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skia / third_party / freetype2 / refs/heads/GSoC-2020-anuj / . / src / sdf / ftsdf.c
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#include <freetype/internal/ftobjs.h>
#include <freetype/internal/ftdebug.h>
#include <freetype/fttrigon.h>
#include "ftsdf.h"
#include "ftsdferrs.h"
/**************************************************************************
*
* A brief technical overview of how the SDF rasterizer works.
* -----------------------------------------------------------
*
* [Notes]:
* * SDF stands for Signed Distance Field everywhere.
*
* * This renderer generate SDF directly from outlines. There is another
* renderer `bsdf' which convert bitmaps to SDF, see `ftbsdf.c' for
* more details on the `bsdf' rasterizer.
*
* * The basic idea of generating the SDF is taken from Viktor Chlumsky's
* research paper. Citation:
* 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 which make the outline of a shape/glyph.
* Each contour comprises of several edges and the edges can be of
* three types i.e.
*
* * Line Segments
* * Conic Bezier Curves
* * Cubic Bezier Curves
*
* 2 - Apart from the outlines we also have a 2D grid namely the bitmap
* which is used to represent the final SDF data.
*
* 3 - Now, 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 it's
* sign will be positive, otherwise it will be 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 this the bitmap will contain information about the closest
* point from each point to the outline of the shape. Of course, this
* is the most straightforward way of generating SDF, in this raster-
* izer we use various optimizations, to checkout how they works
* see the `sdf_generate_' functions in this file.
*
* The optimization currently used by default is the subdivision opt-
* imization, see `sdf_generate_subdivision' for more details.
*
* Also, to see how we compute the shortest distance from a point to
* each type of edge checkout the `get_min_distance_' functions.
*
*/
/**************************************************************************
*
* for tracking memory used
*
*/
/* The memory tracker only works when `FT_DEBUG_MEMORY' is defined */
/* because some variables such as `_ft_debug_file' are defined when */
/* `FT_DEBUG_MEMORY' is defined. */
#if defined(FT_DEBUG_LEVEL_TRACE) && defined(FT_DEBUG_MEMORY)
#undef FT_DEBUG_INNER
#undef FT_ASSIGNP_INNER
#define FT_DEBUG_INNER( exp ) ( _ft_debug_file = __FILE__, \
_ft_debug_lineno = line, \
(exp) )
#define FT_ASSIGNP_INNER( p, exp ) ( _ft_debug_file = __FILE__, \
_ft_debug_lineno = line, \
FT_ASSIGNP( p, exp ) )
/* To be used with `FT_Memory::user' in order to track */
/* memory allocations. */
typedef struct SDF_MemoryUser_
{
void* prev_user;
FT_Long total_usage;
} SDF_MemoryUser;
/* Use these functions while allocating and deallocating */
/* memory. These macros restore the previous user pointer */
/* before calling the allocation functions, which is ess- */
/* ential if the program is compiled with macro */
/* `FT_DEBUG_MEMORY'. */
static FT_Pointer
sdf_alloc( FT_Memory memory,
FT_Long size,
FT_Error* err,
FT_Int line )
{
SDF_MemoryUser* current_user;
FT_Pointer ptr;
FT_Error error;
current_user = (SDF_MemoryUser*)memory->user;
memory->user = current_user->prev_user;
if ( !FT_QALLOC( ptr, size ) )
current_user->total_usage += size;
memory->user = (void*)current_user;
*err = error;
return ptr;
}
static void
sdf_free( FT_Memory memory,
FT_Pointer ptr,
FT_Int line )
{
SDF_MemoryUser* current_user;
current_user = (SDF_MemoryUser*)memory->user;
memory->user = current_user->prev_user;
FT_FREE( ptr );
memory->user = (void*)current_user;
}
#define SDF_ALLOC( ptr, size ) \
( ptr = sdf_alloc( memory, size, \
&error, __LINE__ ), \
error != 0 )
#define SDF_FREE( ptr ) \
sdf_free( memory, ptr, __LINE__ ) \
#define SDF_MEMORY_TRACKER_DECLARE() SDF_MemoryUser sdf_memory_user
#define SDF_MEMORY_TRACKER_SETUP() \
sdf_memory_user.prev_user = memory->user; \
sdf_memory_user.total_usage = 0; \
memory->user = &sdf_memory_user
#define SDF_MEMORY_TRACKER_DONE() \
memory->user = sdf_memory_user.prev_user; \
FT_TRACE0(( "[sdf] sdf_raster_render: " \
"Total memory used = %ld\n", \
sdf_memory_user.total_usage ))
#else
/* Use the native allocation functions. */
#define SDF_ALLOC FT_QALLOC
#define SDF_FREE FT_FREE
/* Do nothing */
#define SDF_MEMORY_TRACKER_DECLARE() FT_DUMMY_STMNT
#define SDF_MEMORY_TRACKER_SETUP() FT_DUMMY_STMNT
#define SDF_MEMORY_TRACKER_DONE() FT_DUMMY_STMNT
#endif
/**************************************************************************
*
* definitions
*
*/
/* If it is defined to 1 then the rasterizer will use Newton-Raphson's */
/* method for finding shortest distance from a point to a conic curve. */
/* The other method is an analytical method which find the roots of a */
/* cubic polynomial to find the shortest distance. But the analytical */
/* method has underflow as of now. So, use the Newton's method if there */
/* is any visible artifacts. */
#ifndef USE_NEWTON_FOR_CONIC
# define USE_NEWTON_FOR_CONIC 1
#endif
/* `MAX_NEWTON_DIVISIONS' is the number of intervals the bezier curve */
/* is sampled and checked for shortest distance. */
#define MAX_NEWTON_DIVISIONS 4
/* `MAX_NEWTON_STEPS' is the number of steps of Newton's iterations in */
/* each interval of the bezier curve. Basically for each division we */
/* run the Newton's approximation (i.e. x -= Q( t ) / Q'( t )) to get */
/* the shortest distance. */
#define MAX_NEWTON_STEPS 4
/* This is the distance in 16.16 which is used for corner resolving. If */
/* the difference of two distance is less than `CORNER_CHECK_EPSILON' */
/* then they will be checked for corner if they have ambiguity. */
#define CORNER_CHECK_EPSILON 32
#if 0
/* Coarse grid dimension. Probably will be removed in the future cause */
/* coarse grid optimization is the slowest. */
#define CG_DIMEN 8
#endif
/**************************************************************************
*
* macros
*
*/
#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 ) )
/**************************************************************************
*
* structures and enums
*
*/
/**************************************************************************
*
* @Struct:
* SDF_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_Render_Func' function, which then can be
* used however we want.
*
* @Fields:
* memory ::
* Used internally to allocate intermediate memory while raterizing.
*
*/
typedef struct SDF_TRaster_
{
FT_Memory memory;
} SDF_TRaster;
/**************************************************************************
*
* @Enum:
* SDF_Edge_Type
*
* @Description:
* Enumeration of all the types of curve present in fonts.
*
* @Fields:
* SDF_EDGE_UNDEFINED ::
* Undefined edge, simply used to initialize and detect errors.
*
* SDF_EDGE_LINE ::
* Line segment with start and end point.
*
* SDF_EDGE_CONIC ::
* A conic/quadratic bezier curve with start, end and on control
* point.
*
* SDF_EDGE_CUBIC ::
* A cubic bezier curve with start, end and two control points.
*
*/
typedef enum SDF_Edge_Type_
{
SDF_EDGE_UNDEFINED = 0,
SDF_EDGE_LINE = 1,
SDF_EDGE_CONIC = 2,
SDF_EDGE_CUBIC = 3
} SDF_Edge_Type;
/**************************************************************************
*
* @Enum:
* SDF_Contour_Orientation
*
* @Description:
* Enumeration of all the orientation of a contour. We determine the
* orientation by calculating the area covered by a contour.
*
* @Fields:
* SDF_ORIENTATION_NONE ::
* Undefined orientation, simply used to initialize and detect errors.
*
* SDF_ORIENTATION_CW ::
* Clockwise orientation. (positive area covered)
*
* SDF_ORIENTATION_ACW ::
* Anti-clockwise orientation. (negative area covered)
*
* @Note:
* The orientation is independent of the fill rule of a `FT_Outline',
* that means the fill will be different for different font formats.
* For example, for TrueType fonts clockwise contours are filled, while
* for OpenType fonts anti-clockwise contours are filled. To determine
* the propert fill rule use `FT_Outline_Get_Orientation'.
*
*/
typedef enum SDF_Contour_Orientation_
{
SDF_ORIENTATION_NONE = 0,
SDF_ORIENTATION_CW = 1,
SDF_ORIENTATION_ACW = 2
} SDF_Contour_Orientation;
/**************************************************************************
*
* @Enum:
* SDF_Edge
*
* @Description:
* Represent an edge of a contour.
*
* @Fields:
* start_pos ::
* Start position of an edge. Valid for all types of edges.
*
* end_pos ::
* Etart position of an edge. Valid for all types of edges.
*
* control_a ::
* A control point of the edge. Valid only for `SDF_EDGE_CONIC'
* and `SDF_EDGE_CUBIC'.
*
* control_b ::
* Another control point of the edge. Valid only for `SDF_EDGE_CONIC'.
*
* edge_type ::
* Type of the edge, see `SDF_Edge_Type' for all possible edge types.
*
* next ::
* Used to create a singly linked list, which can be interpreted
* as a contour.
*
*/
typedef struct SDF_Edge_
{
FT_26D6_Vec start_pos;
FT_26D6_Vec end_pos;
FT_26D6_Vec control_a;
FT_26D6_Vec control_b;
SDF_Edge_Type edge_type;
struct SDF_Edge_* next;
} SDF_Edge;
/**************************************************************************
*
* @Enum:
* SDF_Contour
*
* @Description:
* Represent a complete contour, which contains a list of edges.
*
* @Fields:
* last_pos ::
* Contains the position of the `end_pos' of the last edge
* in the list of edges. Useful while decomposing the outline
* using `FT_Outline_Decompose'.
*
* edges ::
* Linked list of all the edges that make the contour.
*
* next ::
* Used to create a singly linked list, which can be interpreted
* as a complete shape or `FT_Outline'.
*
*/
typedef struct SDF_Contour_
{
FT_26D6_Vec last_pos;
SDF_Edge* edges;
struct SDF_Contour_* next;
} SDF_Contour;
/**************************************************************************
*
* @Enum:
* SDF_Shape
*
* @Description:
* Represent a complete shape which is the decomposition of `FT_Outline'.
*
* @Fields:
* memory ::
* Used internally to allocate memory.
*
* contours ::
* Linked list of all the contours that make the shape.
*
*/
typedef struct SDF_Shape_
{
FT_Memory memory;
SDF_Contour* contours;
} SDF_Shape;
/**************************************************************************
*
* @Enum:
* SDF_Signed_Distance
*
* @Description:
* Represent signed distance of a point, i.e. the distance of the
* edge nearest to the point.
*
* @Fields:
* distance ::
* Distance of the point from the nearest edge. Can be squared or
* absolute depending on the `USE_SQUARED_DISTANCES' parameter
* defined in `ftsdfcommon.h'.
*
* cross ::
* Cross product of the shortest distance vector (i.e. the vector
* the point to the nearest edge) and the direction of the edge
* at the nearest point. This is used to resolve any ambiguity
* in the sign.
*
* sign ::
* Represent weather the distance vector is outside or inside the
* contour corresponding to the edge.
*
* @Note:
* The `sign' may or may not be correct, therefore it must be checked
* properly in case there is an ambiguity.
*
*/
typedef struct SDF_Signed_Distance_
{
FT_16D16 distance;
FT_16D16 cross;
FT_Char sign;
} SDF_Signed_Distance;
/**************************************************************************
*
* @Enum:
* SDF_Params
*
* @Description:
* Yet another internal parameters required by the rasterizer.
*
* @Fields:
* orientation ::
* This is not the `SDF_Contour_Orientation', this is the
* `FT_Orientation', which determine weather clockwise is to
* be filled or anti-clockwise.
*
* flip_sign ::
* Simply flip the sign if this is true. By default the points
* filled by the outline are positive.
*
* flip_y ::
* If set to true the output bitmap will be upside down. Can be
* useful because OpenGL and DirectX have different coordinate
* system for textures.
*
* overload_sign ::
* In the subdivision and bounding box optimization, the default
* outside sign is taken as -1. This parameter can be used to
* modify that behaviour. For example, while generating SDF for
* single counter-clockwise contour the outside sign should be 1.
*
*/
typedef struct SDF_Params_
{
FT_Orientation orientation;
FT_Bool flip_sign;
FT_Bool flip_y;
FT_Int overload_sign;
} SDF_Params;
/**************************************************************************
*
* 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, NULL };
static
const SDF_Contour null_contour = { { 0, 0 }, NULL, NULL };
static
const SDF_Shape null_shape = { NULL, NULL };
static
const SDF_Signed_Distance max_sdf = { INT_MAX, 0, 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 ( !SDF_ALLOC( ptr, sizeof( *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;
SDF_FREE( *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 ( !SDF_ALLOC( ptr, sizeof( *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 )
{
SDF_Edge* edges;
SDF_Edge* temp;
if ( !memory || !contour || !*contour )
return;
edges = (*contour)->edges;
/* release all the edges */
while ( edges )
{
temp = edges;
edges = edges->next;
sdf_edge_done( memory, &temp );
}
SDF_FREE( *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 ( !SDF_ALLOC( ptr, sizeof( *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( SDF_Shape** shape )
{
FT_Memory memory;
SDF_Contour* contours;
SDF_Contour* temp;
if ( !shape || !*shape )
return;
memory = (*shape)->memory;
contours = (*shape)->contours;
if ( !memory )
return;
/* release all the contours */
while ( contours )
{
temp = contours;
contours = contours->next;
sdf_contour_done( memory, &temp );
}
/* release the allocated shape struct */
SDF_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_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
FT_CALL( sdf_contour_new( memory, &contour ) );
contour->last_pos = *to;
contour->next = shape->contours;
shape->contours = contour;
Exit:
return error;
}
/* This function is called when there is a line in the */
/* contour. The line is from the previous edge point to */
/* the parameter `to'. */
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_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contour = shape->contours;
if ( contour->last_pos.x == to->x &&
contour->last_pos.y == to->y )
goto Exit;
FT_CALL( sdf_edge_new( memory, &edge ) );
edge->edge_type = SDF_EDGE_LINE;
edge->start_pos = contour->last_pos;
edge->end_pos = *to;
edge->next = contour->edges;
contour->edges = edge;
contour->last_pos = *to;
Exit:
return error;
}
/* This function is called when there is a conic bezier */
/* curve in the contour. The bezier is from the previous */
/* edge point to the parameter `to' with the control */
/* point being `control_1'. */
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_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
if ( !control_1 || !to || !user )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contour = shape->contours;
FT_CALL( sdf_edge_new( memory, &edge ) );
edge->edge_type = SDF_EDGE_CONIC;
edge->start_pos = contour->last_pos;
edge->control_a = *control_1;
edge->end_pos = *to;
edge->next = contour->edges;
contour->edges = edge;
contour->last_pos = *to;
Exit:
return error;
}
/* This function is called when there is a cubic bezier */
/* curve in the contour. The bezier is from the previous */
/* edge point to the parameter `to' with one control */
/* point being `control_1' and another `control_2'. */
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_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 = shape->contours;
FT_CALL( sdf_edge_new( memory, &edge ) );
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;
edge->next = contour->edges;
contour->edges = edge;
contour->last_pos = *to;
Exit:
return error;
}
/* Construct the struct to hold all four outline */
/* decomposition functions. */
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 */
)
/* The 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;
}
/**************************************************************************
*
* utility functions
*
*/
/* The function returns the control box of a edge. */
/* The control box is a rectangle in which all the */
/* control points can fit tightly. */
static FT_CBox
get_control_box( SDF_Edge edge )
{
FT_CBox cbox;
FT_Bool is_set = 0;
switch (edge.edge_type) {
case SDF_EDGE_CUBIC:
{
cbox.xMin = edge.control_b.x;
cbox.xMax = edge.control_b.x;
cbox.yMin = edge.control_b.y;
cbox.yMax = edge.control_b.y;
is_set = 1;
/* To avoid warning [-Wimplicit-fallthrough=] add */
/* a break statement but jump to next edge before. */
goto conic;
break;
}
case SDF_EDGE_CONIC:
{
conic:
if ( is_set )
{
cbox.xMin = edge.control_a.x < cbox.xMin ?
edge.control_a.x : cbox.xMin;
cbox.xMax = edge.control_a.x > cbox.xMax ?
edge.control_a.x : cbox.xMax;
cbox.yMin = edge.control_a.y < cbox.yMin ?
edge.control_a.y : cbox.yMin;
cbox.yMax = edge.control_a.y > cbox.yMax ?
edge.control_a.y : cbox.yMax;
}
else
{
cbox.xMin = edge.control_a.x;
cbox.xMax = edge.control_a.x;
cbox.yMin = edge.control_a.y;
cbox.yMax = edge.control_a.y;
is_set = 1;
}
goto line;
break;
}
case SDF_EDGE_LINE:
{
line:
if ( is_set )
{
cbox.xMin = edge.start_pos.x < cbox.xMin ?
edge.start_pos.x : cbox.xMin;
cbox.xMax = edge.start_pos.x > cbox.xMax ?
edge.start_pos.x : cbox.xMax;
cbox.yMin = edge.start_pos.y < cbox.yMin ?
edge.start_pos.y : cbox.yMin;
cbox.yMax = edge.start_pos.y > cbox.yMax ?
edge.start_pos.y : cbox.yMax;
}
else
{
cbox.xMin = edge.start_pos.x;
cbox.xMax = edge.start_pos.x;
cbox.yMin = edge.start_pos.y;
cbox.yMax = edge.start_pos.y;
}
cbox.xMin = edge.end_pos.x < cbox.xMin ?
edge.end_pos.x : cbox.xMin;
cbox.xMax = edge.end_pos.x > cbox.xMax ?
edge.end_pos.x : cbox.xMax;
cbox.yMin = edge.end_pos.y < cbox.yMin ?
edge.end_pos.y : cbox.yMin;
cbox.yMax = edge.end_pos.y > cbox.yMax ?
edge.end_pos.y : cbox.yMax;
break;
}
default:
break;
}
return cbox;
}
/* The function returns the orientation for a single contour. */
/* Note that the orientation is independent of the fill rule. */
/* So, for ttf the clockwise has to be filled and the opposite */
/* for otf fonts. */
static SDF_Contour_Orientation
get_contour_orientation ( SDF_Contour* contour )
{
SDF_Edge* head = NULL;
FT_26D6 area = 0;
/* return none if invalid parameters */
if ( !contour || !contour->edges )
return SDF_ORIENTATION_NONE;
head = contour->edges;
/* Simply calculate the area of the control box for */
/* all the edges. */
while ( head )
{
switch ( head->edge_type ) {
case SDF_EDGE_LINE:
{
area += MUL_26D6( ( head->end_pos.x - head->start_pos.x ),
( head->end_pos.y + head->start_pos.y ) );
break;
}
case SDF_EDGE_CONIC:
{
area += MUL_26D6( head->control_a.x - head->start_pos.x,
head->control_a.y + head->start_pos.y );
area += MUL_26D6( head->end_pos.x - head->control_a.x,
head->end_pos.y + head->control_a.y );
break;
}
case SDF_EDGE_CUBIC:
{
area += MUL_26D6( head->control_a.x - head->start_pos.x,
head->control_a.y + head->start_pos.y );
area += MUL_26D6( head->control_b.x - head->control_a.x,
head->control_b.y + head->control_a.y );
area += MUL_26D6( head->end_pos.x - head->control_b.x,
head->end_pos.y + head->control_b.y );
break;
}
default:
return SDF_ORIENTATION_NONE;
}
head = head->next;
}
/* Clockwise contour cover a positive area, and Anti-Clockwise */
/* contour cover a negitive area. */
if ( area > 0 )
return SDF_ORIENTATION_CW;
else
return SDF_ORIENTATION_ACW;
}
/* The function is exactly same as the one */
/* in the smooth renderer. It splits a conic */
/* into two conic exactly half way at t = 0.5 */
static void
split_conic( FT_26D6_Vec* base )
{
FT_26D6 a, b;
base[4].x = base[2].x;
a = base[0].x + base[1].x;
b = base[1].x + base[2].x;
base[3].x = b / 2;
base[2].x = ( a + b ) / 4;
base[1].x = a / 2;
base[4].y = base[2].y;
a = base[0].y + base[1].y;
b = base[1].y + base[2].y;
base[3].y = b / 2;
base[2].y = ( a + b ) / 4;
base[1].y = a / 2;
}
/* The function is exactly same as the one */
/* in the smooth renderer. It splits a cubic */
/* into two cubic exactly half way at t = 0.5 */
static void
split_cubic( FT_26D6_Vec* base )
{
FT_26D6 a, b, c;
base[6].x = base[3].x;
a = base[0].x + base[1].x;
b = base[1].x + base[2].x;
c = base[2].x + base[3].x;
base[5].x = c / 2;
c += b;
base[4].x = c / 4;
base[1].x = a / 2;
a += b;
base[2].x = a / 4;
base[3].x = ( a + c ) / 8;
base[6].y = base[3].y;
a = base[0].y + base[1].y;
b = base[1].y + base[2].y;
c = base[2].y + base[3].y;
base[5].y = c / 2;
c += b;
base[4].y = c / 4;
base[1].y = a / 2;
a += b;
base[2].y = a / 4;
base[3].y = ( a + c ) / 8;
}
/* the function splits a conic bezier curve */
/* into a number of lines and adds them to */
/* a list `out'. The function uses recursion */
/* that is why a `max_splits' param is required */
/* for stopping. */
static FT_Error
split_sdf_conic( FT_Memory memory,
FT_26D6_Vec* control_points,
FT_Int max_splits,
SDF_Edge** out )
{
FT_Error error = FT_Err_Ok;
FT_26D6_Vec cpos[5];
SDF_Edge* left,* right;
if ( !memory || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
/* split the conic */
cpos[0] = control_points[0];
cpos[1] = control_points[1];
cpos[2] = control_points[2];
split_conic( cpos );
/* If max number of splits is done */
/* then stop and add the lines to */
/* the list. */
if ( max_splits <= 2 )
goto Append;
/* If not max splits then keep splitting */
FT_CALL( split_sdf_conic( memory, &cpos[0], max_splits / 2, out ) );
FT_CALL( split_sdf_conic( memory, &cpos[2], max_splits / 2, out ) );
/* [NOTE]: This is not an efficient way of */
/* splitting the curve. Check the deviation */
/* instead and stop if the deviation is less */
/* than a pixel. */
goto Exit;
Append:
/* Allocation and add the lines to the list. */
FT_CALL( sdf_edge_new( memory, &left) );
FT_CALL( sdf_edge_new( memory, &right) );
left->start_pos = cpos[0];
left->end_pos = cpos[2];
left->edge_type = SDF_EDGE_LINE;
right->start_pos = cpos[2];
right->end_pos = cpos[4];
right->edge_type = SDF_EDGE_LINE;
left->next = right;
right->next = (*out);
*out = left;
Exit:
return error;
}
/* the function splits a cubic bezier curve */
/* into a number of lines and adds them to */
/* a list `out'. The function uses recursion */
/* that is why a `max_splits' param is required */
/* for stopping. */
static FT_Error
split_sdf_cubic( FT_Memory memory,
FT_26D6_Vec* control_points,
FT_Int max_splits,
SDF_Edge** out )
{
FT_Error error = FT_Err_Ok;
FT_26D6_Vec cpos[7];
SDF_Edge* left,* right;
if ( !memory || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
/* split the conic */
cpos[0] = control_points[0];
cpos[1] = control_points[1];
cpos[2] = control_points[2];
cpos[3] = control_points[3];
split_cubic( cpos );
/* If max number of splits is done */
/* then stop and add the lines to */
/* the list. */
if ( max_splits <= 2 )
goto Append;
/* If not max splits then keep splitting */
FT_CALL( split_sdf_cubic( memory, &cpos[0], max_splits / 2, out ) );
FT_CALL( split_sdf_cubic( memory, &cpos[3], max_splits / 2, out ) );
/* [NOTE]: This is not an efficient way of */
/* splitting the curve. Check the deviation */
/* instead and stop if the deviation is less */
/* than a pixel. */
goto Exit;
Append:
/* Allocation and add the lines to the list. */
FT_CALL( sdf_edge_new( memory, &left) );
FT_CALL( sdf_edge_new( memory, &right) );
left->start_pos = cpos[0];
left->end_pos = cpos[3];
left->edge_type = SDF_EDGE_LINE;
right->start_pos = cpos[3];
right->end_pos = cpos[6];
right->edge_type = SDF_EDGE_LINE;
left->next = right;
right->next = (*out);
*out = left;
Exit:
return error;
}
/* This function subdivide and entire shape */
/* into line segment such that it doesn't */
/* look visually different from the original */
/* curve. */
static FT_Error
split_sdf_shape( SDF_Shape* shape )
{
FT_Error error = FT_Err_Ok;
FT_Memory memory;
SDF_Contour* contours;
SDF_Contour* new_contours = NULL;
if ( !shape || !shape->memory )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contours = shape->contours;
memory = shape->memory;
/* for each contour */
while ( contours )
{
SDF_Edge* edges = contours->edges;
SDF_Edge* new_edges = NULL;
SDF_Contour* tempc;
/* for each edge */
while ( edges )
{
SDF_Edge* edge = edges;
SDF_Edge* temp;
switch ( edge->edge_type )
{
case SDF_EDGE_LINE:
{
/* Just create a duplicate edge in case */
/* it is a line. We can use the same edge. */
FT_CALL( sdf_edge_new( memory, &temp ) );
ft_memcpy( temp, edge, sizeof( *edge ) );
temp->next = new_edges;
new_edges = temp;
break;
}
case SDF_EDGE_CONIC:
{
/* Subdivide the curve and add to the list. */
FT_26D6_Vec ctrls[3];
ctrls[0] = edge->start_pos;
ctrls[1] = edge->control_a;
ctrls[2] = edge->end_pos;
error = split_sdf_conic( memory, ctrls, 32, &new_edges );
break;
}
case SDF_EDGE_CUBIC:
{
/* Subdivide the curve and add to the list. */
FT_26D6_Vec ctrls[4];
ctrls[0] = edge->start_pos;
ctrls[1] = edge->control_a;
ctrls[2] = edge->control_b;
ctrls[3] = edge->end_pos;
error = split_sdf_cubic( memory, ctrls, 32, &new_edges );
break;
}
default:
error = FT_THROW( Invalid_Argument );
goto Exit;
}
edges = edges->next;
}
/* add to the contours list */
FT_CALL( sdf_contour_new( memory, &tempc ) );
tempc->next = new_contours;
tempc->edges = new_edges;
new_contours = tempc;
new_edges = NULL;
/* deallocate the contour */
tempc = contours;
contours = contours->next;
sdf_contour_done( memory, &tempc );
}
shape->contours = new_contours;
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_UInt total_lines = 0;
FT_UInt total_conic = 0;
FT_UInt total_cubic = 0;
SDF_Contour* 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 )
{
FT_UInt num_edges = 0;
SDF_Edge* edge_list;
SDF_Contour* contour = contour_list;
edge_list = contour->edges;
FT_TRACE5(( "Contour %d\n", num_contours ));
while ( edge_list )
{
SDF_Edge* edge = edge_list;
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: %ld, %ld\n", edge->start_pos.x,
edge->start_pos.y ));
FT_TRACE5(( " End Pos : %ld, %ld\n", edge->end_pos.x,
edge->end_pos.y ));
total_lines++;
break;
case SDF_EDGE_CONIC:
FT_TRACE5(( " Edge Type: Conic Bezier\n" ));
FT_TRACE5(( " -----------------------\n" ));
FT_TRACE5(( " Start Pos: %ld, %ld\n", edge->start_pos.x,
edge->start_pos.y ));
FT_TRACE5(( " Ctrl1 Pos: %ld, %ld\n", edge->control_a.x,
edge->control_a.y ));
FT_TRACE5(( " End Pos : %ld, %ld\n", edge->end_pos.x,
edge->end_pos.y ));
total_conic++;
break;
case SDF_EDGE_CUBIC:
FT_TRACE5(( " Edge Type: Cubic Bezier\n" ));
FT_TRACE5(( " -----------------------\n" ));
FT_TRACE5(( " Start Pos: %ld, %ld\n", edge->start_pos.x,
edge->start_pos.y ));
FT_TRACE5(( " Ctrl1 Pos: %ld, %ld\n", edge->control_a.x,
edge->control_a.y ));
FT_TRACE5(( " Ctrl2 Pos: %ld, %ld\n", edge->control_b.x,
edge->control_b.y ));
FT_TRACE5(( " End Pos : %ld, %ld\n", edge->end_pos.x,
edge->end_pos.y ));
total_cubic++;
break;
default:
break;
}
num_edges++;
total_edges++;
edge_list = edge_list->next;
}
num_contours++;
contour_list = contour_list->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(( " |__lines = %d\n", total_lines ));
FT_TRACE5(( " |__conic = %d\n", total_conic ));
FT_TRACE5(( " |__cubic = %d\n", total_cubic ));
FT_TRACE5(( "[sdf] sdf_shape_dump complete\n" ));
FT_TRACE5(( "-------------------------------------------------\n" ));
}
#endif
/**************************************************************************
*
* math functions
*
*/
#if !USE_NEWTON_FOR_CONIC
/* [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;
}
}
#endif
/*************************************************************************/
/*************************************************************************/
/** **/
/** RASTERIZER **/
/** **/
/*************************************************************************/
/*************************************************************************/
/**************************************************************************
*
* @Function:
* resolve_corner
*
* @Description:
* At some places on the grid two edges can give opposite direction,
* this happens when the closest point is on one 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.
* The orthogonality is nothing but the sinus of the two vectors (i.e.
* ( x - o ) and the corresponding direction. The orthogonality is pre
* computed by the corresponding `get_min_distance_' functions efficiently.
*
* @Input:
* sdf1 ::
* First signed distance. (can be any of `a' or `b')
*
* sdf1 ::
* Second signed distance. (can be any of `a' or `b')
*
* @Return:
* The correct signed distance, which is checked using
* the above algorithm.
*
* @Note:
* The function does not care about the actual distance, it simply
* returns the signed distance which has a larger cross product.
* So, do not call this function if the two distances are fairly
* apart. In that case simply use the signed distance with shorter
* absolute distance.
*
*/
static SDF_Signed_Distance
resolve_corner( SDF_Signed_Distance sdf1,
SDF_Signed_Distance sdf2 )
{
return FT_ABS( sdf1.cross ) > FT_ABS( sdf2.cross ) ? 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:
* line ::
* The line segment to which the shortest distance is to be
* computed.
*
* point ::
* Point from which the shortest distance is to be computed.
*
* @Return:
* out ::
* Signed distance from the `point' to the `line'.
*
* FT_Error ::
* FreeType error, 0 means success.
*
* @Note:
* The `line' parameter must have a `edge_type' of `SDF_EDGE_LINE'.
*
*/
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 );
/* assign the output */
out->sign = cross < 0 ? 1 : -1;
out->distance = VECTOR_LENGTH_16D16( nearest_vector );
/* Instead of finding cross for checking corner we */
/* directly set it here. This is more efficient */
/* because if the distance is perpendicular we can */
/* directly set it to 1. */
if ( factor != 0 && factor != FT_INT_16D16( 1 ) )
out->cross = FT_INT_16D16( 1 );
else
{
/* [OPTIMIZATION]: Pre-compute this direction. */
/* if not perpendicular then compute the cross */
FT_Vector_NormLen( &line_segment );
FT_Vector_NormLen( &nearest_vector );
out->cross = FT_MulFix( line_segment.x, nearest_vector.y ) -
FT_MulFix( line_segment.y, nearest_vector.x );
}
Exit:
return error;
}
#if !USE_NEWTON_FOR_CONIC
/**************************************************************************
*
* @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:
* conic ::
* The conic bezier to which the shortest distance is to be
* computed.
*
* point ::
* Point from which the shortest distance is to be computed.
*
* @Return:
* out ::
* Signed distance from the `point' to the `conic'.
*
* FT_Error ::
* FreeType error, 0 means success.
*
* @Note:
* The function uses analytical method to find shortest distance
* which is faster than the Newton-Raphson's method, but has
* underflows at the moment. Use Newton's method if you can
* see artifacts in the SDF.
*
* The `conic' parameter must have a `edge_type' of `SDF_EDGE_CONIC'.
*
*/
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 determine 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 );
if ( num_roots == 0 )
{
roots[0] = 0;
roots[1] = FT_INT_16D16( 1 );
num_roots = 2;
}
/* [OPTIMIZATION]: Check the roots, clamp them and discard */
/* duplicate 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;
/* Ideally we should discard the roots which are outside the */
/* range [0.0, 1.0] and check the endpoints of the bezier, but */
/* Behdad gave me a lemma: */
/* Lemma: */
/* * If the closest point on the curve [0, 1] is to the endpoint */
/* at t = 1 and the cubic has no real roots at t = 1 then, the */
/* cubic must have a real root at some t > 1. */
/* * Similarly, */
/* If the closest point on the curve [0, 1] is to the endpoint */
/* at t = 0 and the cubic has no real roots at t = 0 then, the */
/* cubic must have a real root at some t < 0. */
/* */
/* Now because of this lemma we only need to clamp the roots and */
/* that will take care of the endpoints. */
/* */
/* For proof contact: behdad@behdad.org */
/* For more details check message: */
/* https://lists.nongnu.org/archive/html/freetype-devel/2020-06/msg00147.html */
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 = VECTOR_LENGTH_16D16( dist_vector );
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->distance = min;
out->sign = cross < 0 ? 1 : -1;
if ( min_factor != 0 && min_factor != FT_INT_16D16( 1 ) )
out->cross = FT_INT_16D16( 1 ); /* the two are perpendicular */
else
{
/* convert to nearest vector */
nearest_point.x -= FT_26D6_16D16( p.x );
nearest_point.y -= FT_26D6_16D16( p.y );
/* if not perpendicular then compute the cross */
FT_Vector_NormLen( &direction );
FT_Vector_NormLen( &nearest_point );
out->cross = FT_MulFix( direction.x, nearest_point.y ) -
FT_MulFix( direction.y, nearest_point.x );
}
Exit:
return error;
}
#else
/**************************************************************************
*
* @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:
* conic ::
* The conic bezier to which the shortest distance is to be
* computed.
*
* point ::
* Point from which the shortest distance is to be computed.
*
* @Return:
* out ::
* Signed distance from the `point' to the `conic'.
*
* FT_Error ::
* FreeType error, 0 means success.
*
* @Note:
* The function uses Newton's approximation to find the shortest
* distance, which is a bit slower than the analytical method but
* doesn't cause underflow. Use is upto your needs.
*
* The `conic' parameter must have a `edge_type' of `SDF_EDGE_CONIC'.
*
*/
static FT_Error
get_min_distance_conic( SDF_Edge* conic,
FT_26D6_Vec point,
SDF_Signed_Distance* out )
{
/* This method uses Newton-Raphson's approximation to find the */
/* shortest distance from a point to conic curve which does */
/* not involve solving any cubic equation, that is why there */
/* is no risk of underflow. The method is as follows: */
/* */
/* p0 = first endpoint */
/* p1 = control point */
/* p3 = 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 = 2( p1 - p0 ) */
/* B( t ) = t^2( A ) + t( B ) + p0 */
/* */
/* => the derivative of the above equation is written as */
/* B'( t ) = 2t( A ) + B */
/* */
/* => further derivative of the above equation is written as */
/* B''( t ) = 2A */
/* */
/* => the equation of distance from point `p' to the curve */
/* P( t ) can be written as */
/* P( t ) = t^2( A ) + t^2( B ) + p0 - p */
/* Now let C = ( p0 - p ) */
/* P( t ) = t^2( A ) + t( B ) + C */
/* */
/* => finally the equation of angle between curve B( t ) and */
/* point to curve distance P( t ) can be written as */
/* Q( t ) = P( t ).B'( t ) */
/* */
/* => now our task is to find a value of t such that the above */
/* equation Q( t ) becomes zero. in other words the point */
/* to curve vector makes 90 degree with curve. this is done */
/* by Newton-Raphson's method. */
/* */
/* => we first assume a arbitary value of the factor `t' and */
/* then we improve it using Newton's equation such as */
/* */
/* t -= Q( t ) / Q'( t ) */
/* putting value of Q( t ) from the above equation gives */
/* */
/* t -= P( t ).B'( t ) / derivative( P( t ).B'( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( P'( t )B'( t ) + P( t ).B''( t ) ) */
/* */
/* P'( t ) is noting but B'( t ) because the constant are */
/* gone due to derivative */
/* */
/* => finally we get the equation to improve the factor as */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* */
/* [note]: B and B( t ) are different in the above equations */
FT_Error error = FT_Err_Ok;
FT_26D6_Vec aA, bB, cC; /* A, B, C 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_16D16 min_factor = 0; /* factor at `nearest_point' */
FT_16D16 cross; /* to determine the sign */
FT_16D16 min = FT_INT_MAX; /* shortest squared distance */
FT_UShort iterations;
FT_UShort steps;
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 = 2 * ( p1.x - p0.x );
bB.y = 2 * ( p1.y - p0.y );
cC.x = p0.x;
cC.y = p0.y;
/* do newton's iterations */
for ( iterations = 0; iterations <= MAX_NEWTON_DIVISIONS; iterations++ )
{
FT_16D16 factor = FT_INT_16D16( iterations ) / MAX_NEWTON_DIVISIONS;
FT_16D16 factor2;
FT_16D16 length;
FT_16D16_Vec curve_point; /* point on the curve */
FT_16D16_Vec dist_vector; /* `curve_point' - `p' */
FT_26D6_Vec d1; /* first derivative */
FT_26D6_Vec d2; /* second derivative */
FT_16D16 temp1;
FT_16D16 temp2;
for ( steps = 0; steps < MAX_NEWTON_STEPS; steps++ )
{
factor2 = FT_MulFix( factor, factor );
/* B( t ) = t^2( A ) + t( B ) + p0 */
curve_point.x = FT_MulFix( aA.x, factor2 ) +
FT_MulFix( bB.x, factor ) + cC.x;
curve_point.y = FT_MulFix( aA.y, factor2 ) +
FT_MulFix( bB.y, factor ) + cC.y;
/* convert to 16.16 */
curve_point.x = FT_26D6_16D16( curve_point.x );
curve_point.y = FT_26D6_16D16( curve_point.y );
/* B( t ) = t^2( A ) + t( B ) + p0 - p. P( t ) in the comment */
dist_vector.x = curve_point.x - FT_26D6_16D16( p.x );
dist_vector.y = curve_point.y - FT_26D6_16D16( p.y );
length = VECTOR_LENGTH_16D16( dist_vector );
if ( length < min )
{
min = length;
min_factor = factor;
nearest_point = curve_point;
}
/* This the actual Newton's approximation. */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* B'( t ) = 2tA + B */
d1.x = FT_MulFix( aA.x, 2 * factor ) + bB.x;
d1.y = FT_MulFix( aA.y, 2 * factor ) + bB.y;
/* B''( t ) = 2A */
d2.x = 2 * aA.x;
d2.y = 2 * aA.y;
dist_vector.x /= 1024;
dist_vector.y /= 1024;
/* temp1 = P( t ).B'( t ) */
temp1 = VEC_26D6_DOT( dist_vector, d1 );
/* temp2 = ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
temp2 = VEC_26D6_DOT( d1, d1 ) +
VEC_26D6_DOT( dist_vector, d2 );
factor -= FT_DivFix( temp1, temp2 );
if ( factor < 0 || factor > FT_INT_16D16( 1 ) )
break;
}
}
/* B'( t ) = 2tA + B */
direction.x = 2 * FT_MulFix( aA.x, min_factor ) + bB.x;
direction.y = 2 * FT_MulFix( aA.y, min_factor ) + bB.y;
/* determine the sign */
cross = FT_MulFix( nearest_point.x - FT_26D6_16D16( p.x ), direction.y ) -
FT_MulFix( nearest_point.y - FT_26D6_16D16( p.y ), direction.x );
/* assign the values */
out->distance = min;
out->sign = cross < 0 ? 1 : -1;
if ( min_factor != 0 && min_factor != FT_INT_16D16( 1 ) )
out->cross = FT_INT_16D16( 1 ); /* the two are perpendicular */
else
{
/* convert to nearest vector */
nearest_point.x -= FT_26D6_16D16( p.x );
nearest_point.y -= FT_26D6_16D16( p.y );
/* if not perpendicular then compute the cross */
FT_Vector_NormLen( &direction );
FT_Vector_NormLen( &nearest_point );
out->cross = FT_MulFix( direction.x, nearest_point.y ) -
FT_MulFix( direction.y, nearest_point.x );
}
Exit:
return error;
}
#endif
/**************************************************************************
*
* @Function:
* get_min_distance_cubic
*
* @Description:
* This function find the shortest distance from the `cubic' bezier
* curve to a given `point' and assigns it to `out'. Only use it for
* cubic curves.
*
* @Input:
* cubic ::
* The cubic bezier to which the shortest distance is to be
* computed.
*
* point ::
* Point from which the shortest distance is to be computed.
*
* @Return:
* out ::
* Signed distance from the `point' to the `cubic'.
*
* FT_Error ::
* FreeType error, 0 means success.
*
* @Note:
* The function uses Newton's approximation to find the shortest
* distance. Another way would be to divide the cubic into conic
* or subdivide the curve into lines, but that is not implemented.
*
* The `cubic' parameter must have a `edge_type' of `SDF_EDGE_CUBIC'.
*
*/
static FT_Error
get_min_distance_cubic( SDF_Edge* cubic,
FT_26D6_Vec point,
SDF_Signed_Distance* out )
{
/* the procedure to find the shortest distance from a point to */
/* a cubic bezier curve is similar to a quadratic curve. */
/* The only difference is that while calculating the factor */
/* `t', instead of a cubic polynomial equation we have to find */
/* the roots of a 5th degree polynomial equation. */
/* But since solving a 5th degree polynomial equation require */
/* significant amount of time and still the results may not be */
/* accurate, we are going to directly approximate the value of */
/* `t' using Newton-Raphson method */
/* */
/* p0 = first endpoint */
/* p1 = first control point */
/* p2 = second control point */
/* p3 = second endpoint */
/* p = point from which shortest distance is to be calculated */
/* ----------------------------------------------------------- */
/* => the equation of a cubic bezier curve can be written as: */
/* B( t ) = ( ( 1 - t )^3 )p0 + 3( ( 1 - t )^2 )tp1 + */
/* 3( 1 - t )( t^2 )p2 + ( t^3 )p3 */
/* The equation can be expanded and written as: */
/* B( t ) = ( t^3 )( -p0 + 3p1 - 3p2 + p3 ) + */
/* 3( t^2 )( p0 - 2p1 + p2 ) + 3t( -p0 + p1 ) + p0 */
/* */
/* Now let A = ( -p0 + 3p1 - 3p2 + p3 ), */
/* B = 3( p0 - 2p1 + p2 ), C = 3( -p0 + p1 ) */
/* B( t ) = t^3( A ) + t^2( B ) + tC + p0 */
/* */
/* => the derivative of the above equation is written as */
/* B'( t ) = 3t^2( A ) + 2t( B ) + C */
/* */
/* => further derivative of the above equation is written as */
/* B''( t ) = 6t( A ) + 2B */
/* */
/* => the equation of distance from point `p' to the curve */
/* P( t ) can be written as */
/* P( t ) = t^3( A ) + t^2( B ) + tC + p0 - p */
/* Now let D = ( p0 - p ) */
/* P( t ) = t^3( A ) + t^2( B ) + tC + D */
/* */
/* => finally the equation of angle between curve B( t ) and */
/* point to curve distance P( t ) can be written as */
/* Q( t ) = P( t ).B'( t ) */
/* */
/* => now our task is to find a value of t such that the above */
/* equation Q( t ) becomes zero. in other words the point */
/* to curve vector makes 90 degree with curve. this is done */
/* by Newton-Raphson's method. */
/* */
/* => we first assume a arbitary value of the factor `t' and */
/* then we improve it using Newton's equation such as */
/* */
/* t -= Q( t ) / Q'( t ) */
/* putting value of Q( t ) from the above equation gives */
/* */
/* t -= P( t ).B'( t ) / derivative( P( t ).B'( t ) ) */
/* t -= P( t ).B'( t ) / */
/* ( P'( t )B'( t ) + P( t ).B''( t ) ) */
/* */
/* P'( t ) is noting but B'( t ) because the constant are */
/* gone due to derivative */
/* */
/* => finally we get the equation to improve the factor as */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* */
/* [note]: B and B( t ) are different in the above equations */
FT_Error error = FT_Err_Ok;
FT_26D6_Vec aA, bB, cC, dD; /* A, B, C in the above comment */
FT_16D16_Vec nearest_point; /* point on curve nearest to `point' */
FT_16D16_Vec direction; /* direction of curve at `nearest_point' */
FT_26D6_Vec p0, p1, p2, p3; /* control points of a cubic curve */
FT_26D6_Vec p; /* `point' to which shortest distance */
FT_16D16 min = FT_INT_MAX; /* shortest distance */
FT_16D16 min_factor = 0; /* factor at shortest distance */
FT_16D16 min_factor_sq = 0; /* factor at shortest distance */
FT_16D16 cross; /* to determine the sign */
FT_UShort iterations;
FT_UShort steps;
if ( !cubic || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( cubic->edge_type != SDF_EDGE_CUBIC )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
/* assign the values after checking pointer */
p0 = cubic->start_pos;
p1 = cubic->control_a;
p2 = cubic->control_b;
p3 = cubic->end_pos;
p = point;
/* compute substitution coefficients */
aA.x = -p0.x + 3 * ( p1.x - p2.x ) + p3.x;
aA.y = -p0.y + 3 * ( p1.y - p2.y ) + p3.y;
bB.x = 3 * ( p0.x - 2 * p1.x + p2.x );
bB.y = 3 * ( p0.y - 2 * p1.y + p2.y );
cC.x = 3 * ( p1.x - p0.x );
cC.y = 3 * ( p1.y - p0.y );
dD.x = p0.x;
dD.y = p0.y;
for ( iterations = 0; iterations <= MAX_NEWTON_DIVISIONS; iterations++ )
{
FT_16D16 factor = FT_INT_16D16( iterations ) / MAX_NEWTON_DIVISIONS;
FT_16D16 factor2; /* factor^2 */
FT_16D16 factor3; /* factor^3 */
FT_16D16 length;
FT_16D16_Vec curve_point; /* point on the curve */
FT_16D16_Vec dist_vector; /* `curve_point' - `p' */
FT_26D6_Vec d1; /* first derivative */
FT_26D6_Vec d2; /* second derivative */
FT_16D16 temp1;
FT_16D16 temp2;
for ( steps = 0; steps < MAX_NEWTON_STEPS; steps++ )
{
factor2 = FT_MulFix( factor, factor );
factor3 = FT_MulFix( factor2, factor );
/* B( t ) = t^3( A ) + t^2( B ) + tC + D */
curve_point.x = FT_MulFix( aA.x, factor3 ) +
FT_MulFix( bB.x, factor2 ) +
FT_MulFix( cC.x, factor ) + dD.x;
curve_point.y = FT_MulFix( aA.y, factor3 ) +
FT_MulFix( bB.y, factor2 ) +
FT_MulFix( cC.y, factor ) + dD.y;
/* convert to 16.16 */
curve_point.x = FT_26D6_16D16( curve_point.x );
curve_point.y = FT_26D6_16D16( curve_point.y );
/* P( t ) in the comment */
dist_vector.x = curve_point.x - FT_26D6_16D16( p.x );
dist_vector.y = curve_point.y - FT_26D6_16D16( p.y );
length = VECTOR_LENGTH_16D16( dist_vector );
if ( length < min )
{
min = length;
min_factor = factor;
min_factor_sq = factor2;
nearest_point = curve_point;
}
/* This the actual Newton's approximation. */
/* t -= P( t ).B'( t ) / */
/* ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
/* B'( t ) = 3t^2( A ) + 2t( B ) + C */
d1.x = FT_MulFix( aA.x, 3 * factor2 ) +
FT_MulFix( bB.x, 2 * factor ) + cC.x;
d1.y = FT_MulFix( aA.y, 3 * factor2 ) +
FT_MulFix( bB.y, 2 * factor ) + cC.y;
/* B''( t ) = 6t( A ) + 2B */
d2.x = FT_MulFix( aA.x, 6 * factor ) + 2 * bB.x;
d2.y = FT_MulFix( aA.y, 6 * factor ) + 2 * bB.y;
dist_vector.x /= 1024;
dist_vector.y /= 1024;
/* temp1 = P( t ).B'( t ) */
temp1 = VEC_26D6_DOT( dist_vector, d1 );
/* temp2 = ( B'( t ).B'( t ) + P( t ).B''( t ) ) */
temp2 = VEC_26D6_DOT( d1, d1 ) +
VEC_26D6_DOT( dist_vector, d2 );
factor -= FT_DivFix( temp1, temp2 );
if ( factor < 0 || factor > FT_INT_16D16( 1 ) )
break;
}
}
/* B'( t ) = 3t^2( A ) + 2t( B ) + C */
direction.x = FT_MulFix( aA.x, 3 * min_factor_sq ) +
FT_MulFix( bB.x, 2 * min_factor ) + cC.x;
direction.y = FT_MulFix( aA.y, 3 * min_factor_sq ) +
FT_MulFix( bB.y, 2 * min_factor ) + cC.y;
/* determine the sign */
cross = FT_MulFix( nearest_point.x - FT_26D6_16D16( p.x ), direction.y ) -
FT_MulFix( nearest_point.y - FT_26D6_16D16( p.y ), direction.x );
/* assign the values */
out->distance = min;
out->sign = cross < 0 ? 1 : -1;
if ( min_factor != 0 && min_factor != FT_INT_16D16( 1 ) )
out->cross = FT_INT_16D16( 1 ); /* the two are perpendicular */
else
{
/* convert to nearest vector */
nearest_point.x -= FT_26D6_16D16( p.x );
nearest_point.y -= FT_26D6_16D16( p.y );
/* if not perpendicular then compute the cross */
FT_Vector_NormLen( &direction );
FT_Vector_NormLen( &nearest_point );
out->cross = FT_MulFix( direction.x, nearest_point.y ) -
FT_MulFix( direction.y, nearest_point.x );
}
Exit:
return error;
}
/**************************************************************************
*
* @Function:
* sdf_edge_get_min_distance
*
* @Description:
* This is a handy function which can be used to find shortest distance
* from a `point' to any type of `edge'. It checks the edge type and
* then calls the relevant `get_min_distance_' function.
*
* @Input:
* edge ::
* An edge to which the shortest distance is to be computed.
*
* point ::
* Point from which the shortest distance is to be computed.
*
* @Return:
* out ::
* Signed distance from the `point' to the `edge'.
*
* FT_Error ::
* FreeType error, 0 means success.
*
*/
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:
get_min_distance_cubic( edge, point, out );
break;
default:
error = FT_THROW( Invalid_Argument );
}
Exit:
return error;
}
/* `sdf_generate' is not used at the moment */
#if 0
/**************************************************************************
*
* @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:
* contour ::
* A contour to which the shortest distance is to be computed.
*
* point ::
* Point from which the shortest distance is to be computed.
*
* @Return:
* out ::
* Signed distance from the `point' to the `contour'.
*
* FT_Error ::
* FreeType error, 0 means success.
*
* @Note:
* The function does not return signed distance for each edge
* which make up the contour, it simply returns the shortest
* of all the edges.
*
*/
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;
SDF_Edge* 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 ) {
SDF_Signed_Distance current_dist = max_sdf;
FT_16D16 diff;
FT_CALL( sdf_edge_get_min_distance(
edge_list,
point, &current_dist ) );
if ( current_dist.distance >= 0 )
{
diff = current_dist.distance - min_dist.distance;
if ( FT_ABS(diff ) < CORNER_CHECK_EPSILON )
min_dist = resolve_corner( min_dist, current_dist );
else if ( diff < 0 )
min_dist = current_dist;
}
else
{
FT_TRACE0(( "sdf_contour_get_min_distance: Overflowed.\n" ));
}
edge_list = edge_list->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:
* internal_params ::
* Internal parameters and properties required by the rasterizer.
* See `SDF_Params' for the actual parameters.
*
* shape ::
* A complete shape which is used to generate SDF.
*
* spread ::
* Maximum distances to be allowed inthe output bitmap.
*
* @Return
* bitmap ::
* The output bitmap which will contain the SDF information.
*
* FT_Error ::
* FreeType error, 0 means success.
*
*/
static FT_Error
sdf_generate( const SDF_Params internal_params,
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;
if ( USE_SQUARED_DISTANCES )
sp_sq = FT_INT_16D16( spread * spread );
else
sp_sq = FT_INT_16D16( 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;
SDF_Contour* 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;
/* iterate through all the contours manually */
while ( contour_list ) {
SDF_Signed_Distance current_dist = max_sdf;
FT_CALL( sdf_contour_get_min_distance(
contour_list,
grid_point, &current_dist ) );
if ( current_dist.distance < min_dist.distance )
min_dist = current_dist;
contour_list = contour_list->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.distance > sp_sq )
min_dist.distance = sp_sq;
/* square_root the values and fit in a 6.10 fixed point */
if ( USE_SQUARED_DISTANCES )
min_dist.distance = square_root( min_dist.distance );
if ( internal_params.orientation == FT_ORIENTATION_FILL_LEFT )
min_dist.sign = -min_dist.sign;
if ( internal_params.flip_sign )
min_dist.sign = -min_dist.sign;
min_dist.distance /= 64; /* convert from 16.16 to 22.10 */
value = min_dist.distance & 0x0000FFFF; /* truncate to 6.10 */
value *= min_dist.sign;
if ( internal_params.flip_y )
index = y * width + x;
else
index = ( rows - y - 1 ) * width + x;
buffer[index] = value;
}
}
Exit:
return error;
}
#endif
/**************************************************************************
*
* @Function:
* sdf_generate_bounding_box
*
* @Description:
* This function does basically the same thing as the above
* `sdf_generate' but more efficiently.
* Instead of checking all the pixels against all the edges, we loop
* through all the edges and only check the pixels around the control
* box of the edge, the control box is increased by the spread in all
* all the directions. Anything outside the control box will naturally
* be more than the `spread' and shouldn't be computed.
* Lastly to determine the sign of unchecked pixels we do a single pass
* of all the rows starting with a '+' sign and flipping when we come
* across a '-' sign and continue.
* This also eliminate the chance of overflow because we only check the
* proximity of the curve. Therefore we can use squared distanced
* safely.
*
* @Input:
* internal_params ::
* Internal parameters and properties required by the rasterizer.
* See `SDF_Params' for the actual parameters.
*
* shape ::
* A complete shape which is used to generate SDF.
*
* spread ::
* Maximum distances to be allowed inthe output bitmap.
*
* @Return
* bitmap ::
* The output bitmap which will contain the SDF information.
*
* FT_Error ::
* FreeType error, 0 means success.
*
*/
static FT_Error
sdf_generate_bounding_box( const SDF_Params internal_params,
const SDF_Shape* shape,
FT_UInt spread,
const FT_Bitmap* bitmap )
{
FT_Error error = FT_Err_Ok;
FT_Memory memory = NULL;
FT_Int width, rows, i, j;
FT_Int sp_sq; /* max value to check */
SDF_Contour* contours; /* list of all contours */
FT_Short* buffer; /* the bitmap buffer */
/* This buffer has the same size in indices as the */
/* bitmap buffer. When we check a pixel position for */
/* shortest distance we keep it in this buffer. */
/* This way we check find out which pixel is set, */
/* and also determine the signs properly. */
SDF_Signed_Distance* dists = NULL;
if ( !shape || !bitmap )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
if ( spread < MIN_SPREAD || spread > MAX_SPREAD )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
memory = shape->memory;
if ( !memory ){
error = FT_THROW( Invalid_Argument );
goto Exit;
}
contours = shape->contours;
width = (FT_Int)bitmap->width;
rows = (FT_Int)bitmap->rows;
buffer = (FT_Short*)bitmap->buffer;
if ( SDF_ALLOC( dists, width * rows * sizeof( *dists ) ) )
goto Exit;
FT_MEM_ZERO( dists, width * rows * sizeof(*dists) );
if ( USE_SQUARED_DISTANCES )
sp_sq = FT_INT_16D16( spread * spread );
else
sp_sq = FT_INT_16D16( 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 contours */
while ( contours ) {
SDF_Edge* edges = contours->edges;
/* loop through all the edges */
while ( edges )
{
FT_CBox cbox;
FT_Int x, y;
/* get the control box and increase by `spread' */
cbox = get_control_box( *edges );
cbox.xMin = ( cbox.xMin - 63 ) / 64 - ( FT_Pos )spread;
cbox.xMax = ( cbox.xMax + 63 ) / 64 + ( FT_Pos )spread;
cbox.yMin = ( cbox.yMin - 63 ) / 64 - ( FT_Pos )spread;
cbox.yMax = ( cbox.yMax + 63 ) / 64 + ( FT_Pos )spread;
/* now loop the pixels in the control box. */
for ( y = cbox.yMin; y < cbox.yMax; y++ )
{
for ( x = cbox.xMin; x < cbox.xMax; x++ )
{
FT_26D6_Vec grid_point = zero_vector;
SDF_Signed_Distance dist = max_sdf;
FT_UInt index = 0;
if ( x < 0 || x >= width ) continue;
if ( y < 0 || y >= rows ) continue;
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;
FT_CALL( sdf_edge_get_min_distance( edges,
grid_point,
&dist ) );
if ( internal_params.orientation == FT_ORIENTATION_FILL_LEFT )
dist.sign = -dist.sign;
/* ignore if the distance is greater than spread */
/* otherwise it creates artifacts due to wrong sign */
if ( dist.distance > sp_sq ) continue;
/* square_root the values and fit in a 6.10 fixed point */
if ( USE_SQUARED_DISTANCES )
dist.distance = square_root( dist.distance );
if ( internal_params.flip_y )
index = y * width + x;
else
index = ( rows - y - 1 ) * width + x;
/* check weather the pixel is set or not */
if ( dists[index].sign == 0 )
dists[index] = dist;
else if ( dists[index].distance > dist.distance )
dists[index] = dist;
else if ( FT_ABS(dists[index].distance - dist.distance ) < CORNER_CHECK_EPSILON )
dists[index] = resolve_corner( dists[index], dist );
}
}
edges = edges->next;
}
contours = contours->next;
}
/* final pass */
for ( j = 0; j < rows; j++ )
{
/* We assume the starting pixel of each row */
/* will be outside. */
FT_Char current_sign = -1;
FT_UInt index;
if ( internal_params.overload_sign != 0 )
current_sign = internal_params.overload_sign < 0 ? -1 : 1;
for ( i = 0; i < width; i++ )
{
index = j * width + i;
/* if the pixel is not set that means it's */
/* shortest distance is more than spread */
if ( dists[index].sign == 0 )
dists[index].distance = FT_INT_16D16( spread );
else
current_sign = dists[index].sign;
/* clamp the values */
if ( dists[index].distance > (FT_Int)FT_INT_16D16( spread ) )
dists[index].distance = FT_INT_16D16( spread );
/* convert from 16.16 to 6.10 */
dists[index].distance /= 64;
if ( internal_params.flip_sign )
buffer[index] = (FT_Short)dists[index].distance * -current_sign;
else
buffer[index] = (FT_Short)dists[index].distance * current_sign;
}
}
Exit:
SDF_FREE( dists );
return error;
}
/**************************************************************************
*
* @Function:
* sdf_generate_subdivision
*
* @Description:
* This function subdivide the shape into a number of straight lines
* and then simply use the above `sdf_generate_bounding_box' to generate
* the SDF.
* Note: After calling this function the `shape' will no longer have the
* original edges, it will only contain lines.
*
* @Input:
* internal_params ::
* Internal parameters and properties required by the rasterizer.
* See `SDF_Params' for the actual parameters.
*
* shape ::
* A complete shape which is used to generate SDF.
*
* spread ::
* Maximum distances to be allowed inthe output bitmap.
*
* @Return
* bitmap ::
* The output bitmap which will contain the SDF information.
*
* FT_Error ::
* FreeType error, 0 means success.
*
*/
static FT_Error
sdf_generate_subdivision( const SDF_Params internal_params,
SDF_Shape* shape,
FT_UInt spread,
const FT_Bitmap* bitmap )
{
/* Thanks to Alexei for providing the idea of this optimization. */
/* */
/* This optimiztion mode take advantage of two facts: */
/* */
/* - Computing shortest distance froma point to a line segment */
/* is super fast. */
/* - We don't have to compute shortest distance for the entire */
/* 2D grid. */
/* */
/* This is how it works: */
/* */
/* - We split the outlines into a number of line segments. */
/* */
/* - For each line segment we only process the neighborhood of */
/* the line segment. */
/* */
/* - Now, only for the neighborhood grid points we compute the */
/* closest distance to the line. */
/* */
/* - This way we do not have to check all grid points against */
/* all the edges. Instead for each line's neighborhood we */
/* only compute shortest distance for that one line only. */
/* */
/* All in all, it reduces the number of grid point to edge check */
/* */
FT_Error error = FT_Err_Ok;
FT_CALL( split_sdf_shape( shape ) );
FT_CALL( sdf_generate_bounding_box( internal_params,
shape, spread, bitmap ) );
Exit:
return error;
}
/**************************************************************************
*
* @Function:
* sdf_generate_with_overlaps
*
* @Description:
* This function can be used to generate SDF for glyphs with
* overlapping contours. The function generate SDF for contours
* seperately on seperate bitmaps (to generate SDF it uses
* `sdf_generate_subdivision'). And at the end it simply combine
* all the SDF into the output bitmap, this fixes all the signs
* and removes overlaps.
*
* @Input:
* internal_params ::
* Internal parameters and properties required by the rasterizer.
* See `SDF_Params' for the actual parameters.
*
* shape ::
* A complete shape which is used to generate SDF.
*
* spread ::
* Maximum distances to be allowed inthe output bitmap.
*
* @Return
* bitmap ::
* The output bitmap which will contain the SDF information.
*
* FT_Error ::
* FreeType error, 0 means success.
*
* @Note
* The function cannot generate proper SDF for glyphs with self
* intersecting contours because we cannot seperate them into two
* seperate bitmaps. In case of self intersecting contours it is
* simply remove the overlaps and then generate SDF.
*
*/
static FT_Error
sdf_generate_with_overlaps( SDF_Params internal_params,
SDF_Shape* shape,
FT_UInt spread,
const FT_Bitmap* bitmap )
{
FT_Error error = FT_Err_Ok;
FT_Int num_contours; /* total number of contours */
FT_Int i, j; /* iterators */
FT_Int width, rows; /* width and rows of the bitmap */
FT_Bitmap* bitmaps; /* seperate bitmaps for contours */
SDF_Contour* contour; /* temporary variable to iterate */
SDF_Contour* temp_contour; /* temporary contour */
SDF_Contour* head; /* head of the contour list */
SDF_Shape temp_shape; /* temporary shape */
FT_Memory memory; /* to allocate memory */
FT_6D10* t; /* target bitmap buffer */
FT_Bool flip_sign; /* filp sign? */
/* orientation of all the seperate contours */
SDF_Contour_Orientation* orientations;
bitmaps = NULL;
orientations = NULL;
head = NULL;
if ( !shape || !bitmap || !shape->memory )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
/* assign the necessary variables */
contour = shape->contours;
memory = shape->memory;
temp_shape.memory = memory;
width = (FT_Int)bitmap->width;
rows = (FT_Int)bitmap->rows;
num_contours = 0;
/* find the number of contours in the shape */
while ( contour )
{
num_contours++;
contour = contour->next;
}
/* allocate the bitmaps to generate SDF for seperate contours */
if ( SDF_ALLOC( bitmaps, num_contours * sizeof( *bitmaps ) ) )
goto Exit;
/* zero the memory */
ft_memset( bitmaps, 0, num_contours * sizeof( *bitmaps ) );
/* allocate array to hold orientation for all contours */
if ( SDF_ALLOC( orientations, num_contours * sizeof( *orientations ) ) )
goto Exit;
/* zero the memory */
ft_memset( orientations, 0, num_contours * sizeof( *orientations ) );
/* Disable the flip_sign to avoid extra complication */
/* during the combination phase. */
flip_sign = internal_params.flip_sign;
internal_params.flip_sign = 0;
contour = shape->contours;
/* Iterate through all the contours */
/* and generate SDF seperately. */
for ( i = 0; i < num_contours; i++ )
{
/* initialize the corresponding bitmap */
FT_Bitmap_Init( &bitmaps[i] );
bitmaps[i].width = bitmap->width;
bitmaps[i].rows = bitmap->rows;
bitmaps[i].pitch = bitmap->pitch;
bitmaps[i].num_grays = bitmap->num_grays;
bitmaps[i].pixel_mode = bitmap->pixel_mode;
/* allocate memory for the buffer */
if ( SDF_ALLOC( bitmaps[i].buffer, bitmap->rows * bitmap->pitch ) )
goto Exit;
/* determine the orientation */
orientations[i] = get_contour_orientation( contour );
/* The `overload_sign; property is specific to */
/* sdf_generate_bounding_box. This basically */
/* overload the default sign of the outside */
/* pixels. Which is necessary for counter clock */
/* wise contours. */
if ( orientations[i] == SDF_ORIENTATION_ACW &&
internal_params.orientation == FT_ORIENTATION_FILL_RIGHT )
internal_params.overload_sign = 1;
else if ( orientations[i] == SDF_ORIENTATION_CW &&
internal_params.orientation == FT_ORIENTATION_FILL_LEFT )
internal_params.overload_sign = 1;
else
internal_params.overload_sign = 0;
/* Make `contour->next' NULL so that there is */
/* one contour in the list. Also hold the next */
/* contour in a temporary variable so as to */
/* restore the original value. */
temp_contour = contour->next;
contour->next = NULL;
/* Use the `temp_shape' to hold the new contour. */
/* Now, the `temp_shape' has only one contour. */
temp_shape.contours = contour;
/* finally generate the SDF */
FT_CALL( sdf_generate_subdivision( internal_params,
&temp_shape,
spread,
&bitmaps[i] ) );
/* Restore the original next variable. */
contour->next = temp_contour;
/* Since `slpit_sdf_shape' deallocated the original */
/* contours list, we need to assign the new value to */
/* the shape's contour. */
temp_shape.contours->next = head;
head = temp_shape.contours;
/* Simply flip the orientation in case of post-scritp fonts, */
/* so as to avoid modificatons in the combining phase. */
if ( internal_params.orientation == FT_ORIENTATION_FILL_LEFT )
{
if ( orientations[i] == SDF_ORIENTATION_CW )
orientations[i] = SDF_ORIENTATION_ACW;
else if ( orientations[i] == SDF_ORIENTATION_ACW )
orientations[i] = SDF_ORIENTATION_CW;
}
contour = contour->next;
}
/* assign the new contour list to `shape->contours' */
shape->contours = head;
/* cast the output bitmap buffer */
t = (FT_6D10*)bitmap->buffer;
/* Iterate through all the pixels and combine all the */
/* seperate contours. This is the rule for combining: */
/* */
/* => For all clockwise contours compute the largest */
/* value. Name this as `val_c'. */
/* => For all counter clockwise contours compute the */
/* smallest value. Name this as `val_ac'. */
/* => Now, finally use the smaller of `val_c' and */
/* `val_ac'. */
for ( j = 0; j < rows; j++ )
{
for ( i = 0; i < width; i++ )
{
FT_Int id = j * width + i; /* index of current pixel */
FT_Int c; /* contour iterator */
FT_6D10 val_c = SHRT_MIN; /* max clockwise value */
FT_6D10 val_ac = SHRT_MAX; /* min anti-clockwise value */
/* iterate through all the contours */
for ( c = 0; c < num_contours; c++ )
{
/* current contour value */
FT_6D10 temp = ((FT_6D10*)bitmaps[c].buffer)[id];
if ( orientations[c] == SDF_ORIENTATION_CW )
val_c = FT_MAX( val_c, temp ); /* for clockwise */
else
val_ac = FT_MIN( val_ac, temp ); /* for anti-clockwise */
}
/* Finally find the smaller of two and assign to output. */
/* Also apply the flip_sign if set. */
t[id] = FT_MIN( val_c, val_ac ) * ( flip_sign ? -1 : 1 );
}
}
Exit:
/* deallocate the orientations array */
if ( orientations )
SDF_FREE( orientations );
/* deallocate the temporary bitmaps */
if ( bitmaps )
{
if ( num_contours == 0 )
error = FT_THROW( Raster_Corrupted );
else
{
for ( i = 0; i < num_contours; i++ )
SDF_FREE( bitmaps[i].buffer );
SDF_FREE( bitmaps );
}
}
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;
FT_Int line = __LINE__;
/* in non debugging mode this is not used */
FT_UNUSED( line );
*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;
SDF_Params internal_params;
SDF_MEMORY_TRACKER_DECLARE();
/* 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;
}
/* setup the params */
internal_params.orientation = FT_Outline_Get_Orientation( outline );
internal_params.flip_sign = sdf_params->flip_sign;
internal_params.flip_y = sdf_params->flip_y;
internal_params.overload_sign = 0;
/* assign a custom user pointer to `FT_Memory' */
/* also keep a reference of the old user pointer */
/* in order to debug the memory while compiling */
/* with `FT_DEBUG_MEMORY'. */
SDF_MEMORY_TRACKER_SETUP();
FT_CALL( sdf_shape_new( memory, &shape ) );
FT_CALL( sdf_outline_decompose( outline, shape ) );
if ( sdf_params->overlaps )
FT_CALL( sdf_generate_with_overlaps( internal_params,
shape, sdf_params->spread,
sdf_params->root.target ) );
else
FT_CALL( sdf_generate_subdivision( internal_params,
shape, sdf_params->spread,
sdf_params->root.target ) );
if ( shape )
sdf_shape_done( &shape );
/* restore the memory->user */
SDF_MEMORY_TRACKER_DONE();
Exit:
return error;
}
static void
sdf_raster_done( FT_Raster raster )
{
FT_Memory memory = (FT_Memory)((SDF_TRaster*)raster)->memory;
FT_Int line = __LINE__;
/* in non debugging mode this is not used */
FT_UNUSED( line );
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 */