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-/****************************************************************************
- *
- * 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,
- &current_dist ) );
-
- if ( current_dist.distance >= 0 )
- {
- diff = current_dist.distance - min_dist.distance;
-
-
- if ( FT_ABS(diff ) < CORNER_CHECK_EPSILON )
- min_dist = resolve_corner( min_dist, current_dist );
- else if ( diff < 0 )
- min_dist = current_dist;
- }
- else
- FT_TRACE0(( "sdf_contour_get_min_distance: 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,
- &current_dist ) );
-
- if ( current_dist.distance < min_dist.distance )
- min_dist = current_dist;
-
- contour_list = contour_list->next;
- }
-
- /* [OPTIMIZATION]: if (min_dist > sp_sq) then simply clamp */
- /* the value to spread to avoid square_root */
-
- /* clamp the values to spread */
- if ( min_dist.distance > sp_sq )
- min_dist.distance = sp_sq;
-
- /* square_root the values and fit in a 6.10 fixed point */
- if ( USE_SQUARED_DISTANCES )
- min_dist.distance = square_root( min_dist.distance );
-
- if ( internal_params.orientation == FT_ORIENTATION_FILL_LEFT )
- min_dist.sign = -min_dist.sign;
- if ( internal_params.flip_sign )
- min_dist.sign = -min_dist.sign;
-
- min_dist.distance /= 64; /* convert from 16.16 to 22.10 */
-
- value = min_dist.distance & 0x0000FFFF; /* truncate to 6.10 */
- value *= min_dist.sign;
-
- if ( internal_params.flip_y )
- index = y * width + x;
- else
- index = ( rows - y - 1 ) * width + x;
-
- buffer[index] = value;
- }
- }
-
- Exit:
- return error;
- }
-
-#endif /* 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 */