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freetype2/src/sdf/ftsdf.c

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#include <freetype/internal/ftobjs.h>
#include <freetype/internal/ftdebug.h>
#include <freetype/ftlist.h>
#include <freetype/fttrigon.h>
#include "ftsdf.h"
#include "ftsdferrs.h"
/**************************************************************************
*
* macros
*
*/
#define FT_INT_26D6( x ) ( x * 64 ) /* convert int to 26.6 fixed point */
#define FT_INT_16D16( x ) ( x * 65536 ) /* convert int to 16.16 fixed point */
#define FT_26D6_16D16( x ) ( x * 1024 ) /* convert 26.6 to 16.16 fixed point */
/* Convenient macro which calls the function */
/* and returns if any error occurs. */
#define FT_CALL( x ) do \
{ \
error = ( x ); \
if ( error != FT_Err_Ok ) \
goto Exit; \
} while ( 0 )
#define MUL_26D6( a, b ) ( ( a * b ) / 64 )
#define VEC_26D6_DOT( p, q ) ( MUL_26D6( p.x, q.x ) + \
MUL_26D6( p.y, q.y ) )
/**************************************************************************
*
* typedefs
*
*/
typedef FT_Vector FT_26D6_Vec; /* with 26.6 fixed point components */
typedef FT_Vector FT_16D16_Vec; /* with 16.16 fixed point components */
typedef FT_Fixed FT_16D16; /* 16.16 fixed point representation */
typedef FT_Fixed FT_26D6; /* 26.6 fixed point representation */
/**************************************************************************
*
* structures and enums
*
*/
typedef struct SDF_TRaster_
{
FT_Memory memory; /* used internally to allocate memory */
} SDF_TRaster;
/* enumeration of all the types of curve present in vector fonts */
typedef enum SDF_Edge_Type_
{
SDF_EDGE_UNDEFINED = 0, /* undefined, used to initialize */
SDF_EDGE_LINE = 1, /* straight line segment */
SDF_EDGE_CONIC = 2, /* second order bezier curve */
SDF_EDGE_CUBIC = 3 /* third order bezier curve */
} SDF_Edge_Type;
/* represent a single edge in a contour */
typedef struct SDF_Edge_
{
FT_26D6_Vec start_pos; /* start position of the edge */
FT_26D6_Vec end_pos; /* end position of the edge */
FT_26D6_Vec control_a; /* first control point of a bezier curve */
FT_26D6_Vec control_b; /* second control point of a bezier curve */
SDF_Edge_Type edge_type; /* edge identifier */
} SDF_Edge;
/* A contour represent a set of edges which make a closed */
/* loop. */
typedef struct SDF_Contour_
{
FT_26D6_Vec last_pos; /* end position of the last edge */
FT_ListRec edges; /* list of all edges in the contour */
} SDF_Contour;
/* Represent a set a contours which makes up a complete */
/* glyph outline. */
typedef struct SDF_Shape_
{
FT_Memory memory; /* used internally to allocate memory */
FT_ListRec contours; /* list of all contours in the outline */
} SDF_Shape;
typedef struct SDF_Signed_Distance_
{
/* Nearest point the outline to a given point. */
/* [note]: This is not a *direction* vector, this */
/* simply a *point* vector on the grid. */
FT_16D16_Vec nearest_point;
/* The normalized direction of the curve at the */
/* above point. */
/* [note]: This is a *direction* vector. */
FT_16D16_Vec direction;
/* Unsigned shortest squared distance from the */
/* point to the above `nearest_point'. */
FT_16D16 squared_distance;
/* Represent weather the `nearest_point' is outside */
/* or inside the contour corresponding to the edge. */
/* [note]: This sign may or may not be correct, */
/* therefore it must be checked properly in */
/* case there is an ambiguity. */
FT_Char sign;
} SDF_Signed_Distance;
/**************************************************************************
*
* constants, initializer and destructor
*
*/
static
const FT_Vector zero_vector = { 0, 0 };
static
const SDF_Edge null_edge = { { 0, 0 }, { 0, 0 },
{ 0, 0 }, { 0, 0 },
SDF_EDGE_UNDEFINED };
static
const SDF_Contour null_contour = { { 0, 0 }, { NULL, NULL } };
static
const SDF_Shape null_shape = { NULL, { NULL, NULL } };
static
const SDF_Signed_Distance max_sdf = { { 0, 0 }, { 0, 0 },
INT_MAX, 0 };
/* Creates a new `SDF_Edge' on the heap and assigns the `edge' */
/* pointer to the newly allocated memory. */
static FT_Error
sdf_edge_new( FT_Memory memory,
SDF_Edge** edge )
{
FT_Error error = FT_Err_Ok;
SDF_Edge* ptr = NULL;
if ( !memory || !edge )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( !FT_QNEW( ptr ) )
{
*ptr = null_edge;
*edge = ptr;
}
Exit:
return error;
}
/* Frees the allocated `edge' variable. */
static void
sdf_edge_done( FT_Memory memory,
SDF_Edge** edge )
{
if ( !memory || !edge || !*edge )
return;
FT_FREE( *edge );
}
/* Used in `FT_List_Finalize'. */
static void
sdf_edge_destructor( FT_Memory memory,
void* data,
void* user )
{
SDF_Edge* edge = (SDF_Edge*)data;
sdf_edge_done( memory, &edge );
}
/* Creates a new `SDF_Contour' on the heap and assigns */
/* the `contour' pointer to the newly allocated memory. */
static FT_Error
sdf_contour_new( FT_Memory memory,
SDF_Contour** contour )
{
FT_Error error = FT_Err_Ok;
SDF_Contour* ptr = NULL;
if ( !memory || !contour )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( !FT_QNEW( ptr ) )
{
*ptr = null_contour;
*contour = ptr;
}
Exit:
return error;
}
/* Frees the allocated `contour' variable and also frees */
/* the list of edges. */
static void
sdf_contour_done( FT_Memory memory,
SDF_Contour** contour )
{
if ( !memory || !contour || !*contour )
return;
/* */
FT_List_Finalize( &(*contour)->edges, sdf_edge_destructor,
memory, NULL );
FT_FREE( *contour );
}
/* Used in `FT_List_Finalize'. */
static void
sdf_contour_destructor( FT_Memory memory,
void* data,
void* user )
{
SDF_Contour* contour = (SDF_Contour*)data;
sdf_contour_done( memory, &contour );
}
/* Creates a new `SDF_Shape' on the heap and assigns */
/* the `shape' pointer to the newly allocated memory. */
static FT_Error
sdf_shape_new( FT_Memory memory,
SDF_Shape** shape )
{
FT_Error error = FT_Err_Ok;
SDF_Shape* ptr = NULL;
if ( !memory || !shape )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( !FT_QNEW( ptr ) )
{
*ptr = null_shape;
ptr->memory = memory;
*shape = ptr;
}
Exit:
return error;
}
/* Frees the allocated `shape' variable and also frees */
/* the list of contours. */
static void
sdf_shape_done( FT_Memory memory,
SDF_Shape** shape )
{
if ( !memory || !shape || !*shape )
return;
/* release the list of contours */
FT_List_Finalize( &(*shape)->contours, sdf_contour_destructor,
memory, NULL );
/* release the allocated shape struct */
FT_FREE( *shape );
}
/**************************************************************************
*
* shape decomposition functions
*
*/
/* This function is called when walking along a new contour */
/* so add a new contour to the shape's list. */
static FT_Error
sdf_move_to( const FT_26D6_Vec* to,
void* user )
{
SDF_Shape* shape = ( SDF_Shape* )user;
SDF_Contour* contour = NULL;
FT_ListNode node = NULL;
FT_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
error = sdf_contour_new( memory, &contour );
if ( error != FT_Err_Ok )
goto Exit;
if ( FT_QNEW( node ) )
goto Exit;
contour->last_pos = *to;
node->data = contour;
FT_List_Add( &shape->contours, node );
Exit:
return error;
}
static FT_Error
sdf_line_to( const FT_26D6_Vec* to,
void* user )
{
SDF_Shape* shape = ( SDF_Shape* )user;
SDF_Edge* edge = NULL;
SDF_Contour* contour = NULL;
FT_ListNode node = NULL;
FT_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contour = ( SDF_Contour* )shape->contours.tail->data;
if ( contour->last_pos.x == to->x &&
contour->last_pos.y == to->y )
goto Exit;
error = sdf_edge_new( memory, &edge );
if ( error != FT_Err_Ok )
goto Exit;
if ( FT_QNEW( node ) )
goto Exit;
edge->edge_type = SDF_EDGE_LINE;
edge->start_pos = contour->last_pos;
edge->end_pos = *to;
contour->last_pos = *to;
node->data = edge;
FT_List_Add( &contour->edges, node );
Exit:
return error;
}
static FT_Error
sdf_conic_to( const FT_26D6_Vec* control_1,
const FT_26D6_Vec* to,
void* user )
{
SDF_Shape* shape = ( SDF_Shape* )user;
SDF_Edge* edge = NULL;
SDF_Contour* contour = NULL;
FT_ListNode node = NULL;
FT_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !control_1 || !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contour = ( SDF_Contour* )shape->contours.tail->data;
error = sdf_edge_new( memory, &edge );
if ( error != FT_Err_Ok )
goto Exit;
if ( FT_QNEW( node ) )
goto Exit;
edge->edge_type = SDF_EDGE_CONIC;
edge->start_pos = contour->last_pos;
edge->control_a = *control_1;
edge->end_pos = *to;
contour->last_pos = *to;
node->data = edge;
FT_List_Add( &contour->edges, node );
Exit:
return error;
}
static FT_Error
sdf_cubic_to( const FT_26D6_Vec* control_1,
const FT_26D6_Vec* control_2,
const FT_26D6_Vec* to,
void* user )
{
SDF_Shape* shape = ( SDF_Shape* )user;
SDF_Edge* edge = NULL;
SDF_Contour* contour = NULL;
FT_ListNode node = NULL;
FT_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !control_2 || !control_1 || !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contour = ( SDF_Contour* )shape->contours.tail->data;
error = sdf_edge_new( memory, &edge );
if ( error != FT_Err_Ok )
goto Exit;
if ( FT_QNEW( node ) )
goto Exit;
edge->edge_type = SDF_EDGE_CUBIC;
edge->start_pos = contour->last_pos;
edge->control_a = *control_1;
edge->control_b = *control_2;
edge->end_pos = *to;
contour->last_pos = *to;
node->data = edge;
FT_List_Add( &contour->edges, node );
Exit:
return error;
}
FT_DEFINE_OUTLINE_FUNCS(
sdf_decompose_funcs,
(FT_Outline_MoveTo_Func) sdf_move_to, /* move_to */
(FT_Outline_LineTo_Func) sdf_line_to, /* line_to */
(FT_Outline_ConicTo_Func) sdf_conic_to, /* conic_to */
(FT_Outline_CubicTo_Func) sdf_cubic_to, /* cubic_to */
0, /* shift */
0 /* delta */
)
/* function decomposes the outline and puts it into the `shape' struct */
static FT_Error
sdf_outline_decompose( FT_Outline* outline,
SDF_Shape* shape )
{
FT_Error error = FT_Err_Ok;
if ( !outline || !shape )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
error = FT_Outline_Decompose( outline, &sdf_decompose_funcs, (void*)shape );
Exit:
return error;
}
/**************************************************************************
*
* for debugging
*
*/
#ifdef FT_DEBUG_LEVEL_TRACE
static void
sdf_shape_dump( SDF_Shape* shape )
{
FT_UInt num_contours = 0;
FT_UInt total_edges = 0;
FT_ListRec contour_list;
if ( !shape )
{
FT_TRACE5(( "[sdf] sdf_shape_dump: null shape\n" ));
return;
}
contour_list = shape->contours;
FT_TRACE5(( "-------------------------------------------------\n" ));
FT_TRACE5(( "[sdf] sdf_shape_dump:\n" ));
while ( contour_list.head != NULL )
{
FT_UInt num_edges = 0;
FT_ListRec edge_list;
SDF_Contour* contour = (SDF_Contour*)contour_list.head->data;
edge_list = contour->edges;
FT_TRACE5(( "Contour %d\n", num_contours ));
while ( edge_list.head != NULL )
{
SDF_Edge* edge = (SDF_Edge*)edge_list.head->data;
FT_TRACE5(( " Edge %d\n", num_edges ));
switch (edge->edge_type) {
case SDF_EDGE_LINE:
FT_TRACE5(( " Edge Type: Line\n" ));
FT_TRACE5(( " ---------------\n" ));
FT_TRACE5(( " Start Pos: %d, %d\n", edge->start_pos.x,
edge->start_pos.y ));
FT_TRACE5(( " End Pos : %d, %d\n", edge->end_pos.x,
edge->end_pos.y ));
break;
case SDF_EDGE_CONIC:
FT_TRACE5(( " Edge Type: Conic Bezier\n" ));
FT_TRACE5(( " -----------------------\n" ));
FT_TRACE5(( " Start Pos: %d, %d\n", edge->start_pos.x,
edge->start_pos.y ));
FT_TRACE5(( " Ctrl1 Pos: %d, %d\n", edge->control_a.x,
edge->control_a.y ));
FT_TRACE5(( " End Pos : %d, %d\n", edge->end_pos.x,
edge->end_pos.y ));
break;
case SDF_EDGE_CUBIC:
FT_TRACE5(( " Edge Type: Cubic Bezier\n" ));
FT_TRACE5(( " -----------------------\n" ));
FT_TRACE5(( " Start Pos: %d, %d\n", edge->start_pos.x,
edge->start_pos.y ));
FT_TRACE5(( " Ctrl1 Pos: %d, %d\n", edge->control_a.x,
edge->control_a.y ));
FT_TRACE5(( " Ctrl2 Pos: %d, %d\n", edge->control_b.x,
edge->control_b.y ));
FT_TRACE5(( " End Pos : %d, %d\n", edge->end_pos.x,
edge->end_pos.y ));
break;
default:
break;
}
num_edges++;
total_edges++;
edge_list.head = edge_list.head->next;
}
num_contours++;
contour_list.head = contour_list.head->next;
}
FT_TRACE5(( "\n" ));
FT_TRACE5(( "*note: the above values are in 26.6 fixed point format*\n" ));
FT_TRACE5(( "total number of contours = %d\n", num_contours ));
FT_TRACE5(( "total number of edges = %d\n", total_edges ));
FT_TRACE5(( "[sdf] sdf_shape_dump complete\n" ));
FT_TRACE5(( "-------------------------------------------------\n" ));
}
#endif
/**************************************************************************
*
* math functions
*
*/
/* Original Algorithm: https://github.com/chmike/fpsqrt */
static FT_16D16
square_root( FT_16D16 val )
{
FT_ULong t, q, b, r;
r = val;
b = 0x40000000;
q = 0;
while( b > 0x40 )
{
t = q + b;
if( r >= t )
{
r -= t;
q = t + b;
}
r <<= 1;
b >>= 1;
}
q >>= 8;
return q;
}
/* [NOTE]: All the functions below down until rasterizer */
/* can be avoided if we decide to subdivide the */
/* curve into lines. */
/* This function uses newton's iteration to find */
/* cube root of a fixed point integer. */
static FT_16D16
cube_root( FT_16D16 val )
{
/* [IMPORTANT]: This function is not good as it may */
/* not break, so use a lookup table instead. Or we */
/* can use algorithm similar to `square_root'. */
FT_Int v, g, c;
if ( val == 0 ||
val == -FT_INT_16D16( 1 ) ||
val == FT_INT_16D16( 1 ) )
return val;
v = val < 0 ? -val : val;
g = square_root( v );
c = 0;
while ( 1 )
{
c = FT_MulFix( FT_MulFix( g, g ), g ) - v;
c = FT_DivFix( c, 3 * FT_MulFix( g, g ) );
g -= c;
if ( ( c < 0 ? -c : c ) < 30 )
break;
}
return val < 0 ? -g : g;
}
/* The function calculate the perpendicular */
/* using 1 - ( base ^ 2 ) and then use arc */
/* tan to compute the angle. */
static FT_16D16
arc_cos( FT_16D16 val )
{
FT_16D16 p, b = val;
FT_16D16 one = FT_INT_16D16( 1 );
if ( b > one ) b = one;
if ( b < -one ) b = -one;
p = one - FT_MulFix( b, b );
p = square_root( p );
return FT_Atan2( b, p );
}
/* The function compute the roots of a quadratic */
/* polynomial, assigns it to `out' and returns the */
/* number of real roots of the equation. */
/* The procedure can be found at: */
/* https://mathworld.wolfram.com/QuadraticFormula.html */
static FT_UShort
solve_quadratic_equation( FT_26D6 a,
FT_26D6 b,
FT_26D6 c,
FT_16D16 out[2] )
{
FT_16D16 discriminant = 0;
a = FT_26D6_16D16( a );
b = FT_26D6_16D16( b );
c = FT_26D6_16D16( c );
if ( a == 0 )
{
if ( b == 0 )
return 0;
else
{
out[0] = FT_DivFix( -c, b );
return 1;
}
}
discriminant = FT_MulFix( b, b ) - 4 * FT_MulFix( a, c );
if ( discriminant < 0 )
return 0;
else if ( discriminant == 0 )
{
out[0] = FT_DivFix( -b, 2 * a );
return 1;
}
else
{
discriminant = square_root( discriminant );
out[0] = FT_DivFix( -b + discriminant, 2 * a );
out[1] = FT_DivFix( -b - discriminant, 2 * a );
return 2;
}
}
/* The function compute the roots of a cubic polynomial */
/* assigns it to `out' and returns the number of real */
/* roots of the equation. */
/* The procedure can be found at: */
/* https://mathworld.wolfram.com/CubicFormula.html */
static FT_UShort
solve_cubic_equation( FT_26D6 a,
FT_26D6 b,
FT_26D6 c,
FT_26D6 d,
FT_16D16 out[3] )
{
FT_16D16 q = 0; /* intermediate */
FT_16D16 r = 0; /* intermediate */
FT_16D16 a2 = b; /* x^2 coefficients */
FT_16D16 a1 = c; /* x coefficients */
FT_16D16 a0 = d; /* constant */
FT_16D16 q3 = 0;
FT_16D16 r2 = 0;
FT_16D16 a23 = 0;
FT_16D16 a22 = 0;
FT_16D16 a1x2 = 0;
/* cutoff value for `a' to be a cubic otherwise solve quadratic*/
if ( a == 0 || FT_ABS( a ) < 16 )
return solve_quadratic_equation( b, c, d, out );
if ( d == 0 )
{
out[0] = 0;
return solve_quadratic_equation( a, b, c, out + 1 ) + 1;
}
/* normalize the coefficients, this also makes them 16.16 */
a2 = FT_DivFix( a2, a );
a1 = FT_DivFix( a1, a );
a0 = FT_DivFix( a0, a );
/* compute intermediates */
a1x2 = FT_MulFix( a1, a2 );
a22 = FT_MulFix( a2, a2 );
a23 = FT_MulFix( a22, a2 );
q = ( 3 * a1 - a22 ) / 9;
r = ( 9 * a1x2 - 27 * a0 - 2 * a23 ) / 54;
/* [BUG]: `q3' and `r2' still causes underflow. */
q3 = FT_MulFix( q, q );
q3 = FT_MulFix( q3, q );
r2 = FT_MulFix( r, r );
if ( q3 < 0 && r2 < -q3 )
{
FT_16D16 t = 0;
q3 = square_root( -q3 );
t = FT_DivFix( r, q3 );
if ( t > ( 1 << 16 ) ) t = ( 1 << 16 );
if ( t < -( 1 << 16 ) ) t = -( 1 << 16 );
t = arc_cos( t );
a2 /= 3;
q = 2 * square_root( -q );
out[0] = FT_MulFix( q, FT_Cos( t / 3 ) ) - a2;
out[1] = FT_MulFix( q, FT_Cos( ( t + FT_ANGLE_PI * 2 ) / 3 ) ) - a2;
out[2] = FT_MulFix( q, FT_Cos( ( t + FT_ANGLE_PI * 4 ) / 3 ) ) - a2;
return 3;
}
else if ( r2 == -q3 )
{
FT_16D16 s = 0;
s = cube_root( r );
a2 /= -3;
out[0] = a2 + ( 2 * s );
out[1] = a2 - s;
return 2;
}
else
{
FT_16D16 s = 0;
FT_16D16 t = 0;
FT_16D16 dis = 0;
if ( q3 == 0 )
dis = FT_ABS( r );
else
dis = square_root( q3 + r2 );
s = cube_root( r + dis );
t = cube_root( r - dis );
a2 /= -3;
out[0] = ( a2 + ( s + t ) );
return 1;
}
}
/*************************************************************************/
/*************************************************************************/
/** **/
/** RASTERIZER **/
/** **/
/*************************************************************************/
/*************************************************************************/
/**************************************************************************
*
* @Function:
* resolve_corner
*
* @Description:
* At some places on the grid two edges can give opposite direction
* this happens when the closes point is on of the endpoint, in that
* case we need to check the proper sign.
*
* This can be visualized by an example:
*
* x
*
* o
* ^ \
* / \
* / \
* (a) / \ (b)
* / \
* / \
* / v
*
* Suppose `x' is the point whose shortest distance from an arbitrary
* contour we want to find out. It is clear that `o' is the nearest
* point on the contour. Now to determine the sign we do a cross
* product of shortest distance vector and the edge direction. i.e.
*
* => sign = cross( ( x - o ), direction( a ) )
*
* From right hand thumb rule we can see that the sign will be positive
* and if check for `b'.
*
* => sign = cross( ( x - o ), direction( b ) )
*
* In this case the sign will be negative. So, to determine the correct
* sign we divide the plane in half and check in which plane the point
* lies.
*
* Divide:
*
* |
* x |
* |
* o
* ^|\
* / | \
* / | \
* (a) / | \ (b)
* / | \
* / \
* / v
*
* We can see that `x' lies in the plane of `a', so we take the sign
* determined by `a'. This can be easily done by calculating the
* orthogonality and taking the greater one.
*
* @Input:
* [TODO]
*
* @Return:
* [TODO]
*/
static SDF_Signed_Distance
resolve_corner( SDF_Signed_Distance sdf1,
SDF_Signed_Distance sdf2,
FT_26D6_Vec point )
{
FT_16D16_Vec dist;
FT_16D16 ortho1;
FT_16D16 ortho2;
/* if they are not equal return the shorter */
if ( sdf1.squared_distance != sdf2.squared_distance )
return sdf1.squared_distance < sdf2.squared_distance ?
sdf1 : sdf2;
/* if there is not ambiguity in the sign return any */
if ( sdf1.sign == sdf2.sign )
return sdf1;
/* final check: Make sure nearest point is same. If not */
/* then return any, it is not the shortest distance. */
if ( sdf1.nearest_point.x != sdf2.nearest_point.x ||
sdf1.nearest_point.y != sdf2.nearest_point.y )
return sdf1;
/* calculate the distance vectors, will be same for both */
dist.x = sdf1.nearest_point.x - FT_26D6_16D16( point.x );
dist.y = sdf1.nearest_point.y - FT_26D6_16D16( point.y );
FT_Vector_NormLen( &dist );
/* use cross product to find orthogonality */
ortho1 = FT_MulFix( sdf1.direction.x, dist.y ) -
FT_MulFix( sdf1.direction.y, dist.x );
ortho1 = FT_ABS( ortho1 );
ortho2 = FT_MulFix( sdf2.direction.x, dist.y ) -
FT_MulFix( sdf2.direction.y, dist.x );
ortho2 = FT_ABS( ortho2 );
return ortho1 > ortho2 ? sdf1 : sdf2;
}
/**************************************************************************
*
* @Function:
* get_min_distance_line
*
* @Description:
* This function find the shortest distance from the `line' to
* a given `point' and assigns it to `out'. Only use it for line
* segments.
*
* @Input:
* [TODO]
*
* @Return:
* [TODO]
*/
static FT_Error
get_min_distance_line( SDF_Edge* line,
FT_26D6_Vec point,
SDF_Signed_Distance* out )
{
/* in order to calculate the shortest distance from a point to */
/* a line segment. */
/* */
/* a = start point of the line segment */
/* b = end point of the line segment */
/* p = point from which shortest distance is to be calculated */
/* ----------------------------------------------------------- */
/* => we first write the parametric equation of the line */
/* point_on_line = a + ( b - a ) * t ( t is the factor ) */
/* */
/* => next we find the projection of point p on the line. the */
/* projection will be perpendicular to the line, that is */
/* why we can find it by making the dot product zero. */
/* ( point_on_line - a ) . ( p - point_on_line ) = 0 */
/* */
/* ( point_on_line ) */
/* ( a ) x-------o----------------x ( b ) */
/* |_| */
/* | */
/* | */
/* ( p ) */
/* */
/* => by simplifying the above equation we get the factor of */
/* point_on_line such that */
/* t = ( ( p - a ) . ( b - a ) ) / ( |b - a| ^ 2 ) */
/* */
/* => we clamp the factor t between [0.0f, 1.0f], because the */
/* point_on_line can be outside the line segment. */
/* */
/* ( point_on_line ) */
/* ( a ) x------------------------x ( b ) -----o--- */
/* |_| */
/* | */
/* | */
/* ( p ) */
/* */
/* => finally the distance becomes | point_on_line - p | */
FT_Error error = FT_Err_Ok;
FT_Vector a; /* start position */
FT_Vector b; /* end position */
FT_Vector p; /* current point */
FT_26D6_Vec line_segment; /* `b' - `a'*/
FT_26D6_Vec p_sub_a; /* `p' - `a' */
FT_26D6 sq_line_length; /* squared length of `line_segment' */
FT_16D16 factor; /* factor of the nearest point */
FT_26D6 cross; /* used to determine sign */
FT_16D16_Vec nearest_point; /* `point_on_line' */
FT_16D16_Vec nearest_vector; /* `p' - `nearest_point' */
if ( !line || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( line->edge_type != SDF_EDGE_LINE )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
a = line->start_pos;
b = line->end_pos;
p = point;
line_segment.x = b.x - a.x;
line_segment.y = b.y - a.y;
p_sub_a.x = p.x - a.x;
p_sub_a.y = p.y - a.y;
sq_line_length = ( line_segment.x * line_segment.x ) / 64 +
( line_segment.y * line_segment.y ) / 64;
/* currently factor is 26.6 */
factor = ( p_sub_a.x * line_segment.x ) / 64 +
( p_sub_a.y * line_segment.y ) / 64;
/* now factor is 16.16 */
factor = FT_DivFix( factor, sq_line_length );
/* clamp the factor between 0.0 and 1.0 in fixed point */
if ( factor > FT_INT_16D16( 1 ) )
factor = FT_INT_16D16( 1 );
if ( factor < 0 )
factor = 0;
nearest_point.x = FT_MulFix( FT_26D6_16D16(line_segment.x),
factor );
nearest_point.y = FT_MulFix( FT_26D6_16D16(line_segment.y),
factor );
nearest_point.x = FT_26D6_16D16( a.x ) + nearest_point.x;
nearest_point.y = FT_26D6_16D16( a.y ) + nearest_point.y;
nearest_vector.x = nearest_point.x - FT_26D6_16D16( p.x );
nearest_vector.y = nearest_point.y - FT_26D6_16D16( p.y );
cross = FT_MulFix( nearest_vector.x, line_segment.y ) -
FT_MulFix( nearest_vector.y, line_segment.x );
/* [OPTIMIZATION]: Pre-compute this direction. */
FT_Vector_NormLen( &line_segment );
/* assign the output */
out->nearest_point = nearest_point;
out->sign = cross < 0 ? 1 : -1;
out->squared_distance = FT_MulFix( nearest_vector.x, nearest_vector.x ) +
FT_MulFix( nearest_vector.y, nearest_vector.y );
out->direction = line_segment;
Exit:
return error;
}
/**************************************************************************
*
* @Function:
* get_min_distance_conic
*
* @Description:
* This function find the shortest distance from the `conic' bezier
* curve to a given `point' and assigns it to `out'. Only use it for
* conic/quadratic curves.
*
* @Input:
* [TODO]
*
* @Return:
* [TODO]
*/
static FT_Error
get_min_distance_conic( SDF_Edge* conic,
FT_26D6_Vec point,
SDF_Signed_Distance* out )
{
/* The procedure to find the shortest distance from a point to */
/* a quadratic bezier curve is similar to a line segment. the */
/* shortest distance will be perpendicular to the bezier curve */
/* The only difference from line is that there can be more */
/* than one perpendicular and we also have to check the endpo- */
/* -ints, because the perpendicular may not be the shortest. */
/* */
/* p0 = first endpoint */
/* p1 = control point */
/* p2 = second endpoint */
/* p = point from which shortest distance is to be calculated */
/* ----------------------------------------------------------- */
/* => the equation of a quadratic bezier curve can be written */
/* B( t ) = ( ( 1 - t )^2 )p0 + 2( 1 - t )tp1 + t^2p2 */
/* here t is the factor with range [0.0f, 1.0f] */
/* the above equation can be rewritten as */
/* B( t ) = t^2( p0 - 2p1 + p2 ) + 2t( p1 - p0 ) + p0 */
/* */
/* now let A = ( p0 - 2p1 + p2), B = ( p1 - p0 ) */
/* B( t ) = t^2( A ) + 2t( B ) + p0 */
/* */
/* => the derivative of the above equation is written as */
/* B`( t ) = 2( tA + B ) */
/* */
/* => now to find the shortest distance from p to B( t ), we */
/* find the point on the curve at which the shortest */
/* distance vector ( i.e. B( t ) - p ) and the direction */
/* ( i.e. B`( t )) makes 90 degrees. in other words we make */
/* the dot product zero. */
/* ( B( t ) - p ).( B`( t ) ) = 0 */
/* ( t^2( A ) + 2t( B ) + p0 - p ).( 2( tA + B ) ) = 0 */
/* */
/* after simplifying we get a cubic equation as */
/* at^3 + bt^2 + ct + d = 0 */
/* a = ( A.A ), b = ( 3A.B ), c = ( 2B.B + A.p0 - A.p ) */
/* d = ( p0.B - p.B ) */
/* */
/* => now the roots of the equation can be computed using the */
/* `Cardano's Cubic formula' we clamp the roots in range */
/* [0.0f, 1.0f]. */
/* */
/* [note]: B and B( t ) are different in the above equations */
FT_Error error = FT_Err_Ok;
FT_26D6_Vec aA, bB; /* A, B in the above comment */
FT_26D6_Vec nearest_point; /* point on curve nearest to `point' */
FT_26D6_Vec direction; /* direction of curve at `nearest_point' */
FT_26D6_Vec p0, p1, p2; /* control points of a conic curve */
FT_26D6_Vec p; /* `point' to which shortest distance */
FT_26D6 a, b, c, d; /* cubic coefficients */
FT_16D16 roots[3] = { 0, 0, 0 }; /* real roots of the cubic eq */
FT_16D16 min_factor; /* factor at `nearest_point' */
FT_16D16 cross; /* to determin the sign */
FT_16D16 min = FT_INT_MAX; /* shortest squared distance */
FT_UShort num_roots; /* number of real roots of cubic */
FT_UShort i;
if ( !conic || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( conic->edge_type != SDF_EDGE_CONIC )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
/* assign the values after checking pointer */
p0 = conic->start_pos;
p1 = conic->control_a;
p2 = conic->end_pos;
p = point;
/* compute substitution coefficients */
aA.x = p0.x - 2 * p1.x + p2.x;
aA.y = p0.y - 2 * p1.y + p2.y;
bB.x = p1.x - p0.x;
bB.y = p1.y - p0.y;
/* compute cubic coefficients */
a = VEC_26D6_DOT( aA, aA );
b = 3 * VEC_26D6_DOT( aA, bB );
c = 2 * VEC_26D6_DOT( bB, bB ) +
VEC_26D6_DOT( aA, p0 ) -
VEC_26D6_DOT( aA, p );
d = VEC_26D6_DOT( p0, bB ) -
VEC_26D6_DOT( p, bB );
/* find the roots */
num_roots = solve_cubic_equation( a, b, c, d, roots );
/* convert these values to 16.16 for further computation */
aA.x = FT_26D6_16D16( aA.x );
aA.y = FT_26D6_16D16( aA.y );
bB.x = FT_26D6_16D16( bB.x );
bB.y = FT_26D6_16D16( bB.y );
p0.x = FT_26D6_16D16( p0.x );
p0.y = FT_26D6_16D16( p0.y );
p.x = FT_26D6_16D16( p.x );
p.y = FT_26D6_16D16( p.y );
for ( i = 0; i < num_roots; i++ )
{
FT_16D16 t = roots[i];
FT_16D16 t2 = 0;
FT_16D16 dist = 0;
FT_16D16_Vec curve_point;
FT_16D16_Vec dist_vector;
/* check this: https://lists.nongnu.org/archive/html/freetype-devel/2020-06/msg00147.html */
/* to see why we clamp the values and not check the endpoints */
if ( t < 0 )
t = 0;
if ( t > FT_INT_16D16( 1 ) )
t = FT_INT_16D16( 1 );
t2 = FT_MulFix( t, t );
/* B( t ) = t^2( A ) + 2t( B ) + p0 - p */
curve_point.x = FT_MulFix( aA.x, t2 ) +
2 * FT_MulFix( bB.x, t ) + p0.x;
curve_point.y = FT_MulFix( aA.y, t2 ) +
2 * FT_MulFix( bB.y, t ) + p0.y;
/* `curve_point' - `p' */
dist_vector.x = curve_point.x - p.x;
dist_vector.y = curve_point.y - p.y;
dist = FT_MulFix( dist_vector.x, dist_vector.x ) +
FT_MulFix( dist_vector.y, dist_vector.y );
if ( dist < min )
{
min = dist;
nearest_point = curve_point;
min_factor = t;
}
}
/* B`( t ) = 2( tA + B ) */
direction.x = 2 * FT_MulFix( aA.x, min_factor ) + 2 * bB.x;
direction.y = 2 * FT_MulFix( aA.y, min_factor ) + 2 * bB.y;
/* determine the sign */
cross = FT_MulFix( nearest_point.x - p.x, direction.y ) -
FT_MulFix( nearest_point.y - p.y, direction.x );
/* assign the values */
out->squared_distance = min;
out->nearest_point = nearest_point;
out->sign = cross < 0 ? 1 : -1;
FT_Vector_NormLen( &direction );
out->direction = direction;
Exit:
return error;
}
/**************************************************************************
*
* @Function:
* sdf_edge_get_min_distance
*
* @Description:
* This function find the shortest distance from the `edge' to
* a given `point' and assigns it to `out'.
*
* @Input:
* [TODO]
*
* @Return:
* [TODO]
*/
static FT_Error
sdf_edge_get_min_distance( SDF_Edge* edge,
FT_26D6_Vec point,
SDF_Signed_Distance* out)
{
FT_Error error = FT_Err_Ok;
if ( !edge || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
/* edge specific distance calculation */
switch ( edge->edge_type ) {
case SDF_EDGE_LINE:
get_min_distance_line( edge, point, out );
break;
case SDF_EDGE_CONIC:
get_min_distance_conic( edge, point, out );
break;
case SDF_EDGE_CUBIC:
default:
error = FT_THROW( Invalid_Argument );
}
Exit:
return error;
}
/**************************************************************************
*
* @Function:
* sdf_contour_get_min_distance
*
* @Description:
* This function iterate through all the edges that make up
* the contour and find the shortest distance from a point to
* this contour and assigns it to `out'.
*
* @Input:
* [TODO]
*
* @Return:
* [TODO]
*/
static FT_Error
sdf_contour_get_min_distance( SDF_Contour* contour,
FT_26D6_Vec point,
SDF_Signed_Distance* out)
{
FT_Error error = FT_Err_Ok;
SDF_Signed_Distance min_dist = max_sdf;
FT_ListRec edge_list;
if ( !contour || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
edge_list = contour->edges;
/* iterate through all the edges manually */
while ( edge_list.head ) {
SDF_Signed_Distance current_dist = max_sdf;
FT_CALL( sdf_edge_get_min_distance(
(SDF_Edge*)edge_list.head->data,
point, &current_dist ) );
if ( current_dist.squared_distance >= 0 &&
current_dist.squared_distance < min_dist.squared_distance )
min_dist = current_dist;
else if ( current_dist.squared_distance ==
min_dist.squared_distance )
min_dist = resolve_corner( min_dist, current_dist, point );
edge_list.head = edge_list.head->next;
}
*out = min_dist;
Exit:
return error;
}
/**************************************************************************
*
* @Function:
* sdf_generate
*
* @Description:
* This is the main function that is responsible for generating
* signed distance fields. The function will not align or compute
* the size of the `bitmap', therefore setup the `bitmap' properly
* and transform the `shape' appropriately before calling this
* function.
* Currently we check all the pixels against all the contours and
* all the edges.
*
* @Input:
* [TODO]
*
* @Return:
* [TODO]
*/
static FT_Error
sdf_generate( const SDF_Shape* shape,
FT_UInt spread,
const FT_Bitmap* bitmap )
{
FT_Error error = FT_Err_Ok;
FT_UInt width = 0;
FT_UInt rows = 0;
FT_UInt x = 0; /* used to loop in x direction i.e. width */
FT_UInt y = 0; /* used to loop in y direction i.e. rows */
FT_UInt sp_sq = 0; /* `spread' * `spread' int 16.16 fixed */
FT_Short* buffer;
if ( !shape || !bitmap )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( spread < MIN_SPREAD || spread > MAX_SPREAD )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
width = bitmap->width;
rows = bitmap->rows;
buffer = (FT_Short*)bitmap->buffer;
sp_sq = FT_INT_16D16( spread * spread );
if ( width == 0 || rows == 0 )
{
FT_TRACE0(( "[sdf] sdf_generate:\n"
" Cannot render glyph with width/height == 0\n"
" (width, height provided [%d, %d])", width, rows ));
error = FT_THROW( Cannot_Render_Glyph );
goto Exit;
}
/* loop through all the rows */
for ( y = 0; y < rows; y++ )
{
/* loop through all the pixels of a row */
for ( x = 0; x < width; x++ )
{
/* `grid_point' is the current pixel position */
/* our task is to find the shortest distance */
/* from this point to the entire shape. */
FT_26D6_Vec grid_point = zero_vector;
SDF_Signed_Distance min_dist = max_sdf;
FT_ListRec contour_list;
FT_UInt index;
FT_Short value;
grid_point.x = FT_INT_26D6( x );
grid_point.y = FT_INT_26D6( y );
/* This `grid_point' is at the corner, but we */
/* use the center of the pixel. */
grid_point.x += FT_INT_26D6( 1 ) / 2;
grid_point.y += FT_INT_26D6( 1 ) / 2;
contour_list = shape->contours;
index = ( rows - y - 1 ) * width + x;
/* iterate through all the contours manually */
while ( contour_list.head ) {
SDF_Signed_Distance current_dist = max_sdf;
FT_CALL( sdf_contour_get_min_distance(
(SDF_Contour*)contour_list.head->data,
grid_point, &current_dist ) );
if ( current_dist.squared_distance < min_dist.squared_distance )
min_dist = current_dist;
contour_list.head = contour_list.head->next;
}
/* [OPTIMIZATION]: if (min_dist > sp_sq) then simply clamp */
/* the value to spread to avoid square_root */
/* clamp the values to spread */
if ( min_dist.squared_distance > sp_sq )
min_dist.squared_distance = sp_sq;
/* square_root the values and fit in a 6.10 fixed point */
min_dist.squared_distance = square_root( min_dist.squared_distance );
min_dist.squared_distance /= 64; /* convert from 16.16 to 22.10 */
value = min_dist.squared_distance & 0x0000FFFF; /* truncate to 6.10 */
value *= min_dist.sign;
buffer[index] = value;
}
}
Exit:
return error;
}
/**************************************************************************
*
* interface functions
*
*/
static FT_Error
sdf_raster_new( FT_Memory memory,
FT_Raster* araster)
{
FT_Error error = FT_Err_Ok;
SDF_TRaster* raster = NULL;
*araster = 0;
if ( !FT_ALLOC( raster, sizeof( SDF_TRaster ) ) )
{
raster->memory = memory;
*araster = (FT_Raster)raster;
}
return error;
}
static void
sdf_raster_reset( FT_Raster raster,
unsigned char* pool_base,
unsigned long pool_size )
{
/* no use of this function */
FT_UNUSED( raster );
FT_UNUSED( pool_base );
FT_UNUSED( pool_size );
}
static FT_Error
sdf_raster_set_mode( FT_Raster raster,
unsigned long mode,
void* args )
{
FT_UNUSED( raster );
FT_UNUSED( mode );
FT_UNUSED( args );
return FT_Err_Ok;
}
static FT_Error
sdf_raster_render( FT_Raster raster,
const FT_Raster_Params* params )
{
FT_Error error = FT_Err_Ok;
SDF_TRaster* sdf_raster = (SDF_TRaster*)raster;
FT_Outline* outline = NULL;
const SDF_Raster_Params* sdf_params = (const SDF_Raster_Params*)params;
FT_Memory memory = NULL;
SDF_Shape* shape = NULL;
/* check for valid arguments */
if ( !sdf_raster || !sdf_params )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
outline = (FT_Outline*)sdf_params->root.source;
/* check if the outline is valid or not */
if ( !outline )
{
error = FT_THROW( Invalid_Outline );
goto Exit;
}
/* if the outline is empty, return */
if ( outline->n_points <= 0 || outline->n_contours <= 0 )
goto Exit;
/* check if the outline has valid fields */
if ( !outline->contours || !outline->points )
{
error = FT_THROW( Invalid_Outline );
goto Exit;
}
/* check if spread is set properly */
if ( sdf_params->spread > MAX_SPREAD ||
sdf_params->spread < MIN_SPREAD )
{
FT_TRACE0((
"[sdf] sdf_raster_render:\n"
" The `spread' field of `SDF_Raster_Params' is invalid,\n"
" the value of this field must be within [%d, %d].\n"
" Also, you must pass `SDF_Raster_Params' instead of the\n"
" default `FT_Raster_Params' while calling this function\n"
" and set the fields properly.\n"
, MIN_SPREAD, MAX_SPREAD) );
error = FT_THROW( Invalid_Argument );
goto Exit;
}
memory = sdf_raster->memory;
if ( !memory )
{
FT_TRACE0(( "[sdf] sdf_raster_render:\n"
" Raster not setup properly, "
"unable to find memory handle.\n" ));
error = FT_THROW( Invalid_Handle );
goto Exit;
}
FT_CALL( sdf_shape_new( memory, &shape ) );
FT_CALL( sdf_outline_decompose( outline, shape ) );
FT_CALL( sdf_generate( shape, sdf_params->spread,
sdf_params->root.target ) );
Exit:
if ( shape )
sdf_shape_done( memory, &shape );
return error;
}
static void
sdf_raster_done( FT_Raster raster )
{
FT_Memory memory = (FT_Memory)((SDF_TRaster*)raster)->memory;
FT_FREE( raster );
}
FT_DEFINE_RASTER_FUNCS(
ft_sdf_raster,
FT_GLYPH_FORMAT_OUTLINE,
(FT_Raster_New_Func) sdf_raster_new, /* raster_new */
(FT_Raster_Reset_Func) sdf_raster_reset, /* raster_reset */
(FT_Raster_Set_Mode_Func) sdf_raster_set_mode, /* raster_set_mode */
(FT_Raster_Render_Func) sdf_raster_render, /* raster_render */
(FT_Raster_Done_Func) sdf_raster_done /* raster_done */
)
/* END */
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