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生体構造を彫像に変換する

ヒトの生体構造の高解像度の3Dモデルが使用できるようになったため，バージョン11の強力なグラフィックスと領域処理の機能を使って，プログラム的に人体をモデルにしたモダンな彫像を構築することが可能である．

以下は，Antony Gormleyの作品である(http://www.antonygormley.com/sculpture/chronology)．

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WikipediaData["Antony Gormley", "ImageList"] // Select[#, Length[Union[#]]/Length[#] &[ImageData[#][[1, 1]]] > 0.8 &] &

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人体の忠実な表現をロードする．

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human = AnatomyData[Entity["AnatomicalStructure", "Skin"], "MeshRegion"]

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領域の関数を使うと，多様な彫像を簡単に作成することができる．

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pts = MeshCoordinates[human]; nf = Nearest[pts]; color := Directive[GrayLevel[RandomReal[{0.5, 0.7}]], Specularity[RandomColor[], RandomInteger[{10, 20}]]]

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With[{dode = N[PolyhedronData["Dodecahedron"][[1]]]}, ballToDodecahedron[Ball[p_, r_]] := Translate[ Scale[Rotate[dode, RandomReal[{-Pi, Pi}], RandomReal[{-1, 1}, 3], {0, 0, 0}], r], p]]

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GraphicsGrid[ Partition[#, 4] &@{Graphics3D[{EdgeForm[], color, Table[BoundingRegion[ nf[RandomChoice[pts], RandomInteger[{100, 1000}]], "MinCuboid"], {200}]}], Graphics3D[{EdgeForm[], color, Table[BoundingRegion[ nf[RandomChoice[pts], RandomInteger[{100, 1000}]], "FastOrientedCuboid"], {250}]}], Graphics3D[{color, EdgeForm[], Table[Show[ BoundingRegion[ RandomChoice[ nf[RandomChoice[pts], RandomInteger[{100, 2000}]], RandomInteger[{4, 12}]], "MinConvexPolyhedron"]][[ 1]] /. _Directive :> {}, {600}]}], Graphics3D[{color, EdgeForm[], Table[ballToDodecahedron@ BoundingRegion[ RandomChoice[nf[RandomChoice[pts], RandomInteger[{100, 600}]], RandomInteger[{4, 12}]], "FastBall"], {300}]}], Graphics3D[{color, Table[BoundingRegion[ RandomChoice[ nf[RandomChoice[pts], RandomInteger[{100, 600}]], RandomInteger[{4, 12}]], "FastBall"], {500}]}], Graphics3D[{color, Table[ BoundingRegion[ RandomChoice[nf[RandomChoice[pts], RandomInteger[{100, 2000}]], RandomInteger[{4, 12}]], "FastEllipsoid"], {350}]}], Graphics3D[{color, EdgeForm[], Table[Cylinder[{#, nf[#, RandomInteger[{2000, 5000}]][[-1]]} &[ RandomChoice[pts]], RandomReal[{5, 25}]], {600}]}], Module[{pts2 = RandomSample[pts, 6000], nf2}, nf2 = Nearest[pts]; Graphics3D[{color, EdgeForm[], CapForm["Round"], Cylinder[{#, nf2[#, 100][[-1]]}, 6] & /@ RandomSample[pts2]}]]}, Spacings -> {-150, Automatic}, ImageSize -> Full ] // Rasterize[#, "Image", ImageSize -> {400, 400}] &

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より古典的な外観の作品を生成することもできる．回転，および脚と腕の部分を引き伸ばす変換を適用して天使のような彫像を作成する．

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nonlinearTransform3D[expr_, g_] := Module[{gD, inv, newNormal, newVertices, newNormals}, gD[x_, y_, z_] = Compile[{x, y, z}, Evaluate[D[g[{x, y, z}], {{x, y, z}}]]]; inv[m_] := With[{im = Inverse[m]}, If[Head[im] === Inverse, m, PseudoInverse[m]]]; newNormal[{vertex_, normal_}] := Quiet[With[{m = inv[Transpose[gD[vertex]]]}, If[Sign[Det[m]] == -1, -1, 1] m.normal]]; expr /. {GraphicsComplex[vertices_, body_, a___, VertexNormals -> normals_, b___] :> (newVertices = g /@ vertices; newNormals = newNormal /@ Transpose[{vertices, normals}]; GraphicsComplex[newVertices, body, a, VertexNormals -> newNormals, b])}]

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doubleTwist[{x_, y_, z_}] := With[{h = 1000, w = 180, H = 1300, \[Xi] = 600, \[Kappa] = 150}, With[{\[CurlyPhi] = 6 Pi If[z > h || (z > \[Xi] && Sqrt[x^2] > w), 0, Cos[Pi/2 (h - z)/h]], \[CurlyTheta] = -1.6 Pi If[(z > \[Xi] && Sqrt[x^2] < w) || z < \[Xi], 0, Cos[Pi/2 (w - x)/w]], f = Piecewise[{{1, z > h}, {1 + (h - z)/h, z < h}}], g = If[(z > \[Xi] && Sqrt[x^2] < w) || z < \[Xi], 1, 1 + (Sqrt[x^2] - w)/\[Kappa]]}, {{g, 0, 0}, {0, Cos[\[CurlyTheta]], Sin[\[CurlyTheta]]}, {0, -Sin[\[CurlyTheta]], Cos[\[CurlyTheta]]}}.({{f Cos[\[CurlyPhi]], f Sin[\[CurlyPhi]], 0}, {-f Sin[\[CurlyPhi]], f Cos[\[CurlyPhi]], 0}, {0, 0, 1}}.{x, y, z} - {0, 0, H}) + {0, 0, H}]]

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smoothHuman = Entity["AnatomicalStructure", "Skin"]["Graphics3D"];

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Show[nonlinearTransform3D[smoothHuman, doubleTwist], ViewPoint -> {-1, -2, 0}, Method -> {"ShrinkWrap" -> True}]

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