aboutsummaryrefslogtreecommitdiff
path: root/libgeometry
diff options
context:
space:
mode:
authorrodri <rgl@antares-labs.eu>2020-04-17 11:37:10 +0000
committerrodri <rgl@antares-labs.eu>2020-04-17 11:37:10 +0000
commite77a34629060abfad8e463efda0c3ffc54379793 (patch)
tree9151e47fab853248f95594e6ef48999a1ff6255f /libgeometry
parent263444216730830b712a4f8f3a087513c5ac93e9 (diff)
download3dee-e77a34629060abfad8e463efda0c3ffc54379793.tar.gz
3dee-e77a34629060abfad8e463efda0c3ffc54379793.tar.bz2
3dee-e77a34629060abfad8e463efda0c3ffc54379793.zip
roll everything back.
Diffstat (limited to 'libgeometry')
-rw-r--r--libgeometry/doc/libgeometry.ms429
-rw-r--r--libgeometry/doc/libgeometry.pdfbin35120 -> 0 bytes
-rw-r--r--libgeometry/doc/libgeometry.ps2799
-rw-r--r--libgeometry/doc/mkfile15
-rw-r--r--libgeometry/matrix.c348
-rw-r--r--libgeometry/mkfile13
-rw-r--r--libgeometry/point.c161
-rw-r--r--libgeometry/quaternion.c90
-rw-r--r--libgeometry/rframe.c51
-rw-r--r--libgeometry/triangle.c9
10 files changed, 0 insertions, 3915 deletions
diff --git a/libgeometry/doc/libgeometry.ms b/libgeometry/doc/libgeometry.ms
deleted file mode 100644
index 47c8d94..0000000
--- a/libgeometry/doc/libgeometry.ms
+++ /dev/null
@@ -1,429 +0,0 @@
-.TL
-libgeometry
-.AU
-Rodrigo G. López
-.sp
-rgl@antares-labs.eu
-.AI
-Antares Telecom Laboratories
-Albatera, Alicante
-.FS
-ACHTUNG! this is a
-.B "WORK IN PROGRESS"
-.FE
-.SH
-Introduction
-.PP
-.I Libgeometry is a computational geometry library that provides all
-the utilities anybody working with graphics or scientific simulations
-could need.
-.NH 1
-Data Structures
-.NH 2
-Point2
-.P1
-struct Point2 {
- double x, y, w;
-};
-.P2
-.PP
-.I Point2
-represents a point in two-dimensional projective space, which itself
-is an extension of the two-dimensional euclidean space that allows us
-to work with vectors and compose affine transformations in a friendly
-manner. A point
-.EQ
-gfont roman
-(x, y, w)
-.EN
-made out of homogenous coordinates
-.I x ,
-.I y ,
-and
-.I w ,
-yields a point with cartesian coordinates
-.EQ
-(x/w, y/w) .
-.EN
-.NH 2
-Point3
-.P1
-struct Point3 {
- double x, y, z, w;
-};
-.P2
-.PP
-.I Point3
-is a point in three-dimensional projective space.
-.NH 2
-Matrix
-.P1
-typedef double Matrix[3][3];
-.P2
-.PP
-.I Matrix
-represents a 3x3 matrix, thought to compose affine transformations to
-apply to homogeneous 2D points.
-.NH 2
-Matrix3
-.P1
-typedef double Matrix3[4][4];
-.P2
-.PP
-.I Matrix3
-represents a 4x4 matrix, thought to compose affine transformations to
-apply to homogeneous 3D points.
-.NH 2
-Quaternion
-.P1
-struct Quaternion {
- double r, i, j, k;
-};
-.P2
-.PP
-.I Quaternions
-are a numbering system that extends the complex numbers up to
-four-dimensional space, and are used to apply rotations and model
-mechanical interactions in 3D space. Their main advantages with
-respect to their matrix relatives are increased computational and
-storage performance and gimbal lock avoidance.
-.NH 2
-RFrame
-.P1
-struct RFrame {
- Point2 p;
- Point2 bx, by;
-};
-.P2
-.PP
-A reference frame (or frame of reference) is
-.NH 2
-RFrame3
-.P1
-struct RFrame3 {
- Point3 p;
- Point3 bx, by, bz;
-};
-.P2
-.PP
-A reference frame (or frame of reference) is
-.NH 1
-Algorithms
-.NH 2
-Point2
-.SH
-Addition
-.P1
-Point2 addpt2(Point2 a, Point2 b)
-.P2
-.EQ
-a + b ~=~ left ( x sub a + x sub b ,~ y sub a + y sub b ,~ w sub a + w sub b right )
-.EN
-.SH
-Substraction
-.P1
-Point2 subpt2(Point2 a, Point2 b)
-.P2
-.EQ
-a - b ~=~ left ( x sub a - x sub b ,~ y sub a - y sub b ,~ w sub a - w sub b right )
-.EN
-.SH
-Multiplication
-.P1
-Point2 mulpt2(Point2 p, double s)
-.P2
-.EQ
-p * s ~=~ left ( xs,~ ys,~ ws right )
-.EN
-.SH
-Division
-.P1
-Point2 divpt2(Point2 p, double s)
-.P2
-.EQ
-p / s ~=~ left ( x over s ,~ y over s ,~ w over s right )
-.EN
-.SH
-Vector Dot Product
-.P1
-double dotvec2(Point2 a, Point2 b)
-.P2
-.EQ
-a vec ~•~ b vec ~=~ x sub a x sub b + y sub a y sub b
-.EN
-.SH
-Vector Magnitude/Length
-.P1
-double vec2len(Point2 v)
-.P2
-.EQ
-| v vec | ~=~ sqrt { x sup 2 + y sup 2 }
-.EN
-.SH
-Vector Normalization
-.P1
-Point2 normvec2(Point2 v)
-.P2
-.EQ
-n vec ~=~ left ( x over {| v vec |},~ y over {| v vec |} right )
-.EN
-.NH 2
-Point3
-.SH
-Addition
-.P1
-Point3 addpt3(Point3 a, Point3 b)
-.P2
-.EQ
-a + b ~=~ left ( x sub a + x sub b ,~ y sub a + y sub b ,~ z sub a + z sub b ,~ w sub a + w sub b right )
-.EN
-.SH
-Substraction
-.P1
-Point3 subpt3(Point3 a, Point3 b)
-.P2
-.EQ
-a - b ~=~ left ( x sub a - x sub b ,~ y sub a - y sub b ,~ z sub a - z sub b ,~ w sub a - w sub b right )
-.EN
-.SH
-Multiplication
-.P1
-Point3 mulpt3(Point3 p, double s)
-.P2
-.EQ
-p * s ~=~ left ( xs,~ ys,~ zs,~ ws right )
-.EN
-.SH
-Division
-.P1
-Point3 divpt3(Point3 p, double s)
-.P2
-.EQ
-p / s ~=~ left ( x over s ,~ y over s ,~ z over s ,~ w over s right )
-.EN
-.SH
-Vector Dot Product
-.P1
-double dotvec3(Point3 a, Point3 b)
-.P2
-.EQ
-a vec ~•~ b vec ~=~ x sub a x sub b + y sub a y sub b + z sub a z sub b
-.EN
-.SH
-Vector Cross Product
-.P1
-double crossvec3(Point3 a, Point3 b)
-.P2
-.EQ
-a vec ~×~ b vec ~=~ left ( y sub a z sub b - z sub a y sub b ,~
- z sub a x sub b - x sub a z sub b ,~
- x sub a y sub b - y sub a x sub b right )
-.EN
-.SH
-Vector Magnitude/Length
-.P1
-double vec3len(Point3 v)
-.P2
-.EQ
-| v vec | ~=~ sqrt { x sup 2 + y sup 2 + z sup 2 }
-.EN
-.SH
-Vector Normalization
-.P1
-Point3 normvec3(Point3 v)
-.P2
-.EQ
-n vec ~=~ left ( x over {| v vec |},~ y over {| v vec |},~ z over {| v vec |} right )
-.EN
-.NH 2
-Matrix
-.SH
-Addition
-.P1
-void addm(Matrix A, Matrix B)
-.P2
-.EQ
-( bold A + bold B ) sub {i,j} ~=~ bold A sub {i,j} + bold B sub {i,j}
-.EN
-.SH
-Substraction
-.P1
-void subm(Matrix A, Matrix B)
-.P2
-.EQ
-( bold A - bold B ) sub {i,j} ~=~ bold A sub {i,j} - bold B sub {i,j}
-.EN
-.SH
-Multiplication
-.P1
-void mulm(Matrix A, Matrix B)
-.P2
-.EQ
-left [ bold A bold B right ] sub {i,j} ~=~ sum from {k = 0} to 3-1 bold A sub {i,k} bold B sub {k,j}
-.EN
-.SH
-Transpose
-.P1
-void transposem(Matrix M)
-.P2
-.EQ
-( bold M sup T ) sub {i,j} ~=~ bold A sub {j,i}
-.EN
-.SH
-Identity
-.P1
-void identity(Matrix M)
-.P2
-.EQ
-bold M ~=~ left [ rpile {
- 1 ~ 0 ~ 0
-above 0 ~ 1 ~ 0
-above 0 ~ 0 ~ 1
-} right ]
-.EN
-.SH
-Determinant
-.P1
-double detm(Matrix M)
-.P2
-.EQ
-det( bold M ) ~=~ lpile {
- m sub 00 ( m sub 11 m sub 22 - m sub 12 m sub 21 ) +
-above m sub 01 ( m sub 12 m sub 20 - m sub 10 m sub 22 ) +
-above m sub 02 ( m sub 10 m sub 21 - m sub 11 m sub 20 )
-}
-.EN
-.NH 2
-Matrix3
-.SH
-Addition
-.P1
-void addm3(Matrix3 A, Matrix3 B)
-.P2
-.EQ
-( bold A + bold B ) sub {i,j} ~=~ bold A sub {i,j} + bold B sub {i,j}
-.EN
-.SH
-Substraction
-.P1
-void subm3(Matrix3 A, Matrix3 B)
-.P2
-.EQ
-( bold A - bold B ) sub {i,j} ~=~ bold A sub {i,j} - bold B sub {i,j}
-.EN
-.SH
-Multiplication
-.P1
-void mulm3(Matrix3 A, Matrix3 B)
-.P2
-.EQ
-left [ bold A bold B right ] sub {i,j} ~=~ sum from {k = 0} to 4-1 bold A sub {i,k} bold B sub {k,j}
-.EN
-.SH
-Transpose
-.P1
-void transposem3(Matrix3 M)
-.P2
-.EQ
-( bold M sup T ) sub {i,j} ~=~ bold A sub {j,i}
-.EN
-.SH
-Identity
-.P1
-void identity3(Matrix3 M)
-.P2
-.EQ
-bold M ~=~ left [ rpile {
- 1 ~ 0 ~ 0 ~ 0
-above 0 ~ 1 ~ 0 ~ 0
-above 0 ~ 0 ~ 1 ~ 0
-above 0 ~ 0 ~ 0 ~ 1
-} right ]
-.EN
-.SH
-Determinant
-.P1
-double detm3(Matrix3 M)
-.P2
-.EQ
-det( bold M ) ~=~ rpile {
- m sub 00 ( m sub 11 ( m sub 22 m sub 33 - m sub 23 m sub 32 ) +
- m sub 12 ( m sub 23 m sub 31 - m sub 21 m sub 33 ) +
- m sub 13 ( m sub 21 m sub 32 - m sub 22 m sub 31 ) )
-above -m sub 01 ( m sub 10 ( m sub 22 m sub 33 - m sub 23 m sub 32 ) +
- m sub 12 ( m sub 23 m sub 30 - m sub 20 m sub 33 ) +
- m sub 13 ( m sub 20 m sub 32 - m sub 22 m sub 30 ) )
-above +m sub 02 ( m sub 10 ( m sub 21 m sub 33 - m sub 23 m sub 31 ) +
- m sub 11 ( m sub 23 m sub 30 - m sub 20 m sub 33 ) +
- m sub 13 ( m sub 20 m sub 31 - m sub 21 m sub 30 ) )
-above -m sub 03 ( m sub 10 ( m sub 21 m sub 32 - m sub 22 m sub 31 ) +
- m sub 11 ( m sub 22 m sub 30 - m sub 20 m sub 32 ) +
- m sub 12 ( m sub 20 m sub 31 - m sub 21 m sub 30 ) )
-}
-.EN
-.NH 2
-Quaternion
-.SH
-Addition
-.P1
-Quaternion addq(Quaternion q, Quaternion r)
-.P2
-.EQ
-q + r ~=~ ( r sub q + r sub r ,~ i sub q + i sub r ,~ j sub q + j sub r ,~ k sub q + k sub r )
-.EN
-.SH
-Substraction
-.P1
-Quaternion subq(Quaternion q, Quaternion r)
-.P2
-.EQ
-q - r ~=~ ( r sub q - r sub r ,~ i sub q - i sub r ,~ j sub q - j sub r ,~ k sub q - k sub r )
-.EN
-.SH
-Multiplication
-.P1
-Quaternion mulq(Quaternion q, Quaternion r)
-.P2
-.EQ
-q ~=~ [ r sub q ,~ v vec sub q ]
-r ~=~ [ r sub r ,~ v vec sub r ]
-qr ~=~ [ r sub q r sub r - v vec sub q • v vec sub r ,~ v vec sub r r sub q + v vec sub q r sub r + v vec sub q X v vec sub r ]
-.EN
-.SH
-Scalar Multiplication
-.P1
-Quaternion smulq(Quaternion q, double s)
-.P2
-.EQ
-qs ~=~ [ r sub q s ,~ i sub q s ,~ j sub q s ,~ k sub q s ]
-.EN
-.SH
-Inverse
-.P1
-Quaternion invq(Quaternion q)
-.P2
-.EQ
-q sup -1 ~=~ left ( r over {| q | sup 2} ,~ -i over {| q | sup 2} ,~ -j over {| q | sup 2} ,~ -k over {| q | sup 2} right )
-.EN
-.SH
-Magnitude/Length
-.P1
-double qlen(Quaternion q)
-.P2
-.EQ
-| q | ~=~ sqrt { r sup 2 + i sup 2 + j sup 2 + k sup 2 }
-.EN
-.NH 2
-RFrame
-.SH
-Change of reference
-.P1
-Point2 rframexform(Point2 p, RFrame rf)
-.P2
-.NH 2
-RFrame3
-.SH
-Change of reference
-.P1
-Point3 rframexform3(Point3 p, RFrame3 rf)
-.P2
diff --git a/libgeometry/doc/libgeometry.pdf b/libgeometry/doc/libgeometry.pdf
deleted file mode 100644
index 3a49480..0000000
--- a/libgeometry/doc/libgeometry.pdf
+++ /dev/null
Binary files differ
diff --git a/libgeometry/doc/libgeometry.ps b/libgeometry/doc/libgeometry.ps
deleted file mode 100644
index 635b9cd..0000000
--- a/libgeometry/doc/libgeometry.ps
+++ /dev/null
@@ -1,2799 +0,0 @@
-%!PS-Adobe-2.0
-%%Version: 0.1
-%%Creator: troff, Plan 9 edition
-%%DocumentFonts: (atend)
-%%Pages: (atend)
-%%EndComments
-%
-% Version 3.3.2 prologue for troff files.
-%
-
-/#copies 1 store
-/aspectratio 1 def
-/formsperpage 1 def
-/landscape false def
-/linewidth .3 def
-/magnification 1 def
-/margin 0 def
-/orientation 0 def
-/resolution 720 def
-/rotation 1 def
-/xoffset 0 def
-/yoffset 0 def
-
-/roundpage true def
-/useclippath true def
-/pagebbox [0 0 612 792] def
-
-/R /Times-Roman def
-/I /Times-Italic def
-/B /Times-Bold def
-/BI /Times-BoldItalic def
-/H /Helvetica def
-/HI /Helvetica-Oblique def
-/HB /Helvetica-Bold def
-/HX /Helvetica-BoldOblique def
-/CW /Courier def
-/CO /Courier def
-/CI /Courier-Oblique def
-/CB /Courier-Bold def
-/CX /Courier-BoldOblique def
-/PA /Palatino-Roman def
-/PI /Palatino-Italic def
-/PB /Palatino-Bold def
-/PX /Palatino-BoldItalic def
-/Hr /Helvetica-Narrow def
-/Hi /Helvetica-Narrow-Oblique def
-/Hb /Helvetica-Narrow-Bold def
-/Hx /Helvetica-Narrow-BoldOblique def
-/KR /Bookman-Light def
-/KI /Bookman-LightItalic def
-/KB /Bookman-Demi def
-/KX /Bookman-DemiItalic def
-/AR /AvantGarde-Book def
-/AI /AvantGarde-BookOblique def
-/AB /AvantGarde-Demi def
-/AX /AvantGarde-DemiOblique def
-/NR /NewCenturySchlbk-Roman def
-/NI /NewCenturySchlbk-Italic def
-/NB /NewCenturySchlbk-Bold def
-/NX /NewCenturySchlbk-BoldItalic def
-/ZD /ZapfDingbats def
-/ZI /ZapfChancery-MediumItalic def
-/S /S def
-/S1 /S1 def
-/GR /Symbol def
-
-/inch {72 mul} bind def
-/min {2 copy gt {exch} if pop} bind def
-
-/setup {
- counttomark 2 idiv {def} repeat pop
-
- landscape {/orientation 90 orientation add def} if
- /scaling 72 resolution div def
- linewidth setlinewidth
- 1 setlinecap
-
- pagedimensions
- xcenter ycenter translate
- orientation rotation mul rotate
- width 2 div neg height 2 div translate
- xoffset inch yoffset inch neg translate
- margin 2 div dup neg translate
- magnification dup aspectratio mul scale
- scaling scaling scale
-
- addmetrics
- 0 0 moveto
-} def
-
-/pagedimensions {
- useclippath userdict /gotpagebbox known not and {
- /pagebbox [clippath pathbbox newpath] def
- roundpage currentdict /roundpagebbox known and {roundpagebbox} if
- } if
- pagebbox aload pop
- 4 -1 roll exch 4 1 roll 4 copy
- landscape {4 2 roll} if
- sub /width exch def
- sub /height exch def
- add 2 div /xcenter exch def
- add 2 div /ycenter exch def
- userdict /gotpagebbox true put
-} def
-
-/addmetrics {
- /Symbol /S null Sdefs cf
- /Times-Roman /S1 StandardEncoding dup length array copy S1defs cf
-} def
-
-/pagesetup {
- /page exch def
- currentdict /pagedict known currentdict page known and {
- page load pagedict exch get cvx exec
- } if
-} def
-
-/decodingdefs [
- {counttomark 2 idiv {y moveto show} repeat}
- {neg /y exch def counttomark 2 idiv {y moveto show} repeat}
- {neg moveto {2 index stringwidth pop sub exch div 0 32 4 -1 roll widthshow} repeat}
- {neg moveto {spacewidth sub 0.0 32 4 -1 roll widthshow} repeat}
- {counttomark 2 idiv {y moveto show} repeat}
- {neg setfunnytext}
-] def
-
-/setdecoding {/t decodingdefs 3 -1 roll get bind def} bind def
-
-/w {neg moveto show} bind def
-/m {neg dup /y exch def moveto} bind def
-/done {/lastpage where {pop lastpage} if} def
-
-/f {
- dup /font exch def findfont exch
- dup /ptsize exch def scaling div dup /size exch def scalefont setfont
- linewidth ptsize mul scaling 10 mul div setlinewidth
- /spacewidth ( ) stringwidth pop def
-} bind def
-
-/changefont {
- /fontheight exch def
- /fontslant exch def
- currentfont [
- 1 0
- fontheight ptsize div fontslant sin mul fontslant cos div
- fontheight ptsize div
- 0 0
- ] makefont setfont
-} bind def
-
-/sf {f} bind def
-
-/cf {
- dup length 2 idiv
- /entries exch def
- /chtab exch def
- /newencoding exch def
- /newfont exch def
-
- findfont dup length 1 add dict
- /newdict exch def
- {1 index /FID ne {newdict 3 1 roll put}{pop pop} ifelse} forall
-
- newencoding type /arraytype eq {newdict /Encoding newencoding put} if
-
- newdict /Metrics entries dict put
- newdict /Metrics get
- begin
- chtab aload pop
- 1 1 entries {pop def} for
- newfont newdict definefont pop
- end
-} bind def
-
-%
-% A few arrays used to adjust reference points and character widths in some
-% of the printer resident fonts. If square roots are too high try changing
-% the lines describing /radical and /radicalex to,
-%
-% /radical [0 -75 550 0]
-% /radicalex [-50 -75 500 0]
-%
-% Move braceleftbt a bit - default PostScript character is off a bit.
-%
-
-/Sdefs [
- /bracketlefttp [201 500]
- /bracketleftbt [201 500]
- /bracketrighttp [-81 380]
- /bracketrightbt [-83 380]
- /braceleftbt [203 490]
- /bracketrightex [220 -125 500 0]
- /radical [0 0 550 0]
- /radicalex [-50 0 500 0]
- /parenleftex [-20 -170 0 0]
- /integral [100 -50 500 0]
- /infinity [10 -75 730 0]
-] def
-
-/S1defs [
- /underscore [0 80 500 0]
- /endash [7 90 650 0]
-] def
-%
-% Tries to round clipping path dimensions, as stored in array pagebbox, so they
-% match one of the known sizes in the papersizes array. Lower left coordinates
-% are always set to 0.
-%
-
-/roundpagebbox {
- 7 dict begin
- /papersizes [8.5 inch 11 inch 14 inch 17 inch] def
-
- /mappapersize {
- /val exch def
- /slop .5 inch def
- /diff slop def
- /j 0 def
- 0 1 papersizes length 1 sub {
- /i exch def
- papersizes i get val sub abs
- dup diff le {/diff exch def /j i def} {pop} ifelse
- } for
- diff slop lt {papersizes j get} {val} ifelse
- } def
-
- pagebbox 0 0 put
- pagebbox 1 0 put
- pagebbox dup 2 get mappapersize 2 exch put
- pagebbox dup 3 get mappapersize 3 exch put
- end
-} bind def
-
-%%EndProlog
-%%BeginSetup
-mark
-%
-% Encoding vector and redefinition of findfont for the ISO Latin1 standard.
-% The 18 characters missing from ROM based fonts on older printers are noted
-% below.
-%
-
-/ISOLatin1Encoding [
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /space
- /exclam
- /quotedbl
- /numbersign
- /dollar
- /percent
- /ampersand
- /quoteright
- /parenleft
- /parenright
- /asterisk
- /plus
- /comma
- /minus
- /period
- /slash
- /zero
- /one
- /two
- /three
- /four
- /five
- /six
- /seven
- /eight
- /nine
- /colon
- /semicolon
- /less
- /equal
- /greater
- /question
- /at
- /A
- /B
- /C
- /D
- /E
- /F
- /G
- /H
- /I
- /J
- /K
- /L
- /M
- /N
- /O
- /P
- /Q
- /R
- /S
- /T
- /U
- /V
- /W
- /X
- /Y
- /Z
- /bracketleft
- /backslash
- /bracketright
- /asciicircum
- /underscore
- /quoteleft
- /a
- /b
- /c
- /d
- /e
- /f
- /g
- /h
- /i
- /j
- /k
- /l
- /m
- /n
- /o
- /p
- /q
- /r
- /s
- /t
- /u
- /v
- /w
- /x
- /y
- /z
- /braceleft
- /bar
- /braceright
- /asciitilde
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /.notdef
- /dotlessi
- /grave
- /acute
- /circumflex
- /tilde
- /macron
- /breve
- /dotaccent
- /dieresis
- /.notdef
- /ring
- /cedilla
- /.notdef
- /hungarumlaut
- /ogonek
- /caron
- /space
- /exclamdown
- /cent
- /sterling
- /currency
- /yen
- /brokenbar % missing
- /section
- /dieresis
- /copyright
- /ordfeminine
- /guillemotleft
- /logicalnot
- /hyphen
- /registered
- /macron
- /degree % missing
- /plusminus % missing
- /twosuperior % missing
- /threesuperior % missing
- /acute
- /mu % missing
- /paragraph
- /periodcentered
- /cedilla
- /onesuperior % missing
- /ordmasculine
- /guillemotright
- /onequarter % missing
- /onehalf % missing
- /threequarters % missing
- /questiondown
- /Agrave
- /Aacute
- /Acircumflex
- /Atilde
- /Adieresis
- /Aring
- /AE
- /Ccedilla
- /Egrave
- /Eacute
- /Ecircumflex
- /Edieresis
- /Igrave
- /Iacute
- /Icircumflex
- /Idieresis
- /Eth % missing
- /Ntilde
- /Ograve
- /Oacute
- /Ocircumflex
- /Otilde
- /Odieresis
- /multiply % missing
- /Oslash
- /Ugrave
- /Uacute
- /Ucircumflex
- /Udieresis
- /Yacute % missing
- /Thorn % missing
- /germandbls
- /agrave
- /aacute
- /acircumflex
- /atilde
- /adieresis
- /aring
- /ae
- /ccedilla
- /egrave
- /eacute
- /ecircumflex
- /edieresis
- /igrave
- /iacute
- /icircumflex
- /idieresis
- /eth % missing
- /ntilde
- /ograve
- /oacute
- /ocircumflex
- /otilde
- /odieresis
- /divide % missing
- /oslash
- /ugrave
- /uacute
- /ucircumflex
- /udieresis
- /yacute % missing
- /thorn % missing
- /ydieresis
-] def
-
-/NewFontDirectory FontDirectory maxlength dict def
-
-%
-% Apparently no guarantee findfont is defined in systemdict so the obvious
-%
-% systemdict /findfont get exec
-%
-% can generate an error. So far the only exception is a VT600 (version 48.0).
-%
-
-userdict /@RealFindfont known not {
- userdict begin
- /@RealFindfont systemdict begin /findfont load end def
- end
-} if
-
-/findfont {
- dup NewFontDirectory exch known not {
- dup
- %dup systemdict /findfont get exec % not always in systemdict
- dup userdict /@RealFindfont get exec
- dup /Encoding get StandardEncoding eq {
- dup length dict begin
- {1 index /FID ne {def}{pop pop} ifelse} forall
- /Encoding ISOLatin1Encoding def
- currentdict
- end
- /DummyFontName exch definefont
- } if
- NewFontDirectory 3 1 roll put
- } if
- NewFontDirectory exch get
-} bind def
-
-%%Patch from lp
-%%EndPatch from lp
-
-setup
-%%EndSetup
-%%Page: 1 1
-/saveobj save def
-mark
-1 pagesetup
-12 /LucidaSans-Demi f
-(libgeometry) 2507 1220 w
-10 /LucidaSans-Italic f
-(Rodrigo G. L\363pez) 2469 1480 w
-(rgl@antares-labs.eu) 2377 1760 w
-10 /LucidaSansUnicode00 f
-(Antares Telecom Laboratories) 2156 1960 w
-(Albatera, Alicante) 2451 2100 w
-10 /LucidaSans-Demi f
-(1.) 720 2700 w
-(Data Structures) 873 2700 w
-(1.1.) 720 2940 w
-(Point2) 962 2940 w
-9 /LucidaTypewriter f
-(struct) 920 3110 w
-(Point2) 1375 3110 w
-({) 1830 3110 w
-(double) 1440 3220 w
-(x,) 1895 3220 w
-(y,) 2090 3220 w
-(w;) 2285 3220 w
-(};) 920 3330 w
-10 /LucidaSans-Italic f
-(Point2) 970 3546 w
-10 /LucidaSansUnicode00 f
-(represents) 1324 3546 w
-(a) 1886 3546 w
-(point) 1989 3546 w
-(in) 2289 3546 w
-(two-dimensional) 2428 3546 w
-(projective) 3299 3546 w
-(space,) 3823 3546 w
-(which) 4179 3546 w
-(itself) 4508 3546 w
-(is) 4795 3546 w
-(an) 4923 3546 w
-(extension) 720 3666 w
-(of) 1240 3666 w
-(the) 1383 3666 w
-(two-dimensional) 1583 3666 w
-(euclidean) 2451 3666 w
-(space) 2959 3666 w
-(that) 3280 3666 w
-(allows) 3516 3666 w
-(us) 3862 3666 w
-(to) 4019 3666 w
-(work) 4161 3666 w
-(with) 4442 3666 w
-(vectors) 4691 3666 w
-(and compose affine transformations in a friendly manner.) 720 3786 w
-(A point) 3589 3786 w
-(\() 2696 3966 w
-(x) 2737 3966 w
-(,) 2806 3966 w
-(y) 2846 3966 w
-(,) 2906 3966 w
-(w) 2946 3966 w
-(\)) 3031 3966 w
-(made) 720 4146 w
-(out) 1027 4146 w
-(of) 1227 4146 w
-(homogenous) 1365 4146 w
-(coordinates) 2036 4146 w
-10 /LucidaSans-Italic f
-(x) 2643 4146 w
-10 /LucidaSansUnicode00 f
-(,) 2697 4146 w
-10 /LucidaSans-Italic f
-(y) 2769 4146 w
-10 /LucidaSansUnicode00 f
-(,) 2824 4146 w
-(and) 2896 4146 w
-10 /LucidaSans-Italic f
-(w) 3116 4146 w
-10 /LucidaSansUnicode00 f
-(,) 3194 4146 w
-(yields) 3267 4146 w
-(a) 3588 4146 w
-(point) 3684 4146 w
-(with) 3977 4146 w
-(cartesian) 4223 4146 w
-(coordi\255) 4701 4146 w
-(nates) 720 4266 w
-(\() 2588 4446 w
-(x) 2629 4446 w
-(/) 2698 4446 w
-(w) 2759 4446 w
-(,) 2844 4446 w
-(y) 2884 4446 w
-(/) 2944 4446 w
-(w) 3005 4446 w
-(\)) 3090 4446 w
-(.) 3139 4446 w
-10 /LucidaSans-Demi f
-(1.2.) 720 4746 w
-(Point3) 962 4746 w
-9 /LucidaTypewriter f
-(struct) 920 4916 w
-(Point3) 1375 4916 w
-({) 1830 4916 w
-(double) 1440 5026 w
-(x,) 1895 5026 w
-(y,) 2090 5026 w
-(z,) 2285 5026 w
-(w;) 2480 5026 w
-(};) 920 5136 w
-10 /LucidaSans-Italic f
-(Point3) 970 5352 w
-10 /LucidaSansUnicode00 f
-(is a point in three-dimensional projective space.) 1309 5352 w
-10 /LucidaSans-Demi f
-(1.3.) 720 5592 w
-(Matrix) 962 5592 w
-9 /LucidaTypewriter f
-(typedef) 920 5762 w
-(double) 1440 5762 w
-(Matrix[3][3];) 1895 5762 w
-10 /LucidaSans-Italic f
-(Matrix) 970 5978 w
-10 /LucidaSansUnicode00 f
-(represents) 1341 5978 w
-(a) 1914 5978 w
-(3x3) 2028 5978 w
-(matrix,) 2274 5978 w
-(thought) 2681 5978 w
-(to) 3123 5978 w
-(compose) 3280 5978 w
-(affine) 3775 5978 w
-(transformations) 4110 5978 w
-(to) 4942 5978 w
-(apply to homogeneous 2D points.) 720 6098 w
-10 /LucidaSans-Demi f
-(1.4.) 720 6338 w
-(Matrix3) 962 6338 w
-9 /LucidaTypewriter f
-(typedef) 920 6508 w
-(double) 1440 6508 w
-(Matrix3[4][4];) 1895 6508 w
-10 /LucidaSans-Italic f
-(Matrix3) 970 6724 w
-10 /LucidaSansUnicode00 f
-(represents) 1398 6724 w
-(a) 1964 6724 w
-(4x4) 2071 6724 w
-(matrix,) 2310 6724 w
-(thought) 2711 6724 w
-(to) 3147 6724 w
-(compose) 3298 6724 w
-(affine) 3787 6724 w
-(transformations) 4116 6724 w
-(to) 4942 6724 w
-(apply to homogeneous 3D points.) 720 6844 w
-8 /S1 f
-(__________________) 720 6980 w
-8 /LucidaSansUnicode00 f
-(ACHTUNG!) 720 7080 w
-(this) 1163 7080 w
-(is) 1333 7080 w
-(a) 1423 7080 w
-8 /LucidaSans-Demi f
-(WORK) 1493 7080 w
-(IN) 1769 7080 w
-(PROGRESS) 1883 7080 w
-cleartomark
-showpage
-saveobj restore
-%%EndPage: 1 1
-%%Page: 2 2
-/saveobj save def
-mark
-2 pagesetup
-10 /LucidaSansUnicode00 f
-(\255 2 \255) 2783 480 w
-10 /LucidaSans-Demi f
-(1.5.) 720 840 w
-(Quaternion) 962 840 w
-9 /LucidaTypewriter f
-(struct) 920 1010 w
-(Quaternion) 1375 1010 w
-({) 2090 1010 w
-(double) 1440 1120 w
-(r,) 1895 1120 w
-(i,) 2090 1120 w
-(j,) 2285 1120 w
-(k;) 2480 1120 w
-(};) 920 1230 w
-10 /LucidaSans-Italic f
-(Quaternions) 970 1446 w
-10 /LucidaSansUnicode00 f
-(are) 1623 1446 w
-(a) 1829 1446 w
-(numbering) 1938 1446 w
-(system) 2522 1446 w
-(that) 2916 1446 w
-(extends) 3161 1446 w
-(the) 3601 1446 w
-(complex) 3810 1446 w
-(numbers) 4279 1446 w
-(up) 4762 1446 w
-(to) 4942 1446 w
-(four-dimensional) 720 1566 w
-(space,) 1607 1566 w
-(and) 1953 1566 w
-(are) 2171 1566 w
-(used) 2361 1566 w
-(to) 2631 1566 w
-(apply) 2767 1566 w
-(rotations) 3067 1566 w
-(and) 3539 1566 w
-(model) 3757 1566 w
-(mechanical) 4096 1566 w
-(interac\255) 4676 1566 w
-(tions) 720 1686 w
-(in) 1015 1686 w
-(3D) 1161 1686 w
-(space.) 1354 1686 w
-(Their) 1749 1686 w
-(main) 2055 1686 w
-(advantages) 2349 1686 w
-(with) 2952 1686 w
-(respect) 3212 1686 w
-(to) 3622 1686 w
-(their) 3775 1686 w
-(matrix) 4055 1686 w
-(relatives) 4426 1686 w
-(are) 4888 1686 w
-(increased computational and storage performance and gimbal lock avoidance.) 720 1806 w
-10 /LucidaSans-Demi f
-(2.) 720 2046 w
-(Algorithms) 873 2046 w
-(2.1.) 720 2286 w
-(Point2) 962 2286 w
-(Addition) 720 2526 w
-9 /LucidaTypewriter f
-(Point2) 920 2696 w
-(addpt2\(Point2) 1375 2696 w
-(a,) 2285 2696 w
-(Point2) 2480 2696 w
-(b\)) 2935 2696 w
-10 /LucidaSansUnicode00 f
-(a) 2051 2971 w
-10 /S f
-(+) 2122 2971 w
-10 /LucidaSansUnicode00 f
-(b) 2193 2971 w
-10 /S f
-(=) 2312 2971 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2431 2934 w
-(\356) 2431 3034 w
-10 /LucidaSansUnicode00 f
-(x) 2480 2971 w
-7 /LucidaSansUnicode00 f
-(a) 2552 2991 w
-10 /S f
-(+) 2615 2971 w
-10 /LucidaSansUnicode00 f
-(x) 2686 2971 w
-7 /LucidaSansUnicode00 f
-(b) 2758 2991 w
-10 /LucidaSansUnicode00 f
-(,) 2818 2971 w
-(y) 2898 2971 w
-7 /LucidaSansUnicode00 f
-(a) 2961 2991 w
-10 /S f
-(+) 3024 2971 w
-10 /LucidaSansUnicode00 f
-(y) 3095 2971 w
-7 /LucidaSansUnicode00 f
-(b) 3158 2991 w
-10 /LucidaSansUnicode00 f
-(,) 3218 2971 w
-(w) 3298 2971 w
-7 /LucidaSansUnicode00 f
-(a) 3386 2991 w
-10 /S f
-(+) 3449 2971 w
-10 /LucidaSansUnicode00 f
-(w) 3520 2971 w
-7 /LucidaSansUnicode00 f
-(b) 3608 2991 w
-10 /S f
-(\374) 3660 2934 w
-(\376) 3660 3034 w
-10 /LucidaSans-Demi f
-(Substraction) 720 3326 w
-9 /LucidaTypewriter f
-(Point2) 920 3496 w
-(subpt2\(Point2) 1375 3496 w
-(a,) 2285 3496 w
-(Point2) 2480 3496 w
-(b\)) 2935 3496 w
-10 /LucidaSansUnicode00 f
-(a) 2051 3771 w
-10 /S f
-(-) 2122 3771 w
-10 /LucidaSansUnicode00 f
-(b) 2193 3771 w
-10 /S f
-(=) 2312 3771 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2431 3734 w
-(\356) 2431 3834 w
-10 /LucidaSansUnicode00 f
-(x) 2480 3771 w
-7 /LucidaSansUnicode00 f
-(a) 2552 3791 w
-10 /S f
-(-) 2615 3771 w
-10 /LucidaSansUnicode00 f
-(x) 2686 3771 w
-7 /LucidaSansUnicode00 f
-(b) 2758 3791 w
-10 /LucidaSansUnicode00 f
-(,) 2818 3771 w
-(y) 2898 3771 w
-7 /LucidaSansUnicode00 f
-(a) 2961 3791 w
-10 /S f
-(-) 3024 3771 w
-10 /LucidaSansUnicode00 f
-(y) 3095 3771 w
-7 /LucidaSansUnicode00 f
-(b) 3158 3791 w
-10 /LucidaSansUnicode00 f
-(,) 3218 3771 w
-(w) 3298 3771 w
-7 /LucidaSansUnicode00 f
-(a) 3386 3791 w
-10 /S f
-(-) 3449 3771 w
-10 /LucidaSansUnicode00 f
-(w) 3520 3771 w
-7 /LucidaSansUnicode00 f
-(b) 3608 3791 w
-10 /S f
-(\374) 3660 3734 w
-(\376) 3660 3834 w
-10 /LucidaSans-Demi f
-(Multiplication) 720 4126 w
-9 /LucidaTypewriter f
-(Point2) 920 4296 w
-(mulpt2\(Point2) 1375 4296 w
-(p,) 2285 4296 w
-(double) 2480 4296 w
-(s\)) 2935 4296 w
-10 /LucidaSansUnicode00 f
-(p) 2395 4536 w
-(*) 2466 4536 w
-(s) 2522 4536 w
-10 /S f
-(=) 2629 4536 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2748 4499 w
-(\356) 2748 4599 w
-10 /LucidaSansUnicode00 f
-(xs) 2797 4546 w
-(,) 2917 4546 w
-(ys) 2997 4546 w
-(,) 3108 4546 w
-(ws) 3188 4546 w
-10 /S f
-(\374) 3316 4499 w
-(\376) 3316 4599 w
-10 /LucidaSans-Demi f
-(Division) 720 4841 w
-9 /LucidaTypewriter f
-(Point2) 920 5011 w
-(divpt2\(Point2) 1375 5011 w
-(p,) 2285 5011 w
-(double) 2480 5011 w
-(s\)) 2935 5011 w
-10 /LucidaSansUnicode00 f
-(p) 2394 5336 w
-(/) 2465 5336 w
-(s) 2526 5336 w
-10 /S f
-(=) 2633 5336 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2752 5249 w
-(\357) 2752 5349 w
-(\356) 2752 5449 w
-10 /LucidaSansUnicode00 f
-(s) 2831 5406 w
-(x) 2826 5276 w
-10 /S1 f
-(_) 2811 5306 w
-(_) 2852 5306 w
-10 /LucidaSansUnicode00 f
-(,) 2920 5336 w
-(s) 3025 5406 w
-(y) 3025 5276 w
-10 /S1 f
-(_) 3010 5306 w
-(_) 3042 5306 w
-10 /LucidaSansUnicode00 f
-(,) 3110 5336 w
-(s) 3228 5406 w
-(w) 3215 5276 w
-10 /S1 f
-(_) 3200 5306 w
-(__) 3207 5306 w
-10 /S f
-(\374) 3317 5249 w
-(\357) 3317 5349 w
-(\376) 3317 5449 w
-10 /LucidaSans-Demi f
-(Vector Dot Product) 720 5741 w
-9 /LucidaTypewriter f
-(double) 920 5911 w
-(dotvec2\(Point2) 1375 5911 w
-(a,) 2350 5911 w
-(Point2) 2545 5911 w
-(b\)) 3000 5911 w
-10 /LucidaSansUnicode00 f
-(a) 2375 6156 w
-7 /LucidaSansUnicode21 f
-(\222) 2370 6106 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSansUnicode20 f
-(") 2479 6156 w
-10 /LucidaSansUnicode00 f
-(b) 2583 6156 w
-7 /LucidaSansUnicode21 f
-(\222) 2582 6081 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2703 6156 w
-10 /LucidaSansUnicode00 f
-(x) 2814 6156 w
-7 /LucidaSansUnicode00 f
-(a) 2886 6176 w
-10 /LucidaSansUnicode00 f
-(x) 2941 6156 w
-7 /LucidaSansUnicode00 f
-(b) 3013 6176 w
-10 /S f
-(+) 3081 6156 w
-10 /LucidaSansUnicode00 f
-(y) 3152 6156 w
-7 /LucidaSansUnicode00 f
-(a) 3215 6176 w
-10 /LucidaSansUnicode00 f
-(y) 3270 6156 w
-7 /LucidaSansUnicode00 f
-(b) 3333 6176 w
-10 /LucidaSans-Demi f
-(Vector Magnitude/Length) 720 6456 w
-9 /LucidaTypewriter f
-(double) 920 6626 w
-(vec2len\(Point2) 1375 6626 w
-(v\)) 2350 6626 w
-10 /LucidaSansUnicode00 f
-(|) 2509 6901 w
-(v) 2557 6884 w
-7 /LucidaSansUnicode21 f
-(\222) 2550 6834 w
-10 /LucidaSansUnicode00 f
-(|) 2609 6901 w
-10 /S f
-(=) 2705 6884 w
-10 /LucidaSansUnicode00 f
-12 /LucidaSansUnicode22 f
-(\032) 2816 6884 w
-12 /S f
-(`) 2913 6884 w
-(`````) 2943 6884 w
-10 /LucidaSansUnicode00 f
-(x) 2921 6884 w
-7 /LucidaSansUnicode00 f
-(2) 2987 6844 w
-10 /S f
-(+) 3055 6884 w
-10 /LucidaSansUnicode00 f
-(y) 3126 6884 w
-7 /LucidaSansUnicode00 f
-(2) 3183 6844 w
-cleartomark
-showpage
-saveobj restore
-%%EndPage: 2 2
-%%Page: 3 3
-/saveobj save def
-mark
-3 pagesetup
-10 /LucidaSansUnicode00 f
-(\255 3 \255) 2783 480 w
-10 /LucidaSans-Demi f
-(Vector Normalization) 720 840 w
-9 /LucidaTypewriter f
-(Point2) 920 1010 w
-(normvec2\(Point2) 1375 1010 w
-(v\)) 2415 1010 w
-10 /LucidaSansUnicode00 f
-(n) 2502 1335 w
-7 /LucidaSansUnicode21 f
-(\222) 2500 1285 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2620 1335 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2739 1248 w
-(\357) 2739 1348 w
-(\356) 2739 1448 w
-10 /LucidaSansUnicode00 f
-(|) 2813 1447 w
-(v) 2861 1430 w
-7 /LucidaSansUnicode21 f
-(\222) 2854 1380 w
-10 /LucidaSansUnicode00 f
-(|) 2913 1447 w
-(x) 2841 1275 w
-10 /S1 f
-(_) 2799 1305 w
-(__) 2845 1305 w
-10 /LucidaSansUnicode00 f
-(,) 2963 1335 w
-(|) 3068 1447 w
-(v) 3116 1430 w
-7 /LucidaSansUnicode21 f
-(\222) 3109 1380 w
-10 /LucidaSansUnicode00 f
-(|) 3168 1447 w
-(y) 3100 1275 w
-10 /S1 f
-(_) 3053 1305 w
-(__) 3099 1305 w
-10 /S f
-(\374) 3209 1248 w
-(\357) 3209 1348 w
-(\376) 3209 1448 w
-10 /LucidaSans-Demi f
-(2.2.) 720 1740 w
-(Point3) 962 1740 w
-(Addition) 720 1980 w
-9 /LucidaTypewriter f
-(Point3) 920 2150 w
-(addpt3\(Point3) 1375 2150 w
-(a,) 2285 2150 w
-(Point3) 2480 2150 w
-(b\)) 2935 2150 w
-10 /LucidaSansUnicode00 f
-(a) 1846 2425 w
-10 /S f
-(+) 1917 2425 w
-10 /LucidaSansUnicode00 f
-(b) 1988 2425 w
-10 /S f
-(=) 2107 2425 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2226 2388 w
-(\356) 2226 2488 w
-10 /LucidaSansUnicode00 f
-(x) 2275 2425 w
-7 /LucidaSansUnicode00 f
-(a) 2347 2445 w
-10 /S f
-(+) 2410 2425 w
-10 /LucidaSansUnicode00 f
-(x) 2481 2425 w
-7 /LucidaSansUnicode00 f
-(b) 2553 2445 w
-10 /LucidaSansUnicode00 f
-(,) 2613 2425 w
-(y) 2693 2425 w
-7 /LucidaSansUnicode00 f
-(a) 2756 2445 w
-10 /S f
-(+) 2819 2425 w
-10 /LucidaSansUnicode00 f
-(y) 2890 2425 w
-7 /LucidaSansUnicode00 f
-(b) 2953 2445 w
-10 /LucidaSansUnicode00 f
-(,) 3013 2425 w
-(z) 3093 2425 w
-7 /LucidaSansUnicode00 f
-(a) 3161 2445 w
-10 /S f
-(+) 3224 2425 w
-10 /LucidaSansUnicode00 f
-(z) 3295 2425 w
-7 /LucidaSansUnicode00 f
-(b) 3363 2445 w
-10 /LucidaSansUnicode00 f
-(,) 3423 2425 w
-(w) 3503 2425 w
-7 /LucidaSansUnicode00 f
-(a) 3591 2445 w
-10 /S f
-(+) 3654 2425 w
-10 /LucidaSansUnicode00 f
-(w) 3725 2425 w
-7 /LucidaSansUnicode00 f
-(b) 3813 2445 w
-10 /S f
-(\374) 3865 2388 w
-(\376) 3865 2488 w
-10 /LucidaSans-Demi f
-(Substraction) 720 2780 w
-9 /LucidaTypewriter f
-(Point3) 920 2950 w
-(subpt3\(Point3) 1375 2950 w
-(a,) 2285 2950 w
-(Point3) 2480 2950 w
-(b\)) 2935 2950 w
-10 /LucidaSansUnicode00 f
-(a) 1846 3225 w
-10 /S f
-(-) 1917 3225 w
-10 /LucidaSansUnicode00 f
-(b) 1988 3225 w
-10 /S f
-(=) 2107 3225 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2226 3188 w
-(\356) 2226 3288 w
-10 /LucidaSansUnicode00 f
-(x) 2275 3225 w
-7 /LucidaSansUnicode00 f
-(a) 2347 3245 w
-10 /S f
-(-) 2410 3225 w
-10 /LucidaSansUnicode00 f
-(x) 2481 3225 w
-7 /LucidaSansUnicode00 f
-(b) 2553 3245 w
-10 /LucidaSansUnicode00 f
-(,) 2613 3225 w
-(y) 2693 3225 w
-7 /LucidaSansUnicode00 f
-(a) 2756 3245 w
-10 /S f
-(-) 2819 3225 w
-10 /LucidaSansUnicode00 f
-(y) 2890 3225 w
-7 /LucidaSansUnicode00 f
-(b) 2953 3245 w
-10 /LucidaSansUnicode00 f
-(,) 3013 3225 w
-(z) 3093 3225 w
-7 /LucidaSansUnicode00 f
-(a) 3161 3245 w
-10 /S f
-(-) 3224 3225 w
-10 /LucidaSansUnicode00 f
-(z) 3295 3225 w
-7 /LucidaSansUnicode00 f
-(b) 3363 3245 w
-10 /LucidaSansUnicode00 f
-(,) 3423 3225 w
-(w) 3503 3225 w
-7 /LucidaSansUnicode00 f
-(a) 3591 3245 w
-10 /S f
-(-) 3654 3225 w
-10 /LucidaSansUnicode00 f
-(w) 3725 3225 w
-7 /LucidaSansUnicode00 f
-(b) 3813 3245 w
-10 /S f
-(\374) 3865 3188 w
-(\376) 3865 3288 w
-10 /LucidaSans-Demi f
-(Multiplication) 720 3580 w
-9 /LucidaTypewriter f
-(Point3) 920 3750 w
-(mulpt3\(Point3) 1375 3750 w
-(p,) 2285 3750 w
-(double) 2480 3750 w
-(s\)) 2935 3750 w
-10 /LucidaSansUnicode00 f
-(p) 2297 3990 w
-(*) 2368 3990 w
-(s) 2424 3990 w
-10 /S f
-(=) 2531 3990 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2650 3953 w
-(\356) 2650 4053 w
-10 /LucidaSansUnicode00 f
-(xs) 2699 4000 w
-(,) 2819 4000 w
-(ys) 2899 4000 w
-(,) 3010 4000 w
-(zs) 3090 4000 w
-(,) 3206 4000 w
-(ws) 3286 4000 w
-10 /S f
-(\374) 3414 3953 w
-(\376) 3414 4053 w
-10 /LucidaSans-Demi f
-(Division) 720 4295 w
-9 /LucidaTypewriter f
-(Point3) 920 4465 w
-(divpt3\(Point3) 1375 4465 w
-(p,) 2285 4465 w
-(double) 2480 4465 w
-(s\)) 2935 4465 w
-10 /LucidaSansUnicode00 f
-(p) 2296 4790 w
-(/) 2367 4790 w
-(s) 2428 4790 w
-10 /S f
-(=) 2535 4790 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2654 4703 w
-(\357) 2654 4803 w
-(\356) 2654 4903 w
-10 /LucidaSansUnicode00 f
-(s) 2733 4860 w
-(x) 2728 4730 w
-10 /S1 f
-(_) 2713 4760 w
-(_) 2754 4760 w
-10 /LucidaSansUnicode00 f
-(,) 2822 4790 w
-(s) 2927 4860 w
-(y) 2927 4730 w
-10 /S1 f
-(_) 2912 4760 w
-(_) 2944 4760 w
-10 /LucidaSansUnicode00 f
-(,) 3012 4790 w
-(s) 3120 4860 w
-(z) 3117 4730 w
-10 /S1 f
-(_) 3102 4760 w
-(_) 3139 4760 w
-10 /LucidaSansUnicode00 f
-(,) 3207 4790 w
-(s) 3325 4860 w
-(w) 3312 4730 w
-10 /S1 f
-(_) 3297 4760 w
-(__) 3304 4760 w
-10 /S f
-(\374) 3414 4703 w
-(\357) 3414 4803 w
-(\376) 3414 4903 w
-10 /LucidaSans-Demi f
-(Vector Dot Product) 720 5195 w
-9 /LucidaTypewriter f
-(double) 920 5365 w
-(dotvec3\(Point3) 1375 5365 w
-(a,) 2350 5365 w
-(Point3) 2545 5365 w
-(b\)) 3000 5365 w
-10 /LucidaSansUnicode00 f
-(a) 2210 5610 w
-7 /LucidaSansUnicode21 f
-(\222) 2205 5560 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSansUnicode20 f
-(") 2314 5610 w
-10 /LucidaSansUnicode00 f
-(b) 2418 5610 w
-7 /LucidaSansUnicode21 f
-(\222) 2417 5535 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2538 5610 w
-10 /LucidaSansUnicode00 f
-(x) 2649 5610 w
-7 /LucidaSansUnicode00 f
-(a) 2721 5630 w
-10 /LucidaSansUnicode00 f
-(x) 2776 5610 w
-7 /LucidaSansUnicode00 f
-(b) 2848 5630 w
-10 /S f
-(+) 2916 5610 w
-10 /LucidaSansUnicode00 f
-(y) 2987 5610 w
-7 /LucidaSansUnicode00 f
-(a) 3050 5630 w
-10 /LucidaSansUnicode00 f
-(y) 3105 5610 w
-7 /LucidaSansUnicode00 f
-(b) 3168 5630 w
-10 /S f
-(+) 3236 5610 w
-10 /LucidaSansUnicode00 f
-(z) 3307 5610 w
-7 /LucidaSansUnicode00 f
-(a) 3375 5630 w
-10 /LucidaSansUnicode00 f
-(z) 3430 5610 w
-7 /LucidaSansUnicode00 f
-(b) 3498 5630 w
-10 /LucidaSans-Demi f
-(Vector Cross Product) 720 5910 w
-9 /LucidaTypewriter f
-(double) 920 6080 w
-(crossvec3\(Point3) 1375 6080 w
-(a,) 2480 6080 w
-(Point3) 2675 6080 w
-(b\)) 3130 6080 w
-10 /LucidaSansUnicode00 f
-(a) 1650 6355 w
-7 /LucidaSansUnicode21 f
-(\222) 1645 6305 w
-10 /LucidaSansUnicode00 f
-(\327) 1754 6355 w
-(b) 1882 6355 w
-7 /LucidaSansUnicode21 f
-(\222) 1881 6280 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2002 6355 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2121 6318 w
-(\356) 2121 6418 w
-10 /LucidaSansUnicode00 f
-(y) 2170 6355 w
-7 /LucidaSansUnicode00 f
-(a) 2233 6375 w
-10 /LucidaSansUnicode00 f
-(z) 2288 6355 w
-7 /LucidaSansUnicode00 f
-(b) 2356 6375 w
-10 /S f
-(-) 2424 6355 w
-10 /LucidaSansUnicode00 f
-(z) 2495 6355 w
-7 /LucidaSansUnicode00 f
-(a) 2563 6375 w
-10 /LucidaSansUnicode00 f
-(y) 2618 6355 w
-7 /LucidaSansUnicode00 f
-(b) 2681 6375 w
-10 /LucidaSansUnicode00 f
-(,) 2741 6355 w
-(z) 2821 6355 w
-7 /LucidaSansUnicode00 f
-(a) 2889 6375 w
-10 /LucidaSansUnicode00 f
-(x) 2944 6355 w
-7 /LucidaSansUnicode00 f
-(b) 3016 6375 w
-10 /S f
-(-) 3084 6355 w
-10 /LucidaSansUnicode00 f
-(x) 3155 6355 w
-7 /LucidaSansUnicode00 f
-(a) 3227 6375 w
-10 /LucidaSansUnicode00 f
-(z) 3282 6355 w
-7 /LucidaSansUnicode00 f
-(b) 3350 6375 w
-10 /LucidaSansUnicode00 f
-(,) 3410 6355 w
-(x) 3490 6355 w
-7 /LucidaSansUnicode00 f
-(a) 3562 6375 w
-10 /LucidaSansUnicode00 f
-(y) 3617 6355 w
-7 /LucidaSansUnicode00 f
-(b) 3680 6375 w
-10 /S f
-(-) 3748 6355 w
-10 /LucidaSansUnicode00 f
-(y) 3819 6355 w
-7 /LucidaSansUnicode00 f
-(a) 3882 6375 w
-10 /LucidaSansUnicode00 f
-(x) 3937 6355 w
-7 /LucidaSansUnicode00 f
-(b) 4009 6375 w
-10 /S f
-(\374) 4061 6318 w
-(\376) 4061 6418 w
-10 /LucidaSans-Demi f
-(Vector Magnitude/Length) 720 6710 w
-9 /LucidaTypewriter f
-(double) 920 6880 w
-(vec3len\(Point3) 1375 6880 w
-(v\)) 2350 6880 w
-10 /LucidaSansUnicode00 f
-(|) 2408 7155 w
-(v) 2456 7138 w
-7 /LucidaSansUnicode21 f
-(\222) 2449 7088 w
-10 /LucidaSansUnicode00 f
-(|) 2508 7155 w
-10 /S f
-(=) 2604 7138 w
-10 /LucidaSansUnicode00 f
-12 /LucidaSansUnicode22 f
-(\032) 2715 7138 w
-12 /S f
-(`) 2812 7138 w
-(````````) 2863 7138 w
-10 /LucidaSansUnicode00 f
-(x) 2820 7138 w
-7 /LucidaSansUnicode00 f
-(2) 2886 7098 w
-10 /S f
-(+) 2954 7138 w
-10 /LucidaSansUnicode00 f
-(y) 3025 7138 w
-7 /LucidaSansUnicode00 f
-(2) 3082 7098 w
-10 /S f
-(+) 3150 7138 w
-10 /LucidaSansUnicode00 f
-(z) 3221 7138 w
-7 /LucidaSansUnicode00 f
-(2) 3283 7098 w
-cleartomark
-showpage
-saveobj restore
-%%EndPage: 3 3
-%%Page: 4 4
-/saveobj save def
-mark
-4 pagesetup
-10 /LucidaSansUnicode00 f
-(\255 4 \255) 2783 480 w
-10 /LucidaSans-Demi f
-(Vector Normalization) 720 840 w
-9 /LucidaTypewriter f
-(Point3) 920 1010 w
-(normvec3\(Point3) 1375 1010 w
-(v\)) 2415 1010 w
-10 /LucidaSansUnicode00 f
-(n) 2374 1335 w
-7 /LucidaSansUnicode21 f
-(\222) 2372 1285 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2492 1335 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2611 1248 w
-(\357) 2611 1348 w
-(\356) 2611 1448 w
-10 /LucidaSansUnicode00 f
-(|) 2685 1447 w
-(v) 2733 1430 w
-7 /LucidaSansUnicode21 f
-(\222) 2726 1380 w
-10 /LucidaSansUnicode00 f
-(|) 2785 1447 w
-(x) 2713 1275 w
-10 /S1 f
-(_) 2671 1305 w
-(__) 2717 1305 w
-10 /LucidaSansUnicode00 f
-(,) 2835 1335 w
-(|) 2940 1447 w
-(v) 2988 1430 w
-7 /LucidaSansUnicode21 f
-(\222) 2981 1380 w
-10 /LucidaSansUnicode00 f
-(|) 3040 1447 w
-(y) 2972 1275 w
-10 /S1 f
-(_) 2925 1305 w
-(__) 2971 1305 w
-10 /LucidaSansUnicode00 f
-(,) 3089 1335 w
-(|) 3194 1447 w
-(v) 3242 1430 w
-7 /LucidaSansUnicode21 f
-(\222) 3235 1380 w
-10 /LucidaSansUnicode00 f
-(|) 3294 1447 w
-(z) 3224 1275 w
-10 /S1 f
-(_) 3180 1305 w
-(__) 3226 1305 w
-10 /S f
-(\374) 3336 1248 w
-(\357) 3336 1348 w
-(\376) 3336 1448 w
-10 /LucidaSans-Demi f
-(2.3.) 720 1740 w
-(Matrix) 962 1740 w
-(Addition) 720 1980 w
-9 /LucidaTypewriter f
-(void) 920 2150 w
-(addm\(Matrix) 1245 2150 w
-(A,) 2025 2150 w
-(Matrix) 2220 2150 w
-(B\)) 2675 2150 w
-10 /LucidaSansUnicode00 f
-(\() 2393 2390 w
-10 /LucidaSans-Demi f
-(A) 2434 2390 w
-10 /S f
-(+) 2524 2390 w
-10 /LucidaSans-Demi f
-(B) 2595 2390 w
-10 /LucidaSansUnicode00 f
-(\)) 2666 2390 w
-7 /LucidaSansUnicode00 f
-(i) 2710 2410 w
-(,) 2735 2410 w
-(j) 2762 2410 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2847 2390 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSans-Demi f
-(A) 2958 2390 w
-7 /LucidaSansUnicode00 f
-(i) 3043 2410 w
-(,) 3068 2410 w
-(j) 3095 2410 w
-10 /S f
-(+) 3140 2390 w
-10 /LucidaSans-Demi f
-(B) 3211 2390 w
-7 /LucidaSansUnicode00 f
-(i) 3285 2410 w
-(,) 3310 2410 w
-(j) 3337 2410 w
-10 /LucidaSans-Demi f
-(Substraction) 720 2690 w
-9 /LucidaTypewriter f
-(void) 920 2860 w
-(subm\(Matrix) 1245 2860 w
-(A,) 2025 2860 w
-(Matrix) 2220 2860 w
-(B\)) 2675 2860 w
-10 /LucidaSansUnicode00 f
-(\() 2393 3100 w
-10 /LucidaSans-Demi f
-(A) 2434 3100 w
-10 /S f
-(-) 2524 3100 w
-10 /LucidaSans-Demi f
-(B) 2595 3100 w
-10 /LucidaSansUnicode00 f
-(\)) 2666 3100 w
-7 /LucidaSansUnicode00 f
-(i) 2710 3120 w
-(,) 2735 3120 w
-(j) 2762 3120 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2847 3100 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSans-Demi f
-(A) 2958 3100 w
-7 /LucidaSansUnicode00 f
-(i) 3043 3120 w
-(,) 3068 3120 w
-(j) 3095 3120 w
-10 /S f
-(-) 3140 3100 w
-10 /LucidaSans-Demi f
-(B) 3211 3100 w
-7 /LucidaSansUnicode00 f
-(i) 3285 3120 w
-(,) 3310 3120 w
-(j) 3337 3120 w
-10 /LucidaSans-Demi f
-(Multiplication) 720 3400 w
-9 /LucidaTypewriter f
-(void) 920 3570 w
-(mulm\(Matrix) 1245 3570 w
-(A,) 2025 3570 w
-(Matrix) 2220 3570 w
-(B\)) 2675 3570 w
-10 /S f
-(\351) 2370 3823 w
-(\353) 2370 3923 w
-10 /LucidaSans-Demi f
-(AB) 2420 3870 w
-10 /S f
-(\371) 2557 3823 w
-(\373) 2557 3923 w
-7 /LucidaSansUnicode00 f
-(i) 2606 3905 w
-(,) 2631 3905 w
-(j) 2658 3905 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2743 3860 w
-10 /LucidaSansUnicode00 f
-7 /LucidaSansUnicode00 f
-(k) 2847 3960 w
-7 /S f
-(=) 2899 3960 w
-7 /LucidaSansUnicode00 f
-(0) 2949 3960 w
-15 /S f
-(S) 2876 3890 w
-7 /LucidaSansUnicode00 f
-(3) 2846 3760 w
-7 /S f
-(-) 2901 3760 w
-7 /LucidaSansUnicode00 f
-(1) 2951 3760 w
-10 /LucidaSans-Demi f
-(A) 3027 3860 w
-7 /LucidaSansUnicode00 f
-(i) 3112 3880 w
-(,) 3137 3880 w
-(k) 3164 3880 w
-10 /LucidaSans-Demi f
-(B) 3221 3860 w
-7 /LucidaSansUnicode00 f
-(k) 3295 3880 w
-(,) 3341 3880 w
-(j) 3368 3880 w
-10 /LucidaSans-Demi f
-(Transpose) 720 4240 w
-9 /LucidaTypewriter f
-(void) 920 4410 w
-(transposem\(Matrix) 1245 4410 w
-(M\)) 2415 4410 w
-10 /LucidaSansUnicode00 f
-(\() 2552 4650 w
-10 /LucidaSans-Demi f
-(M) 2593 4650 w
-7 /LucidaSansUnicode00 f
-(T) 2689 4610 w
-10 /LucidaSansUnicode00 f
-(\)) 2749 4650 w
-7 /LucidaSansUnicode00 f
-(i) 2793 4670 w
-(,) 2818 4670 w
-(j) 2845 4670 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2930 4650 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSans-Demi f
-(A) 3041 4650 w
-7 /LucidaSansUnicode00 f
-(j) 3126 4670 w
-(,) 3152 4670 w
-(i) 3179 4670 w
-10 /LucidaSans-Demi f
-(Identity) 720 4950 w
-9 /LucidaTypewriter f
-(void) 920 5120 w
-(identity\(Matrix) 1245 5120 w
-(M\)) 2285 5120 w
-10 /LucidaSans-Demi f
-(M) 2560 5495 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2707 5495 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\351) 2826 5358 w
-(\357) 2826 5458 w
-(\357) 2826 5558 w
-(\353) 2826 5658 w
-10 /LucidaSansUnicode00 f
-(0) 2876 5645 w
-(0) 2987 5645 w
-(1) 3098 5645 w
-(0) 2876 5505 w
-(1) 2987 5505 w
-(0) 3098 5505 w
-(1) 2876 5365 w
-(0) 2987 5365 w
-(0) 3098 5365 w
-10 /S f
-(\371) 3161 5358 w
-(\357) 3161 5458 w
-(\357) 3161 5558 w
-(\373) 3161 5658 w
-10 /LucidaSans-Demi f
-(Determinant) 720 5950 w
-9 /LucidaTypewriter f
-(double) 920 6120 w
-(detm\(Matrix) 1375 6120 w
-(M\)) 2155 6120 w
-10 /LucidaSansUnicode00 f
-(det) 1992 6500 w
-(\() 2156 6500 w
-10 /LucidaSans-Demi f
-(M) 2197 6500 w
-10 /LucidaSansUnicode00 f
-(\)) 2296 6500 w
-10 /S f
-(=) 2393 6500 w
-10 /LucidaSansUnicode00 f
-(m) 2504 6660 w
-7 /LucidaSansUnicode00 f
-(02) 2608 6680 w
-10 /LucidaSansUnicode00 f
-(\() 2712 6660 w
-(m) 2753 6660 w
-7 /LucidaSansUnicode00 f
-(10) 2857 6680 w
-10 /LucidaSansUnicode00 f
-(m) 2961 6660 w
-7 /LucidaSansUnicode00 f
-(21) 3065 6680 w
-10 /S f
-(-) 3177 6660 w
-10 /LucidaSansUnicode00 f
-(m) 3248 6660 w
-7 /LucidaSansUnicode00 f
-(11) 3352 6680 w
-10 /LucidaSansUnicode00 f
-(m) 3456 6660 w
-7 /LucidaSansUnicode00 f
-(20) 3560 6680 w
-10 /LucidaSansUnicode00 f
-(\)) 3664 6660 w
-(m) 2504 6500 w
-7 /LucidaSansUnicode00 f
-(01) 2608 6520 w
-10 /LucidaSansUnicode00 f
-(\() 2712 6500 w
-(m) 2753 6500 w
-7 /LucidaSansUnicode00 f
-(12) 2857 6520 w
-10 /LucidaSansUnicode00 f
-(m) 2961 6500 w
-7 /LucidaSansUnicode00 f
-(20) 3065 6520 w
-10 /S f
-(-) 3177 6500 w
-10 /LucidaSansUnicode00 f
-(m) 3248 6500 w
-7 /LucidaSansUnicode00 f
-(10) 3352 6520 w
-10 /LucidaSansUnicode00 f
-(m) 3456 6500 w
-7 /LucidaSansUnicode00 f
-(22) 3560 6520 w
-10 /LucidaSansUnicode00 f
-(\)) 3664 6500 w
-10 /S f
-(+) 3713 6500 w
-10 /LucidaSansUnicode00 f
-(m) 2504 6340 w
-7 /LucidaSansUnicode00 f
-(00) 2608 6360 w
-10 /LucidaSansUnicode00 f
-(\() 2712 6340 w
-(m) 2753 6340 w
-7 /LucidaSansUnicode00 f
-(11) 2857 6360 w
-10 /LucidaSansUnicode00 f
-(m) 2961 6340 w
-7 /LucidaSansUnicode00 f
-(22) 3065 6360 w
-10 /S f
-(-) 3177 6340 w
-10 /LucidaSansUnicode00 f
-(m) 3248 6340 w
-7 /LucidaSansUnicode00 f
-(12) 3352 6360 w
-10 /LucidaSansUnicode00 f
-(m) 3456 6340 w
-7 /LucidaSansUnicode00 f
-(21) 3560 6360 w
-10 /LucidaSansUnicode00 f
-(\)) 3664 6340 w
-10 /S f
-(+) 3713 6340 w
-cleartomark
-showpage
-saveobj restore
-%%EndPage: 4 4
-%%Page: 5 5
-/saveobj save def
-mark
-5 pagesetup
-10 /LucidaSansUnicode00 f
-(\255 5 \255) 2783 480 w
-10 /LucidaSans-Demi f
-(2.4.) 720 840 w
-(Matrix3) 962 840 w
-(Addition) 720 1080 w
-9 /LucidaTypewriter f
-(void) 920 1250 w
-(addm3\(Matrix3) 1245 1250 w
-(A,) 2155 1250 w
-(Matrix3) 2350 1250 w
-(B\)) 2870 1250 w
-10 /LucidaSansUnicode00 f
-(\() 2393 1490 w
-10 /LucidaSans-Demi f
-(A) 2434 1490 w
-10 /S f
-(+) 2524 1490 w
-10 /LucidaSans-Demi f
-(B) 2595 1490 w
-10 /LucidaSansUnicode00 f
-(\)) 2666 1490 w
-7 /LucidaSansUnicode00 f
-(i) 2710 1510 w
-(,) 2735 1510 w
-(j) 2762 1510 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2847 1490 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSans-Demi f
-(A) 2958 1490 w
-7 /LucidaSansUnicode00 f
-(i) 3043 1510 w
-(,) 3068 1510 w
-(j) 3095 1510 w
-10 /S f
-(+) 3140 1490 w
-10 /LucidaSans-Demi f
-(B) 3211 1490 w
-7 /LucidaSansUnicode00 f
-(i) 3285 1510 w
-(,) 3310 1510 w
-(j) 3337 1510 w
-10 /LucidaSans-Demi f
-(Substraction) 720 1790 w
-9 /LucidaTypewriter f
-(void) 920 1960 w
-(subm3\(Matrix3) 1245 1960 w
-(A,) 2155 1960 w
-(Matrix3) 2350 1960 w
-(B\)) 2870 1960 w
-10 /LucidaSansUnicode00 f
-(\() 2393 2200 w
-10 /LucidaSans-Demi f
-(A) 2434 2200 w
-10 /S f
-(-) 2524 2200 w
-10 /LucidaSans-Demi f
-(B) 2595 2200 w
-10 /LucidaSansUnicode00 f
-(\)) 2666 2200 w
-7 /LucidaSansUnicode00 f
-(i) 2710 2220 w
-(,) 2735 2220 w
-(j) 2762 2220 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2847 2200 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSans-Demi f
-(A) 2958 2200 w
-7 /LucidaSansUnicode00 f
-(i) 3043 2220 w
-(,) 3068 2220 w
-(j) 3095 2220 w
-10 /S f
-(-) 3140 2200 w
-10 /LucidaSans-Demi f
-(B) 3211 2200 w
-7 /LucidaSansUnicode00 f
-(i) 3285 2220 w
-(,) 3310 2220 w
-(j) 3337 2220 w
-10 /LucidaSans-Demi f
-(Multiplication) 720 2500 w
-9 /LucidaTypewriter f
-(void) 920 2670 w
-(mulm3\(Matrix3) 1245 2670 w
-(A,) 2155 2670 w
-(Matrix3) 2350 2670 w
-(B\)) 2870 2670 w
-10 /S f
-(\351) 2374 2923 w
-(\353) 2374 3023 w
-10 /LucidaSans-Demi f
-(AB) 2424 2970 w
-10 /S f
-(\371) 2561 2923 w
-(\373) 2561 3023 w
-7 /LucidaSansUnicode00 f
-(i) 2610 3005 w
-(,) 2635 3005 w
-(j) 2662 3005 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2747 2960 w
-10 /LucidaSansUnicode00 f
-7 /LucidaSansUnicode00 f
-(k) 2859 3060 w
-7 /S f
-(=) 2911 3060 w
-7 /LucidaSansUnicode00 f
-(0) 2961 3060 w
-15 /S f
-(S) 2888 2990 w
-7 /LucidaSansUnicode00 f
-(4) 2858 2860 w
-7 /S f
-(-) 2913 2860 w
-7 /LucidaSansUnicode00 f
-(1) 2963 2860 w
-10 /LucidaSans-Demi f
-(A) 3023 2960 w
-7 /LucidaSansUnicode00 f
-(i) 3108 2980 w
-(,) 3133 2980 w
-(k) 3160 2980 w
-10 /LucidaSans-Demi f
-(B) 3217 2960 w
-7 /LucidaSansUnicode00 f
-(k) 3291 2980 w
-(,) 3337 2980 w
-(j) 3364 2980 w
-10 /LucidaSans-Demi f
-(Transpose) 720 3340 w
-9 /LucidaTypewriter f
-(void) 920 3510 w
-(transposem3\(Matrix3) 1245 3510 w
-(M\)) 2545 3510 w
-10 /LucidaSansUnicode00 f
-(\() 2552 3750 w
-10 /LucidaSans-Demi f
-(M) 2593 3750 w
-7 /LucidaSansUnicode00 f
-(T) 2689 3710 w
-10 /LucidaSansUnicode00 f
-(\)) 2749 3750 w
-7 /LucidaSansUnicode00 f
-(i) 2793 3770 w
-(,) 2818 3770 w
-(j) 2845 3770 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2930 3750 w
-10 /LucidaSansUnicode00 f
-10 /LucidaSans-Demi f
-(A) 3041 3750 w
-7 /LucidaSansUnicode00 f
-(j) 3126 3770 w
-(,) 3152 3770 w
-(i) 3179 3770 w
-10 /LucidaSans-Demi f
-(Identity) 720 4050 w
-9 /LucidaTypewriter f
-(void) 920 4220 w
-(identity3\(Matrix3) 1245 4220 w
-(M\)) 2415 4220 w
-10 /LucidaSans-Demi f
-(M) 2505 4695 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2652 4695 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\351) 2771 4458 w
-(\357) 2771 4558 w
-(\357) 2771 4658 w
-(\357) 2771 4758 w
-(\357) 2771 4858 w
-(\353) 2771 4958 w
-10 /LucidaSansUnicode00 f
-(0) 2821 4915 w
-(0) 2932 4915 w
-(0) 3043 4915 w
-(1) 3154 4915 w
-(0) 2821 4775 w
-(0) 2932 4775 w
-(1) 3043 4775 w
-(0) 3154 4775 w
-(0) 2821 4635 w
-(1) 2932 4635 w
-(0) 3043 4635 w
-(0) 3154 4635 w
-(1) 2821 4495 w
-(0) 2932 4495 w
-(0) 3043 4495 w
-(0) 3154 4495 w
-10 /S f
-(\371) 3217 4458 w
-(\357) 3217 4558 w
-(\357) 3217 4658 w
-(\357) 3217 4758 w
-(\357) 3217 4858 w
-(\373) 3217 4958 w
-10 /LucidaSans-Demi f
-(Determinant) 720 5250 w
-9 /LucidaTypewriter f
-(double) 920 5420 w
-(detm3\(Matrix3) 1375 5420 w
-(M\)) 2285 5420 w
-10 /LucidaSansUnicode00 f
-(det) 567 5910 w
-(\() 731 5910 w
-10 /LucidaSans-Demi f
-(M) 772 5910 w
-10 /LucidaSansUnicode00 f
-(\)) 871 5910 w
-10 /S f
-(=) 968 5910 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(-) 1079 6120 w
-10 /LucidaSansUnicode00 f
-(m) 1150 6120 w
-7 /LucidaSansUnicode00 f
-(03) 1254 6140 w
-10 /LucidaSansUnicode00 f
-(\() 1358 6120 w
-(m) 1399 6120 w
-7 /LucidaSansUnicode00 f
-(10) 1503 6140 w
-10 /LucidaSansUnicode00 f
-(\() 1607 6120 w
-(m) 1648 6120 w
-7 /LucidaSansUnicode00 f
-(21) 1752 6140 w
-10 /LucidaSansUnicode00 f
-(m) 1856 6120 w
-7 /LucidaSansUnicode00 f
-(32) 1960 6140 w
-10 /S f
-(-) 2072 6120 w
-10 /LucidaSansUnicode00 f
-(m) 2143 6120 w
-7 /LucidaSansUnicode00 f
-(22) 2247 6140 w
-10 /LucidaSansUnicode00 f
-(m) 2351 6120 w
-7 /LucidaSansUnicode00 f
-(31) 2455 6140 w
-10 /LucidaSansUnicode00 f
-(\)) 2559 6120 w
-10 /S f
-(+) 2608 6120 w
-10 /LucidaSansUnicode00 f
-(m) 2679 6120 w
-7 /LucidaSansUnicode00 f
-(11) 2783 6140 w
-10 /LucidaSansUnicode00 f
-(\() 2887 6120 w
-(m) 2928 6120 w
-7 /LucidaSansUnicode00 f
-(22) 3032 6140 w
-10 /LucidaSansUnicode00 f
-(m) 3136 6120 w
-7 /LucidaSansUnicode00 f
-(30) 3240 6140 w
-10 /S f
-(-) 3352 6120 w
-10 /LucidaSansUnicode00 f
-(m) 3423 6120 w
-7 /LucidaSansUnicode00 f
-(20) 3527 6140 w
-10 /LucidaSansUnicode00 f
-(m) 3631 6120 w
-7 /LucidaSansUnicode00 f
-(32) 3735 6140 w
-10 /LucidaSansUnicode00 f
-(\)) 3839 6120 w
-10 /S f
-(+) 3888 6120 w
-10 /LucidaSansUnicode00 f
-(m) 3959 6120 w
-7 /LucidaSansUnicode00 f
-(12) 4063 6140 w
-10 /LucidaSansUnicode00 f
-(\() 4167 6120 w
-(m) 4208 6120 w
-7 /LucidaSansUnicode00 f
-(20) 4312 6140 w
-10 /LucidaSansUnicode00 f
-(m) 4416 6120 w
-7 /LucidaSansUnicode00 f
-(31) 4520 6140 w
-10 /S f
-(-) 4632 6120 w
-10 /LucidaSansUnicode00 f
-(m) 4703 6120 w
-7 /LucidaSansUnicode00 f
-(21) 4807 6140 w
-10 /LucidaSansUnicode00 f
-(m) 4911 6120 w
-7 /LucidaSansUnicode00 f
-(30) 5015 6140 w
-10 /LucidaSansUnicode00 f
-(\)) 5119 6120 w
-(\)) 5160 6120 w
-10 /S f
-(+) 1079 5960 w
-10 /LucidaSansUnicode00 f
-(m) 1150 5960 w
-7 /LucidaSansUnicode00 f
-(02) 1254 5980 w
-10 /LucidaSansUnicode00 f
-(\() 1358 5960 w
-(m) 1399 5960 w
-7 /LucidaSansUnicode00 f
-(10) 1503 5980 w
-10 /LucidaSansUnicode00 f
-(\() 1607 5960 w
-(m) 1648 5960 w
-7 /LucidaSansUnicode00 f
-(21) 1752 5980 w
-10 /LucidaSansUnicode00 f
-(m) 1856 5960 w
-7 /LucidaSansUnicode00 f
-(33) 1960 5980 w
-10 /S f
-(-) 2072 5960 w
-10 /LucidaSansUnicode00 f
-(m) 2143 5960 w
-7 /LucidaSansUnicode00 f
-(23) 2247 5980 w
-10 /LucidaSansUnicode00 f
-(m) 2351 5960 w
-7 /LucidaSansUnicode00 f
-(31) 2455 5980 w
-10 /LucidaSansUnicode00 f
-(\)) 2559 5960 w
-10 /S f
-(+) 2608 5960 w
-10 /LucidaSansUnicode00 f
-(m) 2679 5960 w
-7 /LucidaSansUnicode00 f
-(11) 2783 5980 w
-10 /LucidaSansUnicode00 f
-(\() 2887 5960 w
-(m) 2928 5960 w
-7 /LucidaSansUnicode00 f
-(23) 3032 5980 w
-10 /LucidaSansUnicode00 f
-(m) 3136 5960 w
-7 /LucidaSansUnicode00 f
-(30) 3240 5980 w
-10 /S f
-(-) 3352 5960 w
-10 /LucidaSansUnicode00 f
-(m) 3423 5960 w
-7 /LucidaSansUnicode00 f
-(20) 3527 5980 w
-10 /LucidaSansUnicode00 f
-(m) 3631 5960 w
-7 /LucidaSansUnicode00 f
-(33) 3735 5980 w
-10 /LucidaSansUnicode00 f
-(\)) 3839 5960 w
-10 /S f
-(+) 3888 5960 w
-10 /LucidaSansUnicode00 f
-(m) 3959 5960 w
-7 /LucidaSansUnicode00 f
-(13) 4063 5980 w
-10 /LucidaSansUnicode00 f
-(\() 4167 5960 w
-(m) 4208 5960 w
-7 /LucidaSansUnicode00 f
-(20) 4312 5980 w
-10 /LucidaSansUnicode00 f
-(m) 4416 5960 w
-7 /LucidaSansUnicode00 f
-(31) 4520 5980 w
-10 /S f
-(-) 4632 5960 w
-10 /LucidaSansUnicode00 f
-(m) 4703 5960 w
-7 /LucidaSansUnicode00 f
-(21) 4807 5980 w
-10 /LucidaSansUnicode00 f
-(m) 4911 5960 w
-7 /LucidaSansUnicode00 f
-(30) 5015 5980 w
-10 /LucidaSansUnicode00 f
-(\)) 5119 5960 w
-(\)) 5160 5960 w
-10 /S f
-(-) 1079 5800 w
-10 /LucidaSansUnicode00 f
-(m) 1150 5800 w
-7 /LucidaSansUnicode00 f
-(01) 1254 5820 w
-10 /LucidaSansUnicode00 f
-(\() 1358 5800 w
-(m) 1399 5800 w
-7 /LucidaSansUnicode00 f
-(10) 1503 5820 w
-10 /LucidaSansUnicode00 f
-(\() 1607 5800 w
-(m) 1648 5800 w
-7 /LucidaSansUnicode00 f
-(22) 1752 5820 w
-10 /LucidaSansUnicode00 f
-(m) 1856 5800 w
-7 /LucidaSansUnicode00 f
-(33) 1960 5820 w
-10 /S f
-(-) 2072 5800 w
-10 /LucidaSansUnicode00 f
-(m) 2143 5800 w
-7 /LucidaSansUnicode00 f
-(23) 2247 5820 w
-10 /LucidaSansUnicode00 f
-(m) 2351 5800 w
-7 /LucidaSansUnicode00 f
-(32) 2455 5820 w
-10 /LucidaSansUnicode00 f
-(\)) 2559 5800 w
-10 /S f
-(+) 2608 5800 w
-10 /LucidaSansUnicode00 f
-(m) 2679 5800 w
-7 /LucidaSansUnicode00 f
-(12) 2783 5820 w
-10 /LucidaSansUnicode00 f
-(\() 2887 5800 w
-(m) 2928 5800 w
-7 /LucidaSansUnicode00 f
-(23) 3032 5820 w
-10 /LucidaSansUnicode00 f
-(m) 3136 5800 w
-7 /LucidaSansUnicode00 f
-(30) 3240 5820 w
-10 /S f
-(-) 3352 5800 w
-10 /LucidaSansUnicode00 f
-(m) 3423 5800 w
-7 /LucidaSansUnicode00 f
-(20) 3527 5820 w
-10 /LucidaSansUnicode00 f
-(m) 3631 5800 w
-7 /LucidaSansUnicode00 f
-(33) 3735 5820 w
-10 /LucidaSansUnicode00 f
-(\)) 3839 5800 w
-10 /S f
-(+) 3888 5800 w
-10 /LucidaSansUnicode00 f
-(m) 3959 5800 w
-7 /LucidaSansUnicode00 f
-(13) 4063 5820 w
-10 /LucidaSansUnicode00 f
-(\() 4167 5800 w
-(m) 4208 5800 w
-7 /LucidaSansUnicode00 f
-(20) 4312 5820 w
-10 /LucidaSansUnicode00 f
-(m) 4416 5800 w
-7 /LucidaSansUnicode00 f
-(32) 4520 5820 w
-10 /S f
-(-) 4632 5800 w
-10 /LucidaSansUnicode00 f
-(m) 4703 5800 w
-7 /LucidaSansUnicode00 f
-(22) 4807 5820 w
-10 /LucidaSansUnicode00 f
-(m) 4911 5800 w
-7 /LucidaSansUnicode00 f
-(30) 5015 5820 w
-10 /LucidaSansUnicode00 f
-(\)) 5119 5800 w
-(\)) 5160 5800 w
-(m) 1150 5640 w
-7 /LucidaSansUnicode00 f
-(00) 1254 5660 w
-10 /LucidaSansUnicode00 f
-(\() 1358 5640 w
-(m) 1399 5640 w
-7 /LucidaSansUnicode00 f
-(11) 1503 5660 w
-10 /LucidaSansUnicode00 f
-(\() 1607 5640 w
-(m) 1648 5640 w
-7 /LucidaSansUnicode00 f
-(22) 1752 5660 w
-10 /LucidaSansUnicode00 f
-(m) 1856 5640 w
-7 /LucidaSansUnicode00 f
-(33) 1960 5660 w
-10 /S f
-(-) 2072 5640 w
-10 /LucidaSansUnicode00 f
-(m) 2143 5640 w
-7 /LucidaSansUnicode00 f
-(23) 2247 5660 w
-10 /LucidaSansUnicode00 f
-(m) 2351 5640 w
-7 /LucidaSansUnicode00 f
-(32) 2455 5660 w
-10 /LucidaSansUnicode00 f
-(\)) 2559 5640 w
-10 /S f
-(+) 2608 5640 w
-10 /LucidaSansUnicode00 f
-(m) 2679 5640 w
-7 /LucidaSansUnicode00 f
-(12) 2783 5660 w
-10 /LucidaSansUnicode00 f
-(\() 2887 5640 w
-(m) 2928 5640 w
-7 /LucidaSansUnicode00 f
-(23) 3032 5660 w
-10 /LucidaSansUnicode00 f
-(m) 3136 5640 w
-7 /LucidaSansUnicode00 f
-(31) 3240 5660 w
-10 /S f
-(-) 3352 5640 w
-10 /LucidaSansUnicode00 f
-(m) 3423 5640 w
-7 /LucidaSansUnicode00 f
-(21) 3527 5660 w
-10 /LucidaSansUnicode00 f
-(m) 3631 5640 w
-7 /LucidaSansUnicode00 f
-(33) 3735 5660 w
-10 /LucidaSansUnicode00 f
-(\)) 3839 5640 w
-10 /S f
-(+) 3888 5640 w
-10 /LucidaSansUnicode00 f
-(m) 3959 5640 w
-7 /LucidaSansUnicode00 f
-(13) 4063 5660 w
-10 /LucidaSansUnicode00 f
-(\() 4167 5640 w
-(m) 4208 5640 w
-7 /LucidaSansUnicode00 f
-(21) 4312 5660 w
-10 /LucidaSansUnicode00 f
-(m) 4416 5640 w
-7 /LucidaSansUnicode00 f
-(32) 4520 5660 w
-10 /S f
-(-) 4632 5640 w
-10 /LucidaSansUnicode00 f
-(m) 4703 5640 w
-7 /LucidaSansUnicode00 f
-(22) 4807 5660 w
-10 /LucidaSansUnicode00 f
-(m) 4911 5640 w
-7 /LucidaSansUnicode00 f
-(31) 5015 5660 w
-10 /LucidaSansUnicode00 f
-(\)) 5119 5640 w
-(\)) 5160 5640 w
-10 /LucidaSans-Demi f
-(2.5.) 720 6420 w
-(Quaternion) 962 6420 w
-(Addition) 720 6660 w
-9 /LucidaTypewriter f
-(Quaternion) 920 6830 w
-(addq\(Quaternion) 1635 6830 w
-(q,) 2675 6830 w
-(Quaternion) 2870 6830 w
-(r\)) 3585 6830 w
-10 /LucidaSansUnicode00 f
-(q) 1974 7070 w
-10 /S f
-(+) 2053 7070 w
-10 /LucidaSansUnicode00 f
-(r) 2124 7070 w
-10 /S f
-(=) 2221 7070 w
-10 /LucidaSansUnicode00 f
-(\() 2332 7070 w
-(r) 2373 7070 w
-7 /LucidaSansUnicode00 f
-(q) 2425 7090 w
-10 /S f
-(+) 2493 7070 w
-10 /LucidaSansUnicode00 f
-(r) 2564 7070 w
-7 /LucidaSansUnicode00 f
-(r) 2616 7090 w
-10 /LucidaSansUnicode00 f
-(,) 2661 7070 w
-(i) 2741 7070 w
-7 /LucidaSansUnicode00 f
-(q) 2781 7090 w
-10 /S f
-(+) 2849 7070 w
-10 /LucidaSansUnicode00 f
-(i) 2920 7070 w
-7 /LucidaSansUnicode00 f
-(r) 2960 7090 w
-10 /LucidaSansUnicode00 f
-(,) 3005 7070 w
-(j) 3085 7070 w
-7 /LucidaSansUnicode00 f
-(q) 3126 7090 w
-10 /S f
-(+) 3194 7070 w
-10 /LucidaSansUnicode00 f
-(j) 3265 7070 w
-7 /LucidaSansUnicode00 f
-(r) 3306 7090 w
-10 /LucidaSansUnicode00 f
-(,) 3351 7070 w
-(k) 3431 7070 w
-7 /LucidaSansUnicode00 f
-(q) 3500 7090 w
-10 /S f
-(+) 3568 7070 w
-10 /LucidaSansUnicode00 f
-(k) 3639 7070 w
-7 /LucidaSansUnicode00 f
-(r) 3708 7090 w
-10 /LucidaSansUnicode00 f
-(\)) 3753 7070 w
-cleartomark
-showpage
-saveobj restore
-%%EndPage: 5 5
-%%Page: 6 6
-/saveobj save def
-mark
-6 pagesetup
-10 /LucidaSansUnicode00 f
-(\255 6 \255) 2783 480 w
-10 /LucidaSans-Demi f
-(Substraction) 720 840 w
-9 /LucidaTypewriter f
-(Quaternion) 920 1010 w
-(subq\(Quaternion) 1635 1010 w
-(q,) 2675 1010 w
-(Quaternion) 2870 1010 w
-(r\)) 3585 1010 w
-10 /LucidaSansUnicode00 f
-(q) 1974 1250 w
-10 /S f
-(-) 2053 1250 w
-10 /LucidaSansUnicode00 f
-(r) 2124 1250 w
-10 /S f
-(=) 2221 1250 w
-10 /LucidaSansUnicode00 f
-(\() 2332 1250 w
-(r) 2373 1250 w
-7 /LucidaSansUnicode00 f
-(q) 2425 1270 w
-10 /S f
-(-) 2493 1250 w
-10 /LucidaSansUnicode00 f
-(r) 2564 1250 w
-7 /LucidaSansUnicode00 f
-(r) 2616 1270 w
-10 /LucidaSansUnicode00 f
-(,) 2661 1250 w
-(i) 2741 1250 w
-7 /LucidaSansUnicode00 f
-(q) 2781 1270 w
-10 /S f
-(-) 2849 1250 w
-10 /LucidaSansUnicode00 f
-(i) 2920 1250 w
-7 /LucidaSansUnicode00 f
-(r) 2960 1270 w
-10 /LucidaSansUnicode00 f
-(,) 3005 1250 w
-(j) 3085 1250 w
-7 /LucidaSansUnicode00 f
-(q) 3126 1270 w
-10 /S f
-(-) 3194 1250 w
-10 /LucidaSansUnicode00 f
-(j) 3265 1250 w
-7 /LucidaSansUnicode00 f
-(r) 3306 1270 w
-10 /LucidaSansUnicode00 f
-(,) 3351 1250 w
-(k) 3431 1250 w
-7 /LucidaSansUnicode00 f
-(q) 3500 1270 w
-10 /S f
-(-) 3568 1250 w
-10 /LucidaSansUnicode00 f
-(k) 3639 1250 w
-7 /LucidaSansUnicode00 f
-(r) 3708 1270 w
-10 /LucidaSansUnicode00 f
-(\)) 3753 1250 w
-10 /LucidaSans-Demi f
-(Multiplication) 720 1550 w
-9 /LucidaTypewriter f
-(Quaternion) 920 1720 w
-(mulq\(Quaternion) 1635 1720 w
-(q,) 2675 1720 w
-(Quaternion) 2870 1720 w
-(r\)) 3585 1720 w
-10 /LucidaSansUnicode00 f
-(q) 1321 1965 w
-10 /S f
-(=) 1440 1965 w
-10 /LucidaSansUnicode00 f
-([) 1551 1965 w
-(r) 1592 1965 w
-7 /LucidaSansUnicode00 f
-(q) 1644 1985 w
-10 /LucidaSansUnicode00 f
-(,) 1704 1965 w
-(v) 1784 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 1777 1915 w
-7 /LucidaSansUnicode00 f
-(q) 1847 1985 w
-10 /LucidaSansUnicode00 f
-(]) 1907 1965 w
-(r) 1956 1965 w
-10 /S f
-(=) 2053 1965 w
-10 /LucidaSansUnicode00 f
-([) 2164 1965 w
-(r) 2205 1965 w
-7 /LucidaSansUnicode00 f
-(r) 2257 1985 w
-10 /LucidaSansUnicode00 f
-(,) 2302 1965 w
-(v) 2382 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 2375 1915 w
-7 /LucidaSansUnicode00 f
-(r) 2445 1985 w
-10 /LucidaSansUnicode00 f
-(]) 2490 1965 w
-(qr) 2539 1965 w
-10 /S f
-(=) 2699 1965 w
-10 /LucidaSansUnicode00 f
-([) 2810 1965 w
-(r) 2851 1965 w
-7 /LucidaSansUnicode00 f
-(q) 2903 1985 w
-10 /LucidaSansUnicode00 f
-(r) 2963 1965 w
-7 /LucidaSansUnicode00 f
-(r) 3015 1985 w
-10 /S f
-(-) 3068 1965 w
-10 /LucidaSansUnicode00 f
-(v) 3139 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 3132 1915 w
-7 /LucidaSansUnicode00 f
-(q) 3202 1985 w
-10 /LucidaSansUnicode20 f
-(") 3262 1965 w
-10 /LucidaSansUnicode00 f
-(v) 3326 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 3319 1915 w
-7 /LucidaSansUnicode00 f
-(r) 3389 1985 w
-10 /LucidaSansUnicode00 f
-(,) 3434 1965 w
-(v) 3514 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 3507 1915 w
-7 /LucidaSansUnicode00 f
-(r) 3577 1985 w
-10 /LucidaSansUnicode00 f
-(r) 3622 1965 w
-7 /LucidaSansUnicode00 f
-(q) 3674 1985 w
-10 /S f
-(+) 3742 1965 w
-10 /LucidaSansUnicode00 f
-(v) 3813 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 3806 1915 w
-7 /LucidaSansUnicode00 f
-(q) 3876 1985 w
-10 /LucidaSansUnicode00 f
-(r) 3936 1965 w
-7 /LucidaSansUnicode00 f
-(r) 3988 1985 w
-10 /S f
-(+) 4041 1965 w
-10 /LucidaSansUnicode00 f
-(v) 4112 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 4105 1915 w
-7 /LucidaSansUnicode00 f
-(q) 4175 1985 w
-10 /LucidaSansUnicode00 f
-(Xv) 4235 1965 w
-7 /LucidaSansUnicode21 f
-(\222) 4291 1915 w
-7 /LucidaSansUnicode00 f
-(r) 4361 1985 w
-10 /LucidaSansUnicode00 f
-(]) 4406 1965 w
-10 /LucidaSans-Demi f
-(Scalar Multiplication) 720 2265 w
-9 /LucidaTypewriter f
-(Quaternion) 920 2435 w
-(smulq\(Quaternion) 1635 2435 w
-(q,) 2740 2435 w
-(double) 2935 2435 w
-(s\)) 3390 2435 w
-10 /LucidaSansUnicode00 f
-(qs) 2243 2675 w
-10 /S f
-(=) 2413 2675 w
-10 /LucidaSansUnicode00 f
-([) 2524 2675 w
-(r) 2565 2675 w
-7 /LucidaSansUnicode00 f
-(q) 2617 2695 w
-10 /LucidaSansUnicode00 f
-(s) 2677 2675 w
-(,) 2736 2675 w
-(i) 2816 2675 w
-7 /LucidaSansUnicode00 f
-(q) 2856 2695 w
-10 /LucidaSansUnicode00 f
-(s) 2916 2675 w
-(,) 2975 2675 w
-(j) 3055 2675 w
-7 /LucidaSansUnicode00 f
-(q) 3096 2695 w
-10 /LucidaSansUnicode00 f
-(s) 3156 2675 w
-(,) 3215 2675 w
-(k) 3295 2675 w
-7 /LucidaSansUnicode00 f
-(q) 3364 2695 w
-10 /LucidaSansUnicode00 f
-(s) 3424 2675 w
-(]) 3483 2675 w
-10 /LucidaSans-Demi f
-(Inverse) 720 2975 w
-9 /LucidaTypewriter f
-(Quaternion) 920 3145 w
-(invq\(Quaternion) 1635 3145 w
-(q\)) 2675 3145 w
-10 /LucidaSansUnicode00 f
-(q) 2009 3470 w
-7 /S f
-(-) 2083 3430 w
-7 /LucidaSansUnicode00 f
-(1) 2133 3430 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(=) 2241 3470 w
-10 /LucidaSansUnicode00 f
-10 /S f
-(\354) 2360 3383 w
-(\357) 2360 3483 w
-(\356) 2360 3583 w
-10 /LucidaSansUnicode00 f
-(|) 2434 3567 w
-(q) 2482 3550 w
-(|) 2545 3567 w
-7 /LucidaSansUnicode00 f
-(2) 2583 3510 w
-10 /LucidaSansUnicode00 f
-(r) 2514 3410 w
-10 /S1 f
-(_) 2419 3440 w
-(____) 2450 3440 w
-10 /LucidaSansUnicode00 f
-(,) 2668 3470 w
-(|) 2781 3567 w
-(q) 2829 3550 w
-(|) 2892 3567 w
-7 /LucidaSansUnicode00 f
-(2) 2930 3510 w
-10 /S f
-(-) 2832 3410 w
-10 /LucidaSansUnicode00 f
-(i) 2903 3410 w
-10 /S1 f
-(_) 2767 3440 w
-(____) 2798 3440 w
-10 /LucidaSansUnicode00 f
-(,) 3016 3470 w
-(|) 3129 3567 w
-(q) 3177 3550 w
-(|) 3240 3567 w
-7 /LucidaSansUnicode00 f
-(2) 3278 3510 w
-10 /S f
-(-) 3179 3410 w
-10 /LucidaSansUnicode00 f
-(j) 3250 3410 w
-10 /S1 f
-(_) 3114 3440 w
-(____) 3145 3440 w
-10 /LucidaSansUnicode00 f
-(,) 3363 3470 w
-(|) 3476 3567 w
-(q) 3524 3550 w
-(|) 3587 3567 w
-7 /LucidaSansUnicode00 f
-(2) 3625 3510 w
-10 /S f
-(-) 3512 3410 w
-10 /LucidaSansUnicode00 f
-(k) 3583 3410 w
-10 /S1 f
-(_) 3461 3440 w
-(____) 3492 3440 w
-10 /S f
-(\374) 3702 3383 w
-(\357) 3702 3483 w
-(\376) 3702 3583 w
-10 /LucidaSans-Demi f
-(Magnitude/Length) 720 3875 w
-9 /LucidaTypewriter f
-(double) 920 4045 w
-(qlen\(Quaternion) 1375 4045 w
-(q\)) 2415 4045 w
-10 /LucidaSansUnicode00 f
-(|) 2337 4320 w
-(q) 2385 4303 w
-(|) 2448 4320 w
-10 /S f
-(=) 2544 4303 w
-10 /LucidaSansUnicode00 f
-12 /LucidaSansUnicode22 f
-(\032) 2655 4303 w
-12 /S f
-(`) 2752 4303 w
-(```````````) 2755 4303 w
-10 /LucidaSansUnicode00 f
-(r) 2760 4303 w
-7 /LucidaSansUnicode00 f
-(2) 2806 4263 w
-10 /S f
-(+) 2874 4303 w
-10 /LucidaSansUnicode00 f
-(i) 2945 4303 w
-7 /LucidaSansUnicode00 f
-(2) 2979 4263 w
-10 /S f
-(+) 3047 4303 w
-10 /LucidaSansUnicode00 f
-(j) 3118 4303 w
-7 /LucidaSansUnicode00 f
-(2) 3153 4263 w
-10 /S f
-(+) 3221 4303 w
-10 /LucidaSansUnicode00 f
-(k) 3292 4303 w
-7 /LucidaSansUnicode00 f
-(2) 3355 4263 w
-cleartomark
-showpage
-saveobj restore
-%%EndPage: 6 6
-%%Trailer
-done
-%%DocumentFonts: LucidaSansUnicode20 LucidaSansUnicode21 LucidaSansUnicode22 S1 S LucidaSansUnicode00 LucidaSans-Demi LucidaSans-Italic LucidaTypewriter
-%%Pages: 6
diff --git a/libgeometry/doc/mkfile b/libgeometry/doc/mkfile
deleted file mode 100644
index 8fb6d1c..0000000
--- a/libgeometry/doc/mkfile
+++ /dev/null
@@ -1,15 +0,0 @@
-FONTS='.FP lucidasans'
-DOCNAME=libgeometry
-
-all:VQ: $DOCNAME.ps $DOCNAME.pdf
-
-clean:VQ:
- rm -f $DOCNAME.ps $DOCNAME.pdf
-
-$DOCNAME.ps:V: $DOCNAME.ms
- {echo $FONTS; cat $prereq}> _$prereq
- eval `{doctype _$prereq} | lp -dstdout > $target && rm -f _$prereq
-
-$DOCNAME.pdf:V: $DOCNAME.ps
- cat /sys/doc/docfonts $prereq > _$prereq
- ps2pdf _$prereq $target && rm -f _$prereq
diff --git a/libgeometry/matrix.c b/libgeometry/matrix.c
deleted file mode 100644
index b7efc84..0000000
--- a/libgeometry/matrix.c
+++ /dev/null
@@ -1,348 +0,0 @@
-#include <u.h>
-#include <libc.h>
-#include "../geometry.h"
-
-/* 2D */
-
-void
-identity(Matrix m)
-{
- memset(m, 0, 3*3*sizeof(double));
- m[0][0] = m[1][1] = m[2][2] = 1;
-}
-
-void
-addm(Matrix a, Matrix b)
-{
- int i, j;
-
- for(i = 0; i < 3; i++)
- for(j = 0; j < 3; j++)
- a[i][j] += b[i][j];
-}
-
-void
-subm(Matrix a, Matrix b)
-{
- int i, j;
-
- for(i = 0; i < 3; i++)
- for(j = 0; j < 3; j++)
- a[i][j] -= b[i][j];
-}
-
-void
-mulm(Matrix a, Matrix b)
-{
- int i, j, k;
- Matrix tmp;
-
- for(i = 0; i < 3; i++)
- for(j = 0; j < 3; j++){
- tmp[i][j] = 0;
- for(k = 0; k < 3; k++)
- tmp[i][j] += a[i][k]*b[k][j];
- }
- memmove(a, tmp, 3*3*sizeof(double));
-}
-
-void
-smulm(Matrix m, double s)
-{
- int i, j;
-
- for(i = 0; i < 3; i++)
- for(j = 0; j < 3; j++)
- m[i][j] *= s;
-}
-
-void
-transposem(Matrix m)
-{
- int i, j;
- double tmp;
-
- for(i = 0; i < 3; i++)
- for(j = i; j < 3; j++){
- tmp = m[i][j];
- m[i][j] = m[j][i];
- m[j][i] = tmp;
- }
-}
-
-double
-detm(Matrix m)
-{
- return m[0][0]*(m[1][1]*m[2][2] - m[1][2]*m[2][1])+
- m[0][1]*(m[1][2]*m[2][0] - m[1][0]*m[2][2])+
- m[0][2]*(m[1][0]*m[2][1] - m[1][1]*m[2][0]);
-}
-
-double
-tracem(Matrix m)
-{
- return m[0][0] + m[1][1] + m[2][2];
-}
-
-void
-adjm(Matrix m)
-{
- Matrix tmp;
-
- tmp[0][0] = m[1][1]*m[2][2] - m[1][2]*m[2][1];
- tmp[0][1] = -m[0][1]*m[2][2] + m[0][2]*m[2][1];
- tmp[0][2] = m[0][1]*m[1][2] - m[0][2]*m[1][1];
- tmp[1][0] = -m[1][0]*m[2][2] + m[1][2]*m[2][0];
- tmp[1][1] = m[0][0]*m[2][2] - m[0][2]*m[2][0];
- tmp[1][2] = -m[0][0]*m[1][2] + m[0][2]*m[1][0];
- tmp[2][0] = m[1][0]*m[2][1] - m[1][1]*m[2][0];
- tmp[2][1] = -m[0][0]*m[2][1] + m[0][1]*m[2][0];
- tmp[2][2] = m[0][0]*m[1][1] - m[0][1]*m[1][0];
- memmove(m, tmp, 3*3*sizeof(double));
-}
-
-/* Cayley-Hamilton */
-//void
-//invertm(Matrix m)
-//{
-// Matrix m², r;
-// double det, trm, trm²;
-//
-// det = detm(m);
-// if(det == 0)
-// return;
-// trm = tracem(m);
-// memmove(m², m, 3*3*sizeof(double));
-// mulm(m², m²);
-// trm² = tracem(m²);
-// identity(r);
-// smulm(r, (trm*trm - trm²)/2);
-// smulm(m, trm);
-// subm(r, m);
-// addm(r, m²);
-// smulm(r, 1/det);
-// memmove(m, r, 3*3*sizeof(double));
-//}
-
-/* Cramer's */
-void
-invm(Matrix m)
-{
- double det;
-
- det = detm(m);
- if(det == 0)
- return; /* singular matrices are not invertible */
- adjm(m);
- smulm(m, 1/det);
-}
-
-Point2
-xform(Point2 p, Matrix m)
-{
- return (Point2){
- p.x*m[0][0] + p.y*m[0][1] + p.w*m[0][2],
- p.x*m[1][0] + p.y*m[1][1] + p.w*m[1][2],
- p.x*m[2][0] + p.y*m[2][1] + p.w*m[2][2]
- };
-}
-
-/* 3D */
-
-void
-identity3(Matrix3 m)
-{
- memset(m, 0, 4*4*sizeof(double));
- m[0][0] = m[1][1] = m[2][2] = m[3][3] = 1;
-}
-
-void
-addm3(Matrix3 a, Matrix3 b)
-{
- int i, j;
-
- for(i = 0; i < 4; i++)
- for(j = 0; j < 4; j++)
- a[i][j] += b[i][j];
-}
-
-void
-subm3(Matrix3 a, Matrix3 b)
-{
- int i, j;
-
- for(i = 0; i < 4; i++)
- for(j = 0; j < 4; j++)
- a[i][j] -= b[i][j];
-}
-
-void
-mulm3(Matrix3 a, Matrix3 b)
-{
- int i, j, k;
- Matrix3 tmp;
-
- for(i = 0; i < 4; i++)
- for(j = 0; j < 4; j++){
- tmp[i][j] = 0;
- for(k = 0; k < 4; k++)
- tmp[i][j] += a[i][k]*b[k][j];
- }
- memmove(a, tmp, 4*4*sizeof(double));
-}
-
-void
-smulm3(Matrix3 m, double s)
-{
- int i, j;
-
- for(i = 0; i < 4; i++)
- for(j = 0; j < 4; j++)
- m[i][j] *= s;
-}
-
-void
-transposem3(Matrix3 m)
-{
- int i, j;
- double tmp;
-
- for(i = 0; i < 4; i++)
- for(j = i; j < 4; j++){
- tmp = m[i][j];
- m[i][j] = m[j][i];
- m[j][i] = tmp;
- }
-}
-
-double
-detm3(Matrix3 m)
-{
- return m[0][0]*(m[1][1]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
- m[1][2]*(m[2][3]*m[3][1] - m[2][1]*m[3][3])+
- m[1][3]*(m[2][1]*m[3][2] - m[2][2]*m[3][1]))
- -m[0][1]*(m[1][0]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
- m[1][2]*(m[2][3]*m[3][0] - m[2][0]*m[3][3])+
- m[1][3]*(m[2][0]*m[3][2] - m[2][2]*m[3][0]))
- +m[0][2]*(m[1][0]*(m[2][1]*m[3][3] - m[2][3]*m[3][1])+
- m[1][1]*(m[2][3]*m[3][0] - m[2][0]*m[3][3])+
- m[1][3]*(m[2][0]*m[3][1] - m[2][1]*m[3][0]))
- -m[0][3]*(m[1][0]*(m[2][1]*m[3][2] - m[2][2]*m[3][1])+
- m[1][1]*(m[2][2]*m[3][0] - m[2][0]*m[3][2])+
- m[1][2]*(m[2][0]*m[3][1] - m[2][1]*m[3][0]));
-}
-
-double
-tracem3(Matrix3 m)
-{
- return m[0][0] + m[1][1] + m[2][2] + m[3][3];
-}
-
-void
-adjm3(Matrix3 m)
-{
- Matrix3 tmp;
-
- tmp[0][0]=m[1][1]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
- m[2][1]*(m[1][3]*m[3][2] - m[1][2]*m[3][3])+
- m[3][1]*(m[1][2]*m[2][3] - m[1][3]*m[2][2]);
- tmp[0][1]=m[0][1]*(m[2][3]*m[3][2] - m[2][2]*m[3][3])+
- m[2][1]*(m[0][2]*m[3][3] - m[0][3]*m[3][2])+
- m[3][1]*(m[0][3]*m[2][2] - m[0][2]*m[2][3]);
- tmp[0][2]=m[0][1]*(m[1][2]*m[3][3] - m[1][3]*m[3][2])+
- m[1][1]*(m[0][3]*m[3][2] - m[0][2]*m[3][3])+
- m[3][1]*(m[0][2]*m[1][3] - m[0][3]*m[1][2]);
- tmp[0][3]=m[0][1]*(m[1][3]*m[2][2] - m[1][2]*m[2][3])+
- m[1][1]*(m[0][2]*m[2][3] - m[0][3]*m[2][2])+
- m[2][1]*(m[0][3]*m[1][2] - m[0][2]*m[1][3]);
- tmp[1][0]=m[1][0]*(m[2][3]*m[3][2] - m[2][2]*m[3][3])+
- m[2][0]*(m[1][2]*m[3][3] - m[1][3]*m[3][2])+
- m[3][0]*(m[1][3]*m[2][2] - m[1][2]*m[2][3]);
- tmp[1][1]=m[0][0]*(m[2][2]*m[3][3] - m[2][3]*m[3][2])+
- m[2][0]*(m[0][3]*m[3][2] - m[0][2]*m[3][3])+
- m[3][0]*(m[0][2]*m[2][3] - m[0][3]*m[2][2]);
- tmp[1][2]=m[0][0]*(m[1][3]*m[3][2] - m[1][2]*m[3][3])+
- m[1][0]*(m[0][2]*m[3][3] - m[0][3]*m[3][2])+
- m[3][0]*(m[0][3]*m[1][2] - m[0][2]*m[1][3]);
- tmp[1][3]=m[0][0]*(m[1][2]*m[2][3] - m[1][3]*m[2][2])+
- m[1][0]*(m[0][3]*m[2][2] - m[0][2]*m[2][3])+
- m[2][0]*(m[0][2]*m[1][3] - m[0][3]*m[1][2]);
- tmp[2][0]=m[1][0]*(m[2][1]*m[3][3] - m[2][3]*m[3][1])+
- m[2][0]*(m[1][3]*m[3][1] - m[1][1]*m[3][3])+
- m[3][0]*(m[1][1]*m[2][3] - m[1][3]*m[2][1]);
- tmp[2][1]=m[0][0]*(m[2][3]*m[3][1] - m[2][1]*m[3][3])+
- m[2][0]*(m[0][1]*m[3][3] - m[0][3]*m[3][1])+
- m[3][0]*(m[0][3]*m[2][1] - m[0][1]*m[2][3]);
- tmp[2][2]=m[0][0]*(m[1][1]*m[3][3] - m[1][3]*m[3][1])+
- m[1][0]*(m[0][3]*m[3][1] - m[0][1]*m[3][3])+
- m[3][0]*(m[0][1]*m[1][3] - m[0][3]*m[1][1]);
- tmp[2][3]=m[0][0]*(m[1][3]*m[2][1] - m[1][1]*m[2][3])+
- m[1][0]*(m[0][1]*m[2][3] - m[0][3]*m[2][1])+
- m[2][0]*(m[0][3]*m[1][1] - m[0][1]*m[1][3]);
- tmp[3][0]=m[1][0]*(m[2][2]*m[3][1] - m[2][1]*m[3][2])+
- m[2][0]*(m[1][1]*m[3][2] - m[1][2]*m[3][1])+
- m[3][0]*(m[1][2]*m[2][1] - m[1][1]*m[2][2]);
- tmp[3][1]=m[0][0]*(m[2][1]*m[3][2] - m[2][2]*m[3][1])+
- m[2][0]*(m[0][2]*m[3][1] - m[0][1]*m[3][2])+
- m[3][0]*(m[0][1]*m[2][2] - m[0][2]*m[2][1]);
- tmp[3][2]=m[0][0]*(m[1][2]*m[3][1] - m[1][1]*m[3][2])+
- m[1][0]*(m[0][1]*m[3][2] - m[0][2]*m[3][1])+
- m[3][0]*(m[0][2]*m[1][1] - m[0][1]*m[1][2]);
- tmp[3][3]=m[0][0]*(m[1][1]*m[2][2] - m[1][2]*m[2][1])+
- m[1][0]*(m[0][2]*m[2][1] - m[0][1]*m[2][2])+
- m[2][0]*(m[0][1]*m[1][2] - m[0][2]*m[1][1]);
- memmove(m, tmp, 4*4*sizeof(double));
-}
-
-/* Cayley-Hamilton */
-//void
-//invertm3(Matrix3 m)
-//{
-// Matrix3 m², m³, r;
-// double det, trm, trm², trm³;
-//
-// det = detm3(m);
-// if(det == 0)
-// return;
-// trm = tracem3(m);
-// memmove(m³, m, 4*4*sizeof(double));
-// mulm(m³, m³);
-// mulm(m³, m);
-// trm³ = tracem3(m³);
-// memmove(m², m, 4*4*sizeof(double));
-// mulm(m², m²);
-// trm² = tracem3(m²);
-// identity3(r);
-// smulm3(r, (trm*trm*trm - 3*trm*trm² + 2*trm³)/6);
-// smulm3(m, (trm*trm - trm²)/2);
-// smulm3(m², trm);
-// subm(r, m);
-// addm(r, m²);
-// subm(r, m³);
-// smulm(r, 1/det);
-// memmove(m, r, 4*4*sizeof(double));
-//}
-
-/* Cramer's */
-void
-invm3(Matrix3 m)
-{
- double det;
-
- det = detm3(m);
- if(det == 0)
- return; /* singular matrices are not invertible */
- adjm3(m);
- smulm3(m, 1/det);
-}
-
-Point3
-xform3(Point3 p, Matrix3 m)
-{
- return (Point3){
- p.x*m[0][0] + p.y*m[0][1] + p.z*m[0][2] + p.w*m[0][3],
- p.x*m[1][0] + p.y*m[1][1] + p.z*m[1][2] + p.w*m[1][3],
- p.x*m[2][0] + p.y*m[2][1] + p.z*m[2][2] + p.w*m[2][3],
- p.x*m[3][0] + p.y*m[3][1] + p.z*m[3][2] + p.w*m[3][3],
- };
-}
diff --git a/libgeometry/mkfile b/libgeometry/mkfile
deleted file mode 100644
index 5c7d79f..0000000
--- a/libgeometry/mkfile
+++ /dev/null
@@ -1,13 +0,0 @@
-</$objtype/mkfile
-
-LIB=../libgeometry.a$O
-OFILES=\
- point.$O\
- matrix.$O\
- quaternion.$O\
- rframe.$O\
- triangle.$O\
-
-HFILES=../geometry.h
-
-</sys/src/cmd/mklib
diff --git a/libgeometry/point.c b/libgeometry/point.c
deleted file mode 100644
index 657eb4c..0000000
--- a/libgeometry/point.c
+++ /dev/null
@@ -1,161 +0,0 @@
-#include <u.h>
-#include <libc.h>
-#include "../geometry.h"
-
-/* 2D */
-
-Point2
-Pt2(double x, double y, double w)
-{
- return (Point2){x, y, w};
-}
-
-Point2
-Vec2(double x, double y)
-{
- return (Point2){x, y, 0};
-}
-
-Point2
-addpt2(Point2 a, Point2 b)
-{
- return (Point2){a.x+b.x, a.y+b.y, a.w+b.w};
-}
-
-Point2
-subpt2(Point2 a, Point2 b)
-{
- return (Point2){a.x-b.x, a.y-b.y, a.w-b.w};
-}
-
-Point2
-mulpt2(Point2 p, double s)
-{
- return (Point2){p.x*s, p.y*s, p.w*s};
-}
-
-Point2
-divpt2(Point2 p, double s)
-{
- return (Point2){p.x/s, p.y/s, p.w/s};
-}
-
-Point2
-lerp2(Point2 a, Point2 b, double t)
-{
- if(t < 0) t = 0;
- if(t > 1) t = 1;
- return (Point2){
- (1 - t)*a.x + t*b.x,
- (1 - t)*a.y + t*b.y,
- (1 - t)*a.w + t*b.w
- };
-}
-
-double
-dotvec2(Point2 a, Point2 b)
-{
- return a.x*b.x + a.y*b.y;
-}
-
-double
-vec2len(Point2 v)
-{
- return sqrt(dotvec2(v, v));
-}
-
-Point2
-normvec2(Point2 v)
-{
- double len;
-
- len = vec2len(v);
- if(len == 0)
- return (Point2){0, 0, 0};
- return (Point2){v.x/len, v.y/len, 0};
-}
-
-/* 3D */
-
-Point3
-Pt3(double x, double y, double z, double w)
-{
- return (Point3){x, y, z, w};
-}
-
-Point3
-Vec3(double x, double y, double z)
-{
- return (Point3){x, y, z, 0};
-}
-
-Point3
-addpt3(Point3 a, Point3 b)
-{
- return (Point3){a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w};
-}
-
-Point3
-subpt3(Point3 a, Point3 b)
-{
- return (Point3){a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w};
-}
-
-Point3
-mulpt3(Point3 p, double s)
-{
- return (Point3){p.x*s, p.y*s, p.z*s, p.w*s};
-}
-
-Point3
-divpt3(Point3 p, double s)
-{
- return (Point3){p.x/s, p.y/s, p.z/s, p.w/s};
-}
-
-Point3
-lerp3(Point3 a, Point3 b, double t)
-{
- if(t < 0) t = 0;
- if(t > 1) t = 1;
- return (Point3){
- (1 - t)*a.x + t*b.x,
- (1 - t)*a.y + t*b.y,
- (1 - t)*a.z + t*b.z,
- (1 - t)*a.w + t*b.w
- };
-}
-
-double
-dotvec3(Point3 a, Point3 b)
-{
- return a.x*b.x + a.y*b.y + a.z*b.z;
-}
-
-Point3
-crossvec3(Point3 a, Point3 b)
-{
- return (Point3){
- a.y*b.z - a.z*b.y,
- a.z*b.x - a.x*b.z,
- a.x*b.y - a.y*b.x,
- 0
- };
-}
-
-double
-vec3len(Point3 v)
-{
- return sqrt(dotvec3(v, v));
-}
-
-Point3
-normvec3(Point3 v)
-{
- double len;
-
- len = vec3len(v);
- if(len == 0)
- return (Point3){0, 0, 0, 0};
- return (Point3){v.x/len, v.y/len, v.z/len, 0};
-}
diff --git a/libgeometry/quaternion.c b/libgeometry/quaternion.c
deleted file mode 100644
index b8eaa88..0000000
--- a/libgeometry/quaternion.c
+++ /dev/null
@@ -1,90 +0,0 @@
-#include <u.h>
-#include <libc.h>
-#include "../geometry.h"
-
-Quaternion
-Quat(double r, double i, double j, double k)
-{
- return (Quaternion){r, i, j, k};
-}
-
-Quaternion
-Quatvec(double s, Point3 v)
-{
- return (Quaternion){s, v.x, v.y, v.z};
-}
-
-Quaternion
-addq(Quaternion a, Quaternion b)
-{
- return (Quaternion){a.r+b.r, a.i+b.i, a.j+b.j, a.k+b.k};
-}
-
-Quaternion
-subq(Quaternion a, Quaternion b)
-{
- return (Quaternion){a.r-b.r, a.i-b.i, a.j-b.j, a.k-b.k};
-}
-
-Quaternion
-mulq(Quaternion q, Quaternion r)
-{
- Point3 qv, rv, tmp;
-
- qv = Vec3(q.i, q.j, q.k);
- rv = Vec3(r.i, r.j, r.k);
- tmp = addpt3(addpt3(mulpt3(rv, q.r), mulpt3(qv, r.r)), crossvec3(qv, rv));
- return (Quaternion){q.r*r.r - dotvec3(qv, rv), tmp.x, tmp.y, tmp.z};
-}
-
-Quaternion
-smulq(Quaternion q, double s)
-{
- return (Quaternion){q.r*s, q.i*s, q.j*s, q.k*s};
-}
-
-Quaternion
-sdivq(Quaternion q, double s)
-{
- return (Quaternion){q.r/s, q.i/s, q.j/s, q.k/s};
-}
-
-double
-dotq(Quaternion q, Quaternion r)
-{
- return q.r*r.r + q.i*r.i + q.j*r.j + q.k*r.k;
-}
-
-Quaternion
-invq(Quaternion q)
-{
- double len²;
-
- len² = dotq(q, q);
- if(len² == 0)
- return (Quaternion){0, 0, 0, 0};
- return (Quaternion){q.r/len², -q.i/len², -q.j/len², -q.k/len²};
-}
-
-double
-qlen(Quaternion q)
-{
- return sqrt(q.r*q.r + q.i*q.i + q.j*q.j + q.k*q.k);
-}
-
-Quaternion
-normq(Quaternion q)
-{
- return sdivq(q, qlen(q));
-}
-
-Point3
-qrotate(Point3 p, Point3 axis, double angle)
-{
- Quaternion qaxis, qr;
-
- angle /= 2;
- qaxis = Quatvec(cos(angle), mulpt3(axis, sin(angle)));
- qr = mulq(mulq(qaxis, Quatvec(0, p)), invq(qaxis));
- return Vec3(qr.i, qr.j, qr.k);
-}
diff --git a/libgeometry/rframe.c b/libgeometry/rframe.c
deleted file mode 100644
index 06d63f2..0000000
--- a/libgeometry/rframe.c
+++ /dev/null
@@ -1,51 +0,0 @@
-#include <u.h>
-#include <libc.h>
-#include "../geometry.h"
-
-Point2
-rframexform(Point2 p, RFrame rf)
-{
- Matrix m = {
- rf.bx.x, rf.bx.y, -dotvec2(rf.bx, rf.p),
- rf.by.x, rf.by.y, -dotvec2(rf.by, rf.p),
- 0, 0, 1,
- };
- return xform(p, m);
-}
-
-Point3
-rframexform3(Point3 p, RFrame3 rf)
-{
- Matrix3 m = {
- rf.bx.x, rf.bx.y, rf.bx.z, -dotvec3(rf.bx, rf.p),
- rf.by.x, rf.by.y, rf.by.z, -dotvec3(rf.by, rf.p),
- rf.bz.x, rf.bz.y, rf.bz.z, -dotvec3(rf.bz, rf.p),
- 0, 0, 0, 1,
- };
- return xform3(p, m);
-}
-
-Point2
-invrframexform(Point2 p, RFrame rf)
-{
- Matrix m = {
- rf.bx.x, rf.bx.y, -dotvec2(rf.bx, rf.p),
- rf.by.x, rf.by.y, -dotvec2(rf.by, rf.p),
- 0, 0, 1,
- };
- invm(m);
- return xform(p, m);
-}
-
-Point3
-invrframexform3(Point3 p, RFrame3 rf)
-{
- Matrix3 m = {
- rf.bx.x, rf.bx.y, rf.bx.z, -dotvec3(rf.bx, rf.p),
- rf.by.x, rf.by.y, rf.by.z, -dotvec3(rf.by, rf.p),
- rf.bz.x, rf.bz.y, rf.bz.z, -dotvec3(rf.bz, rf.p),
- 0, 0, 0, 1,
- };
- invm3(m);
- return xform3(p, m);
-}
diff --git a/libgeometry/triangle.c b/libgeometry/triangle.c
deleted file mode 100644
index a8bbf0f..0000000
--- a/libgeometry/triangle.c
+++ /dev/null
@@ -1,9 +0,0 @@
-#include <u.h>
-#include <libc.h>
-#include "../geometry.h"
-
-Point3
-centroid(Triangle3 t)
-{
- return divpt3(addpt3(t.p0, addpt3(t.p1, t.p2)), 3);
-}