From 6444875f68b05a906ba91c917970b8df2b436d4a Mon Sep 17 00:00:00 2001 From: Anuj Verma Date: Fri, 21 Aug 2020 03:59:23 -0700 Subject: [PATCH] [sdf] Add brief technical overview of both rasterizers. --- src/sdf/ftbsdf.c | 89 ++++++++++++++++++++++++++++++++++++++++++++++++ src/sdf/ftsdf.c | 77 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 166 insertions(+) diff --git a/src/sdf/ftbsdf.c b/src/sdf/ftbsdf.c index 510273367..13dbd4511 100644 --- a/src/sdf/ftbsdf.c +++ b/src/sdf/ftbsdf.c @@ -9,6 +9,95 @@ #include "ftsdfcommon.h" + /************************************************************************** + * + * A brief technical overview of how the BSDF rasterizer works + * ----------------------------------------------------------- + * + * [Notes]: + * * SDF stands for Signed Distance Field everywhere. + * + * * BSDF stands for Bitmap to Signed Distance Field rasterizer. + * + * * This renderer converts rasterized bitmaps to SDF. There is another + * renderer called 'sdf', which generates SDF directly from outlines; + * see file `ftsdf.c` for more. + * + * * The idea of generating SDF from bitmaps is taken from two research + * papers, where one is dependent on the other: + * + * - Per-Erik Danielsson: Euclidean Distance Mapping + * http://webstaff.itn.liu.se/~stegu/JFA/Danielsson.pdf + * + * From this paper we use the eight-point sequential Euclidean + * distance mapping (8SED). This is the heart of the process used + * in this rasterizer. + * + * - Stefan Gustavson, Robin Strand: Anti-aliased Euclidean distance transform. + * http://weber.itn.liu.se/~stegu/aadist/edtaa_preprint.pdf + * + * The original 8SED algorithm discards the pixels' alpha values, + * which can contain information about the actual outline of the + * glyph. This paper takes advantage of those alpha values and + * approximates outline pretty accurately. + * + * * This rasterizer also works for monochrome bitmaps. However, the + * result is not as accurate since we don't have any way to + * approximate outlines from binary bitmaps. + * + * ======================================================================== + * + * Generating SDF from bitmap is done in several steps. + * + * (1) The only information we have is the bitmap itself. It can + * be monochrome or anti-aliased. If it is anti-aliased, pixel values + * are nothing but coverage values. These coverage values can be used + * to extract information about the outline of the image. For + * example, if the pixel's alpha value is 0.5, then we can safely + * assume that the outline passes through the center of the pixel. + * + * (2) Find edge pixels in the bitmap (see `bsdf_is_edge` for more). For + * all edge pixels we use the Anti-aliased Euclidean distance + * transform algorithm and compute approximate edge distances (see + * `compute_edge_distance` and/or the second paper for more). + * + * (3) Now that we have computed approximate distances for edge pixels we + * use the 8SED algorithm to basically sweep the entire bitmap and + * compute distances for the rest of the pixels. (Since the algorithm + * is pretty convoluted it is only explained briefly in a comment to + * function `edt8`. To see the actual algorithm refer to the first + * paper.) + * + * (4) Finally, compute the sign for each pixel. This is done in function + * `finalize_sdf`. The basic idea is that if a pixel's original + * alpha/coverage value is greater than 0.5 then it is 'inside' (and + * 'outside' otherwise). + * + * Pseudo Code: + * + * ``` + * b = source bitmap; + * t = target bitmap; + * dm = list of distances; // dimension equal to b + * + * foreach grid_point (x, y) in b: + * { + * if (is_edge(x, y)): + * dm = approximate_edge_distance(b, x, y); + * + * // do the 8SED on the distances + * edt8(dm); + * + * // determine the signs + * determine_signs(dm): + * + * // copy SDF data to the target bitmap + * copy(dm to t); + * } + * + */ + + /************************************************************************** * * useful macros diff --git a/src/sdf/ftsdf.c b/src/sdf/ftsdf.c index 29bc0c3ca..1edb00064 100644 --- a/src/sdf/ftsdf.c +++ b/src/sdf/ftsdf.c @@ -7,6 +7,83 @@ #include "ftsdferrs.h" + /************************************************************************** + * + * A brief technical overview of how the SDF rasterizer works + * ---------------------------------------------------------- + * + * [Notes]: + * * SDF stands for Signed Distance Field everywhere. + * + * * This renderer generates SDF directly from outlines. There is + * another renderer called 'bsdf', which converts bitmaps to SDF; see + * file `ftbsdf.c` for more. + * + * * The basic idea of generating the SDF is taken from Viktor Chlumsky's + * research paper. + * + * Chlumsky, Viktor: Shape Decomposition for Multi-channel Distance + * Fields. Master's thesis. Czech Technical University in Prague, + * Faculty of InformationTechnology, 2015. + * + * For more information: https://github.com/Chlumsky/msdfgen + * + * ======================================================================== + * + * Generating SDF from outlines is pretty straightforward. + * + * (1) We have a set of contours that make the outline of a shape/glyph. + * Each contour comprises of several edges, with three types of edges. + * + * * line segments + * * conic Bezier curves + * * cubic Bezier curves + * + * (2) Apart from the outlines we also have a two-dimensional grid, namely + * the bitmap that is used to represent the final SDF data. + * + * (3) In order to generate SDF, our task is to find shortest signed + * distance from each grid point to the outline. The 'signed + * distance' means that if the grid point is filled by any contour + * then its sign is positive, otherwise it is negative. The pseudo + * code is as follows. + * + * ``` + * foreach grid_point (x, y): + * { + * int min_dist = INT_MAX; + * + * foreach contour in outline: + * { + * foreach edge in contour: + * { + * // get shortest distance from point (x, y) to the edge + * d = get_min_dist(x, y, edge); + * + * if (d < min_dist) + * min_dist = d; + * } + * + * bitmap[x, y] = min_dist; + * } + * } + * ``` + * + * (4) After running this algorithm the bitmap contain sinformation about the closest + * point from each point to the outline of the shape. Of course, + * while this is the most straightforward way of generating SDF, we + * use various optimizations in this rasterizer. See the + * `sdf_generate_*' functions in this file for all details. + * + * The optimization currently used by default is subdivision; see + * function `sdf_generate_subdivision` for more. + * + * Also, to see how we compute the shortest distance from a point to + * each type of edge, check out the `get_min_distance_*' functions. + * + */ + + /************************************************************************** * * for tracking used memory