An upcoming commit will delete many of the operators from pixman-combine32.c and rely on the ones in pixman-combine-float.c. The comments about how the operators were derived are still useful though, so copy them into pixman-combine-float.c before the deletion. --- pixman/pixman-combine-float.c | 334 ++++++++++++++++++++++++++++++------------ 1 file changed, 238 insertions(+), 96 deletions(-)
diff --git a/pixman/pixman-combine-float.c b/pixman/pixman-combine-float.c index ff02105..f5145bc 100644 --- a/pixman/pixman-combine-float.c +++ b/pixman/pixman-combine-float.c @@ -319,23 +319,44 @@ MAKE_PD_COMBINERS (conjoint_xor, ONE_MINUS_DA_OVER_SA, ONE_MINUS_SA_OVER_DA) * * 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 - * ar.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 */ #define MAKE_SEPARABLE_PDF_COMBINERS(name) \ @@ -355,18 +376,55 @@ MAKE_PD_COMBINERS (conjoint_xor, ONE_MINUS_DA_OVER_SA, ONE_MINUS_SA_OVER_DA) \ MAKE_COMBINERS (name, combine_ ## name ## _a, combine_ ## name ## _c) +/* + * Multiply + * + * ad * as * B(d / ad, s / as) + * = ad * as * d/ad * s/as + * = d * s + * + */ static force_inline float blend_multiply (float sa, float s, float da, float d) { return d * s; } +/* + * Screen + * + * ad * as * B(d/ad, s/as) + * = ad * as * (d/ad + s/as - s/as * d/ad) + * = ad * s + as * d - s * d + */ static force_inline float blend_screen (float sa, float s, float da, float d) { return d * sa + s * da - s * d; } +/* + * Overlay + * + * 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 force_inline float blend_overlay (float sa, float s, float da, float d) { @@ -376,6 +434,13 @@ blend_overlay (float sa, float s, float da, float d) return sa * da - 2 * (da - d) * (sa - s); } +/* + * Darken + * + * ad * as * B(d/ad, s/as) + * = ad * as * MIN(d/ad, s/as) + * = MIN (as * d, ad * s) + */ static force_inline float blend_darken (float sa, float s, float da, float d) { @@ -388,6 +453,13 @@ blend_darken (float sa, float s, float da, float d) return s; } +/* + * Lighten + * + * ad * as * B(d/ad, s/as) + * = ad * as * MAX(d/ad, s/as) + * = MAX (as * d, ad * s) + */ static force_inline float blend_lighten (float sa, float s, float da, float d) { @@ -400,6 +472,24 @@ blend_lighten (float sa, float s, float da, float d) return d; } +/* + * Color dodge + * + * 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 force_inline float blend_color_dodge (float sa, float s, float da, float d) { @@ -413,6 +503,26 @@ blend_color_dodge (float sa, float s, float da, float d) return sa * sa * d / (sa - s); } +/* + * Color burn + * + * 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 force_inline float blend_color_burn (float sa, float s, float da, float d) { @@ -426,6 +536,23 @@ blend_color_burn (float sa, float s, float da, float d) return sa * (da - sa * (da - d) / s); } +/* + * Hard light + * + * 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 force_inline float blend_hard_light (float sa, float s, float da, float d) { @@ -435,6 +562,23 @@ blend_hard_light (float sa, float s, float da, float d) return sa * da - 2 * (da - d) * (sa - s); } +/* + * Soft light + * + * 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 force_inline float blend_soft_light (float sa, float s, float da, float d) { @@ -461,6 +605,20 @@ blend_soft_light (float sa, float s, float da, float d) } } +/* + * Difference + * + * 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 force_inline float blend_difference (float sa, float s, float da, float d) { @@ -473,6 +631,13 @@ blend_difference (float sa, float s, float da, float d) return sda - dsa; } +/* + * Exclusion + * + * 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 + */ static force_inline float blend_exclusion (float sa, float s, float da, float d) { @@ -492,116 +657,79 @@ MAKE_SEPARABLE_PDF_COMBINERS (difference) MAKE_SEPARABLE_PDF_COMBINERS (exclusion) /* - * PDF nonseperable blend modes. - * - * These are implemented using the following functions to operate in Hsl - * space, with Cmax, Cmid, Cmin referring to the max, mid and min value - * of the red, green and blue components. + * PDF nonseperable blend modes are implemented using the following functions + * to operate in Hsl space, with Cmax, Cmid, Cmin referring to the max, mid + * and min value of the red, green and blue components. * * 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 - LUM (r × 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 they x'es in the fraction for + * 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) * */ - typedef struct { float r; @@ -769,9 +897,12 @@ set_sat (rgb_t *src, float sat) *min = 0.0f; } -/* - * 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 force_inline void blend_hsl_hue (rgb_t *res, @@ -786,9 +917,14 @@ blend_hsl_hue (rgb_t *res, set_lum (res, sa * da, get_lum (dest) * sa); } -/* - * 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 force_inline void blend_hsl_saturation (rgb_t *res, @@ -803,9 +939,12 @@ blend_hsl_saturation (rgb_t *res, set_lum (res, sa * da, get_lum (dest) * sa); } -/* - * 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 force_inline void blend_hsl_color (rgb_t *res, @@ -820,8 +959,11 @@ blend_hsl_color (rgb_t *res, } /* - * 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 force_inline void blend_hsl_luminosity (rgb_t *res, -- 1.8.3.1 _______________________________________________ Pixman mailing list Pixman@lists.freedesktop.org http://lists.freedesktop.org/mailman/listinfo/pixman
