Jul 6, 2020
Flying through a gyroid, an infinitely connected triply periodic minimal surface.
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Flying through a gyroid, an infinitely connected triply periodic minimal surface.
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example files created using karamba 3d for grasshopper & rhino
I somehow managed to find some time and organize the grasshopper definition. As usual its available at the [Sub]Code page. For this definition to work you could use either loft or the minimal surfa...
a great opportunity for learn some minimal surfaces modelling in GH
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MINIMAL SURFACES Paul Nylander
Costa's Minimal Surface [Wikipedia] Scherk-Collins Surface Enneper Surface [Wikipedia]
Minimal surfaces are surfaces that span an arbitrarily shaped boundary with minimal surface area. For example, surface tension can cause soap films to form minimal surfaces. These surfaces can be very beautiful.
(via Minimal Surfaces Artwork)
Soap film surfaces There are many beautiful and mysterious shapes found in nature. Some very fascinating shapes are formed by nothing more than soap films and they have captured the imagination of artists and mathematicians alike. Molecules in the soap film assume a state where the energy required is minimal. The surface tension in soap films create a surface of minimal energy inside the boundary in which they form. This surface is called a minimal surface. Minimal surfaces are formed inside boundary constraints, like a wire frame. The minimal surfaces are created by the soap films between the frame. A bubble or a sphere is not a minimal surface in this sense even though its shape has minimal surface to volume ratio.. The maths behind minimal surfaces is anything but simple and mathematicians have studied the problem of how such surfaces can be expressed extensively. The area of maths that deals with minimal surfaces is called “calculus of variations”. Minimal surfaces have far reaching implications in geometry and engineering. Stadiums and bridges often use the design . The shape is very efficient and naturally beautiful. These tensile structures can be used to span large areas and still remain strong. You can create minimal surfaces yourself by playing around with wire frame objects (spirals, cubes, tetrahedrons) and a soap solution. You can also make the frames with straws or K'nex. To make the soap solution, just add a generous amount of dishwashing liquid to a bucket of water and add a squirt of glycerin. Don't allow froth to form in the solution. The glycerin keeps the bubbles strong. Dip a frame object into the solution and gently lift it out, the soap will form a minimal surface within the frame. Fathom the Universe "Bubble Art " (by A. van der Net)
Scherk’s Minimal Surface
Scherk’s minimal surface arises from the solution to a differential equation that describes a minimal monge patch (i.e., a patch that maps [u, v] to [u, v, f(u, v)]). The plots above were made by plotting the implicit definition of the surface.
http://www.math.hmc.edu