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support isobands
This commit is contained in:
Justin Lin
@@ -130,3 +130,925 @@ function _marching_squares_isolines(points, sigma) =
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ISOLINES Impl End ============================
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*/
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/*
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ISOBANDS Impl Begin ============================
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*/
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function _isobands_tri_label(pts, lower, upper) =
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[
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for(row = pts)
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[
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for(p = row)
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let(label =
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p[2] < lower ? "0" :
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p[2] >= lower && p[2] < upper ? "1" : "2"
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)
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[p[0], p[1], p[2], label]
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]
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];
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function _isobands_corner_value(cell_pts) =
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str(cell_pts[1][3], cell_pts[2][3], cell_pts[3][3], cell_pts[0][3]);
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// single triangle
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function _case2221_isobands(cell_pts, sigma) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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interpolated_pt(cell_pts[0], cell_pts[3], sigma),
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interpolated_pt(cell_pts[0], cell_pts[1], sigma)
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]
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];
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function _case2212_isobands(cell_pts, sigma) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], sigma),
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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interpolated_pt(cell_pts[2], cell_pts[3], sigma)
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]
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];
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function _case2122_isobands(cell_pts, sigma) = [
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[
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interpolated_pt(cell_pts[1], cell_pts[2], sigma),
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interpolated_pt(cell_pts[2], cell_pts[3], sigma),
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]]
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]
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];
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function _case1222_isobands(cell_pts, sigma) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], sigma),
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interpolated_pt(cell_pts[1], cell_pts[2], sigma),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case0001_isobands(cell_pts, sigma) =
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_case2221_isobands(cell_pts, sigma);
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function _case0010_isobands(cell_pts, sigma) =
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_case2212_isobands(cell_pts, sigma);
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function _case0100_isobands(cell_pts, sigma) =
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_case2122_isobands(cell_pts, sigma);
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function _case1000_isobands(cell_pts, sigma) =
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_case1222_isobands(cell_pts, sigma);
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// single trapezoid
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function _case2220_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], lower),
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case2202_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], upper)
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]
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];
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function _case2022_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], upper),
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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interpolated_pt(cell_pts[0], cell_pts[1], lower)
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]
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];
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function _case0222_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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interpolated_pt(cell_pts[2], cell_pts[3], upper),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], lower)
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]
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];
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function _case0002_isobands(cell_pts, lower, upper) =
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_case2220_isobands(cell_pts, upper, lower);
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function _case0020_isobands(cell_pts, lower, upper) =
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_case2202_isobands(cell_pts, upper, lower);
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function _case0200_isobands(cell_pts, lower, upper) =
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_case2022_isobands(cell_pts, upper, lower);
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function _case2000_isobands(cell_pts, lower, upper) =
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_case0222_isobands(cell_pts, upper, lower);
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// single rectangle
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function _case0011_isobands(cell_pts, sigma) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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interpolated_pt(cell_pts[2], cell_pts[3], sigma),
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interpolated_pt(cell_pts[0], cell_pts[1], sigma)
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]
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];
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function _case0110_isobands(cell_pts, sigma) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], sigma),
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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interpolated_pt(cell_pts[1], cell_pts[2], sigma)
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]
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];
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function _case1100_isobands(cell_pts, sigma) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], sigma),
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interpolated_pt(cell_pts[2], cell_pts[3], sigma),
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case1001_isobands(cell_pts, sigma) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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interpolated_pt(cell_pts[0], cell_pts[3], sigma),
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interpolated_pt(cell_pts[1], cell_pts[2], sigma),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case2211_isobands(cell_pts, sigma) =
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_case0011_isobands(cell_pts, sigma);
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function _case2112_isobands(cell_pts, sigma) =
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_case0110_isobands(cell_pts, sigma);
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function _case1122_isobands(cell_pts, sigma) =
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_case1100_isobands(cell_pts, sigma);
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function _case1221_isobands(cell_pts, sigma) =
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_case1001_isobands(cell_pts, sigma);
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function _case2200_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], upper),
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case2002_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], upper)
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]
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];
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function _case0022_isobands(cell_pts, lower, upper) =
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_case2200_isobands(cell_pts, upper, lower);
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function _case0220_isobands(cell_pts, lower, upper) =
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_case2002_isobands(cell_pts, upper, lower);
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// single hexagon
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function _case0211_isobands(cell_pts, lower, upper) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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interpolated_pt(cell_pts[2], cell_pts[3], upper),
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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interpolated_pt(cell_pts[0], cell_pts[1], lower)
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]
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];
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function _case2110_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], lower),
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case1102_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], upper),
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case1021_isobands(cell_pts, lower, upper) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[2], cell_pts[3], upper),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case2011_isobands(cell_pts, lower, upper) =
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_case0211_isobands(cell_pts, upper, lower);
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function _case0112_isobands(cell_pts, lower, upper) =
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_case2110_isobands(cell_pts, upper, lower);
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function _case1120_isobands(cell_pts, lower, upper) =
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_case1102_isobands(cell_pts, upper, lower);
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function _case1201_isobands(cell_pts, lower, upper) =
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_case1021_isobands(cell_pts, upper, lower);
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function _case2101_isobands(cell_pts, lower, upper) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case0121_isobands(cell_pts, lower, upper) =
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_case2101_isobands(cell_pts, upper, lower);
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function _case1012_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case1210_isobands(cell_pts, lower, upper) =
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_case1012_isobands(cell_pts, upper, lower);
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// single pentagon
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function _case1211_isobands(cell_pts, sigma) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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interpolated_pt(cell_pts[2], cell_pts[3], sigma),
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interpolated_pt(cell_pts[1], cell_pts[2], sigma),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case2111_isobands(cell_pts, sigma) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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interpolated_pt(cell_pts[1], cell_pts[2], sigma),
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interpolated_pt(cell_pts[0], cell_pts[1], sigma)
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]
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];
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function _case1112_isobands(cell_pts, sigma) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], sigma),
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
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interpolated_pt(cell_pts[0], cell_pts[1], sigma)
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]
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];
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function _case1121_isobands(cell_pts, sigma) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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interpolated_pt(cell_pts[0], cell_pts[3], sigma),
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interpolated_pt(cell_pts[2], cell_pts[3], sigma),
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case1011_isobands(cell_pts, sigma) =
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_case1211_isobands(cell_pts, sigma);
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function _case0111_isobands(cell_pts, sigma) =
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_case2111_isobands(cell_pts, sigma);
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function _case1110_isobands(cell_pts, sigma) =
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_case1112_isobands(cell_pts, sigma);
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function _case1101_isobands(cell_pts, sigma) =
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_case1121_isobands(cell_pts, sigma);
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function _case1200_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[2], cell_pts[3], upper),
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
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]
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];
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function _case0120_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[2], cell_pts[3], upper),
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[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
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interpolated_pt(cell_pts[1], cell_pts[2], lower)
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]
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];
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function _case0012_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
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interpolated_pt(cell_pts[2], cell_pts[3], lower),
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interpolated_pt(cell_pts[0], cell_pts[1], lower),
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case2001_isobands(cell_pts, lower, upper) = [
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[
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[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], upper),
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case1022_isobands(cell_pts, lower, upper) =
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_case1200_isobands(cell_pts, upper, lower);
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function _case2102_isobands(cell_pts, lower, upper) =
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_case0120_isobands(cell_pts, upper, lower);
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function _case2210_isobands(cell_pts, lower, upper) =
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_case0012_isobands(cell_pts, upper, lower);
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function _case0221_isobands(cell_pts, lower, upper) =
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_case2001_isobands(cell_pts, upper, lower);
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function _case1002_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[3], upper),
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interpolated_pt(cell_pts[0], cell_pts[3], lower),
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interpolated_pt(cell_pts[1], cell_pts[2], lower),
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[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
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interpolated_pt(cell_pts[0], cell_pts[1], upper)
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]
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];
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function _case2100_isobands(cell_pts, lower, upper) = [
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[
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interpolated_pt(cell_pts[0], cell_pts[1], lower),
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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(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < lower ? [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], 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)
|
||||
],
|
||||
[
|
||||
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), interpolated_pt(cell_pts[2], cell_pts[3], lower)
|
||||
]
|
||||
] :
|
||||
mdpz >= lower && mdpz < 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[2], cell_pts[3], upper),
|
||||
interpolated_pt(cell_pts[2], 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)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
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)
|
||||
],
|
||||
[
|
||||
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 _case0202_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < lower ? [
|
||||
[
|
||||
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[0], cell_pts[1], lower)
|
||||
],
|
||||
[
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], 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)
|
||||
]
|
||||
] :
|
||||
mdpz >= lower && mdpz < 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),
|
||||
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)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
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)
|
||||
],
|
||||
[
|
||||
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 _case0101_isobands(cell_pts, sigma) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < sigma ? [
|
||||
[
|
||||
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma)
|
||||
],
|
||||
[
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma),
|
||||
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma),
|
||||
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma)
|
||||
]
|
||||
];
|
||||
|
||||
function _case1010_isobands(cell_pts, sigma) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < sigma ? [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma),
|
||||
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
|
||||
],
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma),
|
||||
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma)
|
||||
]
|
||||
];
|
||||
|
||||
function _case2121_isobands(cell_pts, sigma) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < sigma ? [
|
||||
[
|
||||
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma),
|
||||
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
[cell_pts[0][0], cell_pts[0][1], cell_pts[0][2]],
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma)
|
||||
],
|
||||
[
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma),
|
||||
[cell_pts[2][0], cell_pts[2][1], cell_pts[2][2]],
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma)
|
||||
]
|
||||
];
|
||||
|
||||
function _case1212_isobands(cell_pts, sigma) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < sigma ? [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma),
|
||||
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]],
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], sigma),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], sigma),
|
||||
[cell_pts[1][0], cell_pts[1][1], cell_pts[1][2]]
|
||||
],
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], sigma),
|
||||
[cell_pts[3][0], cell_pts[3][1], cell_pts[3][2]],
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], sigma)
|
||||
]
|
||||
];
|
||||
|
||||
function _case2120_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < 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], upper),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], 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), interpolated_pt(cell_pts[0], cell_pts[1], 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)
|
||||
]
|
||||
];
|
||||
|
||||
function _case0102_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < lower ? [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], upper),
|
||||
interpolated_pt(cell_pts[0], cell_pts[3], lower),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], lower), interpolated_pt(cell_pts[0], cell_pts[1], upper)
|
||||
],
|
||||
[
|
||||
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[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]],
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], lower),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], lower),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], upper)
|
||||
]
|
||||
];
|
||||
|
||||
function _case2021_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < 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),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], 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], 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[1], cell_pts[2], lower),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], upper)
|
||||
]
|
||||
];
|
||||
|
||||
function _case0201_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < 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], 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),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], 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[2], cell_pts[3], lower),
|
||||
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 _case1202_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < 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),
|
||||
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], cell_pts[1], 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[2], cell_pts[3], lower),
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], upper)
|
||||
]
|
||||
];
|
||||
|
||||
function _case1020_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < lower ? [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], 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[2], cell_pts[3], upper),
|
||||
interpolated_pt(cell_pts[2], cell_pts[3], lower)
|
||||
]
|
||||
] : [
|
||||
[
|
||||
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),
|
||||
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], lower)
|
||||
]
|
||||
];
|
||||
|
||||
function _case0212_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < 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[1], cell_pts[2], upper),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], lower),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], lower),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], 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)
|
||||
],
|
||||
[
|
||||
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)
|
||||
]
|
||||
];
|
||||
|
||||
function _case2010_isobands(cell_pts, lower, upper) =
|
||||
let(mdpz = (cell_pts[0][2] + cell_pts[1][2] + cell_pts[2][2] + cell_pts[3][2]) / 4)
|
||||
mdpz < lower ? [
|
||||
[
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], 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)
|
||||
],
|
||||
[
|
||||
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[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[1], cell_pts[2], lower),
|
||||
interpolated_pt(cell_pts[1], cell_pts[2], upper),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], upper),
|
||||
interpolated_pt(cell_pts[0], cell_pts[1], lower)
|
||||
]
|
||||
];
|
||||
|
||||
function _isobands_of(cell_pts, lower, upper) =
|
||||
let(cv = _isobands_corner_value(cell_pts))
|
||||
// no contour
|
||||
cv == "0000" ? [] :
|
||||
// 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) :
|
||||
cv == "1010" ? _case1010_isobands(cell_pts, lower) :
|
||||
cv == "2121" ? _case2121_isobands(cell_pts, upper) :
|
||||
cv == "1212" ? _case1212_isobands(cell_pts, 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) :
|
||||
cv == "2010" ? _case2010_isobands(cell_pts, lower, upper) :
|
||||
// no contour
|
||||
[]; // 2222
|
||||
|
||||
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 ============================
|
||||
*/
|
||||
@@ -1,3 +1,6 @@
|
||||
use <experimental/_impl/_marching_squares_impl.scad>;
|
||||
|
||||
function marching_squares(points, sigma) = _marching_squares_isolines(points, sigma);
|
||||
function marching_squares(points, threshold) =
|
||||
is_undef(threshold[1]) ?
|
||||
_marching_squares_isolines(points, threshold) :
|
||||
_marching_squares_isobands(points, threshold[0], threshold[1]);
|
||||
Reference in New Issue
Block a user