#include #include #include #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, ¤t_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, ¤t_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 */