[Axiom-developer] 20090416.03.tpd.patch (bookvol10.4 update bezier docum

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[Axiom-developer] 20090416.03.tpd.patch (bookvol10.4 update bezier docum

From:	daly
Subject:	[Axiom-developer] 20090416.03.tpd.patch (bookvol10.4 update bezier documentation)
Date:	Thu, 16 Apr 2009 21:15:36 -0500
Add bezier documentation with an example and a graph

======================================================================
diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index 9884d3b..b603e5b 100644
--- a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ -5122,14 +5122,14 @@ BasicOperatorFunctions1(A:SetCategory): Exports == 
Implementation where
 )set message test on
 )set message auto off
 )clear all
---S 1 of 6
+--S 1 of 9
 n:=linearBezier([2.0,2.0],[4.0,4.0])
 --R
 --I   (1)  theMap(BEZIER;linearBezier;2LM;1!0,707)
 --R                                                  Type: (Float -> List 
Float)
 --E 1
 
---S 2 of 6
+--S 2 of 9
 [n(t/10.0) for t in 0..10 by 1]
 --R
 --R   (2)
@@ -5138,14 +5138,14 @@ n:=linearBezier([2.0,2.0],[4.0,4.0])
 --R                                                        Type: List List 
Float
 --E 2
 
---S 3 of 6
+--S 3 of 9
 n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0])
 --R
 --I   (3)  theMap(BEZIER;quadraticBezier;3LM;2!0,291)
 --R                                                  Type: (Float -> List 
Float)
 --E 3
 
---S 4 of 6
+--S 4 of 9
 [n(t/10.0) for t in 0..10 by 1]
 --R
 --R   (4)
@@ -5154,14 +5154,14 @@ n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0])
 --R                                                        Type: List List 
Float
 --E 4
 
---S 5 of 6
+--S 5 of 9
 n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0])
 --R
 --I   (5)  theMap(BEZIER;cubicBezier;4LM;3!0,915)
 --R                                                  Type: (Float -> List 
Float)
 --E 5
 
---S 6 of 6
+--S 6 of 9
 [n(t/10.0) for t in 0..10 by 1]
 --R
 --R   (6)
@@ -5171,7 +5171,28 @@ n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0])
 --R                                                        Type: List List 
Float
 --E 6
 
+--S 7 of 9
+line:=[[i::Float,4.0] for i in -4..4 by 1]
+--E 7
+
+--S 8 of 9
+functions:=[quadraticBezier([2.0,2.0],m,[6.0,2.0]) for m in line]
+--E 8
+
+--S 9 of 9
+graphs:=[[point(((functions.i)(j/100.0))::LIST(DFLOAT)) for j in 0..100] for i 
in 1..9]
+--E 9
+
+-- We do not do these during testing since graphics is not available
+-- The resulting image is in the Bezier section of Volume 10.4
+
+--d1:=draw(graphs.1,title=="Bezier Control Point Motion")
+--others:=[graphs.i for i in 2..9]
+--for i in 2..9 for graph in others repeat putGraph(d1,[graph],i)
+--vp:=makeViewport2D(d1)
+
 @
+\includegraphics[scale=1.50]{ps/v104beziermove.eps}
 <<Bezier.help>>=
 ====================================================================
 Bezier Curve examples
@@ -5226,19 +5247,60 @@ n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0])
     [4.0,3.5], [4.592,3.44], [5.136,3.26], [5.584,2.96], [5.888,2.54],
     [6.0,2.0]]
 
+Bezier curves "move" based on moving their control points, which
+in the case of the three components of a quadratic Bezier curve
+are the three points given. To see this motion we can show what
+happens when you "drag" the middle control point along the line
+from [-4,4] to [4,4] by increments of 1. 
+
+First, we form the line as a list of Floats, 9 in all.
+
+   line:=[[i::Float,4.0] for i in -4..4 by 1]
+
+Next, we form a list of functions, each with a different center control point.
+Notice that the endpoints remain fized so we expect that the curve will
+begin and end at the same point but that the midpoint is pulled around.
+
+  functions:=[quadraticBezier([2.0,2.0],m,[6.0,2.0]) for m in line]
+
+Then we form a list of the graphs by calling each function in the above
+list. Each function call happens 101 times (to include both endpoints).
+Thus we get a List of Lists of Points of DoubleFloats
+
+  graphs:=[ [ point( ( (functions.i)(j/100.0) )::LIST(DFLOAT) ) _
+    for j in 0..100] for i in 1..9]
+
+We draw the first graph to see if it looks reasonable:
+
+  d1:=draw(graphs.1)
+
+Since it does we add the other 8 graphs. The 2D graphs can hold up to
+9 simultaneous graphs.
+
+  others:=[graphs.i for i in 2..9]
+  for i in 2..9 for graph in others repeat putGraph(d1,[graph],i)
+
+and now we display them all on one graph.
+
+  vp:=makeViewport2D(d1)
+
 See Also:
 o )show Bezier
+o )show TwoDimensionalViewport
+o )d op draw
+o )d op point
+o )d op putGraph
+o )d op makeViewport2D
 
 @
 \pagehead{Bezier}{BEZIER}
 \pagepic{ps/v104bezier.ps}{BEZIER}{1.00}
 
 {\bf Exports:}\\
-\begin{tabular}{llll}
-\cross{BEZIER}{bezoutDiscriminant} &
-\cross{BEZIER}{bezoutMatrix} &
-\cross{BEZIER}{bezoutResultant} &
-\cross{BEZIER}{sylvesterMatrix} 
+\begin{tabular}{lll}
+\cross{BEZIER}{linearBezier} &
+\cross{BEZIER}{quadraticBezier} &
+\cross{BEZIER}{cubicBezier} 
 \end{tabular}
 
 <<package BEZIER Bezier>>=
@@ -5248,35 +5310,35 @@ o )show Bezier
 ++ Description: Provide linear, quadratic, and cubic spline bezier curves
 Bezier(R:Ring): with
    linearBezier: (x:List R,y:List R) -> Mapping(List R,R)
-   ++ A linear Bezier curve is a simple interpolation between the 
-   ++ starting point and the ending point based on a parameter t.
-   ++ Given a start point a=[x1,y1] and an endpoint b=[x2,y2]
-   ++ f(t) == [(1-t)*x1 + t*x2, (1-t)*y1 + t*y2]
-   ++
-   ++X n:=linearBezier([2.0,2.0],[4.0,4.0])
-   ++X [n(t/10.0) for t in 0..10 by 1]
+    ++ A linear Bezier curve is a simple interpolation between the 
+    ++ starting point and the ending point based on a parameter t.
+    ++ Given a start point a=[x1,y1] and an endpoint b=[x2,y2]
+    ++ f(t) == [(1-t)*x1 + t*x2, (1-t)*y1 + t*y2]
+    ++
+    ++X n:=linearBezier([2.0,2.0],[4.0,4.0])
+    ++X [n(t/10.0) for t in 0..10 by 1]
    quadraticBezier: (x:List R,y:List R,z:List R) -> Mapping(List R,R)
-   ++ A quadratic Bezier curve is a simple interpolation between the 
-   ++ starting point, a middle point, and the ending point based on 
-   ++ a parameter t.
-   ++ Given a start point a=[x1,y1], a middle point b=[x2,y2], 
-   ++ and an endpoint c=[x3,y3]
-   ++ f(t) == [(1-t)^2 x1 + 2t(1-t) x2 + t^2 x3,
-   ++          (1-t)^2 y1 + 2t(1-t) y2 + t^2 y3]
-   ++
-   ++X n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0])
-   ++X [n(t/10.0) for t in 0..10 by 1]
+    ++ A quadratic Bezier curve is a simple interpolation between the 
+    ++ starting point, a middle point, and the ending point based on 
+    ++ a parameter t.
+    ++ Given a start point a=[x1,y1], a middle point b=[x2,y2], 
+    ++ and an endpoint c=[x3,y3]
+    ++ f(t) == [(1-t)^2 x1 + 2t(1-t) x2 + t^2 x3,
+    ++          (1-t)^2 y1 + 2t(1-t) y2 + t^2 y3]
+    ++
+    ++X n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0])
+    ++X [n(t/10.0) for t in 0..10 by 1]
    cubicBezier: (w:List R,x:List R,y:List R,z:List R) -> Mapping(List R,R)
-   ++ A cubic Bezier curve is a simple interpolation between the 
-   ++ starting point, a left-middle point,, a right-middle point,
-   ++ and the ending point based on a parameter t.
-   ++ Given a start point a=[x1,y1], the left-middle point b=[x2,y2],
-   ++ the right-middle point c=[x3,y3] and an endpoint d=[x4,y4]
-   ++ f(t) == [(1-t)^3 x1 + 3t(1-t)^2 x2 + 3t^2 (1-t) x3 + t^3 x4,
-   ++          (1-t)^3 y1 + 3t(1-t)^2 y2 + 3t^2 (1-t) y3 + t^3 y4]
-   ++
-   ++X n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0])
-   ++X [n(t/10.0) for t in 0..10 by 1]
+    ++ A cubic Bezier curve is a simple interpolation between the 
+    ++ starting point, a left-middle point,, a right-middle point,
+    ++ and the ending point based on a parameter t.
+    ++ Given a start point a=[x1,y1], the left-middle point b=[x2,y2],
+    ++ the right-middle point c=[x3,y3] and an endpoint d=[x4,y4]
+    ++ f(t) == [(1-t)^3 x1 + 3t(1-t)^2 x2 + 3t^2 (1-t) x3 + t^3 x4,
+    ++          (1-t)^3 y1 + 3t(1-t)^2 y2 + 3t^2 (1-t) y3 + t^3 y4]
+    ++
+    ++X n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0])
+    ++X [n(t/10.0) for t in 0..10 by 1]
  == add
    linearBezier(a,b) == 
     [(1-#1)*(a.1) + #1*(b.1), (1-#1)*(a.2) + #1*(b.2)]
diff --git a/books/ps/v104beziermove.eps b/books/ps/v104beziermove.eps
new file mode 100644
index 0000000..3ac95e6
--- /dev/null
+++ b/books/ps/v104beziermove.eps
@@ -0,0 +1,2342 @@
+%!PS-Adobe-3.0 EPSF-3.0
+%%Creator: GIMP PostScript file plugin V 1.17 by Peter Kirchgessner
+%%Title: v104beziermove.eps
+%%CreationDate: Mon Mar 30 14:51:49 2009
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
+%%Pages: 1
+%%BoundingBox: 14 14 142 146
+%%EndComments
+%%BeginProlog
+% Use own dictionary to avoid conflicts
+10 dict begin
+%%EndProlog
+%%Page: 1 1
+% Translate for offset
+14.173228346456694 14.173228346456694 translate
+% Translate to begin of first scanline
+0 131.17539273108105 translate
+127.10551181102363 -131.17539273108105 scale
+% Image geometry
+406 419 8
+% Transformation matrix
+[ 406 0 0 419 0 0 ]
+% Strings to hold RGB-samples per scanline
+/rstr 406 string def
+/gstr 406 string def
+/bstr 406 string def
+{currentfile /ASCII85Decode filter /RunLengthDecode filter rstr readstring pop}
+{currentfile /ASCII85Decode filter /RunLengthDecode filter gstr readstring pop}
+{currentfile /ASCII85Decode filter /RunLengthDecode filter bstr readstring pop}
+true 3
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+%%Trailer
+end
+%%EOF
diff --git a/changelog b/changelog
index a57f6df..7e8e2d2 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,6 @@
+20090416 tpd src/axiom-website/patches.html 20090416.03.tpd.patch
+20090416 tpd books/bookvol10.4 update bezier documentation
+20090416 tpd books/ps/v104beziermove.eps graph the bezier curves
 20090416 tpd src/axiom-website/patches.html 20090416.02.tpd.patch
 20090416 tpd src/interp/vmlisp.lisp move more interpreter code
 20090416 tpd src/interp/spaderror.lisp move more interpreter code
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 6f83681..758d24e 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -1092,5 +1092,7 @@ bookvol5 add \defunsec, section titles, docstrings<br/>
 regress.lisp tighten checks on regression tests<br/>
 <a href="patches/20090416.02.tpd.patch">20090416.02.tpd.patch</a>
 bookvol5 move more interpreter code<br/>
+<a href="patches/20090416.03.tpd.patch">20090416.03.tpd.patch</a>
+bookvol10.4 update bezier documentation<br/>
  </body>
 </html>
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