This commit overhauls the comments in pixman-comine32.c regarding blend modes:
- Add a link to the PDF supplement that clarifies the specification of ColorBurn and ColorDodge - Clarify how the formulas for premultiplied colors are derived form the ones in the PDF specifications - Write out the derivation of the formulas in each blend routine --- pixman/pixman-combine32.c | 330 ++++++++++++++++++++++++++++------------------ 1 file changed, 204 insertions(+), 126 deletions(-) diff --git a/pixman/pixman-combine32.c b/pixman/pixman-combine32.c index be3cfdf..ae9eed4 100644 --- a/pixman/pixman-combine32.c +++ b/pixman/pixman-combine32.c @@ -463,32 +463,59 @@ combine_saturate_u (pixman_implementation_t *imp, } } + /* * PDF blend modes: + * * The following blend modes have been taken from the PDF ISO 32000 * specification, which at this point in time is available from - * http://www.adobe.com/devnet/acrobat/pdfs/PDF32000_2008.pdf - * The relevant chapters are 11.3.5 and 11.3.6. + * + * http://www.adobe.com/devnet/pdf/pdf_reference.html + * + * The specific documents of interest are the PDF spec itself: + * + * http://wwwimages.adobe.com/www.adobe.com/content/dam/Adobe/en/devnet/pdf/pdfs/PDF32000_2008.pdf + * + * chapters 11.3.5 and 11.3.6 and a later supplement for Adobe Acrobat + * 9.1 and Reader 9.1: + * + * http://wwwimages.adobe.com/www.adobe.com/content/dam/Adobe/en/devnet/pdf/pdfs/adobe_supplement_iso32000_1.pdf + * + * that clarifies the specifications for blend modes ColorDodge and + * ColorBurn. + * * The formula for computing the final pixel color given in 11.3.6 is: - * αr × Cr = (1 – αs) × αb × Cb + (1 – αb) × αs × Cs + αb × αs × B(Cb, Cs) - * with B() being the blend function. - * Note that OVER is a special case of this operation, using B(Cb, Cs) = Cs - * - * These blend modes should match the SVG filter draft specification, as - * it has been designed to mirror ISO 32000. Note that at the current point - * no released draft exists that shows this, as the formulas have not been - * updated yet after the release of ISO 32000. - * - * The default implementation here uses the PDF_SEPARABLE_BLEND_MODE and - * PDF_NON_SEPARABLE_BLEND_MODE macros, which take the blend function as an - * argument. Note that this implementation operates on premultiplied colors, - * while the PDF specification does not. Therefore the code uses the formula - * Cra = (1 – as) . Dca + (1 – ad) . Sca + B(Dca, ad, Sca, as) + * + * αr × Cr = (1 – αs) × αb × Cb + (1 – αb) × αs × Cs + αb × αs × B(Cb, Cs) + * + * with B() is the blend function. When B(Cb, Cs) = Cs, this formula + * reduces to the regular OVER operator. + * + * Cs and Cb are not premultiplied, so in our implementation we instead + * use: + * + * cr = (1 – αs) × cb + (1 – αb) × cs + αb × αs × B (cb/αb, cs/αs) + * + * where cr, cs, and cb are premultiplied colors, and where the + * + * αb × αs × B(cb/αb, cs/αs) + * + * part is first arithmetically simplified under the assumption that αb + * and αs are not 0, and then updated to produce a meaningful result when + * they are. + * + * For all the blend mode operators, the alpha channel is given by + * + * αr = αs + αb + αb × αs */ /* * Multiply - * B(Dca, ad, Sca, as) = Dca.Sca + * + * ad * as * B(d / ad, s / as) + * = ad * as * d/ad * s/as + * = d * s + * */ static void combine_multiply_u (pixman_implementation_t *imp, @@ -608,7 +635,10 @@ combine_multiply_ca (pixman_implementation_t *imp, /* * Screen - * B(Dca, ad, Sca, as) = Dca.sa + Sca.da - Dca.Sca + * + * ad * as * B(d/ad, s/as) + * = ad * as * (d/ad + s/as - s/as * d/ad) + * = ad * s + as * d - s * d */ static inline uint32_t blend_screen (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -620,11 +650,25 @@ PDF_SEPARABLE_BLEND_MODE (screen) /* * Overlay - * B(Dca, Da, Sca, Sa) = - * if 2.Dca < Da - * 2.Sca.Dca - * otherwise - * Sa.Da - 2.(Da - Dca).(Sa - Sca) + * + * ad * as * B(d/ad, s/as) + * = ad * as * Hardlight (s, d) + * = if (d / ad < 0.5) + * as * ad * Multiply (s/as, 2 * d/ad) + * else + * as * ad * Screen (s/as, 2 * d / ad - 1) + * = if (d < 0.5 * ad) + * as * ad * s/as * 2 * d /ad + * else + * as * ad * (s/as + 2 * d / ad - 1 - s / as * (2 * d / ad - 1)) + * = if (2 * d < ad) + * 2 * s * d + * else + * ad * s + 2 * as * d - as * ad - ad * s * (2 * d / ad - 1) + * = if (2 * d < ad) + * 2 * s * d + * else + * as * ad - 2 * (ad - d) * (as - s) */ static inline uint32_t blend_overlay (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -642,7 +686,10 @@ PDF_SEPARABLE_BLEND_MODE (overlay) /* * Darken - * B(Dca, Da, Sca, Sa) = min (Sca.Da, Dca.Sa) + * + * ad * as * B(d/ad, s/as) + * = ad * as * MIN(d/ad, s/as) + * = MIN (as * d, ad * s) */ static inline uint32_t blend_darken (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -658,7 +705,10 @@ PDF_SEPARABLE_BLEND_MODE (darken) /* * Lighten - * B(Dca, Da, Sca, Sa) = max (Sca.Da, Dca.Sa) + * + * ad * as * B(d/ad, s/as) + * = ad * as * MAX(d/ad, s/as) + * = MAX (as * d, ad * s) */ static inline uint32_t blend_lighten (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -674,13 +724,21 @@ PDF_SEPARABLE_BLEND_MODE (lighten) /* * Color dodge - * B(Dca, Da, Sca, Sa) = - * if Dca == 0 - * 0 - * if Sca == Sa - * Sa.Da - * otherwise - * Sa.Da. min (1, Dca / Da / (1 - Sca/Sa)) + * + * ad * as * B(d/ad, s/as) + * = if d/ad = 0 + * ad * as * 0 + * else if (d/ad >= (1 - s/as) + * ad * as * 1 + * else + * ad * as * ((d/ad) / (1 - s/as)) + * = if d = 0 + * 0 + * elif as * d >= ad * (as - s) + * ad * as + * else + * as * (as * d / (as - s)) + * */ static inline uint32_t blend_color_dodge (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -700,13 +758,23 @@ PDF_SEPARABLE_BLEND_MODE (color_dodge) /* * Color burn - * B(Dca, Da, Sca, Sa) = - * if Dca == Da - * Sa.Da - * if Sca == 0 - * 0 - * otherwise - * Sa.Da.(1 - min (1, (1 - Dca/Da).Sa / Sca)) + * + * We modify the first clause "if d = 1" to "if d >= 1" since with + * premultiplied colors d > 1 can actually happen. + * + * ad * as * B(d/ad, s/as) + * = if d/ad >= 1 + * ad * as * 1 + * elif (1 - d/ad) >= s/as + * ad * as * 0 + * else + * ad * as * (1 - ((1 - d/ad) / (s/as))) + * = if d >= ad + * ad * as + * elif as * ad - as * d >= ad * s + * 0 + * else + * ad * as - as * as * (ad - d) / s */ static inline uint32_t blend_color_burn (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -726,11 +794,20 @@ PDF_SEPARABLE_BLEND_MODE (color_burn) /* * Hard light - * B(Dca, Da, Sca, Sa) = - * if 2.Sca < Sa - * 2.Sca.Dca - * otherwise - * Sa.Da - 2.(Da - Dca).(Sa - Sca) + * + * ad * as * B(d/ad, s/as) + * = if (s/as <= 0.5) + * ad * as * Multiply (d/ad, 2 * s/as) + * else + * ad * as * Screen (d/ad, 2 * s/as - 1) + * = if 2 * s <= as + * ad * as * d/ad * 2 * s / as + * else + * ad * as * (d/ad + (2 * s/as - 1) + d/ad * (2 * s/as - 1)) + * = if 2 * s <= as + * 2 * s * d + * else + * as * ad - 2 * (ad - d) * (as - s) */ static inline uint32_t blend_hard_light (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -745,13 +822,20 @@ PDF_SEPARABLE_BLEND_MODE (hard_light) /* * Soft light - * B(Dca, Da, Sca, Sa) = - * if (2.Sca <= Sa) - * Dca.(Sa - (1 - Dca/Da).(2.Sca - Sa)) - * otherwise if Dca.4 <= Da - * Dca.(Sa + (2.Sca - Sa).((16.Dca/Da - 12).Dca/Da + 3) - * otherwise - * (Dca.Sa + (SQRT (Dca/Da).Da - Dca).(2.Sca - Sa)) + * + * ad * as * B(d/ad, s/as) + * = if (s/as <= 0.5) + * ad * as * (d/ad - (1 - 2 * s/as) * d/ad * (1 - d/ad)) + * else if (d/ad <= 0.25) + * ad * as * (d/ad + (2 * s/as - 1) * ((((16 * d/ad - 12) * d/ad + 4) * d/ad) - d/ad)) + * else + * ad * as * (d/ad + (2 * s/as - 1) * sqrt (d/ad)) + * = if (2 * s <= as) + * d * as - d * (ad - d) * (as - 2 * s) / ad; + * else if (4 * d <= ad) + * (2 * s - as) * d * ((16 * d / ad - 12) * d / ad + 3); + * else + * d * as + (sqrt (d * ad) - d) * (2 * s - as); */ static inline uint32_t blend_soft_light (uint32_t dca_org, @@ -792,7 +876,17 @@ PDF_SEPARABLE_BLEND_MODE (soft_light) /* * Difference - * B(Dca, Da, Sca, Sa) = abs (Dca.Sa - Sca.Da) + * + * ad * as * B(s/as, d/ad) + * = ad * as * abs (s/as - d/ad) + * = if (s/as <= d/ad) + * ad * as * (d/ad - s/as) + * else + * ad * as * (s/as - d/ad) + * = if (ad * s <= as * d) + * as * d - ad * s + * else + * ad * s - as * d */ static inline uint32_t blend_difference (uint32_t dca, uint32_t da, uint32_t sca, uint32_t sa) @@ -810,7 +904,10 @@ PDF_SEPARABLE_BLEND_MODE (difference) /* * Exclusion - * B(Dca, Da, Sca, Sa) = (Sca.Da + Dca.Sa - 2.Sca.Dca) + * + * ad * as * B(s/as, d/ad) + * = ad * as * (d/ad + s/as - 2 * d/ad * s/as) + * = as * d + ad * s - 2 * s * d */ /* This can be made faster by writing it directly and not using @@ -834,103 +931,70 @@ PDF_SEPARABLE_BLEND_MODE (exclusion) * LUM (C) = 0.3 × Cred + 0.59 × Cgreen + 0.11 × Cblue * * clip_color (C): - * l = LUM (C) - * min = Cmin - * max = Cmax - * if n < 0.0 - * C = l + ( ( ( C – l ) × l ) ⁄ ( l – min ) ) - * if x > 1.0 - * C = l + ( ( ( C – l ) × ( 1 – l ) ) ⁄ ( max – l ) ) - * return C + * l = LUM (C) + * min = Cmin + * max = Cmax + * if n < 0.0 + * C = l + (((C – l) × l) ⁄ (l – min)) + * if x > 1.0 + * C = l + (((C – l) × (1 – l) ) ⁄ (max – l)) + * return C * * set_lum (C, l): - * d = l – LUM (C) - * C += d - * return clip_color (C) + * d = l – LUM (C) + * C += d + * return clip_color (C) * * SAT (C) = CH_MAX (C) - CH_MIN (C) * * set_sat (C, s): - * if Cmax > Cmin - * Cmid = ( ( ( Cmid – Cmin ) × s ) ⁄ ( Cmax – Cmin ) ) - * Cmax = s - * else - * Cmid = Cmax = 0.0 - * Cmin = 0.0 - * return C + * if Cmax > Cmin + * Cmid = ( ( ( Cmid – Cmin ) × s ) ⁄ ( Cmax – Cmin ) ) + * Cmax = s + * else + * Cmid = Cmax = 0.0 + * Cmin = 0.0 + * return C */ /* For premultiplied colors, we need to know what happens when C is * multiplied by a real number. LUM and SAT are linear: * - * LUM (r × C) = r × LUM (C) SAT (r * C) = r * SAT (C) + * LUM (r × C) = r × LUM (C) SAT (r * C) = r * SAT (C) * * If we extend clip_color with an extra argument a and change * - * if x >= 1.0 + * if x >= 1.0 * * into * - * if x >= a + * if x >= a * * then clip_color is also linear: * - * r * clip_color (C, a) = clip_color (r_c, ra); + * r * clip_color (C, a) = clip_color (r * C, r * a); * * for positive r. * * Similarly, we can extend set_lum with an extra argument that is just passed * on to clip_color: * - * r * set_lum ( C, l, a) + * r * set_lum (C, l, a) * - * = r × clip_color ( C + l - LUM (C), a) + * = r × clip_color (C + l - LUM (C), a) * - * = clip_color ( r * C + r × l - r * LUM (C), r * a) + * = clip_color (r * C + r × l - r * LUM (C), r * a) * - * = set_lum ( r * C, r * l, r * a) + * = set_lum (r * C, r * l, r * a) * * Finally, set_sat: * - * r * set_sat (C, s) = set_sat (x * C, r * s) + * r * set_sat (C, s) = set_sat (x * C, r * s) * * The above holds for all non-zero x, because the x'es in the fraction for * C_mid cancel out. Specifically, it holds for x = r: * - * r * set_sat (C, s) = set_sat (r_c, rs) - * - */ - -/* So, for the non-separable PDF blend modes, we have (using s, d for - * non-premultiplied colors, and S, D for premultiplied: - * - * Color: - * - * a_s * a_d * B(s, d) - * = a_s * a_d * set_lum (S/a_s, LUM (D/a_d), 1) - * = set_lum (S * a_d, a_s * LUM (D), a_s * a_d) - * - * - * Luminosity: - * - * a_s * a_d * B(s, d) - * = a_s * a_d * set_lum (D/a_d, LUM(S/a_s), 1) - * = set_lum (a_s * D, a_d * LUM(S), a_s * a_d) - * - * - * Saturation: - * - * a_s * a_d * B(s, d) - * = a_s * a_d * set_lum (set_sat (D/a_d, SAT (S/a_s)), LUM (D/a_d), 1) - * = set_lum (a_s * a_d * set_sat (D/a_d, SAT (S/a_s)), - * a_s * LUM (D), a_s * a_d) - * = set_lum (set_sat (a_s * D, a_d * SAT (S), a_s * LUM (D), a_s * a_d)) - * - * Hue: - * - * a_s * a_d * B(s, d) - * = a_s * a_d * set_lum (set_sat (S/a_s, SAT (D/a_d)), LUM (D/a_d), 1) - * = set_lum (set_sat (a_d * S, a_s * SAT (D)), a_s * LUM (D), a_s * a_d) + * r * set_sat (C, s) = set_sat (r * C, r * s) * */ @@ -958,7 +1022,7 @@ PDF_SEPARABLE_BLEND_MODE (exclusion) uint8_t da = ALPHA_8 (d); \ uint8_t ida = ~da; \ uint32_t result; \ - uint32_t sc[3], dc[3], c[3]; \ + uint32_t sc[3], dc[3], c[3]; \ \ result = d; \ UN8x4_MUL_UN8_ADD_UN8x4_MUL_UN8 (result, isa, s, ida); \ @@ -1104,9 +1168,12 @@ set_sat (uint32_t dest[3], uint32_t src[3], uint32_t sat) } } -/* - * Hue: - * B(Cb, Cs) = set_lum (set_sat (Cs, SAT (Cb)), LUM (Cb)) +/* Hue: + * + * as * ad * B(s/as, d/as) + * = as * ad * set_lum (set_sat (s/as, SAT (d/ad)), LUM (d/ad), 1) + * = set_lum (set_sat (ad * s, as * SAT (d)), as * LUM (d), as * ad) + * */ static inline void blend_hsl_hue (uint32_t c[3], @@ -1124,9 +1191,14 @@ blend_hsl_hue (uint32_t c[3], PDF_NON_SEPARABLE_BLEND_MODE (hsl_hue) -/* - * Saturation: - * B(Cb, Cs) = set_lum (set_sat (Cb, SAT (Cs)), LUM (Cb)) +/* + * Saturation + * + * as * ad * B(s/as, d/ad) + * = as * ad * set_lum (set_sat (d/ad, SAT (s/as)), LUM (d/ad), 1) + * = set_lum (as * ad * set_sat (d/ad, SAT (s/as)), + * as * LUM (d), as * ad) + * = set_lum (set_sat (as * d, ad * SAT (s), as * LUM (d), as * ad)) */ static inline void blend_hsl_saturation (uint32_t c[3], @@ -1144,9 +1216,12 @@ blend_hsl_saturation (uint32_t c[3], PDF_NON_SEPARABLE_BLEND_MODE (hsl_saturation) -/* - * Color: - * B(Cb, Cs) = set_lum (Cs, LUM (Cb)) +/* + * Color + * + * as * ad * B(s/as, d/as) + * = as * ad * set_lum (s/as, LUM (d/ad), 1) + * = set_lum (s * ad, as * LUM (d), as * ad) */ static inline void blend_hsl_color (uint32_t c[3], @@ -1164,8 +1239,11 @@ blend_hsl_color (uint32_t c[3], PDF_NON_SEPARABLE_BLEND_MODE (hsl_color) /* - * Luminosity: - * B(Cb, Cs) = set_lum (Cb, LUM (Cs)) + * Luminosity + * + * as * ad * B(s/as, d/ad) + * = as * ad * set_lum (d/ad, LUM (s/as), 1) + * = set_lum (as * d, ad * LUM (s), as * ad) */ static inline void blend_hsl_luminosity (uint32_t c[3], -- 1.7.11.7 _______________________________________________ Pixman mailing list Pixman@lists.freedesktop.org http://lists.freedesktop.org/mailman/listinfo/pixman