Nils Berglund | Classics revisited: A hyperbolic reflector @NilsBerglund | Uploaded August 2024 | Updated October 2024, 3 minutes ago.
This is a remake of the video youtu.be/9VDU0FcgNLY of a hyperbolic wave reflector, in much higher resolution. It illustrates a property of hyperbolae, which is that waves emitted from the focal points will perfectly "mirror" each other, as if the reflector were absent. In this simulation, waves are emitted at regular time intervals at the two focal points, and reflected on one branch of the hyperbola (or rather one branch of two hyperbolea that are very close and share the same focal points). Therefore, the top and bottom region do not communicate, and still the waves match almost perfectly.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:24
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
The wave source is located at the right apex of the ellipse, and emits pulses at regular time intervals.
Render time: 32 minutes 41 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Through the Crystal" by Jeremy Blake@RedMeansRecording
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #optics #hyperbola
This is a remake of the video youtu.be/9VDU0FcgNLY of a hyperbolic wave reflector, in much higher resolution. It illustrates a property of hyperbolae, which is that waves emitted from the focal points will perfectly "mirror" each other, as if the reflector were absent. In this simulation, waves are emitted at regular time intervals at the two focal points, and reflected on one branch of the hyperbola (or rather one branch of two hyperbolea that are very close and share the same focal points). Therefore, the top and bottom region do not communicate, and still the waves match almost perfectly.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:24
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
The wave source is located at the right apex of the ellipse, and emits pulses at regular time intervals.
Render time: 32 minutes 41 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Through the Crystal" by Jeremy Blake@RedMeansRecording
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #optics #hyperbola
