This is a continuation to the posts listed at: https://community.wolfram.com/web/ggoff/
Abstract
Abstract
Example 1 used the Wolfram Language to create/export/import a slice of a sphere/crown-like object. The slices were rotated around the z-axis in two animations. In Example 2 two grids of superellipsoids were used as basis for animated lamps and other objects.
Experiments
Experiments
Example 1: Metamorph
Example 1: Metamorph
Initialization
Initialization
In[]:=
path0=SetDirectory[NotebookDirectory[]<>"/data/"]
Out[]=
/Users/gg/Desktop/ams12pub/data
From slice to animation
From slice to animation
A vertical slice of a sphere was prepared and exported:
In[]:=
slice=ParametricPlot3D[{Sin[u]Sin[v],Cos[u]Sin[v],Cos[v]},{u,0,Pi/8},{v,-π,0},Boxed->False,Axes->False,PlotRange->{{-1,1},{-1,1},{-1,1}}]
Out[]=
In[]:=
Export[path0<>If[StringTake[$System,3]=="Win","\\","/"]<>"slice.dxf",slice]
Out[]=
/Users/gg/Desktop/ams12pub/data/slice.dxf
The slice was rotated around the z-axis with step-size Pi/8. resulting in a sliced sphere.
In[]:=
slices=Table[Graphics3D[GeometricTransformation[slice[[1]],RotationTransform[iPi/8,{0,0,1}]],Boxed->False,Axes->False,PlotRange->{{-1,1},{-1,1},{-1,1}}],{i,1,16}];Show[slices]
Out[]=
To the first slice another one was added until the sphere was closed.
In[]:=
slices2=Table[Show[slices[[1;;i]],PlotRange->{{-1,1},{-1,1},{-1,1}}],{i,1,Length[slices]}];ListAnimate[slices2]
Out[]=
From imported slice to animation
From imported slice to animation
In Blender the sphere slices were bended along the x-axis. One slice of the resulting object was exported as a stl-file.
In[]:=
slice3=Import[path0<>If[StringTake[$System,3]=="Win","\\","/"]<>"slice2.stl"];Show[slice3,Boxed->True]
Out[]=
Again a bunch of rotated slices was built together. The visualization showed a crown-like object.
In[]:=
slices4=Table[Graphics3D[GeometricTransformation[slice3,RotationTransform[iPi/8,{0,0,1}]],Boxed->False,Axes->False,PlotRange->2{{-1,1},{-1,1},{-1,1}}],{i,1,16}];Show[slices4]
Out[]=
In the next step the development of the “crown” was animated.
An Wolfram Language implementation of bending a cupola
An Wolfram Language implementation of bending a cupola
In an architectural Wolfram Demonstration (by myself, name of project listed below) a pavilion was built and bent with NURBS. The code was adapted to mimic the result from bending in Blender:
With/without control points:
Via ListAnimate the bending was animated :
Blender
Blender
Part 1:
A sliced sphere was imported in Blender and given a scratched gold-like material. In an animation a half sphere was rotated to open the sliced sphere, then moved outside of the camera-view. At the center a small only slightly transparent glass sphere was positioned.
Part 2-4:
Within the small-glass sphere a light-source was placed. Both delivered a soft colored light for the inside of the sliced-half-sphere. In an animation the half-sphere was bent along the x-axis. It formed a half-hyperboloid with teeth. Then the modified hyperboloid was completed in a further animation.
Part 5:
The color of the centered light-source was changed. From above a torus with emissive material was sent through the modified hyperboloid in a last animation.
A sliced sphere was imported in Blender and given a scratched gold-like material. In an animation a half sphere was rotated to open the sliced sphere, then moved outside of the camera-view. At the center a small only slightly transparent glass sphere was positioned.
Part 2-4:
Within the small-glass sphere a light-source was placed. Both delivered a soft colored light for the inside of the sliced-half-sphere. In an animation the half-sphere was bent along the x-axis. It formed a half-hyperboloid with teeth. Then the modified hyperboloid was completed in a further animation.
Part 5:
The color of the centered light-source was changed. From above a torus with emissive material was sent through the modified hyperboloid in a last animation.
Example 2: Interieur
Example 2: Interieur
Initialization
Initialization
Grid of Superellipsoids
Grid of Superellipsoids
A table of superellipsoids was built, then shown in a grid. The parameters for a subset of six objects were chosen and a second grid created and all six of them exported as dxf-files.
The exported dxf-files were imported in Blender.
Partial recreation of the animations done in Blender
Partial recreation of the animations done in Blender
The first lamp showed upwards. A fitting superellisoid was chosen, solidified and given a glass-like material. It’s rotating around the x-axis from up to down was animated. Below this animation is was partially rebuilt in Mathematica:
In the next phase the first lamp was slowly made transparent. Parallel a second lamp was changed to solid and given an abstract multicolored material. A version of it was rebuilt in Mathematica:
A third object with abstract material was placed upwards above the second and connected with a cylinder with the second object positioned downwards. The third object is moved down along the cylinder to a position just above the second object. Again a Wolfram Language version of this animation was developed.
References
References
Collection of animations
Collection of animations
References
Metamorph
Scene: Modified Spheres, Hyperbola & Torus
“Wolfram Language & System Documentation Center,” April 16, 2022. https://reference.wolfram.com/language/.
Audio:
Stock Music & Sound Effects - Royalty Free Audio - Storyblocks
https://storyblocks.com/audio (accessed 2022-04-16)
Media-Music Group. Bells And Strings for Tutorials Explainer 30 Sec. Accessed April 16, 2022. Asset ID: SBA-346556536.
Scene: Modified Spheres, Hyperbola & Torus
“Wolfram Language & System Documentation Center,” April 16, 2022. https://reference.wolfram.com/language/.
Audio:
Stock Music & Sound Effects - Royalty Free Audio - Storyblocks
https://storyblocks.com/audio (accessed 2022-04-16)
Media-Music Group. Bells And Strings for Tutorials Explainer 30 Sec. Accessed April 16, 2022. Asset ID: SBA-346556536.
Interieur
Scene : Modified Superellipsoid & Cylinder
superellipse - Wolfram | Alpha
https://wolframalpha.com (accessed 2022 - 05 - 01) .
“POV-Ray: Documentation: 2.4.1.11 Superquadric Ellipsoid.” Accessed May 1, 2022. http://www.povray.org/documentation/view/3.6.1/285/.
Audio : Stock Music & Sound Effects - Royalty Free Audio - Storyblocks.
https://storyblocks.com/audio (accessed 2022 - 05 - 01)
Gribanova, Valentina . Atmospheric Phenomenon . Accessed May 1, 2022. SBA - 300418824
Scene : Modified Superellipsoid & Cylinder
superellipse - Wolfram | Alpha
https://wolframalpha.com (accessed 2022 - 05 - 01) .
“POV-Ray: Documentation: 2.4.1.11 Superquadric Ellipsoid.” Accessed May 1, 2022. http://www.povray.org/documentation/view/3.6.1/285/.
Audio : Stock Music & Sound Effects - Royalty Free Audio - Storyblocks.
https://storyblocks.com/audio (accessed 2022 - 05 - 01)
Gribanova, Valentina . Atmospheric Phenomenon . Accessed May 1, 2022. SBA - 300418824