Showtime.
\fullpagefigure{showcases/contour-dropshadow.png} \phantomsection \addcontentsline{toc}{chapter}{Filled contours with dropshadows}
Filled contours with dropshadows is a nice effet that allows you to use a sequential colormap (here Viridis) while distinguishing positive and negative values. If you look closely at the figure, you can see that the drop shadow is external for positive values and internal for negative values. To achieve this result, the contours need to be rendered individually twice. In the first pass, I render a contour offscreen and read the resulting image into an array. I then use a Gaussian filter to blur it a bit and transform the image to make it full black but the alpha channel. I can then display the image using imshow and it will gracefully blend with elements already presents in the figure. I then add the same contour using the colormap and I iterate the process. The trick is to start from bottom to top such that dropshadows remain visible.
Sources: showcases/contour-dropshadow.py
\fullpagefigure{showcases/domain-coloring.pdf} \phantomsection \addcontentsline{toc}{chapter}{Domain coloring}
Domain coloring is a "technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the complex plane to different colors and brightness, domain coloring allows for a four dimensional complex function to be easily represented and understood. This provides insight to the fluidity of complex functions and shows natural geometric extensions of real functions" [Wikipedia]. On the figure on the left, I represented the imaginary function
Sources: showcases/domain-coloring.py
\fullpagefigure{showcases/escher.pdf} \phantomsection \addcontentsline{toc}{chapter}{Escher like projections}
Escher like projections can be obtained using the complex exponential function and some specific periods that can be computed quite easily. To do the figure on the left, I mostly followed explanations given by Craig S. Kaplan, professor at the University of Waterloo on his blog post Escher-like Spiral Tilings (2019). The only difficulty in making this figure is line thickness. If you compare this figure with the previous one, you may have noticed that in the previous figure, lines have a constant thickness while in this figure, thickness varies. To achieve such effect, we have to use a polygon made of several segment with varying thickness. This poses no real difficulty, only some geometrical computations.
Sources: showcases/escher.py
\fullpagefigure{showcases/VSOM.png} \phantomsection \addcontentsline{toc}{chapter}{Self-organizing maps}
Self-organizing map (SOM) "is a type of artificial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional), discretized representation of the input spa-ce of the training samples, called a map, and is therefore a method to do dimensionality reduction" [Wikipedia]. I developed with Georgios Detorakis a randomized self-organizing map based on blue noise distribution of neurons. The figure on the left shows the self-organisation of the map when fed with random RGB colors. The figure itself is made of a polygon collection where each polygon is painted with the color of the neuron. No real difficuly but I had to take care fo disabling antialias, else, thin lines appear between polygons.
Sources: github.com/rougier/VSOM
\fullpagefigure{showcases/waterfall-3d.pdf} \phantomsection \addcontentsline{toc}{chapter}{Waterfall plots}
Waterfall plot "is a three-dimensional plot in which multiple curves of data, typically spectra, are displayed simultaneously. Typically the curves are staggered both across the screen and vertically, with 'nearer' curves masking the ones behind. The result is a series of "mountain" shapes that appear to be side by side. The waterfall plot is often used to show how two-dimensional information changes over time or some other variable" [Wikipedia] To do the figure, I used a 3D axis and polygons (i.e. not filled plot). The reason to use polygon is to obtain the color gradient effect on each curve. The only way to do that (to the best of my knowledge), is to slice horizontally each curve in several stripes and to render the slice using a specific color. The difficulty is to compute those irregular slices and this is the reason I use the Shapely library that allows, among many other things, to compute the intersection between polygons.
Sources: showcases/waterfall-3d.py
\fullpagefigure{showcases/windmap.png} \phantomsection \addcontentsline{toc}{chapter}{Streamlines}
Streamlines are a "family of curves that are instantaneously tangent to the velocity vector of the flow. These show the direction in which a massless fluid element will travel at any point in time" [Wikipedia]. The figure on the left shows such stream lines and is actually a still from an animation. Each streamline has been split into line segments and gathered in a line collection such that each segment has its own color. From there, it is easy to suggest stream direction using gradients. Note that I could have used a single line collection for all streamlines. Strangely enough, the only difficulty in this figure are the line round caps. For the reason explained here, I had to create a specific graphic context such as to have round caps.
Sources: showcases/windmap.py
\fullpagefigure{showcases/mandelbrot.png} \phantomsection \addcontentsline{toc}{chapter}{Mandelbrot set}
The Mandelbrot set "is the set of complex numbers
Sources: showcases/mandelbrot.py
\fullpagefigure{showcases/recursive-voronoi.pdf} \phantomsection \addcontentsline{toc}{chapter}{Recursive Voronoi}
This recursive Voronoi set has been quite painful to design because it requires some quite precise settings to obtain what I think is a beautiful result. These settings are the placement of random points with good visual properties and for that, I use the Fast Poisson Disk Sampling by Robert Bridson which is simple and fast. I also use quite extensively the shapely library to clip he different polygons and I discovered in the meantime how to draw random points inside a polygon. Finally, I played with lines thickness, polygons color and transparency to achieve this result, involving 5 levels of recursion. On my computer, it takes around 1 minute to compute.
Sources: showcases/recursive-voronoi.py
\fullpagefigure{showcases/elevation.png} \phantomsection \addcontentsline{toc}{chapter}{3D Heightmap}
A 3D heightmap of Mount St Helens after it exploded. This has been made with my experimental 3D axis. Nothing really complicated here, just a bit slow because it needs to sort a bunch of triangles.
\fullpagefigure{showcases/mosaic.pdf} \phantomsection \addcontentsline{toc}{chapter}{Voronoi mosaic}
This Voronoi mosaic is based on blue noise distribution where each Voronoi cell has been painted according to the color of the center of the Voronoi cell in the original image. This results in a cheap stained glass window effect.
Sources: showcases/mosaic.py
\fullpagefigure{showcases/text-shadow.png} \phantomsection \addcontentsline{toc}{chapter}{Text shadow}
This shadowed text is harder to design than it seems. I started from a text path object and iterated over the segments composing the path in order to create sheared rectangles that constitute the shadow. To make the shadow disappear in the background, I created an image with a vertical gradient using semi-transparent color (fully transparent on top and fully opaque on the bottom). This results in a nice fading shadow effect.
Sources: showcases/text-shadow.py
\fullpagefigure{showcases/text-spiral.pdf} \phantomsection \addcontentsline{toc}{chapter}{Text spiral}
This spiral text has been made using an Archimedean spiral (r = a + bθ) that guarantees a constant speed along a line that rotates with constant angular velocity. Said differently, successive turnings of the spiral have a constant separation distance. Starting from a very long text path representing some of the decimals of pi (using the mpmath library), it's then only a matter of transforming the vertices to follow the spiral.
Sources: showcases/text-spiral.py