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[sdf] Add functions to compute pixel edge distances.

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* src/sdf/ftbsdf.c (compute_edge_distance, bsdf_approximate_edge):
New functions.
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Anuj Verma 2020-08-20 09:25:15 +05:30 committed by Werner Lemberg
parent c576176461
commit 0f644f38e9
2 changed files with 262 additions and 1 deletions
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ChangeLog
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@ -1,3 +1,10 @@
2020-08-20 Anuj Verma <anujv@iitbhilai.ac.in>
[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 <anujv@iitbhilai.ac.in>
[sdf] Add function to find edge pixels in a grid of alpha values.

256
src/sdf/ftbsdf.c
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@ -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 */