How to discretize a surface constructed with multiple components?

Unsuccessful attempts include combining the objects top and hull using the Mathematica commands Graphics3D, Union, and RegionUnion.

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Combine and mesh the surface defined by these two blocks: enter image description here

{length, beam, draft} = {50, 3, 4}
pmin={0, 0, 0};
pmax={length, beam, draft};
hull = Cuboid[pmin, pmax];
{topLength, height} = {30, 3};
pmin = {10, 0, draft};
pmax = pmin + {topLength, beam, height};
top = Cuboid[pmin, pmax];
ohp = RegionUnion[top, hull]

Fails to discretize:

BoundaryDiscretizeRegion[ohp, MaxCellMeasure -> {"Length" -> 5}]
BoundaryDiscretizeRegion: A non-degenerate region is expected at position 1
  • 1
    $\begingroup$ pmin = {10, 0, draft - 10^-9}; make the pmin of the top very slighty stick into the hull and it works. If you want a shaper edge, reduce the MaxCellMeasure to something like 0.25. $\endgroup$
    – flinty
    Jul 15, 2020 at 22:52

2 Answers 2


Here is an option using OpenCascadeLink. OpenCascade is an open source 3D CAD package that often does a better job retaining sharp features with boolean operations and seems to be fairly robust.

{length, beam, draft} = {50, 3, 4};
pmin = {0, 0, 0};
pmax = {length, beam, draft};
hull = Cuboid[pmin, pmax];
{topLength, height} = {30, 3};
pmin = {10, 0, draft};
pmax = pmin + {topLength, beam, height};
top = Cuboid[pmin, pmax];
shape1 = OpenCascadeShape[hull];
shape2 = OpenCascadeShape[top];
union = OpenCascadeShapeUnion[shape1, shape2];
bmesh = OpenCascadeShapeSurfaceMeshToBoundaryMesh[union];
groups = bmesh["BoundaryElementMarkerUnion"];
temp = Most[Range[0, 1, 1/(Length[groups])]];
colors = ColorData["BrightBands"][#] & /@ temp
bmesh["Wireframe"["MeshElementStyle" -> FaceForm /@ colors]]
   ToElementMesh[bmesh, MaxCellMeasure -> {"Length" -> 5}], 1]]]

enter image description here


Here is a slightly different approach also using OpenCascadeLink

bmesh = ToBoundaryMesh[ohp, "BoundaryMeshGenerator" -> "OpenCasdade"]

enter image description here

Note, however, there is a slight difference in the result compared to Tim's answer. In this case the union is created. I.e. no subdivision between the two cuboids. Tim's answer is a more general approach.

  • $\begingroup$ The simplicity of your solution is great. Wish I could split the vote. $\endgroup$
    – dantopa
    Jul 23, 2020 at 5:17
  • $\begingroup$ @dantopa, no worries ;-) $\endgroup$
    – user21
    Jul 23, 2020 at 5:41

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