Geodesic Spherical Lithophane

prusaprinters

<p>This is a python script to map a grayscale image as a height map onto the inside or outside of a hollow sphere. The result is a spherical lithophane.</p> <p>It is an updated version of <a href="https://www.thingiverse.com/thing:2770219">my previous Thing</a>.</p> <p>The first photo shows the progress of geodesic_g27_inside_200_drilled.stl after 6h of printing on my Wanhao i3.</p> <h3>Print Settings</h3> <p><strong>Printer:</strong></p> <p>Wanhao i3 v2</p> <p><strong>Rafts:</strong></p> <p>No</p> <p><strong>Supports:</strong></p> <p>Yes</p> <p><strong>Resolution:</strong></p> <p>0.2</p> <p><strong>Infill:</strong></p> <p>100%</p> <h3>How I Designed This</h3> <p><strong>New approach</strong></p> <p>In <a href="https://www.thingiverse.com/thing:2770219">my previous Thing</a>, I based the sphere on spherical coordinates using a rectangular mesh of latitude and longitude angles. The disadvantage of that approach is the unnecessarily dense mesh it generates at the poles of the globe.</p> <p>Not only does this result in a lot of vertices and faces which need to be handled by the slicer, even the script generating the mesh could easily run for hours in order to get a decent equatorial resolution.</p> <p>In order to circumvent this problem I remembered an object class in the virtual 3D world ov the <a href="http://www.povray.org/">raytracer POV-Ray</a> which I played around with almost 20 years ago: <a href="https://www.sciencetronics.com/geocities/povray/geodesic.html">the geodesic sphere</a>.</p> <p><strong>Meet the Geodesic Sphere</strong></p> <p>A spherical object can be created if you start with a regular <a href="https://en.wikipedia.org/wiki/Icosahedron">icosahedron</a>. As one of the five Platonic solids it consists of 20 equilateral triangles.</p> <p>By subsequent subdivision of each of the faces into smaller triangles you will get smoother and smoother approximations to a sphere. Geodesics are widely used in architecture to construct round dome shapes - often from glass panes and metal struts.</p> <p><strong>Original idea</strong></p> <p>A couple of weeks ago I saw the YouTube video where<em>RCLifeOn</em> presented his <a href="https://youtu.be/YjkP1BcwLNI">spherical lithophane globe</a>. He used Autodesk 3ds Max to design the object, where he placed the height map on the outside of the globe, but I immediately wondered how it would look like when the height map was hidden inside the globe.</p> <p>RCLifeOn has also posted his globe here on <a href="https://www.thingiverse.com/thing:2761284">Thingiverse</a>.</p> <p><strong>Free and open source?</strong></p> <p>Not having access to this piece of software I researched if I could get a similar result using free tools. My favorite OpenSCAD does not (yet?) support mapping of bitmap files onto non-flat surfaces, so I had to look further.</p> <p>I quickly found an example on how to create an .stl file in python and started to experiment. My first output was a simple cube, before I put all pieces together:</p> <ul> <li>scaling an image</li> <li>creating a sphere</li> <li>creating a second sphere</li> <li>putting the two spheres into each other</li> <li>modifying the thickness of the wall by means of the map</li> </ul> <p><strong>Implementation</strong></p> <p>The map I use is the free <a href="https://asterweb.jpl.nasa.gov/gdem.asp">height map image of the world</a> by NASA. I now added the map itself and a modified version with a gamma setting of 2.7 which might give a better contrast between the oceans and continents.</p> <p>In the Python script itself you can modify a couple of things</p> <ul> <li>the outer diameter of the sphere</li> <li>the number of subdivisions of the geodesic object, starting at 10 pixels around the equator for a frequency of 1, this number can be increased e.g. to about 2000 pixels around the equator for a frequency of 200</li> <li>the thickness of the wall for the black portions of the mapped image</li> <li>the depth of the carving from the outside in</li> <li>the depth of the carving from the inside out</li> <li>the filename of the image to be carved out of the wall of the sphere</li> </ul> <p><strong>The files</strong></p> <p>the included files are:</p> <p>// the main script geodesic_mapped_double.py</p> <p>// a 120 mm sphere with the world on the inside at freq=200 // wall thickness 3 mm, carving depth 2.2 mm geodesic_g27_inside_200.stl</p> <p>// - the same sphere with a 15 mm diameter hole at the south pole geodesic_g27_inside_200_drilled.stl</p> <p>// a 120 mm sphere with the world on the outside at freq=200 // wall thickness 3 mm, carving depth 2.2 mm geodesic_g27_outside_200.stl</p> <p>// - the same sphere with a 15 mm diameter hole at the south pole geodesic_g27_outside_200_drilled.stl</p> <p>// checkerboard patterned sphere - carved from the outside, freq=100 geodesic_test_outside_100.stl // checkerboard patterned sphere - carved from the outside, freq=100 geodesic_test_inside_100.stl // checkerboard patterned sphere - carved from the outside, freq=100 geodesic_test_inoutside_100.stl</p> <p>// the same three spheres cut open geodesic_test_outside_100_cut.stl geodesic_test_inside_100_cut.stl geodesic_test_inoutside_100_cut.stl</p> <p>geodesic_demo_1.stl // just a geodesic object, freq=1 geodesic_demo_2.stl // freq=2 geodesic_demo_4.stl // freq=3 geodesic_demo_3.stl // freq=4 geodesic_demo_5.stl // freq=5 geodesic_demo_6.stl // freq=6</p> Category: Sculptures