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+/****************************************************************************
+ *
+ * ftbsdf.c
+ *
+ * Signed Distance Field support for bitmap fonts (body only).
+ *
+ * Copyright (C) 2020-2023 by
+ * David Turner, Robert Wilhelm, and Werner Lemberg.
+ *
+ * Written by Anuj Verma.
+ *
+ * This file is part of the FreeType project, and may only be used,
+ * modified, and distributed under the terms of the FreeType project
+ * license, LICENSE.TXT. By continuing to use, modify, or distribute
+ * this file you indicate that you have read the license and
+ * understand and accept it fully.
+ *
+ */
+
+
+#include <freetype/internal/ftobjs.h>
+#include <freetype/internal/ftdebug.h>
+#include <freetype/internal/ftmemory.h>
+#include <freetype/fttrigon.h>
+
+#include "ftsdf.h"
+#include "ftsdferrs.h"
+#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);
+ * }
+ *
+ */
+
+
+ /**************************************************************************
+ *
+ * The macro FT_COMPONENT is used in trace mode. It is an implicit
+ * parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log
+ * messages during execution.
+ */
+#undef FT_COMPONENT
+#define FT_COMPONENT bsdf
+
+
+ /**************************************************************************
+ *
+ * useful macros
+ *
+ */
+
+#define ONE 65536 /* 1 in 16.16 */
+
+
+ /**************************************************************************
+ *
+ * structs
+ *
+ */
+
+
+ /**************************************************************************
+ *
+ * @Struct:
+ * BSDF_TRaster
+ *
+ * @Description:
+ * This struct is used in place of @FT_Raster and is stored within the
+ * internal FreeType renderer struct. While rasterizing this is passed
+ * to the @FT_Raster_RenderFunc function, which then can be used however
+ * we want.
+ *
+ * @Fields:
+ * memory ::
+ * Used internally to allocate intermediate memory while raterizing.
+ *
+ */
+ typedef struct BSDF_TRaster_
+ {
+ FT_Memory memory;
+
+ } BSDF_TRaster, *BSDF_PRaster;
+
+
+ /**************************************************************************
+ *
+ * @Struct:
+ * ED
+ *
+ * @Description:
+ * Euclidean distance. It gets used for Euclidean distance transforms;
+ * it can also be interpreted as an edge distance.
+ *
+ * @Fields:
+ * dist ::
+ * Vector length of the `prox` parameter. Can be squared or absolute
+ * depending on the `USE_SQUARED_DISTANCES` macro defined in file
+ * `ftsdfcommon.h`.
+ *
+ * prox ::
+ * Vector to the nearest edge. Can also be interpreted as shortest
+ * distance of a point.
+ *
+ * alpha ::
+ * Alpha value of the original bitmap from which we generate SDF.
+ * Needed for computing the gradient and determining the proper sign
+ * of a pixel.
+ *
+ */
+ typedef struct ED_
+ {
+ FT_16D16 dist;
+ FT_16D16_Vec prox;
+ FT_Byte alpha;
+
+ } ED;
+
+
+ /**************************************************************************
+ *
+ * @Struct:
+ * BSDF_Worker
+ *
+ * @Description:
+ * A convenience struct that is passed to functions while generating
+ * SDF; most of those functions require the same parameters.
+ *
+ * @Fields:
+ * distance_map ::
+ * A one-dimensional array that gets interpreted as two-dimensional
+ * one. It contains the Euclidean distances of all points of the
+ * bitmap.
+ *
+ * width ::
+ * Width of the above `distance_map`.
+ *
+ * rows ::
+ * Number of rows in the above `distance_map`.
+ *
+ * params ::
+ * Internal parameters and properties required by the rasterizer. See
+ * file `ftsdf.h` for more.
+ *
+ */
+ typedef struct BSDF_Worker_
+ {
+ ED* distance_map;
+
+ FT_Int width;
+ FT_Int rows;
+
+ SDF_Raster_Params params;
+
+ } BSDF_Worker;
+
+
+ /**************************************************************************
+ *
+ * initializer
+ *
+ */
+
+ static const ED zero_ed = { 0, { 0, 0 }, 0 };
+
+
+ /**************************************************************************
+ *
+ * rasterizer functions
+ *
+ */
+
+ /**************************************************************************
+ *
+ * @Function:
+ * bsdf_is_edge
+ *
+ * @Description:
+ * Check whether a pixel is an edge pixel, i.e., whether it is
+ * surrounded by a completely black pixel (zero alpha), and the current
+ * pixel is not a completely black pixel.
+ *
+ * @Input:
+ * dm ::
+ * Array of distances. The parameter must point to the current
+ * pixel, i.e., the pixel that is to be checked for being an edge.
+ *
+ * x ::
+ * The x position of the current pixel.
+ *
+ * y ::
+ * The y position of the current pixel.
+ *
+ * w ::
+ * Width of the bitmap.
+ *
+ * r ::
+ * Number of rows in the bitmap.
+ *
+ * @Return:
+ * 1~if the current pixel is an edge pixel, 0~otherwise.
+ *
+ */
+
+#ifdef CHECK_NEIGHBOR
+#undef CHECK_NEIGHBOR
+#endif
+
+#define CHECK_NEIGHBOR( x_offset, y_offset ) \
+ do \
+ { \
+ if ( x + x_offset >= 0 && x + x_offset < w && \
+ y + y_offset >= 0 && y + y_offset < r ) \
+ { \
+ num_neighbors++; \
+ \
+ to_check = dm + y_offset * w + x_offset; \
+ if ( to_check->alpha == 0 ) \
+ { \
+ is_edge = 1; \
+ goto Done; \
+ } \
+ } \
+ } while ( 0 )
+
+ static FT_Bool
+ bsdf_is_edge( ED* dm, /* distance map */
+ FT_Int x, /* x index of point to check */
+ FT_Int y, /* y index of point to check */
+ FT_Int w, /* width */
+ FT_Int r ) /* rows */
+ {
+ FT_Bool is_edge = 0;
+ ED* to_check = NULL;
+ FT_Int num_neighbors = 0;
+
+
+ if ( dm->alpha == 0 )
+ goto Done;
+
+ if ( dm->alpha > 0 && dm->alpha < 255 )
+ {
+ is_edge = 1;
+ goto Done;
+ }
+
+ /* up */
+ CHECK_NEIGHBOR( 0, -1 );
+
+ /* down */
+ CHECK_NEIGHBOR( 0, 1 );
+
+ /* left */
+ CHECK_NEIGHBOR( -1, 0 );
+
+ /* right */
+ CHECK_NEIGHBOR( 1, 0 );
+
+ /* up left */
+ CHECK_NEIGHBOR( -1, -1 );
+
+ /* up right */
+ CHECK_NEIGHBOR( 1, -1 );
+
+ /* down left */
+ CHECK_NEIGHBOR( -1, 1 );
+
+ /* down right */
+ CHECK_NEIGHBOR( 1, 1 );
+
+ if ( num_neighbors != 8 )
+ is_edge = 1;
+
+ Done:
+ return is_edge;
+ }
+
+#undef CHECK_NEIGHBOR
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * compute_edge_distance
+ *
+ * @Description:
+ * Approximate the outline and compute the distance from `current`
+ * to the approximated outline.
+ *
+ * @Input:
+ * current ::
+ * Array of Euclidean distances. `current` must point to the position
+ * for which the distance is to be caculated. We treat this array as
+ * a two-dimensional array mapped to a one-dimensional array.
+ *
+ * x ::
+ * The x coordinate of the `current` parameter in the array.
+ *
+ * y ::
+ * The y coordinate of the `current` parameter in the array.
+ *
+ * w ::
+ * The width of the distances array.
+ *
+ * r ::
+ * Number of rows in the distances array.
+ *
+ * @Return:
+ * A vector pointing to the approximate edge distance.
+ *
+ * @Note:
+ * This is a computationally expensive function. Try to reduce the
+ * number of calls to this function. Moreover, this must only be used
+ * for edge pixel positions.
+ *
+ */
+ static FT_16D16_Vec
+ compute_edge_distance( ED* current,
+ FT_Int x,
+ FT_Int y,
+ FT_Int w,
+ FT_Int r )
+ {
+ /*
+ * This function, based on the paper presented by Stefan Gustavson and
+ * Robin Strand, gets used to approximate edge distances from
+ * anti-aliased bitmaps.
+ *
+ * The algorithm is as follows.
+ *
+ * (1) In anti-aliased images, the pixel's alpha value is the coverage
+ * of the pixel by the outline. For example, if the alpha value is
+ * 0.5f we can assume that the outline passes through the center of
+ * the pixel.
+ *
+ * (2) For this reason we can use that alpha value to approximate the real
+ * distance of the pixel to edge pretty accurately. A simple
+ * approximation is `(0.5f - alpha)`, assuming that the outline is
+ * parallel to the x or y~axis. However, in this algorithm we use a
+ * different approximation which is quite accurate even for
+ * non-axis-aligned edges.
+ *
+ * (3) The only remaining piece of information that we cannot
+ * approximate directly from the alpha is the direction of the edge.
+ * This is where we use Sobel's operator to compute the gradient of
+ * the pixel. The gradient give us a pretty good approximation of
+ * the edge direction. We use a 3x3 kernel filter to compute the
+ * gradient.
+ *
+ * (4) After the above two steps we have both the direction and the
+ * distance to the edge which is used to generate the Signed
+ * Distance Field.
+ *
+ * References:
+ *
+ * - Anti-Aliased Euclidean Distance Transform:
+ * http://weber.itn.liu.se/~stegu/aadist/edtaa_preprint.pdf
+ * - Sobel Operator:
+ * https://en.wikipedia.org/wiki/Sobel_operator
+ */
+
+ FT_16D16_Vec g = { 0, 0 };
+ FT_16D16 dist, current_alpha;
+ FT_16D16 a1, temp;
+ FT_16D16 gx, gy;
+ FT_16D16 alphas[9];
+
+
+ /* Since our spread cannot be 0, this condition */
+ /* can never be true. */
+ if ( x <= 0 || x >= w - 1 ||
+ y <= 0 || y >= r - 1 )
+ return g;
+
+ /* initialize the alphas */
+ alphas[0] = 256 * (FT_16D16)current[-w - 1].alpha;
+ alphas[1] = 256 * (FT_16D16)current[-w ].alpha;
+ alphas[2] = 256 * (FT_16D16)current[-w + 1].alpha;
+ alphas[3] = 256 * (FT_16D16)current[ -1].alpha;
+ alphas[4] = 256 * (FT_16D16)current[ 0].alpha;
+ alphas[5] = 256 * (FT_16D16)current[ 1].alpha;
+ alphas[6] = 256 * (FT_16D16)current[ w - 1].alpha;
+ alphas[7] = 256 * (FT_16D16)current[ w ].alpha;
+ alphas[8] = 256 * (FT_16D16)current[ w + 1].alpha;
+
+ current_alpha = alphas[4];
+
+ /* Compute the gradient using the Sobel operator. */
+ /* In this case we use the following 3x3 filters: */
+ /* */
+ /* For x: | -1 0 -1 | */
+ /* | -root(2) 0 root(2) | */
+ /* | -1 0 1 | */
+ /* */
+ /* For y: | -1 -root(2) -1 | */
+ /* | 0 0 0 | */
+ /* | 1 root(2) 1 | */
+ /* */
+ /* [Note]: 92681 is root(2) in 16.16 format. */
+ g.x = -alphas[0] -
+ FT_MulFix( alphas[3], 92681 ) -
+ alphas[6] +
+ alphas[2] +
+ FT_MulFix( alphas[5], 92681 ) +
+ alphas[8];
+
+ g.y = -alphas[0] -
+ FT_MulFix( alphas[1], 92681 ) -
+ alphas[2] +
+ alphas[6] +
+ FT_MulFix( alphas[7], 92681 ) +
+ alphas[8];
+
+ FT_Vector_NormLen( &g );
+
+ /* The gradient gives us the direction of the */
+ /* edge for the current pixel. Once we have the */
+ /* approximate direction of the edge, we can */
+ /* approximate the edge distance much better. */
+
+ if ( g.x == 0 || g.y == 0 )
+ dist = ONE / 2 - alphas[4];
+ else
+ {
+ gx = g.x;
+ gy = g.y;
+
+ gx = FT_ABS( gx );
+ gy = FT_ABS( gy );
+
+ if ( gx < gy )
+ {
+ temp = gx;
+ gx = gy;
+ gy = temp;
+ }
+
+ a1 = FT_DivFix( gy, gx ) / 2;
+
+ if ( current_alpha < a1 )
+ dist = ( gx + gy ) / 2 -
+ square_root( 2 * FT_MulFix( gx,
+ FT_MulFix( gy,
+ current_alpha ) ) );
+
+ else if ( current_alpha < ( ONE - a1 ) )
+ dist = FT_MulFix( ONE / 2 - current_alpha, gx );
+
+ else
+ dist = -( gx + gy ) / 2 +
+ square_root( 2 * FT_MulFix( gx,
+ FT_MulFix( gy,
+ ONE - current_alpha ) ) );
+ }
+
+ g.x = FT_MulFix( g.x, dist );
+ g.y = FT_MulFix( g.y, dist );
+
+ return g;
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * bsdf_approximate_edge
+ *
+ * @Description:
+ * Loops over all the pixels and call `compute_edge_distance` only for
+ * edge pixels. This maked the process a lot faster since
+ * `compute_edge_distance` uses functions such as `FT_Vector_NormLen',
+ * which are quite slow.
+ *
+ * @InOut:
+ * worker ::
+ * Contains the distance map as well as all the relevant parameters
+ * required by the function.
+ *
+ * @Return:
+ * FreeType error, 0 means success.
+ *
+ * @Note:
+ * The function directly manipulates `worker->distance_map`.
+ *
+ */
+ static FT_Error
+ bsdf_approximate_edge( BSDF_Worker* worker )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_Int i, j;
+ FT_Int index;
+ ED* ed;
+
+
+ if ( !worker || !worker->distance_map )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ ed = worker->distance_map;
+
+ for ( j = 0; j < worker->rows; j++ )
+ {
+ for ( i = 0; i < worker->width; i++ )
+ {
+ index = j * worker->width + i;
+
+ if ( bsdf_is_edge( worker->distance_map + index,
+ i, j,
+ worker->width,
+ worker->rows ) )
+ {
+ /* approximate the edge distance for edge pixels */
+ ed[index].prox = compute_edge_distance( ed + index,
+ i, j,
+ worker->width,
+ worker->rows );
+ ed[index].dist = VECTOR_LENGTH_16D16( ed[index].prox );
+ }
+ else
+ {
+ /* for non-edge pixels assign far away distances */
+ ed[index].dist = 400 * ONE;
+ ed[index].prox.x = 200 * ONE;
+ ed[index].prox.y = 200 * ONE;
+ }
+ }
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * bsdf_init_distance_map
+ *
+ * @Description:
+ * Initialize the distance map according to the '8-point sequential
+ * Euclidean distance mapping' (8SED) algorithm. Basically it copies
+ * the `source` bitmap alpha values to the `distance_map->alpha`
+ * parameter of `worker`.
+ *
+ * @Input:
+ * source ::
+ * Source bitmap to copy the data from.
+ *
+ * @Output:
+ * worker ::
+ * Target distance map to copy the data to.
+ *
+ * @Return:
+ * FreeType error, 0 means success.
+ *
+ */
+ static FT_Error
+ bsdf_init_distance_map( const FT_Bitmap* source,
+ BSDF_Worker* worker )
+ {
+ FT_Error error = FT_Err_Ok;
+
+ FT_Int x_diff, y_diff;
+ FT_Int t_i, t_j, s_i, s_j;
+ FT_Byte* s;
+ ED* t;
+
+
+ /* again check the parameters (probably unnecessary) */
+ if ( !source || !worker )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* Because of the way we convert a bitmap to SDF, */
+ /* i.e., aligning the source to the center of the */
+ /* target, the target's width and rows must be */
+ /* checked before copying. */
+ if ( worker->width < (FT_Int)source->width ||
+ worker->rows < (FT_Int)source->rows )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* check pixel mode */
+ if ( source->pixel_mode == FT_PIXEL_MODE_NONE )
+ {
+ FT_ERROR(( "bsdf_copy_source_to_target:"
+ " Invalid pixel mode of source bitmap" ));
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+#ifdef FT_DEBUG_LEVEL_TRACE
+ if ( source->pixel_mode == FT_PIXEL_MODE_MONO )
+ {
+ FT_TRACE0(( "bsdf_copy_source_to_target:"
+ " The `bsdf' renderer can convert monochrome\n" ));
+ FT_TRACE0(( " "
+ " bitmaps to SDF but the results are not perfect\n" ));
+ FT_TRACE0(( " "
+ " because there is no way to approximate actual\n" ));
+ FT_TRACE0(( " "
+ " outlines from monochrome bitmaps. Consider\n" ));
+ FT_TRACE0(( " "
+ " using an anti-aliased bitmap instead.\n" ));
+ }
+#endif
+
+ /* Calculate the width and row differences */
+ /* between target and source. */
+ x_diff = worker->width - (int)source->width;
+ y_diff = worker->rows - (int)source->rows;
+
+ x_diff /= 2;
+ y_diff /= 2;
+
+ t = (ED*)worker->distance_map;
+ s = source->buffer;
+
+ /* For now we only support pixel mode `FT_PIXEL_MODE_MONO` */
+ /* and `FT_PIXEL_MODE_GRAY`. More will be added later. */
+ /* */
+ /* [NOTE]: We can also use @FT_Bitmap_Convert to convert */
+ /* bitmap to 8bpp. To avoid extra allocation and */
+ /* since the target bitmap can be 16bpp we manually */
+ /* convert the source bitmap to the desired bpp. */
+
+ switch ( source->pixel_mode )
+ {
+ case FT_PIXEL_MODE_MONO:
+ {
+ FT_Int t_width = worker->width;
+ FT_Int t_rows = worker->rows;
+ FT_Int s_width = (int)source->width;
+ FT_Int s_rows = (int)source->rows;
+
+
+ for ( t_j = 0; t_j < t_rows; t_j++ )
+ {
+ for ( t_i = 0; t_i < t_width; t_i++ )
+ {
+ FT_Int t_index = t_j * t_width + t_i;
+ FT_Int s_index;
+ FT_Int div, mod;
+ FT_Byte pixel, byte;
+
+
+ t[t_index] = zero_ed;
+
+ s_i = t_i - x_diff;
+ s_j = t_j - y_diff;
+
+ /* Assign 0 to padding similar to */
+ /* the source bitmap. */
+ if ( s_i < 0 || s_i >= s_width ||
+ s_j < 0 || s_j >= s_rows )
+ continue;
+
+ if ( worker->params.flip_y )
+ s_index = ( s_rows - s_j - 1 ) * source->pitch;
+ else
+ s_index = s_j * source->pitch;
+
+ div = s_index + s_i / 8;
+ mod = 7 - s_i % 8;
+
+ pixel = s[div];
+ byte = (FT_Byte)( 1 << mod );
+
+ t[t_index].alpha = pixel & byte ? 255 : 0;
+ }
+ }
+ }
+ break;
+
+ case FT_PIXEL_MODE_GRAY:
+ {
+ FT_Int t_width = worker->width;
+ FT_Int t_rows = worker->rows;
+ FT_Int s_width = (int)source->width;
+ FT_Int s_rows = (int)source->rows;
+
+
+ /* loop over all pixels and assign pixel values from source */
+ for ( t_j = 0; t_j < t_rows; t_j++ )
+ {
+ for ( t_i = 0; t_i < t_width; t_i++ )
+ {
+ FT_Int t_index = t_j * t_width + t_i;
+ FT_Int s_index;
+
+
+ t[t_index] = zero_ed;
+
+ s_i = t_i - x_diff;
+ s_j = t_j - y_diff;
+
+ /* Assign 0 to padding similar to */
+ /* the source bitmap. */
+ if ( s_i < 0 || s_i >= s_width ||
+ s_j < 0 || s_j >= s_rows )
+ continue;
+
+ if ( worker->params.flip_y )
+ s_index = ( s_rows - s_j - 1 ) * s_width + s_i;
+ else
+ s_index = s_j * s_width + s_i;
+
+ /* simply copy the alpha values */
+ t[t_index].alpha = s[s_index];
+ }
+ }
+ }
+ break;
+
+ default:
+ FT_ERROR(( "bsdf_copy_source_to_target:"
+ " unsopported pixel mode of source bitmap\n" ));
+
+ error = FT_THROW( Unimplemented_Feature );
+ break;
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * compare_neighbor
+ *
+ * @Description:
+ * Compare neighbor pixel (which is defined by the offset) and update
+ * `current` distance if the new distance is shorter than the original.
+ *
+ * @Input:
+ * x_offset ::
+ * X offset of the neighbor to be checked. The offset is relative to
+ * the `current`.
+ *
+ * y_offset ::
+ * Y offset of the neighbor to be checked. The offset is relative to
+ * the `current`.
+ *
+ * width ::
+ * Width of the `current` array.
+ *
+ * @InOut:
+ * current ::
+ * Pointer into array of distances. This parameter must point to the
+ * position whose neighbor is to be checked. The array is treated as
+ * a two-dimensional array.
+ *
+ */
+ static void
+ compare_neighbor( ED* current,
+ FT_Int x_offset,
+ FT_Int y_offset,
+ FT_Int width )
+ {
+ ED* to_check;
+ FT_16D16 dist;
+ FT_16D16_Vec dist_vec;
+
+
+ to_check = current + ( y_offset * width ) + x_offset;
+
+ /*
+ * While checking for the nearest point we first approximate the
+ * distance of `current` by adding the deviation (which is sqrt(2) at
+ * most). Only if the new value is less than the current value we
+ * calculate the actual distances using `FT_Vector_Length`. This last
+ * step can be omitted by using squared distances.
+ */
+
+ /*
+ * Approximate the distance. We subtract 1 to avoid precision errors,
+ * which could happen because the two directions can be opposite.
+ */
+ dist = to_check->dist - ONE;
+
+ if ( dist < current->dist )
+ {
+ dist_vec = to_check->prox;
+
+ dist_vec.x += x_offset * ONE;
+ dist_vec.y += y_offset * ONE;
+ dist = VECTOR_LENGTH_16D16( dist_vec );
+
+ if ( dist < current->dist )
+ {
+ current->dist = dist;
+ current->prox = dist_vec;
+ }
+ }
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * first_pass
+ *
+ * @Description:
+ * First pass of the 8SED algorithm. Loop over the bitmap from top to
+ * bottom and scan each row left to right, updating the distances in
+ * `worker->distance_map`.
+ *
+ * @InOut:
+ * worker::
+ * Contains all the relevant parameters.
+ *
+ */
+ static void
+ first_pass( BSDF_Worker* worker )
+ {
+ FT_Int i, j; /* iterators */
+ FT_Int w, r; /* width, rows */
+ ED* dm; /* distance map */
+
+
+ dm = worker->distance_map;
+ w = worker->width;
+ r = worker->rows;
+
+ /* Start scanning from top to bottom and sweep each */
+ /* row back and forth comparing the distances of the */
+ /* neighborhood. Leave the first row as it has no top */
+ /* neighbor; it will be covered in the second scan of */
+ /* the image (from bottom to top). */
+ for ( j = 1; j < r; j++ )
+ {
+ FT_Int index;
+ ED* current;
+
+
+ /* Forward pass of rows (left -> right). Leave the first */
+ /* column, which gets covered in the backward pass. */
+ for ( i = 1; i < w - 1; i++ )
+ {
+ index = j * w + i;
+ current = dm + index;
+
+ /* left-up */
+ compare_neighbor( current, -1, -1, w );
+ /* up */
+ compare_neighbor( current, 0, -1, w );
+ /* up-right */
+ compare_neighbor( current, 1, -1, w );
+ /* left */
+ compare_neighbor( current, -1, 0, w );
+ }
+
+ /* Backward pass of rows (right -> left). Leave the last */
+ /* column, which was already covered in the forward pass. */
+ for ( i = w - 2; i >= 0; i-- )
+ {
+ index = j * w + i;
+ current = dm + index;
+
+ /* right */
+ compare_neighbor( current, 1, 0, w );
+ }
+ }
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * second_pass
+ *
+ * @Description:
+ * Second pass of the 8SED algorithm. Loop over the bitmap from bottom
+ * to top and scan each row left to right, updating the distances in
+ * `worker->distance_map`.
+ *
+ * @InOut:
+ * worker::
+ * Contains all the relevant parameters.
+ *
+ */
+ static void
+ second_pass( BSDF_Worker* worker )
+ {
+ FT_Int i, j; /* iterators */
+ FT_Int w, r; /* width, rows */
+ ED* dm; /* distance map */
+
+
+ dm = worker->distance_map;
+ w = worker->width;
+ r = worker->rows;
+
+ /* Start scanning from bottom to top and sweep each */
+ /* row back and forth comparing the distances of the */
+ /* neighborhood. Leave the last row as it has no down */
+ /* neighbor; it is already covered in the first scan */
+ /* of the image (from top to bottom). */
+ for ( j = r - 2; j >= 0; j-- )
+ {
+ FT_Int index;
+ ED* current;
+
+
+ /* Forward pass of rows (left -> right). Leave the first */
+ /* column, which gets covered in the backward pass. */
+ for ( i = 1; i < w - 1; i++ )
+ {
+ index = j * w + i;
+ current = dm + index;
+
+ /* left-up */
+ compare_neighbor( current, -1, 1, w );
+ /* up */
+ compare_neighbor( current, 0, 1, w );
+ /* up-right */
+ compare_neighbor( current, 1, 1, w );
+ /* left */
+ compare_neighbor( current, -1, 0, w );
+ }
+
+ /* Backward pass of rows (right -> left). Leave the last */
+ /* column, which was already covered in the forward pass. */
+ for ( i = w - 2; i >= 0; i-- )
+ {
+ index = j * w + i;
+ current = dm + index;
+
+ /* right */
+ compare_neighbor( current, 1, 0, w );
+ }
+ }
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * edt8
+ *
+ * @Description:
+ * Compute the distance map of the a bitmap. Execute both first and
+ * second pass of the 8SED algorithm.
+ *
+ * @InOut:
+ * worker::
+ * Contains all the relevant parameters.
+ *
+ * @Return:
+ * FreeType error, 0 means success.
+ *
+ */
+ static FT_Error
+ edt8( BSDF_Worker* worker )
+ {
+ FT_Error error = FT_Err_Ok;
+
+
+ if ( !worker || !worker->distance_map )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* first scan of the image */
+ first_pass( worker );
+
+ /* second scan of the image */
+ second_pass( worker );
+
+ Exit:
+ return error;
+ }
+
+
+ /**************************************************************************
+ *
+ * @Function:
+ * finalize_sdf
+ *
+ * @Description:
+ * Copy the SDF data from `worker->distance_map` to the `target` bitmap.
+ * Also transform the data to output format, (which is 6.10 fixed-point
+ * format at the moment).
+ *
+ * @Input:
+ * worker ::
+ * Contains source distance map and other SDF data.
+ *
+ * @Output:
+ * target ::
+ * Target bitmap to which the SDF data is copied to.
+ *
+ * @Return:
+ * FreeType error, 0 means success.
+ *
+ */
+ static FT_Error
+ finalize_sdf( BSDF_Worker* worker,
+ const FT_Bitmap* target )
+ {
+ FT_Error error = FT_Err_Ok;
+
+ FT_Int w, r;
+ FT_Int i, j;
+
+ FT_SDFFormat* t_buffer;
+ FT_16D16 sp_sq, spread;
+
+
+ if ( !worker || !target )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ w = (int)target->width;
+ r = (int)target->rows;
+ t_buffer = (FT_SDFFormat*)target->buffer;
+
+ if ( w != worker->width ||
+ r != worker->rows )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ spread = (FT_16D16)FT_INT_16D16( worker->params.spread );
+
+#if USE_SQUARED_DISTANCES
+ sp_sq = (FT_16D16)FT_INT_16D16( worker->params.spread *
+ worker->params.spread );
+#else
+ sp_sq = (FT_16D16)FT_INT_16D16( worker->params.spread );
+#endif
+
+ for ( j = 0; j < r; j++ )
+ {
+ for ( i = 0; i < w; i++ )
+ {
+ FT_Int index;
+ FT_16D16 dist;
+ FT_SDFFormat final_dist;
+ FT_Char sign;
+
+
+ index = j * w + i;
+ dist = worker->distance_map[index].dist;
+
+ if ( dist < 0 || dist > sp_sq )
+ dist = sp_sq;
+
+#if USE_SQUARED_DISTANCES
+ dist = square_root( dist );
+#endif
+
+ /* We assume that if the pixel is inside a contour */
+ /* its coverage value must be > 127. */
+ sign = worker->distance_map[index].alpha < 127 ? -1 : 1;
+
+ /* flip the sign according to the property */
+ if ( worker->params.flip_sign )
+ sign = -sign;
+
+ /* concatenate from 16.16 to appropriate format */
+ final_dist = map_fixed_to_sdf( dist * sign, spread );
+
+ t_buffer[index] = final_dist;
+ }
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ /**************************************************************************
+ *
+ * interface functions
+ *
+ */
+
+ /* called when adding a new module through @FT_Add_Module */
+ static FT_Error
+ bsdf_raster_new( void* memory_, /* FT_Memory */
+ FT_Raster* araster_ ) /* BSDF_PRaster* */
+ {
+ FT_Memory memory = (FT_Memory)memory_;
+ BSDF_PRaster* araster = (BSDF_PRaster*)araster_;
+
+ FT_Error error;
+ BSDF_PRaster raster = NULL;
+
+
+ if ( !FT_NEW( raster ) )
+ raster->memory = memory;
+
+ *araster = raster;
+
+ return error;
+ }
+
+
+ /* unused */
+ static void
+ bsdf_raster_reset( FT_Raster raster,
+ unsigned char* pool_base,
+ unsigned long pool_size )
+ {
+ FT_UNUSED( raster );
+ FT_UNUSED( pool_base );
+ FT_UNUSED( pool_size );
+ }
+
+
+ /* unused */
+ static FT_Error
+ bsdf_raster_set_mode( FT_Raster raster,
+ unsigned long mode,
+ void* args )
+ {
+ FT_UNUSED( raster );
+ FT_UNUSED( mode );
+ FT_UNUSED( args );
+
+ return FT_Err_Ok;
+ }
+
+
+ /* called while rendering through @FT_Render_Glyph */
+ static FT_Error
+ bsdf_raster_render( FT_Raster raster,
+ const FT_Raster_Params* params )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_Memory memory = NULL;
+
+ const FT_Bitmap* source = NULL;
+ const FT_Bitmap* target = NULL;
+
+ BSDF_TRaster* bsdf_raster = (BSDF_TRaster*)raster;
+ BSDF_Worker worker;
+
+ const SDF_Raster_Params* sdf_params = (const SDF_Raster_Params*)params;
+
+
+ worker.distance_map = NULL;
+
+ /* check for valid parameters */
+ if ( !raster || !params )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* check whether the flag is set */
+ if ( sdf_params->root.flags != FT_RASTER_FLAG_SDF )
+ {
+ error = FT_THROW( Raster_Corrupted );
+ goto Exit;
+ }
+
+ source = (const FT_Bitmap*)sdf_params->root.source;
+ target = (const FT_Bitmap*)sdf_params->root.target;
+
+ /* check source and target bitmap */
+ if ( !source || !target )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ memory = bsdf_raster->memory;
+ if ( !memory )
+ {
+ FT_TRACE0(( "bsdf_raster_render: Raster not set up properly,\n" ));
+ FT_TRACE0(( " unable to find memory handle.\n" ));
+
+ error = FT_THROW( Invalid_Handle );
+ goto Exit;
+ }
+
+ /* check whether spread is set properly */
+ if ( sdf_params->spread > MAX_SPREAD ||
+ sdf_params->spread < MIN_SPREAD )
+ {
+ FT_TRACE0(( "bsdf_raster_render:"
+ " The `spread' field of `SDF_Raster_Params'\n" ));
+ FT_TRACE0(( " "
+ " is invalid; the value of this field must be\n" ));
+ FT_TRACE0(( " "
+ " within [%d, %d].\n",
+ MIN_SPREAD, MAX_SPREAD ));
+ FT_TRACE0(( " "
+ " Also, you must pass `SDF_Raster_Params'\n" ));
+ FT_TRACE0(( " "
+ " instead of the default `FT_Raster_Params'\n" ));
+ FT_TRACE0(( " "
+ " while calling this function and set the fields\n" ));
+ FT_TRACE0(( " "
+ " accordingly.\n" ));
+
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* set up the worker */
+
+ /* allocate the distance map */
+ if ( FT_QALLOC_MULT( worker.distance_map, target->rows,
+ target->width * sizeof ( *worker.distance_map ) ) )
+ goto Exit;
+
+ worker.width = (int)target->width;
+ worker.rows = (int)target->rows;
+ worker.params = *sdf_params;
+
+ FT_CALL( bsdf_init_distance_map( source, &worker ) );
+ FT_CALL( bsdf_approximate_edge( &worker ) );
+ FT_CALL( edt8( &worker ) );
+ FT_CALL( finalize_sdf( &worker, target ) );
+
+ FT_TRACE0(( "bsdf_raster_render: Total memory used = %ld\n",
+ worker.width * worker.rows *
+ (long)sizeof ( *worker.distance_map ) ));
+
+ Exit:
+ if ( worker.distance_map )
+ FT_FREE( worker.distance_map );
+
+ return error;
+ }
+
+
+ /* called while deleting `FT_Library` only if the module is added */
+ static void
+ bsdf_raster_done( FT_Raster raster )
+ {
+ FT_Memory memory = (FT_Memory)((BSDF_TRaster*)raster)->memory;
+
+
+ FT_FREE( raster );
+ }
+
+
+ FT_DEFINE_RASTER_FUNCS(
+ ft_bitmap_sdf_raster,
+
+ FT_GLYPH_FORMAT_BITMAP,
+
+ (FT_Raster_New_Func) bsdf_raster_new, /* raster_new */
+ (FT_Raster_Reset_Func) bsdf_raster_reset, /* raster_reset */
+ (FT_Raster_Set_Mode_Func)bsdf_raster_set_mode, /* raster_set_mode */
+ (FT_Raster_Render_Func) bsdf_raster_render, /* raster_render */
+ (FT_Raster_Done_Func) bsdf_raster_done /* raster_done */
+ )
+
+
+/* END */