Initial population.

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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input ntube.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1994.
+@
+<<*>>=
+<<license>>
+-- ntube.input
+-- Generalized tubes.
+-- The functions in this file draw a 2-d curve in the normal
+-- planes around a 3-d curve.  The computations are all done
+-- numerically in machine-precision floating point for efficiency.
+
+R3 := Point DoubleFloat                  -- Points in 3-Space
+R2 := Point DoubleFloat                  -- Points in 2-Space
+S := Segment Float              -- Draw ranges
+ThreeCurve := DoubleFloat -> R3          -- type of a space curve function
+TwoCurve := (DoubleFloat, DoubleFloat) -> R2      -- type of a plane curve function
+Surface := (DoubleFloat, DoubleFloat) -> R3   -- type of a parameterized surface function
+
+-- Frenet frames define a coordinate system around a point on a space curve
+FrenetFrame := Record(value: R3, tagent: R3, normal: R3, binormal: R3)
+
+-- Holds current Frenet frame for a point on a curve
+frame: FrenetFrame
+
+-- compile, don't interpret functions
+)set fun compile on
+
+-- Draw a generalized tube.
+-- ntubeDraw(spaceCurve, planeCurve, u0..u1, t0..t1)
+-- draws planeCurve int the normal planes of spaceCurve.  u0..u1 specifies
+-- the paramter range of the planeCurve and t0..t1 specifies the parameter
+-- range of the spaceCurve.  Additionally the plane curve function takes
+-- as a second parameter the current parameter of the spaceCurve.  This
+-- allows the plane curve to evolve as it goes around the space curve.
+-- see "page5.input" for an example of this.
+ntubeDraw: (ThreeCurve, TwoCurve, S, S) -> VIEW3D
+ntubeDraw(spaceCurve, planeCurve, uRange, tRange) ==
+  ntubeDrawOpt(spaceCurve, planeCurve, uRange, tRange, []$List DROPT)
+
+-- ntuberDrawOpt is the same as ntuberDraw, but takes optional
+-- parameters which it passes to the draw command.
+ntubeDrawOpt: (ThreeCurve, TwoCurve, S, S, List DROPT) -> VIEW3D
+ntubeDrawOpt(spaceCurve, planeCurve, uRange,  tRange, l) ==
+  delT:DoubleFloat := (hi(tRange) - lo(tRange))/10000
+  oldT:DoubleFloat := lo(tRange) - 1
+  fun := ngeneralTube(spaceCurve, planeCurve, delT, oldT)
+  draw(fun, uRange, tRange, l)
+
+-- nfrenetFrame(c, t, delT) numerically computes the Frenet Frame
+-- about the curve c at t.  delT is a small number used to
+-- compute derivatives.
+nfrenetFrame(c, t, delT) ==
+  f0 := c(t)
+  f1 := c(t+delT)
+  t0 := f1 - f0                -- the tangent
+  n0 := f1 + f0
+  b := cross(t0, n0)           -- the binormal
+  n := cross(b,t0)             -- the normal
+  ln := length n
+  lb := length b
+  ln = 0 or lb = 0 => error "Frenet Frame not well defined"
+  n := (1/ln)*n                -- make into unit length vectors
+  b := (1/lb)*b
+  [f0, t0, n, b]$FrenetFrame
+
+-- nGeneralTube(spaceCurve, planeCurve, delT, oltT)
+-- creates a function which can be passed to the system draw command.
+-- The function is a parameterized surface for the general tube
+-- around the spaceCurve.  delT is a small number used to compute
+-- derivatives, and oldT is used to hold the current value of the
+-- t parameter for the spaceCurve.  This is an efficiency measure
+-- to ensure that frames are only computed once for every value of t.
+ngeneralTube: (ThreeCurve, TwoCurve, DoubleFloat, DoubleFloat) -> Surface
+ngeneralTube(spaceCurve, planeCurve, delT, oldT) ==
+  free frame
+  (v:DoubleFloat, t: DoubleFloat): R3 +->
+    if (t ~= oldT) then
+      frame := nfrenetFrame(spaceCurve, t, delT)
+      oldT := t
+    p := planeCurve(v, t)
+    frame.value + p.1*frame.normal + p.2*frame.binormal
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}