Find Optimal 3D Print Orientations

With a broad support for mesh-based geometric regions, printability analysis from structural loads to upright orientation is easy to perform.

Find candidate orientations for placing the model on a flat surface.

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cover = TransformedRegion[ MeshRegion[ Import["http://www.thingiverse.com/download:342676", "STL"], PlotTheme -> "Minimal"], TransformationFunction[{{1., 0.5, 0.03, -0.06}, {-0.05, 0.03, 1.1, 0.1}, {0.53, -1.02, 0.05, 0.19}, {0, 0, 0, 1.}}]]; points = MeshCoordinates[cover]; transform[Polygon[points_]] := Module[{proj = points}, proj[[All, 3]] = 0; Last[FindGeometricTransform[proj, points]]]; highlight[convexHull_, cover_] := Show[HighlightMesh[ convexHull, {Style[1, Brown], Style[2, Opacity[0.3, Brown]]}], cover]; Show[cover, Boxed -> True]

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Each face of the convex hull represents a candidate orientation.

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convexHull = ConvexHullMesh[points]; orientations = MeshPrimitives[convexHull, 2]; highlight[convexHull, cover]

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Use the orthogonal projection of the center of mass to further restrict candidate orientations.

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masscenter = RegionCentroid[cover]; projection[polygon_, p_] := RegionNearest[AffineSpace @@ polygon, p]; candidates = Select[orientations, RegionMember[#, projection[#, masscenter]] &];

A candidate orientation.

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Show[ncover = TransformedRegion[cover, transform[Last[SortBy[candidates, Area]]]], Boxed -> True]

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Print the model.

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Printout3D[ncover, "Shapeways"]

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