ref: a255125fe482772feade4334635fc8a3967199b9
dir: /src/sdf/ftsdf.c/
#include <freetype/internal/ftobjs.h>
#include <freetype/internal/ftdebug.h>
#include <freetype/fttrigon.h>
#include "ftsdf.h"
#include "ftsdferrs.h"
/**************************************************************************
*
* for tracking used memory
*
*/
/* The memory tracker only works when `FT_DEBUG_MEMORY` is defined; */
/* we need some variables such as `_ft_debug_file`, which aren't */
/* available otherwise. */
#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;
/*
* These functions are used while allocating and deallocating memory.
* They restore the previous user pointer before calling the allocation
* functions.
*/
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 /* !FT_DEBUG_LEVEL_TRACE */
#define SDF_ALLOC FT_QALLOC
#define SDF_FREE FT_FREE
#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 /* !FT_DEBUG_LEVEL_TRACE */
/**************************************************************************
*
* definitions
*
*/
/*
* If set to 1, the rasterizer uses Newton-Raphson's method for finding
* the shortest distance from a point to a conic curve.
*
* If set to 0, an analytical method gets used instead, which computes the
* roots of a cubic polynomial to find the shortest distance. However,
* the analytical method can currently underflow; we thus use Newton's
* method by default.
*/
#ifndef USE_NEWTON_FOR_CONIC
#define USE_NEWTON_FOR_CONIC 1
#endif
/*
* The number of intervals a Bezier curve gets sampled and checked to find
* the shortest distance.
*/
#define MAX_NEWTON_DIVISIONS 4
/*
* The number of steps of Newton's iterations in each interval of the
* Bezier curve. Basically, we run Newton's approximation
*
* x -= Q(t) / Q'(t)
*
* for each division to get the shortest distance.
*/
#define MAX_NEWTON_STEPS 4
/*
* The epsilon distance (in 16.16 fractional units) used for corner
* resolving. If the difference of two distances is less than this value
* they will be checked for a corner if they are ambiguous.
*/
#define CORNER_CHECK_EPSILON 32
#if 0
/*
* Coarse grid dimension. Will probably be removed in the future because
* coarse grid optimization is the slowest algorithm.
*/
#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 it is passed to
* the @FT_Raster_RenderFunc function, which then can be used however we
* want.
*
* @Fields:
* memory ::
* Used internally to allocate intermediate memory while raterizing.
*
*/
typedef struct SDF_TRaster_
{
FT_Memory memory;
} SDF_TRaster;
/**************************************************************************
*
* @Enum:
* SDF_Edge_Type
*
* @Description:
* Enumeration of all curve types 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 one 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 orientation values of a contour. We determine the
* orientation by calculating the area covered by a contour. Contrary
* to values returned by @FT_Outline_Get_Orientation,
* `SDF_Contour_Orientation` is independent of the fill rule, which can
* be different for different font formats.
*
* @Fields:
* SDF_ORIENTATION_NONE ::
* Undefined orientation, used for initialization and error detection.
*
* SDF_ORIENTATION_CW ::
* Clockwise orientation (positive area covered).
*
* SDF_ORIENTATION_ACW ::
* Anti-clockwise orientation (negative area covered).
*
* @Note:
* See @FT_Outline_Get_Orientation for more details.
*
*/
typedef enum SDF_Contour_Orientation_
{
SDF_ORIENTATION_NONE = 0,
SDF_ORIENTATION_CW = 1,
SDF_ORIENTATION_ACW = 2
} SDF_Contour_Orientation;
/**************************************************************************
*
* @Struct:
* 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;
/**************************************************************************
*
* @Struct:
* SDF_Contour
*
* @Description:
* Represent a complete contour, which contains a list of edges.
*
* @Fields:
* last_pos ::
* Contains the value of `end_pos' of the last edge in the list of
* edges. Useful while decomposing the outline with
* @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;
/**************************************************************************
*
* @Struct:
* 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;
/**************************************************************************
*
* @Struct:
* 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` macro defined in
* file `ftsdfcommon.h`.
*
* cross ::
* Cross product of the shortest distance vector (i.e., the vector
* from the point to the nearest edge) and the direction of the edge
* at the nearest point. This is used to resolve ambiguities of
* `sign`.
*
* sign ::
* A value used to indicate whether the distance vector is outside or
* inside the contour corresponding to the edge.
*
* @Note:
* `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;
/**************************************************************************
*
* @Struct:
* SDF_Params
*
* @Description:
* Yet another internal parameters required by the rasterizer.
*
* @Fields:
* orientation ::
* This is not the @SDF_Contour_Orientation value but @FT_Orientation,
* which determines whether clockwise-oriented outlines are to be
* filled or anti-clockwise-oriented ones.
*
* flip_sign ::
* If set to true, flip the sign. By default the points filled by the
* outline are positive.
*
* flip_y ::
* If set to true the output bitmap is upside-down. Can be useful
* because OpenGL and DirectX use different coordinate systems 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 a 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 };
/* Create 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;
}
/* Free the allocated `edge` variable. */
static void
sdf_edge_done( FT_Memory memory,
SDF_Edge** edge )
{
if ( !memory || !edge || !*edge )
return;
SDF_FREE( *edge );
}
/* Create a new @SDF_Contour on the heap and assign */
/* 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;
}
/* Free the allocated `contour` variable. */
/* Also free 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 edges */
while ( edges )
{
temp = edges;
edges = edges->next;
sdf_edge_done( memory, &temp );
}
SDF_FREE( *contour );
}
/* Create a new @SDF_Shape on the heap and assign */
/* 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;
}
/* Free the allocated `shape` variable. */
/* Also free 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 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 starting a new contour at `to`, */
/* which gets added 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 starts at the previous edge point and */
/* stops at `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 curve starts at the previous edge point */
/* and stops at `to`, with control point `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 curve starts at the previous edge point */
/* and stops at `to`, with two control points `control_1` and */
/* `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 structure 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 */
)
/* Decompose `outline` and put it into the `shape` structure. */
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
*
*/
/* Return 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;
/* fall through */
case SDF_EDGE_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;
}
/* fall through */
case SDF_EDGE_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;
}
/* Return orientation of a single contour. */
/* Note that the orientation is independent of the fill rule! */
/* So, for TTF a clockwise-oriented contour 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;
/* Calculate the area of the control box for all 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 contours cover a positive area, and anti-clockwise */
/* contours cover a negative area. */
if ( area > 0 )
return SDF_ORIENTATION_CW;
else
return SDF_ORIENTATION_ACW;
}
/* This function is exactly the same as the one */
/* in the smooth renderer. It splits a conic */
/* into two conics 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;
}
/* This function is exactly the same as the one */
/* in the smooth renderer. It splits a cubic */
/* into two cubics 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;
}
/* Split a conic Bezier curve into a number of lines */
/* and add them to `out'. */
/* */
/* This function uses recursion; we thus need */
/* parameter `max_splits' 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 conic outline */
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;
/* Otherwise 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:
/* Do 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;
}
/* Split a cubic Bezier curve into a number of lines */
/* and add them to `out`. */
/* */
/* This function uses recursion; we thus need */
/* parameter `max_splits' 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;
/* Otherwise 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:
/* Do 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;
}
/* Subdivide an entire shape into line segments */
/* 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 it 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 it 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;
}
/**************************************************************************
*
* 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 */
/* the 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 an 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;
}
/* Calculate the perpendicular by using '1 - base^2'. */
/* Then use arctan to compute the angle. */
static FT_16D16
arc_cos( FT_16D16 val )
{
FT_16D16 p;
FT_16D16 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 );
}
/* Compute roots of a quadratic polynomial, assign them to `out`, */
/* and return number of real roots. */
/* */
/* 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;
}
}
/* Compute roots of a cubic polynomial, assign them to `out`, */
/* and return number of real roots. */
/* */
/* 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 cause 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 /* !USE_NEWTON_FOR_CONIC */
/* END */