Tag Archives: S-curve

Blender – complexity inside spherical and concave cylindrical mirrors – V – a video of S-curve reflections

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After some months without much Blender activities I now have some days to continue with the experiments in this series.

Blender – complexity inside spherical and concave cylindrical mirrors – I – some impressions
Blender – complexity inside spherical and concave cylindrical mirrors – II – a step towards the S-curve
Blender – complexity inside spherical and concave cylindrical mirrors – III – a second step towards the S-curve
Blender – complexity inside spherical and concave cylindrical mirrors – IV – reflective images of a Blender variant of Mr Kapoor’s S-curve

To get a fresh start I thought it might be funny to get a more dynamic view on the S-curve. I am going to make movies especially for the effects created by a half-sphere later on as we expect some spatial effects there. Look at the NASA movie I referred to in my first post of this series.

The images published in my last posts show that the concave part of the S-curve is the interesting one regarding reflections. The Gaussian curvature is positive there at every point. Therefore we get multiple reflections and large scale reshaping of simple regular figures or bodies. It gives us a first idea about what a half-sphere may create by the reflection of light rays.

A movie

Below I put the video with somewhat reduced resolution but the download of the 1.5 MB may still take some time. An additional link allows you to download an mp4-file with a resolution of 1000×500 px.

Link to movie with a bit higher resolution.
mv_SC_1000_mp40001-0200.mp4

Some remarks

All reflection patterns stem from 3 fully reflective, metallic spheres which are moved in front of the S-curves surface.
The “organic” jelly-like appearance of the pattern dynamics is partially due to the spherical form of the figures. Spherical surfaces lead to soft edges of the reflective patterns. The fully reflective surface of the spheres helps in addition.
The enlargements of some patterns during their object’s movement are due to the curvature of the S-curve in both direction, but especially along the longer symmetry axis, i.e. in the direction of the camera. This curvature increases the area from where light rays emitted from the surface of the spheres can hit the camera.
The separation and merging of some parts of the reflection patterns is due to single reflections of the spheres on fitting upper and lower parts of the S-curve. Such reflective patterns can also merge with reflective patterns emerging from central parts of the S-curve.
Multiple up/down-reflections can be seen in the beginning for the green sphere and at the end of the movie for the red sphere.

Conclusion

Moving objects in front of the S-curve make this surface even more interesting. Again all tribute to Mr Kapoor whose S-curve object at the Kistefoss museet gave me the idea to reconstruct something similar in Blender.
Stay tuned …

Ceterum censeo: The worst living fascist and war criminal today, who must be isolated, denazified and imprisoned, is the Putler.

 

Blender – complexity inside spherical and concave cylindrical mirrors – IV – reflective images of a Blender variant of Mr Kapoor’s S-curve

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The topic of the last post in this series

Blender – complexity inside spherical and concave cylindrical mirrors – I – some impressions
Blender – complexity inside spherical and concave cylindrical mirrors – II – a step towards the S-curve
Blender – complexity inside spherical and concave cylindrical mirrors – III – a second step towards the S-curve

was the construction of a metallic object with basic similarities to the “S-curve” of artist Anish Kapoor. Our object was a bit more extreme than the artists real object; we had a smaller curvature radii in two dimensions and on the outer ends our surface approximated a half circle boundary curve. We therefore could expect multiple reflections of light rays on the concave side(s) of our virtual object when applying ray tracing.

At the end of my last article I already presented some images of the reflection of a far distant horizontal line marked by a sun close to the horizon at dusk or dawn. In this article I am going to add some simple objects – a small red and a small green sphere at varying positions. Plus a point like light source. I take some shots with the virtual Blender camera form different angles and with varying focal length. I present the results below without many comments.

What we see is a rich variation of patterns and figures. Mathematically it is all the result from a single and simple mapping-operation. Each operation maps one point on our surface to another point on the S-curve (or on a hit sphere). The points are given by millions and millions of light rays which in the end reach our virtual camera from different angles. The basic message is:

Simplicity can create a complexity which or brain would not predict without some deeper analysis. And a complex apparition may be based on simple rules and the selection of special circumstances.

So, besides many other philosophical aspects Mr. Kapoor’s “S-curve” reveals a very fundamental idea in physics, certain branches of mathematics and in information theory.

Reflections of a horizon line

Reflections of a horizon line and a red sphere

Reflections of a horizon line, a red and a green sphere

Note that the concave side of the S-curve gives us a first idea about what we can expect from a full half-sphere where even more reflections on the surface are possible before a light ray reaches the camera.

But, in my next article
Blender – complexity inside spherical and concave cylindrical mirrors – V – a video of S-curve reflections
I am first going to produce a movie of objects moving in front of the concave part of the S-curve.