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dotSCAD/src/_impl/_contours_impl.scad
Justin Lin 5d4eec1ad8 elaborate 2010
2021-01-08 12:11:01 +08:00

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OpenSCAD
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use <util/lerp.scad>;
function interpolated_pt(p0, p1, threshold) =
lerp(
[p0[0], p0[1], p0[2]],
[p1[0], p1[1], p1[2]],
(threshold - p0[2]) / (p1[2] - p0[2])
);
/*
Grid indexes
1 － 2
| |
0 － 3
*/
/*
ISOLINES Impl Begin ============================
*/
function _isolines_pn_label(pts, threshold) =
[
for(row = pts)
[for(p = row) [p[0], p[1], p[2], p[2] >= threshold]]
];
function _isolines_corner_value(cell_pts) =
let(
c0 = cell_pts[0][3] ? 1 : 0,
c1 = cell_pts[1][3] ? 2 : 0,
c2 = cell_pts[2][3] ? 4 : 0,
c3 = cell_pts[3][3] ? 8 : 0
)
c0 + c1 + c2 + c3;
function _case1_isolines(cell_pts, threshold) = [
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[0], cell_pts[3], threshold)]
];
function _case2_isolines(cell_pts, threshold) = [
[interpolated_pt(cell_pts[0], cell_pts[3], threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
];
function _case3_isolines(cell_pts, threshold) = [
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
];
function _case4_isolines(cell_pts, threshold) = [
[interpolated_pt(cell_pts[1], cell_pts[2], threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
];
function _case5_isolines(cell_pts, threshold) =
let(center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4)
center_p[2] >= threshold ?
[
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[1], center_p, threshold), interpolated_pt(cell_pts[1], cell_pts[2], threshold)],
[interpolated_pt(cell_pts[0], cell_pts[3], threshold), interpolated_pt(cell_pts[3], center_p, threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
]
:
[
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[0], center_p, threshold), interpolated_pt(cell_pts[0], cell_pts[3], threshold)],
[interpolated_pt(cell_pts[1], cell_pts[2], threshold), interpolated_pt(cell_pts[2], center_p, threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
];
function _case6_isolines(cell_pts, threshold) = [
[interpolated_pt(cell_pts[1], cell_pts[2], threshold), interpolated_pt(cell_pts[0], cell_pts[3], threshold)]
];
function _case7_isolines(cell_pts, threshold) = [
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[1], cell_pts[2], threshold)]
];
function _case8_isolines(cell_pts, threshold) = _case7_isolines(cell_pts, threshold);
function _case9_isolines(cell_pts, threshold) = _case6_isolines(cell_pts, threshold);
function _case10_isolines(cell_pts, threshold) =
let(center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4)
center_p[2] >= threshold ?
[
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[1], center_p, threshold), interpolated_pt(cell_pts[0], cell_pts[3], threshold)],
[interpolated_pt(cell_pts[1], cell_pts[2], threshold), interpolated_pt(cell_pts[2], center_p, threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
]
:
[
[interpolated_pt(cell_pts[0], cell_pts[1], threshold), interpolated_pt(cell_pts[1], center_p, threshold), interpolated_pt(cell_pts[1], cell_pts[2], threshold)],
[interpolated_pt(cell_pts[0], cell_pts[3], threshold), interpolated_pt(cell_pts[3], center_p, threshold), interpolated_pt(cell_pts[2], cell_pts[3], threshold)]
];
function _case11_isolines(cell_pts, threshold) = _case4_isolines(cell_pts, threshold);
function _case12_isolines(cell_pts, threshold) = _case3_isolines(cell_pts, threshold);
function _case13_isolines(cell_pts, threshold) = _case2_isolines(cell_pts, threshold);
function _case14_isolines(cell_pts, threshold) = _case1_isolines(cell_pts, threshold);
function _isolines_of(cell_pts, threshold) =
let(cv = _isolines_corner_value(cell_pts))
cv == 0 || cv == 15 ? [] :
cv == 1 ? _case1_isolines(cell_pts, threshold) :
cv == 8 ? _case2_isolines(cell_pts, threshold) :
cv == 9 ? _case3_isolines(cell_pts, threshold) :
cv == 4 ? _case4_isolines(cell_pts, threshold) :
cv == 5 ? _case5_isolines(cell_pts, threshold) :
cv == 12 ? _case6_isolines(cell_pts, threshold) :
cv == 13 ? _case7_isolines(cell_pts, threshold) :
cv == 2 ? _case8_isolines(cell_pts, threshold) :
cv == 3 ? _case9_isolines(cell_pts, threshold) :
cv == 10 ? _case10_isolines(cell_pts, threshold) :
cv == 11 ? _case11_isolines(cell_pts, threshold) :
cv == 6 ? _case12_isolines(cell_pts, threshold) :
cv == 7 ? _case13_isolines(cell_pts, threshold) :
_case14_isolines(cell_pts, threshold);
function _marching_squares_isolines(points, threshold) =
let(labeled_pts = _isolines_pn_label(points, threshold))
[
for(y = [0:len(labeled_pts) - 2])
for(x = [0:len(labeled_pts[0]) - 2])
let(
p0 = labeled_pts[y][x],
p1 = labeled_pts[y + 1][x],
p2 = labeled_pts[y + 1][x + 1],
p3 = labeled_pts[y][x + 1],
cell_pts = [p0, p1, p2, p3],
isolines_lt = _isolines_of(cell_pts, threshold)
)
if(isolines_lt != [])
each isolines_lt
];
/*
ISOLINES Impl End ============================
*/
/*
ISOBANDS Impl Begin ============================
*/
function _isobands_tri_label(pts, lower, upper) =
[
for(row = pts)
[
for(p = row)
let(label =
p[2] < lower ? "0" :
p[2] >= lower && p[2] <= upper ? "1" : "2"
)
[p[0], p[1], p[2], label]
]
];
function _isobands_corner_value(cell_pts) =
str(cell_pts[1][3], cell_pts[2][3], cell_pts[3][3], cell_pts[0][3]);
// single triangle
function _case2221_isobands(cell_pts, threshold) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], threshold),
interpolated_pt(cell_pts[0], cell_pts[1], threshold)
]
];
function _case2212_isobands(cell_pts, threshold) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], threshold),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], threshold)
]
];
function _case2122_isobands(cell_pts, threshold) = [
[
interpolated_pt(cell_pts[1], cell_pts[2], threshold),
interpolated_pt(cell_pts[2], cell_pts[3], threshold),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]]
]
];
function _case1222_isobands(cell_pts, threshold) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], threshold),
interpolated_pt(cell_pts[1], cell_pts[2], threshold),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case0001_isobands(cell_pts, threshold) =
_case2221_isobands(cell_pts, threshold);
function _case0010_isobands(cell_pts, threshold) =
_case2212_isobands(cell_pts, threshold);
function _case0100_isobands(cell_pts, threshold) =
_case2122_isobands(cell_pts, threshold);
function _case1000_isobands(cell_pts, threshold) =
_case1222_isobands(cell_pts, threshold);
// single trapezoid
function _case2220_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case2202_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper)
]
];
function _case2022_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
];
function _case0222_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
];
function _case0002_isobands(cell_pts, lower, upper) =
_case2220_isobands(cell_pts, upper, lower);
function _case0020_isobands(cell_pts, lower, upper) =
_case2202_isobands(cell_pts, upper, lower);
function _case0200_isobands(cell_pts, lower, upper) =
_case2022_isobands(cell_pts, upper, lower);
function _case2000_isobands(cell_pts, lower, upper) =
_case0222_isobands(cell_pts, upper, lower);
// single rectangle
function _case0011_isobands(cell_pts, threshold) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], threshold),
interpolated_pt(cell_pts[0], cell_pts[1], threshold)
]
];
function _case0110_isobands(cell_pts, threshold) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], threshold),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], threshold)
]
];
function _case1100_isobands(cell_pts, threshold) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], threshold),
interpolated_pt(cell_pts[2], cell_pts[3], threshold),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case1001_isobands(cell_pts, threshold) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], threshold),
interpolated_pt(cell_pts[1], cell_pts[2], threshold),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case2211_isobands(cell_pts, threshold) =
_case0011_isobands(cell_pts, threshold);
function _case2112_isobands(cell_pts, threshold) =
_case0110_isobands(cell_pts, threshold);
function _case1122_isobands(cell_pts, threshold) =
_case1100_isobands(cell_pts, threshold);
function _case1221_isobands(cell_pts, threshold) =
_case1001_isobands(cell_pts, threshold);
function _case2200_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case2002_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper)
]
];
function _case0022_isobands(cell_pts, lower, upper) =
_case2200_isobands(cell_pts, upper, lower);
function _case0220_isobands(cell_pts, lower, upper) =
_case2002_isobands(cell_pts, upper, lower);
// single hexagon
function _case0211_isobands(cell_pts, lower, upper) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
];
function _case2110_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case1102_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case1021_isobands(cell_pts, lower, upper) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case2011_isobands(cell_pts, lower, upper) =
_case0211_isobands(cell_pts, upper, lower);
function _case0112_isobands(cell_pts, lower, upper) =
_case2110_isobands(cell_pts, upper, lower);
function _case1120_isobands(cell_pts, lower, upper) =
_case1102_isobands(cell_pts, upper, lower);
function _case1201_isobands(cell_pts, lower, upper) =
_case1021_isobands(cell_pts, upper, lower);
function _case2101_isobands(cell_pts, lower, upper) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case0121_isobands(cell_pts, lower, upper) =
_case2101_isobands(cell_pts, upper, lower);
function _case1012_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case1210_isobands(cell_pts, lower, upper) =
_case1012_isobands(cell_pts, upper, lower);
// single pentagon
function _case1211_isobands(cell_pts, threshold) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], threshold),
interpolated_pt(cell_pts[1], cell_pts[2], threshold),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case2111_isobands(cell_pts, threshold) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], threshold),
interpolated_pt(cell_pts[0], cell_pts[1], threshold)
]
];
function _case1112_isobands(cell_pts, threshold) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], threshold),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], threshold)
]
];
function _case1121_isobands(cell_pts, threshold) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], threshold),
interpolated_pt(cell_pts[2], cell_pts[3], threshold),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case1011_isobands(cell_pts, threshold) =
_case1211_isobands(cell_pts, threshold);
function _case0111_isobands(cell_pts, threshold) =
_case2111_isobands(cell_pts, threshold);
function _case1110_isobands(cell_pts, threshold) =
_case1112_isobands(cell_pts, threshold);
function _case1101_isobands(cell_pts, threshold) =
_case1121_isobands(cell_pts, threshold);
function _case1200_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
]
];
function _case0120_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
];
function _case0012_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case2001_isobands(cell_pts, lower, upper) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case1022_isobands(cell_pts, lower, upper) =
_case1200_isobands(cell_pts, upper, lower);
function _case2102_isobands(cell_pts, lower, upper) =
_case0120_isobands(cell_pts, upper, lower);
function _case2210_isobands(cell_pts, lower, upper) =
_case0012_isobands(cell_pts, upper, lower);
function _case0221_isobands(cell_pts, lower, upper) =
_case2001_isobands(cell_pts, upper, lower);
function _case1002_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case2100_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
];
function _case0210_isobands(cell_pts, lower, upper) = [
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
];
function _case0021_isobands(cell_pts, lower, upper) = [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
];
function _case1220_isobands(cell_pts, lower, upper) =
_case1002_isobands(cell_pts, upper, lower);
function _case0122_isobands(cell_pts, lower, upper) =
_case2100_isobands(cell_pts, upper, lower);
function _case2012_isobands(cell_pts, lower, upper) =
_case0210_isobands(cell_pts, upper, lower);
function _case2201_isobands(cell_pts, lower, upper) =
_case0021_isobands(cell_pts, upper, lower);
// Saddles
function _case2020_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
],
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
],
[
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
];
function _case0202_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
],
[
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
],
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper)
]
];
function _case0101_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
],
[
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], center_p, lower)
],
[
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]]
]
];
function _case1010_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
],
[
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
] : [
[
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
],
[
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[0], center_p, upper)
]
];
function _case2121_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]]
],
[
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[1], center_p, lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
] : [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
],
[
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[2], center_p, upper)
]
];
function _case1212_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
],
[
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], center_p, lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
],
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper)
]
];
function _case2120_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]]
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower)
],
[
interpolated_pt(cell_pts[2], cell_pts[3], upper),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[3], center_p, upper)
]
];
function _case0102_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper)
],
[
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
] : [
[
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]]
]
];
function _case2021_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
]
] : [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
],
[
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[2], center_p, upper)
]
];
function _case0201_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
],
[
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[2], center_p, lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
]
] : [
[
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper)
]
];
function _case1202_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
],
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper)
]
];
function _case1020_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
],
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[3], center_p, lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower)
]
] : [
[
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower)
]
];
function _case0212_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], center_p, lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], center_p, upper)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[1], lower)
],
[
interpolated_pt(cell_pts[0], cell_pts[3], upper),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], upper),
interpolated_pt(cell_pts[3], center_p, upper)
]
];
function _case2010_isobands(cell_pts, lower, upper) =
let(
center_p = (cell_pts[0] + cell_pts[1] + cell_pts[2] + cell_pts[3]) / 4,
center_p_z = center_p[2]
)
center_p_z < lower ? [
[
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[1], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper)
],
[
interpolated_pt(cell_pts[3], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower)
]
] :
center_p_z >= lower && center_p_z <= upper ? [
[
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[1], center_p, upper),
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower)
]
] : [
[
interpolated_pt(cell_pts[0], cell_pts[1], upper),
interpolated_pt(cell_pts[0], cell_pts[1], lower),
interpolated_pt(cell_pts[0], center_p, lower),
interpolated_pt(cell_pts[0], cell_pts[3], lower),
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
interpolated_pt(cell_pts[2], cell_pts[3], lower),
interpolated_pt(cell_pts[2], center_p, lower),
interpolated_pt(cell_pts[1], cell_pts[2], lower),
interpolated_pt(cell_pts[1], cell_pts[2], upper),
interpolated_pt(cell_pts[2], center_p, upper),
interpolated_pt(cell_pts[3], center_p, upper),
interpolated_pt(cell_pts[0], center_p, upper)
]
];
function _isobands_of(cell_pts, lower, upper) =
let(cv = _isobands_corner_value(cell_pts))
// no contour
cv == "0000" || cv == "2222" ? [] :
// single square
cv == "1111" ? [[for(i = 3; i >= 0; i = i - 1) [cell_pts[i][0], cell_pts[i][1]]]] :
// single triangle
cv == "2221" ? _case2221_isobands(cell_pts, upper) :
cv == "2212" ? _case2212_isobands(cell_pts, upper) :
cv == "2122" ? _case2122_isobands(cell_pts, upper) :
cv == "1222" ? _case1222_isobands(cell_pts, upper) :
cv == "0001" ? _case0001_isobands(cell_pts, lower) :
cv == "0010" ? _case0010_isobands(cell_pts, lower) :
cv == "0100" ? _case0100_isobands(cell_pts, lower) :
cv == "1000" ? _case1000_isobands(cell_pts, lower) :
// single trapezoid
cv == "2220" ? _case2220_isobands(cell_pts, lower, upper) :
cv == "2202" ? _case2202_isobands(cell_pts, lower, upper) :
cv == "2022" ? _case2022_isobands(cell_pts, lower, upper) :
cv == "0222" ? _case0222_isobands(cell_pts, lower, upper) :
cv == "0002" ? _case0002_isobands(cell_pts, lower, upper) :
cv == "0020" ? _case0020_isobands(cell_pts, lower, upper) :
cv == "0200" ? _case0200_isobands(cell_pts, lower, upper) :
cv == "2000" ? _case2000_isobands(cell_pts, lower, upper) :
// single rectangle
cv == "0011" ? _case0011_isobands(cell_pts, lower) :
cv == "0110" ? _case0110_isobands(cell_pts, lower) :
cv == "1100" ? _case1100_isobands(cell_pts, lower) :
cv == "1001" ? _case1001_isobands(cell_pts, lower) :
cv == "2211" ? _case2211_isobands(cell_pts, upper) :
cv == "2112" ? _case2112_isobands(cell_pts, upper) :
cv == "1122" ? _case1122_isobands(cell_pts, upper) :
cv == "1221" ? _case1221_isobands(cell_pts, upper) :
cv == "2200" ? _case2200_isobands(cell_pts, lower, upper) :
cv == "2002" ? _case2002_isobands(cell_pts, lower, upper) :
cv == "0022" ? _case0022_isobands(cell_pts, lower, upper) :
cv == "0220" ? _case0220_isobands(cell_pts, lower, upper) :
// single hexagon
cv == "0211" ? _case0211_isobands(cell_pts, lower, upper) :
cv == "2110" ? _case2110_isobands(cell_pts, lower, upper) :
cv == "1102" ? _case1102_isobands(cell_pts, lower, upper) :
cv == "1021" ? _case1021_isobands(cell_pts, lower, upper) :
cv == "2011" ? _case2011_isobands(cell_pts, lower, upper) :
cv == "0112" ? _case0112_isobands(cell_pts, lower, upper) :
cv == "1120" ? _case1120_isobands(cell_pts, lower, upper) :
cv == "1201" ? _case1201_isobands(cell_pts, lower, upper) :
cv == "2101" ? _case2101_isobands(cell_pts, lower, upper) :
cv == "0121" ? _case0121_isobands(cell_pts, lower, upper) :
cv == "1012" ? _case1012_isobands(cell_pts, lower, upper) :
cv == "1210" ? _case1210_isobands(cell_pts, lower, upper) :
// single pentagon
cv == "1211" ? _case1211_isobands(cell_pts, upper) :
cv == "2111" ? _case2111_isobands(cell_pts, upper) :
cv == "1112" ? _case1112_isobands(cell_pts, upper) :
cv == "1121" ? _case1121_isobands(cell_pts, upper) :
cv == "1011" ? _case1011_isobands(cell_pts, lower) :
cv == "0111" ? _case0111_isobands(cell_pts, lower) :
cv == "1110" ? _case1110_isobands(cell_pts, lower) :
cv == "1101" ? _case1101_isobands(cell_pts, lower) :
cv == "1200" ? _case1200_isobands(cell_pts, lower, upper) :
cv == "0120" ? _case0120_isobands(cell_pts, lower, upper) :
cv == "0012" ? _case0012_isobands(cell_pts, lower, upper) :
cv == "2001" ? _case2001_isobands(cell_pts, lower, upper) :
cv == "1022" ? _case1022_isobands(cell_pts, lower, upper) :
cv == "2102" ? _case2102_isobands(cell_pts, lower, upper) :
cv == "2210" ? _case2210_isobands(cell_pts, lower, upper) :
cv == "0221" ? _case0221_isobands(cell_pts, lower, upper) :
cv == "1002" ? _case1002_isobands(cell_pts, lower, upper) :
cv == "2100" ? _case2100_isobands(cell_pts, lower, upper) :
cv == "0210" ? _case0210_isobands(cell_pts, lower, upper) :
cv == "0021" ? _case0021_isobands(cell_pts, lower, upper) :
cv == "1220" ? _case1220_isobands(cell_pts, lower, upper) :
cv == "0122" ? _case0122_isobands(cell_pts, lower, upper) :
cv == "2012" ? _case2012_isobands(cell_pts, lower, upper) :
cv == "2201" ? _case2201_isobands(cell_pts, lower, upper) :
// Saddles
cv == "2020" ? _case2020_isobands(cell_pts, lower, upper) :
cv == "0202" ? _case0202_isobands(cell_pts, lower, upper) :
cv == "0101" ? _case0101_isobands(cell_pts, lower, upper) :
cv == "1010" ? _case1010_isobands(cell_pts, lower, upper) :
cv == "2121" ? _case2121_isobands(cell_pts, lower, upper) :
cv == "1212" ? _case1212_isobands(cell_pts, lower, upper) :
cv == "2120" ? _case2120_isobands(cell_pts, lower, upper) :
cv == "0102" ? _case0102_isobands(cell_pts, lower, upper) :
cv == "2021" ? _case2021_isobands(cell_pts, lower, upper) :
cv == "0201" ? _case0201_isobands(cell_pts, lower, upper) :
cv == "1202" ? _case1202_isobands(cell_pts, lower, upper) :
cv == "1020" ? _case1020_isobands(cell_pts, lower, upper) :
cv == "0212" ? _case0212_isobands(cell_pts, lower, upper) :
_case2010_isobands(cell_pts, lower, upper);
function _marching_squares_isobands(points, lower, upper) =
let(labeled_pts = _isobands_tri_label(points, lower, upper))
[
for(y = [0:len(labeled_pts) - 2])
for(x = [0:len(labeled_pts[0]) - 2])
let(
p0 = labeled_pts[y][x],
p1 = labeled_pts[y + 1][x],
p2 = labeled_pts[y + 1][x + 1],
p3 = labeled_pts[y][x + 1],
cell_pts = [p0, p1, p2, p3],
isobands_lt = _isobands_of(cell_pts, lower, upper)
)
if(isobands_lt != [])
each isobands_lt
];
/*
ISOBANDS Impl End ============================
*/
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