This is a continuation to the posts listed at: https://community.wolfram.com/web/ggoff/
Abstract
Abstract
One aspect of Mathematica is the possibility to experiment. In Example 1 the sphere in parametric form was modified by swapping the parameters of the third coordinate. In Example 2 a torse of an ellipsoid was used in parametric form. The parameters were adapted resulting in a cross-like structure.
Blender was utilized to create animations starting with the structures from both examples.
Blender was utilized to create animations starting with the structures from both examples.
Experiments
Experiments
Example 1: Swapped
Example 1: Swapped
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A sphere in parametric form :
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ParametricPlot3D[{aCos[u]Sin[v],aSin[u]Sin[v],aCos[v]}/.{a->2Pi},{u,0,2Pi},{v,-Pi,Pi}]
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Swap the parameters in the third coordinate of the parametric form :
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ParametricPlot3D[{aCos[u]Sin[v],aSin[u]Sin[v],aCos[u]}/.{a->2Pi},{u,0,2Pi},{v,-Pi,Pi}]
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To enrich the surface add v to the third coordinate of the parametric form :
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ParametricPlot3D[{aCos[u]Sin[v],aSin[u]Sin[v],aCos[u]+v}/.{a->2Pi},{u,0,2Pi},{v,-Pi,Pi}]
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Swap the parameters in the third coordinate of the parametric form again:
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ParametricPlot3D[{aCos[u]Sin[v],aSin[u]Sin[v],aCos[v]+u}/.{a->Pi/2},{u,0,2Pi},{v,-Pi,Pi}]
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The result is a corcscrew surface.
For Example 1 create a bunch of curves:
For Example 1 create a bunch of curves:
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term1={aCos[u]Sin[v],aSin[u]Sin[v],aCos[u]+v}/.{a->2Pi};terms=Table[term1/.{v->v1},{v1,-Pi,Pi,Pi/16}];gr1=(ParametricPlot3D[#,{u,0,2Pi}])&@terms;term2={aCos[u]Sin[v],aSin[u]Sin[v],aCos[u]+v}/.{a->Pi,u->0};gr2=ParametricPlot3D[term2,{v,-Pi,Pi}];gr3=Show[{gr1,gr2},PlotRange->All,Boxed->False,Axes->False]
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Export curves and surface as dxf - files :
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SetDirectory[NotebookDirectory[]]
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/Users/gg/Desktop/ship
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Export["curves.dxf",gr3]
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curves.dxf
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term4={aCos[u]Sin[v],aSin[u]Sin[v],aCos[u]+v}/.{a->2Pi};gr4=ParametricPlot3D[term4,{u,0,2Pi},{v,-Pi,Pi},Boxed->False,Axes->False]
In Blender the curves and the surface were imported with the released dfx-addon. The curves were beveled round, given a material and animated through rotation. The surface with a second material was animated from transparent to opaque and included in the rotation.
Example 2: Ship
Example 2: Ship
In animation Ship a torse of an ellipsoid was used as basis. Adapting the values for the parameters delivered following structure:
Both surfaces were exported from Mathematica as dxf-files and imported in Blender.
In Ship animation - part 1 the first cross-like surface was zoomed in/out. The material applied simulates the settings in Mathematica. Part 2 animates the cutting to the second form. It is done by using a boolean modifier. Part 3 closes the top/bottom gap and switches the materials in a gradual animation. Part 4 shows a structure with a camouflage surface, refined with the subsurface-modifier.
In Ship animation - part 1 the first cross-like surface was zoomed in/out. The material applied simulates the settings in Mathematica. Part 2 animates the cutting to the second form. It is done by using a boolean modifier. Part 3 closes the top/bottom gap and switches the materials in a gradual animation. Part 4 shows a structure with a camouflage surface, refined with the subsurface-modifier.
References
References
List of animations
List of animations
Ship (B1, A1)
Swapped (W1, W2, A2))
Swapped (W1, W2, A2))
References
References
Web:
(1) Wolfram Language & System Documentation Center https://reference.wolfram.com/language/ (accessed 2021-07-13).
(2) Corcscrew Surface - Wolfram|Alpha https://www.wolframalpha.com (accessed 2021-07-13).
(1) Wolfram Language & System Documentation Center https://reference.wolfram.com/language/ (accessed 2021-07-13).
(2) Corcscrew Surface - Wolfram|Alpha https://www.wolframalpha.com (accessed 2021-07-13).
Book
(1) Krivoshapko, S.; Ivanov, V. N. Encyclopedia of Analytical Surfaces; Springer International Publishing, 2015. https://doi.org/10.1007/978-3-319-11773-7.
(1) Krivoshapko, S.; Ivanov, V. N. Encyclopedia of Analytical Surfaces; Springer International Publishing, 2015. https://doi.org/10.1007/978-3-319-11773-7.
Audio
Stock Music & Sound Effects - Royalty Free Audio - Storyblocks https://storyblocks.com/audio
(1) -. Lepine, S. Good Chilling Vibe (30 Seconds Intro).
(2) -. Smith, P. Modern Trans 2.
Stock Music & Sound Effects - Royalty Free Audio - Storyblocks https://storyblocks.com/audio
(1) -. Lepine, S. Good Chilling Vibe (30 Seconds Intro).
(2) -. Smith, P. Modern Trans 2.