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Diffstat (limited to 'Build/source/libs/freetype2/freetype-src/src/sdf/ftsdf.c')
-rw-r--r-- | Build/source/libs/freetype2/freetype-src/src/sdf/ftsdf.c | 3878 |
1 files changed, 0 insertions, 3878 deletions
diff --git a/Build/source/libs/freetype2/freetype-src/src/sdf/ftsdf.c b/Build/source/libs/freetype2/freetype-src/src/sdf/ftsdf.c deleted file mode 100644 index d3722b1dc17..00000000000 --- a/Build/source/libs/freetype2/freetype-src/src/sdf/ftsdf.c +++ /dev/null @@ -1,3878 +0,0 @@ -/**************************************************************************** - * - * ftsdf.c - * - * Signed Distance Field support for outline fonts (body). - * - * Copyright (C) 2020-2021 by - * David Turner, Robert Wilhelm, and Werner Lemberg. - * - * Written by Anuj Verma. - * - * This file is part of the FreeType project, and may only be used, - * modified, and distributed under the terms of the FreeType project - * license, LICENSE.TXT. By continuing to use, modify, or distribute - * this file you indicate that you have read the license and - * understand and accept it fully. - * - */ - - -#include <freetype/internal/ftobjs.h> -#include <freetype/internal/ftdebug.h> -#include <freetype/ftoutln.h> -#include <freetype/fttrigon.h> -#include <freetype/ftbitmap.h> -#include "ftsdf.h" - -#include "ftsdferrs.h" - - - /************************************************************************** - * - * A brief technical overview of how the SDF rasterizer works - * ---------------------------------------------------------- - * - * [Notes]: - * * SDF stands for Signed Distance Field everywhere. - * - * * This renderer generates SDF directly from outlines. There is - * another renderer called 'bsdf', which converts bitmaps to SDF; see - * file `ftbsdf.c` for more. - * - * * The basic idea of generating the SDF is taken from Viktor Chlumsky's - * research paper. The paper explains both single and multi-channel - * SDF, however, this implementation only generates single-channel SDF. - * - * 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 that make the outline of a shape/glyph. - * Each contour comprises of several edges, with three types of edges. - * - * * line segments - * * conic Bezier curves - * * cubic Bezier curves - * - * (2) Apart from the outlines we also have a two-dimensional grid, namely - * the bitmap that is used to represent the final SDF data. - * - * (3) 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 its sign is positive, otherwise it is 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 running this algorithm the bitmap contains information about - * the shortest distance from each point to the outline of the shape. - * Of course, while this is the most straightforward way of generating - * SDF, we use various optimizations in our implementation. See the - * `sdf_generate_*' functions in this file for all details. - * - * The optimization currently used by default is subdivision; see - * function `sdf_generate_subdivision` for more. - * - * Also, to see how we compute the shortest distance from a point to - * each type of edge, check out the `get_min_distance_*' functions. - * - */ - - - /************************************************************************** - * - * The macro FT_COMPONENT is used in trace mode. It is an implicit - * parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log - * messages during execution. - */ -#undef FT_COMPONENT -#define FT_COMPONENT sdf - - - /************************************************************************** - * - * 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_CCW :: - * Counter-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_CCW = 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 counter-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 ( !FT_QALLOC( 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; - - FT_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 ( !FT_QALLOC( 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 ); - } - - FT_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 ( !FT_QALLOC( 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 */ - FT_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 counter-clockwise */ - /* contours cover a negative area. */ - if ( area > 0 ) - return SDF_ORIENTATION_CW; - else - return SDF_ORIENTATION_CCW; - } - - - /* 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; - } - - - /************************************************************************** - * - * 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_shape_dump: null shape\n" )); - return; - } - - contour_list = shape->contours; - - FT_TRACE5(( "sdf_shape_dump (values are in 26.6 format):\n" )); - - while ( contour_list ) - { - FT_UInt num_edges = 0; - SDF_Edge* edge_list; - SDF_Contour* contour = contour_list; - - - FT_TRACE5(( " Contour %d\n", num_contours )); - - edge_list = contour->edges; - - while ( edge_list ) - { - SDF_Edge* edge = edge_list; - - - FT_TRACE5(( " %3d: ", num_edges )); - - switch ( edge->edge_type ) - { - case SDF_EDGE_LINE: - FT_TRACE5(( "Line: (%ld, %ld) -- (%ld, %ld)\n", - edge->start_pos.x, edge->start_pos.y, - edge->end_pos.x, edge->end_pos.y )); - total_lines++; - break; - - case SDF_EDGE_CONIC: - FT_TRACE5(( "Conic: (%ld, %ld) .. (%ld, %ld) .. (%ld, %ld)\n", - edge->start_pos.x, edge->start_pos.y, - edge->control_a.x, edge->control_a.y, - edge->end_pos.x, edge->end_pos.y )); - total_conic++; - break; - - case SDF_EDGE_CUBIC: - FT_TRACE5(( "Cubic: (%ld, %ld) .. (%ld, %ld)" - " .. (%ld, %ld) .. (%ld %ld)\n", - edge->start_pos.x, edge->start_pos.y, - edge->control_a.x, edge->control_a.y, - edge->control_b.x, edge->control_b.y, - 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(( " 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 )); - } - -#endif /* FT_DEBUG_LEVEL_TRACE */ - - - /************************************************************************** - * - * 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 */ - - - /*************************************************************************/ - /*************************************************************************/ - /** **/ - /** RASTERIZER **/ - /** **/ - /*************************************************************************/ - /*************************************************************************/ - - /************************************************************************** - * - * @Function: - * resolve_corner - * - * @Description: - * At some places on the grid two edges can give opposite directions; - * 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 the shortest distance vector and the edge direction, i.e., - * - * ``` - * => sign = cross(x - o, direction(a)) - * ``` - * - * Using the right hand thumb rule we can see that the sign will be - * positive. - * - * If we use `b', however, we have - * - * ``` - * => sign = cross(x - o, direction(b)) - * ``` - * - * In this case the sign will be negative. To determine the correct - * sign we thus divide the plane in two halves and check which plane the - * point lies in. - * - * ``` - * | - * 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 test can be easily done by calculating the - * orthogonality and taking the greater one. - * - * The orthogonality is simply the sinus of the two vectors (i.e., - * x - o) and the corresponding direction. We efficiently pre-compute - * the orthogonality with the corresponding `get_min_distance_*` - * functions. - * - * @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 computed by 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. As a - * consequence, this function should not be used if the two distances - * are fairly apart. In that case simply use the signed distance with - * a 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: - * Find the shortest distance from the `line` segment to a given `point` - * and assign it to `out`. Use it for line segments only. - * - * @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. - * - * @Output: - * out :: - * Signed distance from `point` to `line`. - * - * @Return: - * FreeType error, 0 means success. - * - * @Note: - * The `line' parameter must have an 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, we do the following. Let's assume that - * - * ``` - * a = start point of the line segment - * b = end point of the line segment - * p = point from which shortest distance is to be calculated - * ``` - * - * (1) Write the parametric equation of the line. - * - * ``` - * point_on_line = a + (b - a) * t (t is the factor) - * ``` - * - * (2) Find the projection of point `p` on the line. The projection - * will be perpendicular to the line, which allows us to get the - * solution by making the dot product zero. - * - * ``` - * (point_on_line - a) . (p - point_on_line) = 0 - * - * (point_on_line) - * (a) x-------o----------------x (b) - * |_| - * | - * | - * (p) - * ``` - * - * (3) Simplification of the above equation yields the factor of - * `point_on_line`: - * - * ``` - * t = ((p - a) . (b - a)) / |b - a|^2 - * ``` - * - * (4) We clamp factor `t` between [0.0f, 1.0f] because `point_on_line` - * can be outside of the line segment: - * - * ``` - * (point_on_line) - * (a) x------------------------x (b) -----o--- - * |_| - * | - * | - * (p) - * ``` - * - * (5) Finally, the distance we are interested in is - * - * ``` - * |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 `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; - } - - - /************************************************************************** - * - * @Function: - * get_min_distance_conic - * - * @Description: - * Find the shortest distance from the `conic` Bezier curve to a given - * `point` and assign it to `out`. Use it for conic/quadratic curves - * only. - * - * @Input: - * conic :: - * The conic Bezier curve to which the shortest distance is to be - * computed. - * - * point :: - * Point from which the shortest distance is to be computed. - * - * @Output: - * out :: - * Signed distance from `point` to `conic`. - * - * @Return: - * FreeType error, 0 means success. - * - * @Note: - * The `conic` parameter must have an edge type of `SDF_EDGE_CONIC`. - * - */ - -#if !USE_NEWTON_FOR_CONIC - - /* - * The function uses an analytical method to find the shortest distance - * which is faster than the Newton-Raphson method, but has underflows at - * the moment. Use Newton's method if you can see artifacts in the SDF. - */ - 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 the line segment algorithm. The - * shortest distance is 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 endpoints, because the - * perpendicular may not be the shortest. - * - * Let's assume that - * ``` - * p0 = first endpoint - * p1 = control point - * p2 = second endpoint - * p = point from which shortest distance is to be calculated - * ``` - * - * (1) The equation of a quadratic Bezier curve can be written as - * - * ``` - * B(t) = (1 - t)^2 * p0 + 2(1 - t)t * p1 + t^2 * p2 - * ``` - * - * with `t` a factor in the range [0.0f, 1.0f]. This equation can - * be rewritten as - * - * ``` - * B(t) = t^2 * (p0 - 2p1 + p2) + 2t * (p1 - p0) + p0 - * ``` - * - * With - * - * ``` - * A = p0 - 2p1 + p2 - * B = p1 - p0 - * ``` - * - * we have - * - * ``` - * B(t) = t^2 * A + 2t * B + p0 - * ``` - * - * (2) The derivative of the last equation above is - * - * ``` - * B'(t) = 2 *(tA + B) - * ``` - * - * (3) 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)`) make 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 - * - * ``` - * at^3 + bt^2 + ct + d = 0 - * ``` - * - * with - * - * ``` - * a = A.A - * b = 3A.B - * c = 2B.B + A.p0 - A.p - * d = p0.B - p.B - * ``` - * - * (4) Now the roots of the equation can be computed using 'Cardano's - * Cubic formula'; we clamp the roots in the 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; - } - - 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 curve, but Behdad - * Esfahbod proved the following lemma. - * - * Lemma: - * - * (1) 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. - * - * (2) 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 more details see - * - * 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 ); - - /* compute `cross` if not perpendicular */ - 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 /* USE_NEWTON_FOR_CONIC */ - - /* - * 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. - */ - 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 a conic curve. It does not involve solving - * any cubic equation, that is why there is no risk of underflow. - * - * Let's assume that - * - * ``` - * p0 = first endpoint - * p1 = control point - * p3 = second endpoint - * p = point from which shortest distance is to be calculated - * ``` - * - * (1) The equation of a quadratic Bezier curve can be written as - * - * ``` - * B(t) = (1 - t)^2 * p0 + 2(1 - t)t * p1 + t^2 * p2 - * ``` - * - * with `t` the factor in the range [0.0f, 1.0f]. The above - * equation can be rewritten as - * - * ``` - * B(t) = t^2 * (p0 - 2p1 + p2) + 2t * (p1 - p0) + p0 - * ``` - * - * With - * - * ``` - * A = p0 - 2p1 + p2 - * B = 2 * (p1 - p0) - * ``` - * - * we have - * - * ``` - * B(t) = t^2 * A + t * B + p0 - * ``` - * - * (2) The derivative of the above equation is - * - * ``` - * B'(t) = 2t * A + B - * ``` - * - * (3) The second derivative of the above equation is - * - * ``` - * B''(t) = 2A - * ``` - * - * (4) The equation `P(t)` of the distance from point `p` to the curve - * can be written as - * - * ``` - * P(t) = t^2 * A + t^2 * B + p0 - p - * ``` - * - * With - * - * ``` - * C = p0 - p - * ``` - * - * we have - * - * ``` - * P(t) = t^2 * A + t * B + C - * ``` - * - * (5) Finally, the equation of the angle between `B(t)` and `P(t)` can - * be written as - * - * ``` - * Q(t) = P(t) . B'(t) - * ``` - * - * (6) Our task is to find a value of `t` such that the above equation - * `Q(t)` becomes zero, this is, the point-to-curve vector makes - * 90~degrees with the curve. We solve this with the Newton-Raphson - * method. - * - * (7) We first assume an arbitary value of factor `t`, which we then - * improve. - * - * ``` - * t := Q(t) / Q'(t) - * ``` - * - * Putting the 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)) - * ``` - * - * Note that `P'(t)` is the same as `B'(t)` because the constant is - * gone due to the derivative. - * - * (8) 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; - } - - 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 ); - - /* 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 is 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) = 2t * A + 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 ); - - /* compute `cross` if not perpendicular */ - 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 /* USE_NEWTON_FOR_CONIC */ - - - /************************************************************************** - * - * @Function: - * get_min_distance_cubic - * - * @Description: - * Find the shortest distance from the `cubic` Bezier curve to a given - * `point` and assigns it to `out`. Use it for cubic curves only. - * - * @Input: - * cubic :: - * The cubic Bezier curve to which the shortest distance is to be - * computed. - * - * point :: - * Point from which the shortest distance is to be computed. - * - * @Output: - * out :: - * Signed distance from `point` to `cubic`. - * - * @Return: - * 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 an 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 quadratic curve algorithm. The only - * difference is that while calculating factor `t`, instead of a cubic - * polynomial equation we have to find the roots of a 5th degree - * polynomial equation. Solving this would require a significant amount - * of time, and still the results may not be accurate. We are thus - * going to directly approximate the value of `t` using the Newton-Raphson - * method. - * - * Let's assume that - * - * ``` - * p0 = first endpoint - * p1 = first control point - * p2 = second control point - * p3 = second endpoint - * p = point from which shortest distance is to be calculated - * ``` - * - * (1) The equation of a cubic Bezier curve can be written as - * - * ``` - * B(t) = (1 - t)^3 * p0 + 3(1 - t)^2 t * p1 + - * 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) + - * 3t^2 * (p0 - 2p1 + p2) + 3t * (-p0 + p1) + p0 - * ``` - * - * With - * - * ``` - * A = -p0 + 3p1 - 3p2 + p3 - * B = 3(p0 - 2p1 + p2) - * C = 3(-p0 + p1) - * ``` - * - * we have - * - * ``` - * B(t) = t^3 * A + t^2 * B + t * C + p0 - * ``` - * - * (2) The derivative of the above equation is - * - * ``` - * B'(t) = 3t^2 * A + 2t * B + C - * ``` - * - * (3) The second derivative of the above equation is - * - * ``` - * B''(t) = 6t * A + 2B - * ``` - * - * (4) The equation `P(t)` of the distance from point `p` to the curve - * can be written as - * - * ``` - * P(t) = t^3 * A + t^2 * B + t * C + p0 - p - * ``` - * - * With - * - * ``` - * D = p0 - p - * ``` - * - * we have - * - * ``` - * P(t) = t^3 * A + t^2 * B + t * C + D - * ``` - * - * (5) Finally the equation of the angle between `B(t)` and `P(t)` can - * be written as - * - * ``` - * Q(t) = P(t) . B'(t) - * ``` - * - * (6) Our task is to find a value of `t` such that the above equation - * `Q(t)` becomes zero, this is, the point-to-curve vector makes - * 90~degree with curve. We solve this with the Newton-Raphson - * method. - * - * (7) We first assume an arbitary value of factor `t`, which we then - * improve. - * - * ``` - * t := Q(t) / Q'(t) - * ``` - * - * Putting the 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)) - * ``` - * - * Note that `P'(t)` is the same as `B'(t)` because the constant is - * gone due to the derivative. - * - * (8) 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_factor = 0; /* factor at shortest distance */ - FT_16D16 min_factor_sq = 0; /* factor at shortest distance */ - FT_16D16 cross; /* to determine the sign */ - FT_16D16 min = FT_INT_MAX; /* shortest distance */ - - 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; - } - - 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 + t * C + 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 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 ); - - /* compute `cross` if not perpendicular */ - 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: - * Find shortest distance from `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. - * - * @Output: - * out :: - * Signed distance from `point` to `edge`. - * - * @Return: - * 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 - - #error "DO NOT USE THIS!" - #error "The function still outputs 16-bit data, which might cause memory" - #error "corruption. If required I will add this later." - - /************************************************************************** - * - * @Function: - * sdf_contour_get_min_distance - * - * @Description: - * Iterate over all edges that make up the contour, find the shortest - * distance from a point to this contour, and assigns result 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. - * - * @Output: - * out :: - * Signed distance from the `point' to the `contour'. - * - * @Return: - * FreeType error, 0 means success. - * - * @Note: - * The function does not return a signed distance for each edge which - * makes 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 over 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: Overflow.\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 does not align or compute the size of - * `bitmap`; therefore the calling application must set up `bitmap` - * properly and transform the `shape' appropriately in advance. - * - * Currently we check all pixels against all contours and all edges. - * - * @Input: - * internal_params :: - * Internal parameters and properties required by the rasterizer. See - * @SDF_Params for more. - * - * shape :: - * A complete shape which is used to generate SDF. - * - * spread :: - * Maximum distances to be allowed in the output bitmap. - * - * @Output: - * bitmap :: - * The output bitmap which will contain the SDF information. - * - * @Return: - * 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`] as a 16.16 fixed value */ - - 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_generate:" - " Cannot render glyph with width/height == 0\n" )); - FT_TRACE0(( " " - " (width, height provided [%d, %d])\n", - width, rows )); - - error = FT_THROW( Cannot_Render_Glyph ); - goto Exit; - } - - /* loop over all rows */ - for ( y = 0; y < rows; y++ ) - { - /* loop over all 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 over all 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 /* 0 */ - - - /************************************************************************** - * - * @Function: - * sdf_generate_bounding_box - * - * @Description: - * This function does basically the same thing as `sdf_generate` above - * but more efficiently. - * - * Instead of checking all pixels against all edges, we loop over all - * edges and only check pixels around the control box of the edge; the - * control box is increased by the spread in all directions. Anything - * outside of the control box that exceeds `spread` doesn't need to be - * computed. - * - * Lastly, to determine the sign of unchecked pixels, we do a single - * pass of all rows starting with a '+' sign and flipping when we come - * across a '-' sign and continue. This also eliminates the possibility - * 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 more. - * - * shape :: - * A complete shape which is used to generate SDF. - * - * spread :: - * Maximum distances to be allowed in the output bitmap. - * - * @Output: - * bitmap :: - * The output bitmap which will contain the SDF information. - * - * @Return: - * 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_SDFFormat* buffer; /* the bitmap buffer */ - - /* This buffer has the same size in indices as the */ - /* bitmap buffer. When we check a pixel position for */ - /* a shortest distance we keep it in this buffer. */ - /* This way we can find out which pixel is set, */ - /* and also determine the signs properly. */ - SDF_Signed_Distance* dists = NULL; - - const FT_16D16 fixed_spread = FT_INT_16D16( spread ); - - - 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; - } - - if ( FT_ALLOC( dists, - bitmap->width * bitmap->rows * sizeof ( *dists ) ) ) - goto Exit; - - contours = shape->contours; - width = (FT_Int)bitmap->width; - rows = (FT_Int)bitmap->rows; - buffer = (FT_SDFFormat*)bitmap->buffer; - - if ( USE_SQUARED_DISTANCES ) - sp_sq = fixed_spread * fixed_spread; - else - sp_sq = fixed_spread; - - if ( width == 0 || rows == 0 ) - { - FT_TRACE0(( "sdf_generate:" - " Cannot render glyph with width/height == 0\n" )); - FT_TRACE0(( " " - " (width, height provided [%d, %d])", width, rows )); - - error = FT_THROW( Cannot_Render_Glyph ); - goto Exit; - } - - /* loop over all contours */ - while ( contours ) - { - SDF_Edge* edges = contours->edges; - - - /* loop over all edges */ - while ( edges ) - { - FT_CBox cbox; - FT_Int x, y; - - - /* get the control box and increase it 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 over 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 the 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 = (FT_UInt)( y * width + x ); - else - index = (FT_UInt)( ( rows - y - 1 ) * width + x ); - - /* check whether 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 is 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 = (FT_UInt)( j * width + i ); - - /* if the pixel is not set */ - /* its shortest distance is more than `spread` */ - if ( dists[index].sign == 0 ) - dists[index].distance = fixed_spread; - else - current_sign = dists[index].sign; - - /* clamp the values */ - if ( dists[index].distance > fixed_spread ) - dists[index].distance = fixed_spread; - - /* flip sign if required */ - dists[index].distance *= internal_params.flip_sign ? -current_sign - : current_sign; - - /* concatenate to appropriate format */ - buffer[index] = map_fixed_to_sdf( dists[index].distance, - fixed_spread ); - } - } - - Exit: - FT_FREE( dists ); - return error; - } - - - /************************************************************************** - * - * @Function: - * sdf_generate_subdivision - * - * @Description: - * Subdivide the shape into a number of straight lines, then use the - * above `sdf_generate_bounding_box` function to generate the SDF. - * - * Note: After calling this function `shape` no longer has the original - * edges, it only contains lines. - * - * @Input: - * internal_params :: - * Internal parameters and properties required by the rasterizer. - * See @SDF_Params for more. - * - * shape :: - * A complete shape which is used to generate SDF. - * - * spread :: - * Maximum distances to be allowed inthe output bitmap. - * - * @Output: - * bitmap :: - * The output bitmap which will contain the SDF information. - * - * @Return: - * 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. - * - * We take advantage of two facts. - * - * (1) Computing the shortest distance from a point to a line segment is - * very fast. - * (2) We don't have to compute the shortest distance for the entire - * two-dimensional grid. - * - * Both ideas lead to the following optimization. - * - * (1) Split the outlines into a number of line segments. - * - * (2) For each line segment, only process its neighborhood. - * - * (3) Compute the closest distance to the line only for neighborhood - * grid points. - * - * This greatly reduces the number of grid points to 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 generates SDF for contours separately on - * separate bitmaps (to generate SDF it uses - * `sdf_generate_subdivision`). At the end it simply combines 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 more. - * - * shape :: - * A complete shape which is used to generate SDF. - * - * spread :: - * Maximum distances to be allowed in the output bitmap. - * - * @Output: - * bitmap :: - * The output bitmap which will contain the SDF information. - * - * @Return: - * FreeType error, 0 means success. - * - * @Note: - * The function cannot generate a proper SDF for glyphs with - * self-intersecting contours because we cannot separate them into two - * separate bitmaps. In case of self-intersecting contours it is - * necessary to remove the overlaps before generating the 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; /* separate 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_SDFFormat* t; /* target bitmap buffer */ - FT_Bool flip_sign; /* flip sign? */ - - /* orientation of all the separate contours */ - SDF_Contour_Orientation* orientations; - - - bitmaps = NULL; - orientations = NULL; - head = NULL; - - if ( !shape || !bitmap || !shape->memory ) - return FT_THROW( Invalid_Argument ); - - /* Disable `flip_sign` to avoid extra complication */ - /* during the combination phase. */ - flip_sign = internal_params.flip_sign; - internal_params.flip_sign = 0; - - 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 separate contours */ - if ( FT_ALLOC( bitmaps, - (FT_UInt)num_contours * sizeof ( *bitmaps ) ) ) - goto Exit; - - /* allocate array to hold orientation for all contours */ - if ( FT_ALLOC( orientations, - (FT_UInt)num_contours * sizeof ( *orientations ) ) ) - goto Exit; - - contour = shape->contours; - - /* Iterate over all contours and generate SDF separately. */ - 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 ( FT_ALLOC( bitmaps[i].buffer, - bitmap->rows * (FT_UInt)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 */ - /* overloads the default sign of the outside */ - /* pixels, which is necessary for */ - /* counter-clockwise contours. */ - if ( orientations[i] == SDF_ORIENTATION_CCW && - 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 `temp_shape` to hold the new contour. */ - /* Now, `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 `split_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-script 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_CCW; - else if ( orientations[i] == SDF_ORIENTATION_CCW ) - 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_SDFFormat*)bitmap->buffer; - - /* Iterate over all pixels and combine all separate */ - /* contours. These are the rules for combining: */ - /* */ - /* (1) For all clockwise contours, compute the largest */ - /* value. Name this as `val_c`. */ - /* (2) For all counter-clockwise contours, compute the */ - /* smallest value. Name this as `val_ac`. */ - /* (3) Now, finally use the smaller value 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_SDFFormat val_c = 0; /* max clockwise value */ - FT_SDFFormat val_ac = UCHAR_MAX; /* min counter-clockwise val */ - - - /* iterate through all the contours */ - for ( c = 0; c < num_contours; c++ ) - { - /* current contour value */ - FT_SDFFormat temp = ( (FT_SDFFormat*)bitmaps[c].buffer )[id]; - - - if ( orientations[c] == SDF_ORIENTATION_CW ) - val_c = FT_MAX( val_c, temp ); /* clockwise */ - else - val_ac = FT_MIN( val_ac, temp ); /* counter-clockwise */ - } - - /* Finally find the smaller of the two and assign to output. */ - /* Also apply `flip_sign` if set. */ - t[id] = FT_MIN( val_c, val_ac ); - - if ( flip_sign ) - t[id] = invert_sign( t[id] ); - } - } - - Exit: - /* deallocate orientations array */ - if ( orientations ) - FT_FREE( orientations ); - - /* deallocate temporary bitmaps */ - if ( bitmaps ) - { - if ( num_contours == 0 ) - error = FT_THROW( Raster_Corrupted ); - else - { - for ( i = 0; i < num_contours; i++ ) - FT_FREE( bitmaps[i].buffer ); - - FT_FREE( bitmaps ); - } - } - - /* restore the `flip_sign` property */ - internal_params.flip_sign = flip_sign; - - 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 ) - { - 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; - - - /* check for valid arguments */ - if ( !sdf_raster || !sdf_params ) - { - error = FT_THROW( Invalid_Argument ); - goto Exit; - } - - outline = (FT_Outline*)sdf_params->root.source; - - /* check whether outline is valid */ - 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 whether the outline has valid fields */ - if ( !outline->contours || !outline->points ) - { - error = FT_THROW( Invalid_Outline ); - goto Exit; - } - - /* check whether spread is set properly */ - if ( sdf_params->spread > MAX_SPREAD || - sdf_params->spread < MIN_SPREAD ) - { - FT_TRACE0(( "sdf_raster_render:" - " The `spread' field of `SDF_Raster_Params' is invalid,\n" )); - FT_TRACE0(( " " - " the value of this field must be within [%d, %d].\n", - MIN_SPREAD, MAX_SPREAD )); - FT_TRACE0(( " " - " Also, you must pass `SDF_Raster_Params' instead of\n" )); - FT_TRACE0(( " " - " the default `FT_Raster_Params' while calling\n" )); - FT_TRACE0(( " " - " this function and set the fields properly.\n" )); - - error = FT_THROW( Invalid_Argument ); - goto Exit; - } - - memory = sdf_raster->memory; - if ( !memory ) - { - FT_TRACE0(( "sdf_raster_render:" - " Raster not setup properly,\n" )); - FT_TRACE0(( " " - " unable to find memory handle.\n" )); - - error = FT_THROW( Invalid_Handle ); - goto Exit; - } - - /* set up the parameters */ - 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; - - 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 ); - - Exit: - return error; - } - - - static void - sdf_raster_done( FT_Raster raster ) - { - FT_Memory memory = (FT_Memory)((SDF_TRaster*)raster)->memory; - - - FT_FREE( raster ); - } - - - FT_DEFINE_RASTER_FUNCS( - ft_sdf_raster, - - FT_GLYPH_FORMAT_OUTLINE, - - (FT_Raster_New_Func) sdf_raster_new, /* raster_new */ - (FT_Raster_Reset_Func) sdf_raster_reset, /* raster_reset */ - (FT_Raster_Set_Mode_Func)sdf_raster_set_mode, /* raster_set_mode */ - (FT_Raster_Render_Func) sdf_raster_render, /* raster_render */ - (FT_Raster_Done_Func) sdf_raster_done /* raster_done */ - ) - - -/* END */ |