Determining X and Y for the intersection of a conic section and rotated plane given Y

// Given an [x,y] or [x,y,z], transform to a
// [rho, theta] or [rho, theta, phi].
// Note that in mathematical spherical coordinates,
// phi is measured down from vertical.  This is as
// opposed to geographic coordinates, where latitude
// is measured up from the equator.
function topolar(p) =
    len(p) == 3 ? topolar3(p) : topolar2(p);

function topolar2(p) = [
    norm(p),
    atan2(p.y, p.x)
];

function topolar3(p) = [
    norm(p),
    atan2(p.y, p.x),
    atan2(norm([p.x,p.y]), p.z)
];

// Given a [rho, theta] or [rho, theta, phi], transform to
// an [x,y] or [x,y,z].
function torect(p) =
    len(p) == 3 ? torect3(p) : torect2(p);

function torect2(p) = [
    p[0] * cos(p[1]),
    p[0] * sin(p[1])
];

function torect3(p) = [
    p[0] * cos(p[1]) * sin(p[2]),
    p[0] * sin(p[1]) * sin(p[2]),
    p[0] * cos(p[2])
];

echo(topolar([10,0]));
echo(topolar([10,1]));
echo(topolar([10,10]));
echo(topolar([-10,10]));
echo(topolar([-10,-10]));
echo(topolar([10,-10]));
echo();
echo(topolar([10,0,0]));
echo(topolar([10,1,0]));
echo(topolar([10,10,10]));
echo(topolar([-10,10,10]));
echo(topolar([-10,-10,10]));
echo(topolar([10,-10,10]));
echo();

rho = 100;
for (theta = [0:10:70]) for (phi=[0:10:70]) translate(torect([rho, theta, phi])) cube(1);

OpenSCAD mailing list-2 wrote

Drawing the lines first isn't an option --- I need to match a differently cut part and need to get from the left (the tip of the cone) to the right (the ellipse where the cone and plane intersect at X and Z based on knowing Y (I'll be looping through).
I've tried doing it w/ trigonometry, and it's a long series of nested calculations which seem cumbersome and slow to calculate even before I get halfway there. 
William

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OpenSCAD mailing list-2 wrote

Thank you.
What I'm trying to do is to feed X and Z into a module along w/ Y so that I can write out the coordinates.
Unfortunately, I can't figure out how to unwrap your code to fit the requirements of the module I worked up:
include<BOSL2/std.scad>$fn=80;
difference(){
  translate([0, 0.125, 0.25])
    rotate([0, 90, 0])
    cylinder(r1=0, r2=0.125, h=(0.125 / tan(15)), center=false);
  cube([1, 1, 0.25], center=false);
  rotate([0, 45, 0])
     cube([1, 1, 1], center=false);
} plane = plane_from_normal([-1,0,1]);
apex = [0, 1/8, 1/4];
rbase = 0.125;
h = 0.125/tan(15);
N = 16;
//base = [for(i=[0:1:N/2]) let(theta=360*i/N) apex+[h,rbase*cos(theta), rbase*sin(theta)]]; color("red")
//  for(pt=base)
    for(i=[0:1:N/2])
{
//     int = plane_line_intersection(plane, [apex, pt]);
     stroke([apex,plane_line_intersection(plane, [apex, pt])], width=0.005);
  }


I want to have separate access to the X, Y, and, Z coordinates:
module cutv(bx, by, bz, ex, ey, ez, r, a) {
  hull(){
    translate([bx, by, bz]){
      vendmill(r, a);
    }
    translate([ex, ey, ez]){
      vendmill(r, a);
    }
  }
}
(see below for the dependencies)

Eventually the module will be extended to write out the coordinates as G-Code using echo.
Another limitation is I do most of my development in BlockSCAD, which I guess makes my code overly simplistic/procedural/stilted.
William

module vendmill(vr, va) {
  union(){
    removevshape(vr, va);
    translate([0, 0, (calcVdepth(vr, va))]){
      cylinder(r1=vr, r2=vr, h=st, center=false);
    }
  }
}

module removevshape(vr, va) {
  cylinder(r1=0, r2=vr, h=(calcVdepth(vr, va)), center=false);
}
function calcVdepth(rad, an) = rad / tan(an);




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