Klein bottle generator

// Time to sleep between rezzes -- avoids compile errors
float   sleep = 1;
// Number of "slices"
integer m = 120;
// Number of "stripes"
integer n = 8;
// Name of the rezzed object (must exist in inv)
string  edgeprimname = "Cylinder";
 
// Rezz a segment between 2 given points, assign its color color
// Mod of a routine found here: 
//   http://lslwiki.net/lslwiki/wakka.php?wakka=LibraryBezierCurveDemo
// Original credits follow:
//   Bezier Curve Demo 1.0.1
//   Catherine Omega Heavy Industries
//   Modified by Lionel Forager 29-12-2006: 
//     Added segment drawing between points. Corrected minor bugs.
drawLineSegment(vector base, vector p1,vector p2, integer order)
{
    // Calc the position of the center of the segment
    vector center = (p1+p2)/2.;
    vector localZ = p2 - p1;
    // Get distance between points
    float distance= llVecMag(localZ);
    // Normalize the vector
    localZ = localZ / distance;
 
    vector xAxis;
    // Let's choose as x local axis the direction of a vector normal
    // to localZ and contained in the plain given by localZ and global X
    // or global Y, the one that is less parallel to localZ
    if ( localZ.x < localZ.y ) xAxis= <1.,0.,0.>;
    else                       xAxis= <0.,1.,0.>;
 
    // localX is the one contain in the plane given by localZ and xAxis
    // that is normal to localZ. That is, localX = xAxis - localZ*xaxis*localZ.
    // We should normalize the vector to get a unitary one.
    vector localX= xAxis - (localZ * xAxis) * localZ;
    localX= llVecNorm(localX);
 
    // Now get the rotation to put axis Z oriented pointing
    // to the direction between the two given points. 
    rotation rot = llAxes2Rot(localX,localZ % localX, localZ);    
 
    // Rezz the cylinder!
    llRezObject(edgeprimname,base + center,ZERO_VECTOR,rot,(integer) (distance*1000)*100+order);
 
    // Avoid clogging the queue and subsequent compile problems
    llSleep(sleep);
}
 
 
default 
{
 
    touch_start(integer total_number)
    {
 
        llSay(0, "Generating Klein bottle..."); 
 
        integer i;
        integer j;
        float a = 2;
        float b = 7;
        float c = 2;
        float r;
        float u;
        float v;
        float x;
        float y;
        float z;
        list oldcoor = [];
        list firstcoor = [];
        list coor = [];
        vector prevpos;
        rotation rot;
 
        for (i = 0; i <= m; i++) {
            // llSay(0,"Looping I="+(string)i+" of "+(string)m);
 
            for (j = 0; j < n; j++) {
                // llSay(0," Looping J="+(string)j+" of "+(string)n);
 
                u = 2 * PI * i / m;
                v = 2 * PI * j / n;
 
                if (n % 2 == 1) v += PI / n * i/m;
 
                r = c * (1 - llCos(u) / 2);
 
                // See PlanetMath,         
                // http://planetmath.org/?op=getobj&from=objects&id=4249
 
                if (u < PI) {
                    x = a * llCos(u) * (1 + llSin(u)) + r * llCos(u) * llCos(v);
                    y = b * llSin(u) + r * llSin(u) * llCos(v);
                } else {
                    x = a * llCos(u) * (1 + llSin(u)) + r * llCos(v + PI);
                    y = b * llSin(u);
                };
 
                z = r * llSin(v);
 
 
                // draw "horizontal" lines
                if (j > 0) {
                    prevpos = llList2Vector(coor,j-1);
                    drawLineSegment(llGetPos(),prevpos,<x,y,z>,j);
                };
 
                if (j == n-1) {
                    prevpos = llList2Vector(coor,0);
                    drawLineSegment(llGetPos(),prevpos,<x,y,z>,0);
                };
 
 
                // draw "vertical" and diagonal lines
                if (i > 0) { 
 
                    prevpos = llList2Vector(oldcoor,j);
                    drawLineSegment(llGetPos(),prevpos,<x,y,z>,j);
 
                    if (j > 0) prevpos = llList2Vector(oldcoor,j-1);
                    else prevpos = llList2Vector(oldcoor,n-1);
                    drawLineSegment(llGetPos(),prevpos,<x,y,z>,j);
 
                };
 
 
                // if (i < m) llRezObject("Vertex", llGetPos() + <x,y,z>, 
                // <0.0,0.0,0.0>, <0.0,0.0,0.0,1.0>, 0);
 
                coor = coor + [<x,y,z>];
 
            }; 
 
            if (i == 0) firstcoor = coor;
            oldcoor = coor;
            coor = [];
 
        };
        llSay(0, "Done!"); 
    }
}