- /* Name xRed yRed xGreen yGreen xBlue yBlue White point Gamma */
-#if 0 /* UNUSED */
- NTSCsystem = { "NTSC", 0.67, 0.33, 0.21, 0.71, 0.14, 0.08, IlluminantC, GAMMA_REC709 },
- EBUsystem = { "EBU (PAL/SECAM)", 0.64, 0.33, 0.29, 0.60, 0.15, 0.06, IlluminantD65, GAMMA_REC709 },
- SMPTEsystem = { "SMPTE", 0.630, 0.340, 0.310, 0.595, 0.155, 0.070, IlluminantD65, GAMMA_REC709 },
- HDTVsystem = { "HDTV", 0.670, 0.330, 0.210, 0.710, 0.150, 0.060, IlluminantD65, GAMMA_REC709 },
-#endif
-
- CIEsystem = { "CIE", 0.7355, 0.2645, 0.2658, 0.7243, 0.1669, 0.0085, IlluminantE, GAMMA_REC709 };
-
-#if 0 /* UNUSED */
- Rec709system = { "CIE REC 709", 0.64, 0.33, 0.30, 0.60, 0.15, 0.06, IlluminantD65, GAMMA_REC709 };
-#endif
-
-/* UPVP_TO_XY
-
- Given 1976 coordinates u', v', determine 1931 chromaticities x, y
-
-*/
-
-#if 0 /* UNUSED */
-static void upvp_to_xy(double up, double vp, double *xc, double *yc)
-{
- *xc = (9 * up) / ((6 * up) - (16 * vp) + 12);
- *yc = (4 * vp) / ((6 * up) - (16 * vp) + 12);
-}
-#endif
-
-/* XY_TO_UPVP
-
- Given 1931 chromaticities x, y, determine 1976 coordinates u', v'
-
-*/
-
-#if 0 /* UNUSED */
-static void xy_to_upvp(double xc, double yc, double *up, double *vp)
-{
- *up = (4 * xc) / ((-2 * xc) + (12 * yc) + 3);
- *vp = (9 * yc) / ((-2 * xc) + (12 * yc) + 3);
-}
-#endif
-
-/* XYZ_TO_RGB
-
- Given an additive tricolour system CS, defined by the CIE x
- and y chromaticities of its three primaries (z is derived
- trivially as 1-(x+y)), and a desired chromaticity (XC, YC,
- ZC) in CIE space, determine the contribution of each
- primary in a linear combination which sums to the desired
- chromaticity. If the requested chromaticity falls outside
- the Maxwell triangle (colour gamut) formed by the three
- primaries, one of the r, g, or b weights will be negative.
-
- Caller can use constrain_rgb() to desaturate an
- outside-gamut colour to the closest representation within
- the available gamut and/or norm_rgb to normalise the RGB
- components so the largest nonzero component has value 1.
-
-*/
-
-static void xyz_to_rgb(struct colourSystem *cs,
- double xc, double yc, double zc,
- double *r, double *g, double *b)
-{
- double xr, yr, zr, xg, yg, zg, xb, yb, zb;
- double xw, yw, zw;
- double rx, ry, rz, gx, gy, gz, bx, by, bz;
- double rw, gw, bw;
-
- xr = cs->xRed; yr = cs->yRed; zr = 1 - (xr + yr);
- xg = cs->xGreen; yg = cs->yGreen; zg = 1 - (xg + yg);
- xb = cs->xBlue; yb = cs->yBlue; zb = 1 - (xb + yb);
-
- xw = cs->xWhite; yw = cs->yWhite; zw = 1 - (xw + yw);
-
- /* xyz -> rgb matrix, before scaling to white. */
-
- rx = (yg * zb) - (yb * zg); ry = (xb * zg) - (xg * zb); rz = (xg * yb) - (xb * yg);
- gx = (yb * zr) - (yr * zb); gy = (xr * zb) - (xb * zr); gz = (xb * yr) - (xr * yb);
- bx = (yr * zg) - (yg * zr); by = (xg * zr) - (xr * zg); bz = (xr * yg) - (xg * yr);
-
- /* White scaling factors.
- Dividing by yw scales the white luminance to unity, as conventional. */
-
- rw = ((rx * xw) + (ry * yw) + (rz * zw)) / yw;
- gw = ((gx * xw) + (gy * yw) + (gz * zw)) / yw;
- bw = ((bx * xw) + (by * yw) + (bz * zw)) / yw;
-
- /* xyz -> rgb matrix, correctly scaled to white. */
-
- rx = rx / rw; ry = ry / rw; rz = rz / rw;
- gx = gx / gw; gy = gy / gw; gz = gz / gw;
- bx = bx / bw; by = by / bw; bz = bz / bw;
-
- /* rgb of the desired point */
-
- *r = (rx * xc) + (ry * yc) + (rz * zc);
- *g = (gx * xc) + (gy * yc) + (gz * zc);
- *b = (bx * xc) + (by * yc) + (bz * zc);
-}
-
-/* INSIDE_GAMUT
-
- Test whether a requested colour is within the gamut
- achievable with the primaries of the current colour
- system. This amounts simply to testing whether all the
- primary weights are non-negative. */
-
-#if 0 /* UNUSED */
-static int inside_gamut(double r, double g, double b)
-{
- return (r >= 0) && (g >= 0) && (b >= 0);
-}
-#endif
-
-/* CONSTRAIN_RGB
-
- If the requested RGB shade contains a negative weight for
- one of the primaries, it lies outside the colour gamut
- accessible from the given triple of primaries. Desaturate
- it by adding white, equal quantities of R, G, and B, enough
- to make RGB all positive. The function returns 1 if the
- components were modified, zero otherwise.
-
-*/
-
-static int constrain_rgb(double *r, double *g, double *b)
-{
- double w;
-
- /* Amount of white needed is w = - min(0, *r, *g, *b) */
-
- w = (0 < *r) ? 0 : *r;
- w = (w < *g) ? w : *g;
- w = (w < *b) ? w : *b;
- w = -w;
-
- /* Add just enough white to make r, g, b all positive. */
-
- if (w > 0) {
- *r += w; *g += w; *b += w;
- return 1; /* Colour modified to fit RGB gamut */
- }
-
- return 0; /* Colour within RGB gamut */
-}
-
-/* GAMMA_CORRECT_RGB
-
- Transform linear RGB values to nonlinear RGB values. Rec.
- 709 is ITU-R Recommendation BT. 709 (1990) ``Basic
- Parameter Values for the HDTV Standard for the Studio and
- for International Programme Exchange'', formerly CCIR Rec.
- 709. For details see
-
- http://www.poynton.com/ColorFAQ.html
- http://www.poynton.com/GammaFAQ.html
-*/
-
-#if 0 /* UNUSED */
-static void gamma_correct(const struct colourSystem *cs, double *c)
-{
- double gamma;
-
- gamma = cs->gamma;
-
- if (gamma == GAMMA_REC709) {
- /* Rec. 709 gamma correction. */
- double cc = 0.018;
-
- if (*c < cc) {
- *c *= ((1.099 * pow(cc, 0.45)) - 0.099) / cc;
- } else {
- *c = (1.099 * pow(*c, 0.45)) - 0.099;
- }
- } else {
- /* Nonlinear colour = (Linear colour)^(1/gamma) */
- *c = pow(*c, 1.0 / gamma);
- }
-}
-
-static void gamma_correct_rgb(const struct colourSystem *cs, double *r, double *g, double *b)
-{
- gamma_correct(cs, r);
- gamma_correct(cs, g);
- gamma_correct(cs, b);
-}
-#endif
-
-/* NORM_RGB
-
- Normalise RGB components so the most intense (unless all
- are zero) has a value of 1.
-
-*/
-
-static void norm_rgb(double *r, double *g, double *b)
-{
-#define Max(a, b) (((a) > (b)) ? (a) : (b))
- double greatest = Max(*r, Max(*g, *b));
-
- if (greatest > 0) {
- *r /= greatest;
- *g /= greatest;
- *b /= greatest;
- }
-#undef Max
-}
-
-/* SPECTRUM_TO_XYZ
-
- Calculate the CIE X, Y, and Z coordinates corresponding to
- a light source with spectral distribution given by the
- function SPEC_INTENS, which is called with a series of
- wavelengths between 380 and 780 nm (the argument is
- expressed in meters), which returns emittance at that
- wavelength in arbitrary units. The chromaticity
- coordinates of the spectrum are returned in the x, y, and z
- arguments which respect the identity:
-
- x + y + z = 1.
-*/
-
-static void spectrum_to_xyz(double (*spec_intens)(double wavelength),
- double *x, double *y, double *z)
-{
- int i;
- double lambda, X = 0, Y = 0, Z = 0, XYZ;
-
- /* CIE colour matching functions xBar, yBar, and zBar for
- wavelengths from 380 through 780 nanometers, every 5
- nanometers. For a wavelength lambda in this range:
-
- cie_colour_match[(lambda - 380) / 5][0] = xBar
- cie_colour_match[(lambda - 380) / 5][1] = yBar
- cie_colour_match[(lambda - 380) / 5][2] = zBar
-
- To save memory, this table can be declared as floats
- rather than doubles; (IEEE) float has enough
- significant bits to represent the values. It's declared
- as a double here to avoid warnings about "conversion
- between floating-point types" from certain persnickety
- compilers. */
-
- static double cie_colour_match[81][3] = {
- {0.0014,0.0000,0.0065}, {0.0022,0.0001,0.0105}, {0.0042,0.0001,0.0201},
- {0.0076,0.0002,0.0362}, {0.0143,0.0004,0.0679}, {0.0232,0.0006,0.1102},
- {0.0435,0.0012,0.2074}, {0.0776,0.0022,0.3713}, {0.1344,0.0040,0.6456},
- {0.2148,0.0073,1.0391}, {0.2839,0.0116,1.3856}, {0.3285,0.0168,1.6230},
- {0.3483,0.0230,1.7471}, {0.3481,0.0298,1.7826}, {0.3362,0.0380,1.7721},
- {0.3187,0.0480,1.7441}, {0.2908,0.0600,1.6692}, {0.2511,0.0739,1.5281},
- {0.1954,0.0910,1.2876}, {0.1421,0.1126,1.0419}, {0.0956,0.1390,0.8130},
- {0.0580,0.1693,0.6162}, {0.0320,0.2080,0.4652}, {0.0147,0.2586,0.3533},
- {0.0049,0.3230,0.2720}, {0.0024,0.4073,0.2123}, {0.0093,0.5030,0.1582},
- {0.0291,0.6082,0.1117}, {0.0633,0.7100,0.0782}, {0.1096,0.7932,0.0573},
- {0.1655,0.8620,0.0422}, {0.2257,0.9149,0.0298}, {0.2904,0.9540,0.0203},
- {0.3597,0.9803,0.0134}, {0.4334,0.9950,0.0087}, {0.5121,1.0000,0.0057},
- {0.5945,0.9950,0.0039}, {0.6784,0.9786,0.0027}, {0.7621,0.9520,0.0021},
- {0.8425,0.9154,0.0018}, {0.9163,0.8700,0.0017}, {0.9786,0.8163,0.0014},
- {1.0263,0.7570,0.0011}, {1.0567,0.6949,0.0010}, {1.0622,0.6310,0.0008},
- {1.0456,0.5668,0.0006}, {1.0026,0.5030,0.0003}, {0.9384,0.4412,0.0002},
- {0.8544,0.3810,0.0002}, {0.7514,0.3210,0.0001}, {0.6424,0.2650,0.0000},
- {0.5419,0.2170,0.0000}, {0.4479,0.1750,0.0000}, {0.3608,0.1382,0.0000},
- {0.2835,0.1070,0.0000}, {0.2187,0.0816,0.0000}, {0.1649,0.0610,0.0000},
- {0.1212,0.0446,0.0000}, {0.0874,0.0320,0.0000}, {0.0636,0.0232,0.0000},
- {0.0468,0.0170,0.0000}, {0.0329,0.0119,0.0000}, {0.0227,0.0082,0.0000},
- {0.0158,0.0057,0.0000}, {0.0114,0.0041,0.0000}, {0.0081,0.0029,0.0000},
- {0.0058,0.0021,0.0000}, {0.0041,0.0015,0.0000}, {0.0029,0.0010,0.0000},
- {0.0020,0.0007,0.0000}, {0.0014,0.0005,0.0000}, {0.0010,0.0004,0.0000},
- {0.0007,0.0002,0.0000}, {0.0005,0.0002,0.0000}, {0.0003,0.0001,0.0000},
- {0.0002,0.0001,0.0000}, {0.0002,0.0001,0.0000}, {0.0001,0.0000,0.0000},
- {0.0001,0.0000,0.0000}, {0.0001,0.0000,0.0000}, {0.0000,0.0000,0.0000}
- };
-
- for (i = 0, lambda = 380; lambda < 780.1; i++, lambda += 5) {
- double Me;
-
- Me = (*spec_intens)(lambda);
- X += Me * cie_colour_match[i][0];
- Y += Me * cie_colour_match[i][1];
- Z += Me * cie_colour_match[i][2];
- }
- XYZ = (X + Y + Z);
- *x = X / XYZ;
- *y = Y / XYZ;
- *z = Z / XYZ;
-}
-
-/* BB_SPECTRUM
-
- Calculate, by Planck's radiation law, the emittance of a black body
- of temperature bbTemp at the given wavelength (in metres). */
-
-static double bbTemp = 5000; /* Hidden temperature argument
- to BB_SPECTRUM. */
-static double bb_spectrum(double wavelength)
-{
- double wlm = wavelength * 1e-9; /* Wavelength in meters */
-
- return (3.74183e-16 * pow(wlm, -5.0)) /
- (exp(1.4388e-2 / (wlm * bbTemp)) - 1.0);
-}
-
-static void xyz_to_lms(double x, double y, double z, double* l, double* m, double* s)
-{
- *l = 0.3897*x + 0.6890*y - 0.0787*z;
- *m = -0.2298*x + 1.1834*y + 0.0464*z;
- *s = z;
-}
-
-static void lms_to_xyz(double l, double m, double s, double* x, double *y, double* z)
-{
- *x = 1.9102*l - 1.1121*m + 0.2019*s;
- *y = 0.3709*l + 0.6290*m + 0.0000*s;
- *z = s;
-}
-
-void spectrum(double t1, double t2, int N, unsigned char *d)
-{
- int i,j,dj;
- double X,Y,Z,R,G,B,L,M,S, Lw, Mw, Sw;
- struct colourSystem *cs = &CIEsystem;
-
- j = 0; dj = 1;
- if (t1<t2) {
- double t = t1;
- t1 = t2;
- t2 = t;
- j = N-1; dj=-1;
- }
-
- for (i=0; i<N; i++) {
- bbTemp = t1 + (t2-t1)/N*i;
-
- // integrate blackbody radiation spectrum to XYZ
- spectrum_to_xyz(bb_spectrum, &X, &Y, &Z);
-
- // normalize highest temperature to white (in LMS system)
- xyz_to_lms(X,Y,Z,&L,&M,&S);
- if (i==0) {
- Lw=1/L; Mw=1/M; Sw=1/S;
- }
- L *= Lw; M *= Mw; S *= Sw;
- lms_to_xyz(L,M,S,&X,&Y,&Z);
-
- // convert to RGB
- xyz_to_rgb(cs, X, Y, Z, &R, &G, &B);
- constrain_rgb(&R, &G, &B);
- norm_rgb(&R, &G, &B);
- d[(j<<2)] = (unsigned char) ((double)R*255);
- d[(j<<2)+1] = (unsigned char) ((double)G*255);
- d[(j<<2)+2] = (unsigned char) ((double)B*255);
- d[(j<<2)+3] = (B>0.1)? B*255 : 0;
- j += dj;
- }
-}