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26
ChangeLog.20
26
ChangeLog.20
@ -66,7 +66,7 @@
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* src/pcf/pcf.h (PCF_Done_Face): Removed.
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2002-02-06 Detlef Würkner <TetiSoft@apg.lahn.de>
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2002-02-06 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/pcf/pcfdriver.c (FT_Done_Face): Fixed small memory leak.
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@ -193,7 +193,7 @@
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2002-01-21 Antoine Leca <Antoine-Freetype@Leca-Marti.org>
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* docs/PATENTS: Typo fixed (thanks to Detlef `Hawkeye' Würkner) in
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* docs/PATENTS: Typo fixed (thanks to Detlef `Hawkeye' Würkner) in
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the URL for the online resource.
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2002-01-18 Ian Brown <ian.brown@printsoft.de>
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@ -201,7 +201,7 @@
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* builds/win32/ftdebug.c: New file.
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* builds/win32/visualc/freetype.dsp: Updated.
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2002-01-18 Detlef Würkner <TetiSoft@apg.lahn.de>
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2002-01-18 Detlef Würkner <TetiSoft@apg.lahn.de>
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* builds/amiga/src/base/ftsystem.c: Updated for AmigaOS 3.9.
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* builds/amiga/README: Updated.
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@ -339,7 +339,7 @@
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incorrect glyph advance in the case of mono-width fonts (like
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Courier, Andale Mono, and others).
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2001-12-22 Detlef Würkner <TetiSoft@apg.lahn.de>
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2001-12-22 Detlef Würkner <TetiSoft@apg.lahn.de>
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* builds/amiga/*: Adaptations to latest changes.
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Support added for MorphOS.
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@ -586,7 +586,7 @@
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slightly improper results for `FT_Cos' and `FT_Sin' (example:
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FT_Sin(0) == -1!).
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2001-12-11 Detlef Würkner <TetiSoft@apg.lahn.de>
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2001-12-11 Detlef Würkner <TetiSoft@apg.lahn.de>
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* include/freetype/internal/ftstream.h (GET_LongLE, GET_ULongLE):
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Fixed incorrect argument types.
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@ -694,7 +694,7 @@
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codes and LCIDs as found in MSDN (Passport SDK). Also added
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comments about the meaning of bit 57 of the `OS/2' table
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(TT_UCR_SURROGATES) which (with OpenType v.1.3) now means `there is
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a character beyond 0xFFFF in this font'. Thanks to Detlef Würkner
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a character beyond 0xFFFF in this font'. Thanks to Detlef Würkner
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<TetiSoft@apg.lahn.de> for noticing this.
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2001-11-20 David Turner <david@freetype.org>
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@ -1024,11 +1024,11 @@
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(ftc_manager_init_size, ftc_manager_flush_size): Use
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FT_Activate_Size.
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2001-09-20 Detlef Würkner <TetiSoft@apg.lahn.de>
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2001-09-20 Detlef Würkner <TetiSoft@apg.lahn.de>
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* builds/amiga/*: Added port to Amiga with the SAS/C compiler.
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2001-09-15 Detlef Würkner <TetiSoft@apg.lahn.de>
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2001-09-15 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/type1/t1afm.c (T1_Done_AFM): Free `afm'.
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@ -1216,7 +1216,7 @@
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instead of FT_Int as type for `length' parameter.
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* include/freetype/internal/psaux.h (PSAux_Interface): Updated.
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2001-06-27 Wolfgang Domröse <porthos.domroese@harz.de>
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2001-06-27 Wolfgang Domröse <porthos.domroese@harz.de>
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* src/psaux/psobjs.c, src/psaux/psobjs.h (T1_Decrypt): Use FT_Offset
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instead of FT_Int as type for `length' parameter.
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@ -1242,7 +1242,7 @@
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that the kerning table is correctly sorted (some problem fonts don't
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have a correct kern table).
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2001-06-26 Wolfgang Domröse <porthos.domroese@harz.de>
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2001-06-26 Wolfgang Domröse <porthos.domroese@harz.de>
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* include/freetype/internal/ftstream.h (FT_GET_OFF3_LE): Fix typo.
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@ -1895,7 +1895,7 @@
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* src/type1/t1load.c (parse_font_bbox): Changed to use FT_Fixed
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number handling.
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2001-03-10 Henrik Grubbström <grubba@roxen.com>
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2001-03-10 Henrik Grubbström <grubba@roxen.com>
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* src/*/*.c: Added many casts to make code more 64bit-safe.
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@ -2448,7 +2448,7 @@
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2000-11-29 David Turner <david.turner@freetype.org>
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* src/base/ftbbox.c (BBox_Conic_Check): Fixed a really stupid
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bug in the formula used to compute the conic Bézier extrema
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bug in the formula used to compute the conic Bézier extrema
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of non-monotonous arcs.
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2000-11-29 Werner Lemberg <wl@gnu.org>
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@ -2609,5 +2609,5 @@ fully.
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Local Variables:
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version-control: never
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coding: latin-1
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coding: utf-8
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End:
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80
ChangeLog.21
80
ChangeLog.21
@ -8,7 +8,7 @@
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* src/pcf/readme: Renamed to...
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* src/pcf/README: This.
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2005-06-07 Detlef Würkner <TetiSoft@apg.lahn.de>
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2005-06-07 Detlef Würkner <TetiSoft@apg.lahn.de>
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* builds/amiga/*: Added copyright notes, reworked some comments.
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@ -453,7 +453,7 @@
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* docs/CHANGES, include/freetype/freetype.h: Improve documentation
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of FT_Set_Pixel_Sizes and FT_Set_Char_Size.
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2005-03-26 Detlef Würkner <TetiSoft@apg.lahn.de>
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2005-03-26 Detlef Würkner <TetiSoft@apg.lahn.de>
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* builds/amiga/src/base/ftsystem.c (ft_amiga_stream_io): Fix buffer
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offsets after a large read.
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@ -470,7 +470,7 @@
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* src/sfnt/ttsbit0.h: Dummy file for build with `make'.
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2005-03-26 Detlef Würkner <TetiSoft@apg.lahn.de>
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2005-03-26 Detlef Würkner <TetiSoft@apg.lahn.de>
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Update of the Amiga port.
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@ -478,7 +478,7 @@
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builds/amiga/smakefile: Included the base extension files
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(ftbitmap.c, ftotval.c, ftpfr.c, ftstroke.c, ftxf86.c).
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2005-03-25 Detlef Würkner <TetiSoft@apg.lahn.de>
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2005-03-25 Detlef Würkner <TetiSoft@apg.lahn.de>
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Update of the Amiga port.
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@ -1816,7 +1816,7 @@
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* docs/CHANGES, docs/VERSION.DLL: Updated.
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2004-08-11 Detlef Würkner <TetiSoft@apg.lahn.de>
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2004-08-11 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/base/ftrfork.c (FT_Raccess_Guess)
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[!FT_CONFIG_OPTION_GUESSING_EMBEDDED_FORK]: Remove compiler
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@ -1877,7 +1877,7 @@
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(BDF_Face_Init), src/truetype/ttgxvar (TT_Get_MM_Var,
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tt_face_vary_cvt): Fix compiler warnings.
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2004-07-26 Søren Sandmann <sandmann@daimi.au.dk>
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2004-07-26 Søren Sandmann <sandmann@daimi.au.dk>
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* src/pcf/pcfread.c (pcf_interpret_style): Always allocate memory for
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face->style_name.
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@ -1888,7 +1888,7 @@
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* include/freetype/config/ftconfig.h (FT_SIZEOF_LONG): Recognize
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five-byte `long' (which is avoided then).
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2004-07-25 Detlef Würkner <TetiSoft@apg.lahn.de>
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2004-07-25 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/pcf/pcfdrivr.c (PCF_Set_Pixel_Size): Compare heights, not
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ppem values.
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@ -2083,7 +2083,7 @@
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2004-06-14 Werner Lemberg <wl@gnu.org>
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* src/lzw/zopen.c: Comment out inclusion of signal.h and unistd.h.
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Reported by Hyvärinen Jyrki Juhani.
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Reported by Hyvärinen Jyrki Juhani.
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2004-06-11 Werner Lemberg <wl@gnu.org>
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@ -3422,7 +3422,7 @@
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* src/winfonts/winfnt.c (FNT_Size_Set_Pixels): Fix sign of
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size->metrics.descender.
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2003-12-31 Wolfgang Domröse <porthos.domroese@harz.de>
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2003-12-31 Wolfgang Domröse <porthos.domroese@harz.de>
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* src/cff/cffgload.c (cff_decoder_parse_charstrings)
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[FT_DEBUG_LEVEL_TRACE]: Use `%ld' in FT_TRACE4.
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@ -3516,7 +3516,7 @@
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FT_ENCODING_NONE except for FT_WinFNT_ID_MAC.
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* include/freetype/freetype.h (FT_Encoding): Improve comment,
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based on work by Detlef Würkner <TetiSoft@apg.lahn.de>.
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based on work by Detlef Würkner <TetiSoft@apg.lahn.de>.
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* docs/CHANGES: Updated.
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@ -3661,12 +3661,12 @@
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* docs/CHANGES: Updated.
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2003-12-15 Wolfgang Domröse <porthos.domroese@harz.de>
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2003-12-15 Wolfgang Domröse <porthos.domroese@harz.de>
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* builds/atari/*: New directory for building FreeType 2 on Atari
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with the PureC compiler.
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2003-12-12 Wolfgang Domröse <porthos.domroese@harz.de>
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2003-12-12 Wolfgang Domröse <porthos.domroese@harz.de>
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* src/type1/t1gload.c (T1_Parse_Glyph_And_Get_Char_String): Add
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cast.
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@ -3718,7 +3718,7 @@
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* src/cff/cfftypes.h (CFF_FontRecDictRec): Remove `base_font_name'
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and `postscript'.
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2003-12-10 Detlef Würkner <TetiSoft@apg.lahn.de>
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2003-12-10 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/pcf/pcfdrivr.c (pcf_get_charset_id): New function (a clone
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of the similar BDF function).
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@ -3750,7 +3750,7 @@
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(FT_Open_Face) [!FT_MACINTOSH]: Add conditional
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FT_CONFIG_OPTION_MAC_FONTS.
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2003-12-08 Wolfgang Domröse <porthos.domroese@harz.de>
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2003-12-08 Wolfgang Domröse <porthos.domroese@harz.de>
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* src/autohint/ahhint.c (ah_hinter_hint_edges,
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ah_hinter_align_strong_points): Add some casts.
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@ -3955,7 +3955,7 @@
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* src/base/fttype1.c (FT_Get_PS_Font_Info): Fix incorrectly applied
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patch.
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2003-10-31 Detlef Würkner <TetiSoft@apg.lahn.de>
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2003-10-31 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/base/fttype1.c (FT_Get_PS_Font_Info, FT_Has_PS_Glyph_Names):
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Fix parameter order in calls to FT_FACE_FIND_SERVICE.
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@ -4897,7 +4897,7 @@
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* configure: Set DOC_DIR variable.
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2003-07-07 Patrik Hägglund <patrik.hagglund@bredband.net>
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2003-07-07 Patrik Hägglund <patrik.hagglund@bredband.net>
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* builds/freetype.mk (refdoc): New target to build the
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documentation.
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@ -5139,7 +5139,7 @@
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(winfnt_driver_class), src/bdf/bdfdrivr.c (bdf_driver_class): Add
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the FT_MODULE_DRIVER_NO_OUTLINES flag.
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2003-06-13 Detlef Würkner <TetiSoft@apg.lahn.de>
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2003-06-13 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/pfr/pfrobjs.c (pfr_slot_load): Apply font matrix.
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@ -5216,7 +5216,7 @@
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TrueType specification.
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(Ins_MDRP, Ins_MIRP): Fix single width cut-in test.
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2003-06-09 Detlef Würkner <TetiSoft@apg.lahn.de>
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2003-06-09 Detlef Würkner <TetiSoft@apg.lahn.de>
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* src/gzip/ftgzip.c: (inflate_mask): Replaced with...
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(NO_INFLATE_MASK): This.
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@ -5228,7 +5228,7 @@
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* src/gzip/ftgzip.c (ft_gzip_file_fill_output): Handle Z_STREAM_END
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correctly.
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2003-06-09 Wolfgang Domröse <porthos.domroese@harz.de>
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2003-06-09 Wolfgang Domröse <porthos.domroese@harz.de>
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* src/pshinter/pshglob.c (psh_globals_new): Change calculation of
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dim->stdw.count to avoid compiler problem.
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@ -5294,7 +5294,7 @@
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* devel/ftoption.h: Updated.
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2003-06-07 Detlef Würkner <TetiSoft@apg.lahn.de>
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2003-06-07 Detlef Würkner <TetiSoft@apg.lahn.de>
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* include/freetype/internal/psaux.h, src/truetype/ttgload.h:
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s/index/idx/ to fix compiler warnings.
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@ -5352,7 +5352,7 @@
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* src/pshinter/pshglob.c (psh_globals_new): Fix default value of
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blue_scale.
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2003-06-04 Wolfgang Domröse <porthos.domroese@harz.de>
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2003-06-04 Wolfgang Domröse <porthos.domroese@harz.de>
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* include/freetype/internal/ftdriver.h,
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include/freetype/internal/ftobjs.h,
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@ -6674,7 +6674,7 @@
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* include/freetype/ftcache.h (FT_POINTER_TO_ULONG): New macro.
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(FTC_FACE_ID_HASH): Rewritten, using FT_POINTER_TO_ULONG.
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2002-10-22 Giuseppe Ghibò <ghibo@mandrakesoft.com>
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2002-10-22 Giuseppe Ghibò <ghibo@mandrakesoft.com>
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* include/freetype/freetype.h (FT_Encoding): Fix entry for latin-2.
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@ -6731,7 +6731,7 @@
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Update all casts.
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(gray_render_line): Fix casts for `p' and `first'.
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2002-10-02 Detlef Würkner <TetiSoft@apg.lahn.de>
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2002-10-02 Detlef Würkner <TetiSoft@apg.lahn.de>
|
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* src/bdf/bdflib.c (bdf_load_font): Allocate the _bdf_parse_t
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structure with FT_ALLOC instead of using the stack.
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@ -6745,7 +6745,7 @@
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(find_sbit_image): Remove cast.
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* src/raster/ftrend1.c (ft_raster1_render): Fix cast.
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2002-09-27 Wolfgang Domröse <porthos.domroese@harz.de>
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2002-09-27 Wolfgang Domröse <porthos.domroese@harz.de>
|
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* src/sfnt/ttload.c (tt_face_load_names): Use cast.
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* src/sfnt/ttcmap.c (code_to_next2): Use long constant.
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@ -6811,7 +6811,7 @@
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* src/psnames/psmodule.c (ps_unicode_value, ps_build_unicode_table):
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Updated accordingly.
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2002-09-26 Wolfgang Domröse <porthos.domroese@harz.de>
|
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2002-09-26 Wolfgang Domröse <porthos.domroese@harz.de>
|
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|
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* src/cff/cffdrivr.c (Get_Kerning): Use FT_Long for `middle'.
|
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(cff_get_glyph_name): Use cast for result of ft_strlen.
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@ -6852,7 +6852,7 @@
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* src/sfnt/sfnt_dir_check: Compare `magic' with unsigned long
|
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constant.
|
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|
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2002-09-26 Detlef Würkner <TetiSoft@apg.lahn.de>
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2002-09-26 Detlef Würkner <TetiSoft@apg.lahn.de>
|
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|
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* builds/amiga/include/freetype/config/ftmodule.h: Updated.
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|
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@ -6871,14 +6871,14 @@
|
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charmap that uses offset=0xFFFFU instead of 0x0000 to indicate a
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missing glyph).
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|
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2002-09-21 Wolfgang Domröse <porthos.domroese@harz.de>
|
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2002-09-21 Wolfgang Domröse <porthos.domroese@harz.de>
|
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* src/truetype/ttdriver.c (Load_Glyph): Fourth parameter must be
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FT_Int32.
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* src/truetype/ttgload.c, src/truetype/ttgload.h (TT_Load_Glyph):
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Ditto.
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2002-09-19 Wolfgang Domröse <porthos.domroese@harz.de>
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2002-09-19 Wolfgang Domröse <porthos.domroese@harz.de>
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|
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More 16bit fixes.
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@ -6927,7 +6927,7 @@
|
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|
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2002-09-16 Werner Lemberg <wl@gnu.org>
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|
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16bit fixes from Wolfgang Domröse.
|
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16bit fixes from Wolfgang Domröse.
|
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|
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* src/type1/t1parse.h (T1_ParserRec): Change type of `base_len'
|
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and `private_len' to FT_Long.
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@ -7890,7 +7890,7 @@
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* src/type42/t42objs.h: Include FT_INTERNAL_TYPE42_TYPES_H.
|
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(T42_Face): Removed since it is already in t42types.h.
|
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|
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2002-06-21 Detlef Würkner <TetiSoft@apg.lahn.de>
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2002-06-21 Detlef Würkner <TetiSoft@apg.lahn.de>
|
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|
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* src/pfrgload.c (pfr_glyph_load_compound): Fix loading of composite
|
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glyphs.
|
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@ -7913,7 +7913,7 @@
|
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|
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* README, docs/CHANGES: Preparing the 2.1.2 release.
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||||
|
||||
2002-06-19 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-19 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
* src/base/fttype1.c: Include FT_INTERNAL_TYPE42_TYPES_H.
|
||||
(t1_face_check_cast): Removed.
|
||||
@ -7938,7 +7938,7 @@
|
||||
instead.
|
||||
(T42_GlyphSlot_Load): Remove call to t42_check_size_change.
|
||||
|
||||
2002-06-18 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-18 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
* src/psaux/t1cmap.c (t1_cmap_custom_char_index,
|
||||
t1_cmap_custom_char_next): Fix index computation -- indices start
|
||||
@ -7967,7 +7967,7 @@
|
||||
|
||||
* builds/unix/install.mk (install, uninstall): Handle it.
|
||||
|
||||
2002-06-16 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-16 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
Same fix for PFR driver.
|
||||
|
||||
@ -7975,7 +7975,7 @@
|
||||
Increase return value by 1.
|
||||
* src/pfr/pfrobjs.c (pfr_slot_load): Decrease index by 1.
|
||||
|
||||
2002-06-15 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-15 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
Fix glyph indices to make index zero always the undefined glyph.
|
||||
|
||||
@ -7994,7 +7994,7 @@
|
||||
* src/base/ftobjs.c (FT_Load_Glyph, FT_Get_Glyph_Name): Fix
|
||||
bounding tests.
|
||||
|
||||
2002-06-14 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-14 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
Add new cmap support to BDF driver.
|
||||
|
||||
@ -8068,7 +8068,7 @@
|
||||
bug that caused nasty memory overwrites. The hash table's
|
||||
buckets array wasn't correctly resized when shrinked.
|
||||
|
||||
2002-06-08 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-08 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
* builds/amiga/smakefile, builds/amiga/makefile: Updated.
|
||||
|
||||
@ -8189,11 +8189,11 @@
|
||||
* src/bdf/bdfdrivr.c (BDF_Glyph_Load): Ditto.
|
||||
* src/bdf/README: Updated.
|
||||
|
||||
2002-06-02 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-06-02 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
* src/pfr/pfrload.c (pfr_phy_font_done): Free `blue_values' array.
|
||||
|
||||
2002-05-29 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-05-29 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
* src/bdf/bdflib.c (_bdf_readstream): Allocate `buf' dynamically.
|
||||
(_bdf_parse_glyphs): Use correct size for allocating
|
||||
@ -8212,7 +8212,7 @@
|
||||
compilation.
|
||||
* src/pshglob.c (psh_blues_scale_zones): Fix compiler warning.
|
||||
|
||||
2002-05-28 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
2002-05-28 Detlef Würkner <TetiSoft@apg.lahn.de>
|
||||
|
||||
* builds/amiga/makefile, builds/amiga/smakefile,
|
||||
amiga/include/freetype/config/ftmodule.h: Updated to include
|
||||
@ -9435,5 +9435,5 @@ fully.
|
||||
|
||||
Local Variables:
|
||||
version-control: never
|
||||
coding: latin-1
|
||||
coding: utf-8
|
||||
End:
|
||||
|
@ -30,8 +30,8 @@ I. Introduction
|
||||
A rasterizer is a library in charge of converting a vectorial
|
||||
representation of a shape into a bitmap. The FreeType rasterizer
|
||||
has been originally developed to render the glyphs found in
|
||||
TrueType files, made up of segments and second-order Béziers.
|
||||
Meanwhile it has been extended to render third-order Bézier curves
|
||||
TrueType files, made up of segments and second-order Béziers.
|
||||
Meanwhile it has been extended to render third-order Bézier curves
|
||||
also. This document is an explanation of its design and
|
||||
implementation.
|
||||
|
||||
@ -99,24 +99,24 @@ II. Rendering Technology
|
||||
points indicate a line segment joining the two points.
|
||||
|
||||
One `off' point amidst two `on' points indicates a second-degree
|
||||
(conic) Bézier parametric arc, defined by these three points
|
||||
(conic) Bézier parametric arc, defined by these three points
|
||||
(the `off' point being the control point, and the `on' ones the
|
||||
start and end points). Similarly, a third-degree (cubic) Bézier
|
||||
start and end points). Similarly, a third-degree (cubic) Bézier
|
||||
curve is described by four points (two `off' control points
|
||||
between two `on' points).
|
||||
|
||||
Finally, for second-order curves only, two successive `off'
|
||||
points forces the rasterizer to create, during rendering, an
|
||||
`on' point amidst them, at their exact middle. This greatly
|
||||
facilitates the definition of successive Bézier arcs.
|
||||
facilitates the definition of successive Bézier arcs.
|
||||
|
||||
The parametric form of a second-order Bézier curve is:
|
||||
The parametric form of a second-order Bézier curve is:
|
||||
|
||||
P(t) = (1-t)^2*P1 + 2*t*(1-t)*P2 + t^2*P3
|
||||
|
||||
(P1 and P3 are the end points, P2 the control point.)
|
||||
|
||||
The parametric form of a third-order Bézier curve is:
|
||||
The parametric form of a third-order Bézier curve is:
|
||||
|
||||
P(t) = (1-t)^3*P1 + 3*t*(1-t)^2*P2 + 3*t^2*(1-t)*P3 + t^3*P4
|
||||
|
||||
@ -125,7 +125,7 @@ II. Rendering Technology
|
||||
For both formulae, t is a real number in the range [0..1].
|
||||
|
||||
Note that the rasterizer does not use these formulae directly.
|
||||
They exhibit, however, one very useful property of Bézier arcs:
|
||||
They exhibit, however, one very useful property of Bézier arcs:
|
||||
Each point of the curve is a weighted average of the control
|
||||
points.
|
||||
|
||||
@ -372,7 +372,7 @@ II. Rendering Technology
|
||||
- min scanline = FLOOR ( min y )
|
||||
- max scanline = CEILING( max y )
|
||||
|
||||
A problem arises with Bézier Arcs. While a segment is always
|
||||
A problem arises with Bézier Arcs. While a segment is always
|
||||
necessarily y-monotonic (i.e., flat, ascending, or descending),
|
||||
which makes extrema computations easy, the ascent of an arc can
|
||||
vary between its control points.
|
||||
@ -384,7 +384,7 @@ II. Rendering Technology
|
||||
* off curve
|
||||
__-x--_
|
||||
_-- -_
|
||||
P1 _- - A non y-monotonic Bézier arc.
|
||||
P1 _- - A non y-monotonic Bézier arc.
|
||||
# \
|
||||
- The arc goes from P1 to P3.
|
||||
\
|
||||
@ -431,7 +431,7 @@ II. Rendering Technology
|
||||
* off curve
|
||||
__-x--_
|
||||
_-- -_
|
||||
P1 _- - A non-y-monotonic Bézier arc.
|
||||
P1 _- - A non-y-monotonic Bézier arc.
|
||||
# \
|
||||
- Here we have
|
||||
\ P2.y >= P1.y &&
|
||||
@ -445,10 +445,10 @@ II. Rendering Technology
|
||||
but we rely on a different technique, which use will become
|
||||
apparent soon.
|
||||
|
||||
Bézier arcs have the special property of being very easily
|
||||
decomposed into two sub-arcs, which are themselves Bézier arcs.
|
||||
Bézier arcs have the special property of being very easily
|
||||
decomposed into two sub-arcs, which are themselves Bézier arcs.
|
||||
Moreover, it is easy to prove that there is at most one vertical
|
||||
extremum on each Bézier arc (for second-degree curves; similar
|
||||
extremum on each Bézier arc (for second-degree curves; similar
|
||||
conditions can be found for third-order arcs).
|
||||
|
||||
For instance, the following arc P1P2P3 can be decomposed into
|
||||
@ -461,7 +461,7 @@ II. Rendering Technology
|
||||
* off curve
|
||||
|
||||
|
||||
original Bézier arc P1P2P3.
|
||||
original Bézier arc P1P2P3.
|
||||
__---__
|
||||
_-- --_
|
||||
_- -_
|
||||
@ -492,7 +492,7 @@ II. Rendering Technology
|
||||
tangent to the curve.
|
||||
|
||||
|
||||
We have then decomposed a non-y-monotonic Bézier curve into two
|
||||
We have then decomposed a non-y-monotonic Bézier curve into two
|
||||
smaller sub-arcs. Note that in the above drawing, both sub-arcs
|
||||
are monotonic, and that the extremum is then Q3=R1. However, in
|
||||
a more general case, only one sub-arc is guaranteed to be
|
||||
@ -530,9 +530,9 @@ II. Rendering Technology
|
||||
|
||||
In the case of segments, the computation is straightforward,
|
||||
using the Euclidian algorithm (also known as Bresenham).
|
||||
However, for Bézier arcs, the job is a little more complicated.
|
||||
However, for Bézier arcs, the job is a little more complicated.
|
||||
|
||||
We assume that all Béziers that are part of a profile are the
|
||||
We assume that all Béziers that are part of a profile are the
|
||||
result of flattening the curve, which means that they are all
|
||||
y-monotonic (ascending or descending, and never flat). We now
|
||||
have to compute the intersections of arcs with the profile's
|
||||
@ -631,5 +631,5 @@ accept it fully.
|
||||
--- end of raster.txt ---
|
||||
|
||||
Local Variables:
|
||||
coding: latin-1
|
||||
coding: utf-8
|
||||
End:
|
||||
|
Loading…
Reference in New Issue
Block a user