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+/***************************************************************************/
+/* */
+/* ftbbox.c */
+/* */
+/* FreeType bbox computation (body). */
+/* */
+/* Copyright 1996-2002, 2004, 2006, 2010, 2013 by */
+/* David Turner, Robert Wilhelm, and Werner Lemberg. */
+/* */
+/* 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. */
+/* */
+/***************************************************************************/
+
+
+ /*************************************************************************/
+ /* */
+ /* This component has a _single_ role: to compute exact outline bounding */
+ /* boxes. */
+ /* */
+ /*************************************************************************/
+
+
+#include <ft2build.h>
+#include FT_INTERNAL_DEBUG_H
+
+#include FT_BBOX_H
+#include FT_IMAGE_H
+#include FT_OUTLINE_H
+#include FT_INTERNAL_CALC_H
+#include FT_INTERNAL_OBJECTS_H
+
+
+ typedef struct TBBox_Rec_
+ {
+ FT_Vector last;
+ FT_BBox bbox;
+
+ } TBBox_Rec;
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Move_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `move_to' and `line_to' emitter during */
+ /* FT_Outline_Decompose(). It simply records the destination point */
+ /* in `user->last'; no further computations are necessary since we */
+ /* use the cbox as the starting bbox which must be refined. */
+ /* */
+ /* <Input> */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: A pointer to the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ static int
+ BBox_Move_To( FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ user->last = *to;
+
+ return 0;
+ }
+
+
+#define CHECK_X( p, bbox ) \
+ ( p->x < bbox.xMin || p->x > bbox.xMax )
+
+#define CHECK_Y( p, bbox ) \
+ ( p->y < bbox.yMin || p->y > bbox.yMax )
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Conic_Check */
+ /* */
+ /* <Description> */
+ /* Finds the extrema of a 1-dimensional conic Bezier curve and update */
+ /* a bounding range. This version uses direct computation, as it */
+ /* doesn't need square roots. */
+ /* */
+ /* <Input> */
+ /* y1 :: The start coordinate. */
+ /* */
+ /* y2 :: The coordinate of the control point. */
+ /* */
+ /* y3 :: The end coordinate. */
+ /* */
+ /* <InOut> */
+ /* min :: The address of the current minimum. */
+ /* */
+ /* max :: The address of the current maximum. */
+ /* */
+ static void
+ BBox_Conic_Check( FT_Pos y1,
+ FT_Pos y2,
+ FT_Pos y3,
+ FT_Pos* min,
+ FT_Pos* max )
+ {
+ if ( y1 <= y3 && y2 == y1 ) /* flat arc */
+ goto Suite;
+
+ if ( y1 < y3 )
+ {
+ if ( y2 >= y1 && y2 <= y3 ) /* ascending arc */
+ goto Suite;
+ }
+ else
+ {
+ if ( y2 >= y3 && y2 <= y1 ) /* descending arc */
+ {
+ y2 = y1;
+ y1 = y3;
+ y3 = y2;
+ goto Suite;
+ }
+ }
+
+ y1 = y3 = y1 - FT_MulDiv( y2 - y1, y2 - y1, y1 - 2*y2 + y3 );
+
+ Suite:
+ if ( y1 < *min ) *min = y1;
+ if ( y3 > *max ) *max = y3;
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Conic_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `conic_to' emitter during */
+ /* FT_Outline_Decompose(). It checks a conic Bezier curve with the */
+ /* current bounding box, and computes its extrema if necessary to */
+ /* update it. */
+ /* */
+ /* <Input> */
+ /* control :: A pointer to a control point. */
+ /* */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: The address of the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ /* <Note> */
+ /* In the case of a non-monotonous arc, we compute directly the */
+ /* extremum coordinates, as it is sufficiently fast. */
+ /* */
+ static int
+ BBox_Conic_To( FT_Vector* control,
+ FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ /* we don't need to check `to' since it is always an `on' point, thus */
+ /* within the bbox */
+
+ if ( CHECK_X( control, user->bbox ) )
+ BBox_Conic_Check( user->last.x,
+ control->x,
+ to->x,
+ &user->bbox.xMin,
+ &user->bbox.xMax );
+
+ if ( CHECK_Y( control, user->bbox ) )
+ BBox_Conic_Check( user->last.y,
+ control->y,
+ to->y,
+ &user->bbox.yMin,
+ &user->bbox.yMax );
+
+ user->last = *to;
+
+ return 0;
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Cubic_Check */
+ /* */
+ /* <Description> */
+ /* Finds the extrema of a 1-dimensional cubic Bezier curve and */
+ /* updates a bounding range. This version uses splitting because we */
+ /* don't want to use square roots and extra accuracy. */
+ /* */
+ /* <Input> */
+ /* p1 :: The start coordinate. */
+ /* */
+ /* p2 :: The coordinate of the first control point. */
+ /* */
+ /* p3 :: The coordinate of the second control point. */
+ /* */
+ /* p4 :: The end coordinate. */
+ /* */
+ /* <InOut> */
+ /* min :: The address of the current minimum. */
+ /* */
+ /* max :: The address of the current maximum. */
+ /* */
+
+#if 0
+
+ static void
+ BBox_Cubic_Check( FT_Pos p1,
+ FT_Pos p2,
+ FT_Pos p3,
+ FT_Pos p4,
+ FT_Pos* min,
+ FT_Pos* max )
+ {
+ FT_Pos q1, q2, q3, q4;
+
+
+ q1 = p1;
+ q2 = p2;
+ q3 = p3;
+ q4 = p4;
+
+ /* for a conic segment to possibly reach new maximum */
+ /* one of its off-points must be above the current value */
+ while ( q2 > *max || q3 > *max )
+ {
+ /* determine which half contains the maximum and split */
+ if ( q1 + q2 > q3 + q4 ) /* first half */
+ {
+ q4 = q4 + q3;
+ q3 = q3 + q2;
+ q2 = q2 + q1;
+ q4 = q4 + q3;
+ q3 = q3 + q2;
+ q4 = ( q4 + q3 ) / 8;
+ q3 = q3 / 4;
+ q2 = q2 / 2;
+ }
+ else /* second half */
+ {
+ q1 = q1 + q2;
+ q2 = q2 + q3;
+ q3 = q3 + q4;
+ q1 = q1 + q2;
+ q2 = q2 + q3;
+ q1 = ( q1 + q2 ) / 8;
+ q2 = q2 / 4;
+ q3 = q3 / 2;
+ }
+
+ /* check if either end reached the maximum */
+ if ( q1 == q2 && q1 >= q3 )
+ {
+ *max = q1;
+ break;
+ }
+ if ( q3 == q4 && q2 <= q4 )
+ {
+ *max = q4;
+ break;
+ }
+ }
+
+ q1 = p1;
+ q2 = p2;
+ q3 = p3;
+ q4 = p4;
+
+ /* for a conic segment to possibly reach new minimum */
+ /* one of its off-points must be below the current value */
+ while ( q2 < *min || q3 < *min )
+ {
+ /* determine which half contains the minimum and split */
+ if ( q1 + q2 < q3 + q4 ) /* first half */
+ {
+ q4 = q4 + q3;
+ q3 = q3 + q2;
+ q2 = q2 + q1;
+ q4 = q4 + q3;
+ q3 = q3 + q2;
+ q4 = ( q4 + q3 ) / 8;
+ q3 = q3 / 4;
+ q2 = q2 / 2;
+ }
+ else /* second half */
+ {
+ q1 = q1 + q2;
+ q2 = q2 + q3;
+ q3 = q3 + q4;
+ q1 = q1 + q2;
+ q2 = q2 + q3;
+ q1 = ( q1 + q2 ) / 8;
+ q2 = q2 / 4;
+ q3 = q3 / 2;
+ }
+
+ /* check if either end reached the minimum */
+ if ( q1 == q2 && q1 <= q3 )
+ {
+ *min = q1;
+ break;
+ }
+ if ( q3 == q4 && q2 >= q4 )
+ {
+ *min = q4;
+ break;
+ }
+ }
+ }
+
+#else
+
+ static void
+ test_cubic_extrema( FT_Pos y1,
+ FT_Pos y2,
+ FT_Pos y3,
+ FT_Pos y4,
+ FT_Fixed u,
+ FT_Pos* min,
+ FT_Pos* max )
+ {
+ /* FT_Pos a = y4 - 3*y3 + 3*y2 - y1; */
+ FT_Pos b = y3 - 2*y2 + y1;
+ FT_Pos c = y2 - y1;
+ FT_Pos d = y1;
+ FT_Pos y;
+ FT_Fixed uu;
+
+ FT_UNUSED ( y4 );
+
+
+ /* The polynomial is */
+ /* */
+ /* P(x) = a*x^3 + 3b*x^2 + 3c*x + d , */
+ /* */
+ /* dP/dx = 3a*x^2 + 6b*x + 3c . */
+ /* */
+ /* However, we also have */
+ /* */
+ /* dP/dx(u) = 0 , */
+ /* */
+ /* which implies by subtraction that */
+ /* */
+ /* P(u) = b*u^2 + 2c*u + d . */
+
+ if ( u > 0 && u < 0x10000L )
+ {
+ uu = FT_MulFix( u, u );
+ y = d + FT_MulFix( c, 2*u ) + FT_MulFix( b, uu );
+
+ if ( y < *min ) *min = y;
+ if ( y > *max ) *max = y;
+ }
+ }
+
+
+ static void
+ BBox_Cubic_Check( FT_Pos y1,
+ FT_Pos y2,
+ FT_Pos y3,
+ FT_Pos y4,
+ FT_Pos* min,
+ FT_Pos* max )
+ {
+ /* always compare first and last points */
+ if ( y1 < *min ) *min = y1;
+ else if ( y1 > *max ) *max = y1;
+
+ if ( y4 < *min ) *min = y4;
+ else if ( y4 > *max ) *max = y4;
+
+ /* now, try to see if there are split points here */
+ if ( y1 <= y4 )
+ {
+ /* flat or ascending arc test */
+ if ( y1 <= y2 && y2 <= y4 && y1 <= y3 && y3 <= y4 )
+ return;
+ }
+ else /* y1 > y4 */
+ {
+ /* descending arc test */
+ if ( y1 >= y2 && y2 >= y4 && y1 >= y3 && y3 >= y4 )
+ return;
+ }
+
+ /* There are some split points. Find them. */
+ /* We already made sure that a, b, and c below cannot be all zero. */
+ {
+ FT_Pos a = y4 - 3*y3 + 3*y2 - y1;
+ FT_Pos b = y3 - 2*y2 + y1;
+ FT_Pos c = y2 - y1;
+ FT_Pos d;
+ FT_Fixed t;
+ FT_Int shift;
+
+
+ /* We need to solve `ax^2+2bx+c' here, without floating points! */
+ /* The trick is to normalize to a different representation in order */
+ /* to use our 16.16 fixed-point routines. */
+ /* */
+ /* We compute FT_MulFix(b,b) and FT_MulFix(a,c) after normalization. */
+ /* These values must fit into a single 16.16 value. */
+ /* */
+ /* We normalize a, b, and c to `8.16' fixed-point values to ensure */
+ /* that their product is held in a `16.16' value including the sign. */
+ /* Necessarily, we need to shift `a', `b', and `c' so that the most */
+ /* significant bit of their absolute values is at position 22. */
+ /* */
+ /* This also means that we are using 23 bits of precision to compute */
+ /* the zeros, independently of the range of the original polynomial */
+ /* coefficients. */
+ /* */
+ /* This algorithm should ensure reasonably accurate values for the */
+ /* zeros. Note that they are only expressed with 16 bits when */
+ /* computing the extrema (the zeros need to be in 0..1 exclusive */
+ /* to be considered part of the arc). */
+
+ shift = FT_MSB( FT_ABS( a ) | FT_ABS( b ) | FT_ABS( c ) );
+
+ if ( shift > 22 )
+ {
+ shift -= 22;
+
+ /* this loses some bits of precision, but we use 23 of them */
+ /* for the computation anyway */
+ a >>= shift;
+ b >>= shift;
+ c >>= shift;
+ }
+ else
+ {
+ shift = 22 - shift;
+
+ a <<= shift;
+ b <<= shift;
+ c <<= shift;
+ }
+
+ /* handle a == 0 */
+ if ( a == 0 )
+ {
+ if ( b != 0 )
+ {
+ t = - FT_DivFix( c, b ) / 2;
+ test_cubic_extrema( y1, y2, y3, y4, t, min, max );
+ }
+ }
+ else
+ {
+ /* solve the equation now */
+ d = FT_MulFix( b, b ) - FT_MulFix( a, c );
+ if ( d < 0 )
+ return;
+
+ if ( d == 0 )
+ {
+ /* there is a single split point at -b/a */
+ t = - FT_DivFix( b, a );
+ test_cubic_extrema( y1, y2, y3, y4, t, min, max );
+ }
+ else
+ {
+ /* there are two solutions; we need to filter them */
+ d = FT_SqrtFixed( (FT_Int32)d );
+ t = - FT_DivFix( b - d, a );
+ test_cubic_extrema( y1, y2, y3, y4, t, min, max );
+
+ t = - FT_DivFix( b + d, a );
+ test_cubic_extrema( y1, y2, y3, y4, t, min, max );
+ }
+ }
+ }
+ }
+
+#endif
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Cubic_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `cubic_to' emitter during */
+ /* FT_Outline_Decompose(). It checks a cubic Bezier curve with the */
+ /* current bounding box, and computes its extrema if necessary to */
+ /* update it. */
+ /* */
+ /* <Input> */
+ /* control1 :: A pointer to the first control point. */
+ /* */
+ /* control2 :: A pointer to the second control point. */
+ /* */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: The address of the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ /* <Note> */
+ /* In the case of a non-monotonous arc, we don't compute directly */
+ /* extremum coordinates, we subdivide instead. */
+ /* */
+ static int
+ BBox_Cubic_To( FT_Vector* control1,
+ FT_Vector* control2,
+ FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ /* we don't need to check `to' since it is always an `on' point, thus */
+ /* within the bbox */
+
+ if ( CHECK_X( control1, user->bbox ) ||
+ CHECK_X( control2, user->bbox ) )
+ BBox_Cubic_Check( user->last.x,
+ control1->x,
+ control2->x,
+ to->x,
+ &user->bbox.xMin,
+ &user->bbox.xMax );
+
+ if ( CHECK_Y( control1, user->bbox ) ||
+ CHECK_Y( control2, user->bbox ) )
+ BBox_Cubic_Check( user->last.y,
+ control1->y,
+ control2->y,
+ to->y,
+ &user->bbox.yMin,
+ &user->bbox.yMax );
+
+ user->last = *to;
+
+ return 0;
+ }
+
+FT_DEFINE_OUTLINE_FUNCS(bbox_interface,
+ (FT_Outline_MoveTo_Func) BBox_Move_To,
+ (FT_Outline_LineTo_Func) BBox_Move_To,
+ (FT_Outline_ConicTo_Func)BBox_Conic_To,
+ (FT_Outline_CubicTo_Func)BBox_Cubic_To,
+ 0, 0
+ )
+
+ /* documentation is in ftbbox.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Outline_Get_BBox( FT_Outline* outline,
+ FT_BBox *abbox )
+ {
+ FT_BBox cbox;
+ FT_BBox bbox;
+ FT_Vector* vec;
+ FT_UShort n;
+
+
+ if ( !abbox )
+ return FT_THROW( Invalid_Argument );
+
+ if ( !outline )
+ return FT_THROW( Invalid_Outline );
+
+ /* if outline is empty, return (0,0,0,0) */
+ if ( outline->n_points == 0 || outline->n_contours <= 0 )
+ {
+ abbox->xMin = abbox->xMax = 0;
+ abbox->yMin = abbox->yMax = 0;
+ return 0;
+ }
+
+ /* We compute the control box as well as the bounding box of */
+ /* all `on' points in the outline. Then, if the two boxes */
+ /* coincide, we exit immediately. */
+
+ vec = outline->points;
+ bbox.xMin = bbox.xMax = cbox.xMin = cbox.xMax = vec->x;
+ bbox.yMin = bbox.yMax = cbox.yMin = cbox.yMax = vec->y;
+ vec++;
+
+ for ( n = 1; n < outline->n_points; n++ )
+ {
+ FT_Pos x = vec->x;
+ FT_Pos y = vec->y;
+
+
+ /* update control box */
+ if ( x < cbox.xMin ) cbox.xMin = x;
+ if ( x > cbox.xMax ) cbox.xMax = x;
+
+ if ( y < cbox.yMin ) cbox.yMin = y;
+ if ( y > cbox.yMax ) cbox.yMax = y;
+
+ if ( FT_CURVE_TAG( outline->tags[n] ) == FT_CURVE_TAG_ON )
+ {
+ /* update bbox for `on' points only */
+ if ( x < bbox.xMin ) bbox.xMin = x;
+ if ( x > bbox.xMax ) bbox.xMax = x;
+
+ if ( y < bbox.yMin ) bbox.yMin = y;
+ if ( y > bbox.yMax ) bbox.yMax = y;
+ }
+
+ vec++;
+ }
+
+ /* test two boxes for equality */
+ if ( cbox.xMin < bbox.xMin || cbox.xMax > bbox.xMax ||
+ cbox.yMin < bbox.yMin || cbox.yMax > bbox.yMax )
+ {
+ /* the two boxes are different, now walk over the outline to */
+ /* get the Bezier arc extrema. */
+
+ FT_Error error;
+ TBBox_Rec user;
+
+#ifdef FT_CONFIG_OPTION_PIC
+ FT_Outline_Funcs bbox_interface;
+ Init_Class_bbox_interface(&bbox_interface);
+#endif
+
+ user.bbox = bbox;
+
+ error = FT_Outline_Decompose( outline, &bbox_interface, &user );
+ if ( error )
+ return error;
+
+ *abbox = user.bbox;
+ }
+ else
+ *abbox = bbox;
+
+ return FT_Err_Ok;
+ }
+
+
+/* END */
generated by cgit v1.1-26-g67d0 at 2025-05-18 22:17:49 +0000