In this post, I provide some R code which generates a mesh of the Mandelbulb, a well-known 3D fractal. The Mandelbulb is an isosurface, and I use the rmarchingcubes package to get a mesh of ... [Read more...]

The algebraicMesh function of my package cgalMeshes takes as inputs a trivariate polynomial \(P(x,y,z)\), a number \(\ell\) and some other parameters, and it returns a mesh of the isosurfa... [Read more...]

I made some progress on the cgalMeshes package, that I introduced here. The new version is not on CRAN yet. In particular, one can know assign some properties to the meshes (the cgal... [Read more...]

I presented the ‘Reorient’ rotation in a previous post. I figured out three things: there’s an easy precise definition of this rotation, that I didn’t give; ... [Read more...]

The paper Simple formula for integration of polynomials on a simplex by Jean B. Lasserre provides a method to calculate the exact value of the integral of a multivariate polynomial on a simplex (i.e. a ... [Read more...]

Setting up an environment Example Notes Advanced example Arbitrary HTML ... [Read more...]

In Haskell, for any type T (for example Double), there is a corresponding type Maybe T. An object of this type either has form Just x, where x is of type T, or is Nothing. Thus one can use the May... [Read more...]

Because of a change I did in the lazyNumbers package, I have to post a correction to my previous post. The as.double function, called on a lazy number, was not stable. Now it is. In ... [Read more...]

My new package lazyNumbers is a port of the lazy numbers implemented in the C++ library CGAL. The lazy numbers represent the real numbers and arithmetic on these numbers is exact. ... [Read more...]

My new package cgalMeshes (not on CRAN yet) deals with 3D meshes. All algorithms implemented in this package are performed by the C++ library CGAL. I already wrapped some CGA... [Read more...]

In the ‘shiny’ package, the reactiveConsole function allows to enable reactivity at the console, for the purposes of experimentation and learning (that doesn’t work in a R Markdown document). ... [Read more...]

If you follow my youtube channel then you have certainly seen the “ball” of twenty Hopf tori. Sometimes I call it the “Hopf flower”. How is it done? Well, firstly, I take twenty poin... [Read more...]

Do you know my former blog? It contains four posts about the computation of the Kantorovich distance: Using Julia to compute the Kantorovich distance ... [Read more...]

In this previous post I was wrong when I said I didn’t have a tool to compute the intersection of the compound of five tetrahedra: This can be achieved with th... [Read more...]

The Shiny app below allows to attribute a label to the points of a ‘ggplot’ by double-clicking on the points. library(shiny) library(rhandsontable) library(htmlwidgets) library(colourpicker) library... [Read more...]

Last month, I posted an article showing a way to expand a polynomial in R when the coefficients of the polynomial contain some literal values, with the help of the caracas package. Today I wanted ... [Read more...]

In a previous post, I showed how to draw a 3D slice of a 4D hypersurface when a parameterization of this hypersurface is available. Here we deal with the case when an implicit equation of the hypersurface... [Read more...]

It is possible to search in a ‘DT’ table with a regular expression: datatable( data = dat, options = list( search = list(regex = TRUE) ) ) But it could be desirable to have the possibility t... [Read more...]

Below is a simple example of a ‘ggplot2’ graphic with tooltips in a Shiny application. The tooltips are constructed with the help of the qTip2 JavaScript library. library(shiny) library(ggpl... [Read more...]

The donut torus Given a number \(s \geqslant 1\), the following map: \[ (u, v) \mapsto (x, y, z) = \frac{\Bigl(s\cos\frac{u}{s}, s\sin\frac{u}{s}, \sin v\Bigr)}{\sqrt{s^2+1}-\cos v} \] is ... [Read more...]