Thanks for your help and patience Bart and again for your excellent macros.    I
love the increased readability of spline definitions they bring - I know
probably not for everyone, but for me as a novice thinking about splines as a
series of trace actions is easier to understand and manage then a large pile of
points, for me it gives more focus on shape and dimensions.    Your macros
provide elegant simplicity - I think your suggestions should be an example in
the help file to help novices get started or even a standard include file
"SplinesForDummies.inc" could be put together by someone way above my pay grade.

In case anyone is interested, I've copied my current feeble efforts to
illustrate a) that I know next to nothing about Pov or Beziers! and b) to show
the kind of mechanisms of how I would like to be able to setup splines.  Clearly
I have a long way to go... but having fun ... many thanks again.

Alan




//======================8<======================
// Persistence of Vision Ray Tracer Scene Description File
// File: ?.pov
// Vers: 3.6
// Desc: Basic Scene Example
// Date: mm/dd/yy
// Auth: ?
//

#version 3.6;

#include "colors.inc"

global_settings {
   assumed_gamma 1.0
}

// ----------------------------------------

camera {
   location  <0.0, 18, -4>
   direction 1.5*z
   right     x*image_width/image_height
   look_at   <0.0, 0.0,  2.0>
}

background { color rgb <0.1, 0.3, 0.8> }

light_source {
   <0, 0, 0>            // light's position (translated below)
   color rgb <1, 1, 1>  // light's color
   translate <-30, 30, -30>
}

// ----------------------------------------


plane {
   y, -0.5-1e-6
   pigment { color rgb <0.7,0.5,0.3> }
}

#declare Texture=texture {
     pigment {color rgb <0.2,0.5,0.2> }
     finish {
       ambient 0.1              // ambient surface reflection color [0.1]
       diffuse 0.6              // amount [0.6]
       brilliance 1.0           // tightness of diffuse illumination [1.0]
       phong 0.5                // amount [0.0]
       phong_size 40            // (1.0..250+) (dull->highly polished) [40]
       metallic 0.8 //[Amount]  // give highlight color of surface
       reflection {1.0 metallic 1.0}
     }
   };


#macro BezierLine(A,D)
        #local LineVec = D-A;
        #local B= A + LineVec * 1/3;
        #local C= A + LineVec * 2/3;
        A,B,C,D

        #declare CurrentPoint = D;
        #declare CurrentDirection = vnormalize (LineVec);
        #declare CurrentDirection = <CurrentDirection.x, CurrentDirection.y>;
        #declare LastControl = C;
#end


//Draw a curve to a delta point with a specified exit direction
#macro CurveBy(dx,dy, ExitVec)
        #declare Sharpness =3;
        #local Ev = vnormalize(ExitVec);
        #local Ev = <Ev.x, Ev.y>;
        #local EndPoint = CurrentPoint + <dx,dy>;
        #local VecLen = vlength(EndPoint-CurrentPoint);
        #local Cp1 = CurrentPoint + CurrentDirection*VecLen/Sharpness;
        #local Cp2 = EndPoint - Ev*VecLen/Sharpness;

        CurrentPoint, Cp1, Cp2, EndPoint

        #declare CurrentPoint = EndPoint;
        #declare CurrentDirection = Ev;
        #declare CurrentDirection = <CurrentDirection.x, CurrentDirection.y>;
#end

//Record the start point to allow use of closure statements
#macro SplineStart(Pos)
        #declare StartingPoint = Pos;
        #declare CurrentPoint = Pos;
        #declare CurrentDirection = <1,0>;
#end

//Draw a horizontal line
#macro HLine(dx)
        BezierLine(CurrentPoint, CurrentPoint + <dx,0>)
#end

//Draw a vertical line
#macro VLine(dy)
        BezierLine(CurrentPoint,  CurrentPoint + <0,dy>)
#end

//Draw by a delta amount
#macro LineBy(dx,dy)
        BezierLine(CurrentPoint, CurrentPoint + <dx,dy>)
#end


#macro SplineCloseWithLine()
        BezierLine(CurrentPoint,StartingPoint)
#end



prism {
        linear_sweep            // or conic_sweep for tapering to a point
        bezier_spline           // linear_spline | quadratic_spline |
cubic_spline |
        -0.5,                   // height 1
        0.1,                    // height 2
        10*4,                    // number of points

        SplineStart(<0,0>)
        LineBy(4,4),
        VLine(2),

        CurveBy(-1.5,  2,        < -1, 0>),
        CurveBy(-1.5, -3,        < -1,-1>),

        CurveBy(-1,   -0.5,      < -1, 0>),
        CurveBy(-1,   0.5,       < -1, 1> ),

        CurveBy(-1.5,   3,       < -1, 0> ),
        CurveBy(-1.5,    -2      <  0,-1> ),

        VLine(-2),
        SplineCloseWithLine()
        //open
        texture{Texture}
}


union
{
        #declare dx = -5; #while (dx < 5)  cylinder{ <dx,-0.5,0>  <dx,-0.5,10>
0.01 pigment{Red} } #declare dx = dx + 0.5; #end
        #declare dz = 0;  #while (dz < 10) cylinder{ <-5,-0.5,dz>  <5,-0.5,dz >
0.01 pigment{Blue} } #declare dz = dz + 0.5; #end
        translate .1*y
        no_shadow
}

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