diff --git a/ChangeLog b/ChangeLog index 86a63086b..950d7d5d2 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,10 @@ +2020-08-20 Anuj Verma + + [sdf] Add functions to compute pixel edge distances. + + * src/sdf/ftbsdf.c (compute_edge_distance, bsdf_approximate_edge): + New functions. + 2020-08-20 Anuj Verma [sdf] Add function to find edge pixels in a grid of alpha values. diff --git a/src/sdf/ftbsdf.c b/src/sdf/ftbsdf.c index 2229354ef..9dc6953b7 100644 --- a/src/sdf/ftbsdf.c +++ b/src/sdf/ftbsdf.c @@ -192,7 +192,7 @@ FT_Int w, /* width */ FT_Int r ) /* rows */ { - FT_Bool is_edge = 0; + FT_Bool is_edge = 0; ED* to_check = NULL; FT_Int num_neighbors = 0; @@ -240,4 +240,258 @@ #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].near = compute_edge_distance( ed + index, + i, j, + worker->width, + worker->rows ); + ed[index].dist = VECTOR_LENGTH_16D16( ed[index].near ); + } + else + { + /* for non-edge pixels assign far away distances */ + ed[index].dist = 400 * ONE; + ed[index].near.x = 200 * ONE; + ed[index].near.y = 200 * ONE; + } + } + } + + Exit: + return error; + } + /* END */