/*
On 01/26/2010 12:22 PM, Alan1961 wrote:
 >I would like to create prisms with a combination
 > of straight lines and curves - including circular.
 >For a very very simple example - a 4*4 box shape but with one corner 
 >rounded off with a circular radius of 1.

 >I am struggling to work out how to do this
 >with either a cubic or quadratic
 >spline and cannot find an example.
 >Should I be using beziers?
 >I've tried not to be lazy but would
 >appreciate some kind experienced Pov user showing me the way!

You can probably find better examples,
but this could be a starting point.
Example below demonstrates how to
combine linear and cubic segments to generate a Bezier spline
for the prism shape.

*/
//======================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, 2, -4.0>*4
   direction 1.5*z
   right     x*image_width/image_height
   look_at   <0.0, 0.0,  0.0>
}

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 lighting---)
       diffuse 0.6          // amount [0.6]
       brilliance 1.0       // tightness of diffuse illumination [1.0]
       // (---phong highlight---)
       phong 0.5          // amount [0.0]
       phong_size 40      // (1.0..250+) (dull->highly polished) [40]
       // (---specular highlight---)
       //specular 0.5       // amount [0.0]
       //roughness 0.05     // (~1.0..0.0005) (dull->highly polished) [0.05]
       // (---phong and specular---)
       metallic 0.8 //[Amount]  // give highlight color of surface
       // (---reflection---)
       reflection {

         1.0
         metallic 1.0
       }
     }
   };


#macro BezierLine(A,D)
// Convert linear segment into cubic Bezier form
   #local B=(2*A+D)/3;
   #local C=(A+2*D)/3;
   A,B,C,D
#end

#macro Corner(P,Q,R,S)
//
   #local A=Q;
   #local D=R;
   #local B=Q+(Q-P)/2;
   #local C=R+(R-S)/2;
   A,B,C,D
#end

#declare A=array[8]{
   <-1,-2>
   <1,-2>
   <2,-1>
   <2,1>
   <1,2>
   <-1,2>
   <-2,1>
   <-2,-1>
}


// Prism outline is constructed from linear segments,
// represented as a cubic Bezier
prism {
   linear_sweep  // or conic_sweep for tapering to a point
   bezier_spline // linear_spline | quadratic_spline | cubic_spline | 
bezier_spline
   -0.5,         // height 1
    0.5,         // height 2
   8*4,           // number of points
   // (--- the <u,v> points ---)
   BezierLine(A[0],A[1]),
     BezierLine(A[1],A[2]),
   BezierLine(A[2],A[3]),
     BezierLine(A[3],A[4]),
   BezierLine(A[4],A[5]),
     BezierLine(A[5],A[6]),
   BezierLine(A[6],A[7]),
     BezierLine(A[7],A[0])

   // [open]
   // [sturm]
   texture{Texture}
   translate -x*3
}



// Here some real cubic curves are used for corners

prism {
   linear_sweep  // or conic_sweep for tapering to a point
   bezier_spline // linear_spline | quadratic_spline | cubic_spline | 
bezier_spline
   -0.5,         // height 1
    0.5,         // height 2
   8*4,           // number of points
   // (--- the <u,v> points ---)
   BezierLine(A[0],A[1]),
     Corner(A[0],A[1],A[2],A[3]),
   BezierLine(A[2],A[3]),
     Corner(A[2],A[3],A[4],A[5]),
   BezierLine(A[4],A[5]),
     Corner(A[4],A[5],A[6],A[7]),
   BezierLine(A[6],A[7]),
     Corner(A[6],A[7],A[0],A[1])
   // [open]
   // [sturm]
   texture{Texture}
   translate x*3
}

// And this one uses only one curved corner

prism {
   linear_sweep  // or conic_sweep for tapering to a point
   bezier_spline // linear_spline | quadratic_spline | cubic_spline | 
bezier_spline
   -0.5,         // height 1
    0.5,         // height 2
   8*4,           // number of points
   // (--- the <u,v> points ---)
   BezierLine(A[0],A[1]),
     Corner(A[0],A[1],A[2],A[3]),
   BezierLine(A[2],A[3]),
     BezierLine(A[3],A[4]),
   BezierLine(A[4],A[5]),
     BezierLine(A[5],A[6]),
   BezierLine(A[6],A[7]),
     BezierLine(A[7],A[0])
   // [open]
   // [sturm]
   texture{Texture}
   translate -z*4
}
//======================8<======================

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