// Gabriel's Horn: y = 1/x Surface of Revolution
// 3D slice of PIST pathological manifold

// Finite volume, infinite surface area
// Visualized as hollow shell (the byte container surface)

// Generate horn profile as a polygon
// Then rotate_extrude to create the surface

module horn_profile() {
  points = [
    [0.050, 40.000],
    [0.250, 8.000],
    [0.450, 4.444],
    [0.650, 3.077],
    [0.850, 2.353],
    [1.050, 1.905],
    [1.250, 1.600],
    [1.450, 1.379],
    [1.650, 1.212],
    [1.850, 1.081],
    [2.050, 0.976],
    [2.250, 0.889],
    [2.450, 0.816],
    [2.650, 0.755],
    [2.850, 0.702],
    [3.050, 0.656],
    [3.250, 0.615],
    [3.450, 0.580],
    [3.650, 0.548],
    [3.850, 0.519],
    [4.050, 0.494],
    [4.250, 0.471],
    [4.450, 0.449],
    [4.650, 0.430],
    [4.850, 0.412],
    [5.050, 0.396],
    [5.250, 0.381],
    [5.450, 0.367],
    [5.650, 0.354],
    [5.850, 0.342],
    [6.050, 0.331],
    [6.250, 0.320],
    [6.450, 0.310],
    [6.650, 0.301],
    [6.850, 0.292],
    [7.050, 0.284],
    [7.250, 0.276],
    [7.450, 0.268],
    [7.650, 0.261],
    [7.850, 0.255],
    [8.050, 0.248],
    [8.250, 0.242],
    [8.450, 0.237],
    [8.650, 0.231],
    [8.850, 0.226],
    [9.050, 0.221],
    [9.250, 0.216],
    [9.450, 0.212],
    [9.650, 0.207],
    [9.850, 0.203],
    [10.050, 0.199],
    [10.250, 0.195],
    [10.450, 0.191],
    [10.650, 0.188],
    [10.850, 0.184],
    [11.050, 0.181],
    [11.250, 0.178],
    [11.450, 0.175],
    [11.650, 0.172],
    [11.850, 0.169],
    [12.050, 0.166],
    [12.250, 0.163],
    [12.450, 0.161],
    [12.650, 0.158],
    [12.650, 0],
    [0.05, 0]
  ];
  polygon(points);
}

// Thick-walled horn (byte positions on surface)
difference() {
  rotate_extrude($fn=64) horn_profile();
  scale([0.95, 0.95, 0.95]) rotate_extrude($fn=64) horn_profile();
}

// Byte position markers (sample every 32 positions)
color([1, 0.5, 0]) {
  translate([0.05, -1.89, 39.96]) sphere(r=0.8, $fn=8); // n=1
  translate([1.65, -1.21, 0.01]) sphere(r=0.8, $fn=8); // n=33
  translate([3.25, -0.04, -0.61]) sphere(r=0.8, $fn=8); // n=65
  translate([4.85, 0.41, -0.05]) sphere(r=0.8, $fn=8); // n=97
  translate([6.45, 0.06, 0.30]) sphere(r=0.8, $fn=8); // n=129
  translate([8.05, -0.24, 0.06]) sphere(r=0.8, $fn=8); // n=161
  translate([9.65, -0.06, -0.20]) sphere(r=0.8, $fn=8); // n=193
  translate([11.25, 0.17, -0.06]) sphere(r=0.8, $fn=8); // n=225
}