How am I supposed to get any work done when the maths is so pretty! Look at it flutter by like a butterfly!

This is an animation for "biharmonic spline interpolation" (see also: https://doi.org/10.1007/s11004-011-9346-5).

I'm testing a Julia implementation here which I'd like to use to interpolate the Z-coordinate for meshes that should span a closed curve domain where the x,y, and z are known. Here I created a circle and manipulated the z-coordinates using z=sin(x+a) where a is a phase offset. Next I animated the change of the phase offset to create the wave like motion.

Testing out "Natural Neighbour" interpolation of non-gridded/scattered 3D data. If only there was a fun boundary curve with some sharp features that I could use to test these methods.

https://en.wikipedia.org/wiki/Natural-neighbor_interpolation

See the nice package by Daniel VandenHeuvel: https://github.com/DanielVandH/NaturalNeighbours.jl

A simple parameterised hexahedral mesh of a cylindrical solid.

Coming soon to #Comodo

https://github.com/COMODO-research/Comodo.jl

#opensource #computationalmechanics #geometryprocessing

An animation of a hexahedral mesh for a solid cylinder. The animation shows a cylinder with blue quadrilateral faces on top, yellow ones in the bottom, and red ones on the side. The screen shows 3 sliders. When the first slider is changed the mesh density is increased iteratively (each quad is split into 4 new ones). If the second slider is changed the height of the cylinder is changed and new elements are added to maintain a similar point spacing. If the third slider is changed the radius is changed. When the radius is decreased the point spacing decreases and hence additional elements are also added in the height direction to maintain a homogeneous mesh. This animation therefore shows a full parameterisation of a hexahedral mesh of the cylinder.

Just a bunny rotating according to a uniform set of directions on the sphere. The bunny is colored towards the "overhang" angle with respect to the ground. The black area on the ground is the projection of the bunny onto the ground (a bit like a shadow). This is a simple toy simulation that computes some metrics relevant to the simulation of 3D printing preparation.

Whoopsy

(setting the levelset value too low for a Gyroid shell reconstruction leads to a crummy mess)

A circumcircle is a circle that circumscribes a triangle's corner points. Plotting them for a regular mesh (sphere) looks pretty, for an irregular mesh (rabbit) it looks like it has odd piercings everywhere.

https://en.wikipedia.org/wiki/Circumcircle

Cubic smoothing splines be like.

#Julialang #opensource #GeometryProcessing

Code: https://github.com/COMODO-research/Comodo.jl/blob/main/examples/demo_smoothing_spline.jl

Made possible by: https://github.com/jipolanco/BSplineKit.jl

Meet the n-trapezohedron.

Recipe: put 2*n points around the equator, and 2 more for the poles. Now form n top faces and n bottom faces (all quadrilateral). Now alter the points so that all faces are planar.

High n-values give spiky diamond like things. But the special case with n=3 produces the humble cube!

More here too:
https://en.wikipedia.org/wiki/Trapezohedron

Nice set of equations describing the shapes:
https://mathworld.wolfram.com/Trapezohedron.html

Coming soon to #comodo: constrained #Delaunay triangulations. Which I decided needs parameterized #Batman curves too for testing purposes