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2

a = 1; c = 1; b = -1; d = 1; p = 1; q = -1; f1 = (Exp[-2 r a] p)/(2 r c) + (Exp[-2 r b] p)/(2 r d); f2 = (Exp[-2 r a] q)/(2 r c) + (Exp[-2 r b] q)/(2 r d); a = 1; c = 1; b = -1; d = 1; p = 1; q = -1; f1 = (Exp[-2 r a] p)/(2 r c) + (Exp[-2 r b] p)/(2 r d); f2 = (Exp[-2 r a] q)/(2 r c) + (Exp[-2 r b] q)/(2 r d); Plot[{f1, f2}, {r, -2, 2}, PlotRange -> ...

3

Clear["Global`*"] a = 1; c = 1; b = -1; d = 1; p = 1; q = -1; f1 = (Exp[-2 r a] p)/(2 r c) + (Exp[-2 r b] p)/(2 r d); f2 = (Exp[-2 r a] q)/(2 r c) + (Exp[-2 r b] q)/(2 r d); Plot[Evaluate@Outer[ Tooltip@ConditionalExpression[#2, #1] &, {r > 0, r < 0}, {f1, f2}], {r, -2, 2}, PlotLegends -> {"f1;\[ThinSpace]r\[ThinSpace]&...

5

Here are some modifications to ParametricPlot: Method -> {"BoundaryOffset" -> False} Mesh -> None PlotPoints -> {40, 20} MaxRecursion -> 1 PlotRange -> All The first one is important, since it allows the pairs of boundaries, u == 0, u == 1 and v == 0, v == 1, to match up. The Mesh option is important because it ...

3

The Indexed approach produces: reg = ParametricRegion[ { Indexed[surfacefunc[θ, φ], 1], Indexed[surfacefunc[θ, φ], 2], Indexed[surfacefunc[θ, φ], 3] }, {{θ, 0, 1}, {φ, 0, 1}} ]; mesh = DiscretizeRegion[reg, PerformanceGoal->"Quality"]; FindMeshDefects[mesh]

4

surfacefunc = BSplineFunction[data, SplineClosed -> {True, True}, SplineDegree -> 3]; reg = ParametricPlot3D[surfacefunc[u, v], {u, 0, 1}, {v, 0, 1}, Boxed -> False, Axes -> False]; DiscretizeGraphics[reg]

0

The change of the variables does the job. RegionPlot[({y > 8*(10^-10) (x)^(1/2)*HeavisideTheta[(x)^(-1) - (y)] && x > 6*(10^4) && x < 6*(10^10) && y < (8*(10^-10))^-1 x^(-5/2)*HeavisideTheta[-(x)^(-1) + (y)] && y > 0.6*x^(-3/2)}) /. {x -> Exp[s], y -> Exp[t]}, {s, Log[10^2], Log[10^6]}, {t, Log[10^-6]...

6

You need to give ParametricRegion a list as a first argument. Also, BoundaryDiscretizeRegion is a better choice for visualization of a numerical function: Clear[f] f[r_?NumericQ, th_] := {r Cos[th], r Sin[th]} BoundaryDiscretizeRegion @ ParametricRegion[ {Indexed[f[r, th], 1], Indexed[f[r, th], 2]}, {{th, 0, 2 Pi}, {r, 0, 1}} ]

5

Here we use BoundaryMeshRegion {p0, p1, p2,p3} = {{0, 0, 0}, {Sqrt/2, 1/2, 0}, {Sqrt/2, -(1/2), 0}, {0, 0, -3/2}}; polyhedron = Polyhedron[{{p1, p2, p3}, {p1, p2, p0}, {p1, p0, p3}, {p2, p3, p0}}]; newpolyhedron = BoundaryMeshRegion[polyhedron]; RegionMember[newpolyhedron, {0.1, 0, -0.1}] Graphics3D[{Red, Point[{0.1, 0, -0.1}], Cyan, Opacity[0.1], ...

4

Updated answer to include a single STL file The STL format supports a named solid structure that will allow multiple STL solids to be included in a single file. This will allow us to mesh each disjoint solid separately under a unique name and combine the solids into a single STL file. Note that the STL format is simply a collection of triangles and will not ...

2

Another possibility is to use TransformedRegion with RegionProduct. Here is a function that does this: Options[MinkowskiSum] = Options[BoundaryDiscretizeRegion]; MinkowskiSum[r1_, r2_, opts:OptionsPattern[]] := Module[{d1,d2,func,bounds}, d1=RegionEmbeddingDimension[r1]; d2=RegionEmbeddingDimension[r2]; ( func=Evaluate[Array[Slot, d1] + ...

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