0
$\begingroup$

I have a volume enclosing a certain region. The region is non-convex, and I calculate its convex hull with the built-in Mathematica function. I want to know the difference between the region and its convex hull. The inbuilt RegionDifference function throws the following error:

BoundaryMeshRegion::bsuncl: The boundary surface is not closed because the edges Line[{... ,<<2390>>}] only come from a single face.

Any help would be appreciated.

(* some preliminaries *)
fn[x_, y_] = 
 x^2 + y^2 + 
  2/x^2 (-20 x + 0.4 x^2 + y^2)^2 (1/2 + (
     Sqrt[
      2] (Cos[(x^2)^(1/4)/Sqrt[2]] - 
        Cosh[(x^2)^(1/4)/Sqrt[2]]))/((x^2)^(
      1/4) (Sin[(x^2)^(1/4)/Sqrt[2]] + Sinh[(x^2)^(1/4)/Sqrt[2]])))
fnLimit[x_, y_] = Limit[fn[x, y], x -> 0]
fnPiecewise[x_, y_] = 
 Piecewise[{{fn[x, y], x < 0}, {fnLimit[x, y], x == 0}, {fn[x, y], 
    x > 0}}]

(* the region of interest *)
volToPlot = 
  ImplicitRegion[
   fnPiecewise[x, y] - 100 z < 
    00, {{x, -300, 300}, {y, -300, 300}, {z, 0, 800}}];
vol = BoundaryDiscretizeRegion[
  volToPlot, {{-300, 300}, {-300, 300}, {0, 800}}, 
  MaxCellMeasure -> 1000]

(* Convex hull of the region *)
convexHullVol = ConvexHullMesh[vol]

RegionDifference[convexHullVol, vol]
Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ "RegionDifference is throwing an error" - what error? $\endgroup$
    – MarcoB
    Jun 1, 2022 at 12:26
  • $\begingroup$ Thanks, @MarcoB. I edited the question. $\endgroup$
    – akr
    Jun 1, 2022 at 12:28

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.