Short post today. Did you know that the intersection of the Enneper surface with a sphere looks like the seam of a tennis ball? That’s what we shall see. f [Read more...]

I implemented the framed closed curves exposed in this blog post, in Julia and R. In fact it is useless with R, because the rgl function cylinder3d is faster and better. Here is the Julia imp... [Read more...]

I introduced the Gröbner implicitization and the giacR package in the previous post. We will see an application here. Consider this satellite curve: satelliteCu... [Read more...]

I considerably improved the computation of the Gröbner bases in the qspray package, and I implemented something new: Gröbner implicitization. The Gröbner implicitization is able to transform a sys... [Read more...]

There is something new in the qspray package: Gröbner bases. Gröbner bases have many applications, and we will see one of them now. My package qspray deals with multivariate polynomials with rational coef... [Read more...]

Recall that a Hopf torus is a two-dimensional object in the 4D space defined by a profile curve: a closed curve on the unit sphere. When mapping it to the 3D space with the stereographic projection, we ca... [Read more...]

I translated to R the JavaScipt code for the Doyle spiral written by Robin Houston and kindly provided in this gist. library(rootSolve) # for the function multiroot library(plotrix) # for ... [Read more...]

In the previous post, I showed how to expand a polynomial with symbolic parameters with the help of the spray package. As I said, it has one problem: it doesn’t preserve the rational numbers in the polyno... [Read more...]

In this previous post, this previous post, and this previous post, I showed how to expand a polynomial with symbolic parameters. In the first two posts, I used the R package caracas, a wra... [Read more...]

The RcppCGAL package now contains version 5.5.2 of the CGAL library. There is something new in this version: the 3D alpha wrapping. This is a bit similar to the 3D alpha hull but this can work better. ... [Read more...]

I’ve just discovered the excellent book Convex Optimization written by Stephen Boyd and Lieven Vandenberghe. It gives methods for many interesting geometric problems. In this blog po... [Read more...]

Here is how to have some tooltips for the options and their headers of a selectizeInput in Shiny. library(shiny) ui [Read more...]

The fisheye function below distorts a bitmap image with a fisheye effect or an anti-fisheye effect (rho __ 0.5 or rho __ 0.5). fisheye_xy [Read more...]

Googling “heatmap format excel” returns a lot of results. Here we will see how to do a heatmap formatting with a DT table in R. The dataset we use provides the average monthly temperatures o... [Read more...]

Given a complex number \(z_c\), called the Julia point, the corresponding Julia fractal is obtained by iterating \(z \mapsto z^2 + z_c\) for each complex number \(z\) until the modulus of ... [Read more...]

I still wrapped a part of the C++ library CGAL in a R package, namely interpolation. The purpose of this package is to perform interpolation of bivariate functions. As compared to ex... [Read more...]

The purpose of my package qsplines is to construct quaternions splines. This is a port of the Python library splines, written by Matthias Geier. A quaternions spline is a sequence of quaternions interpola... [Read more...]

Denoting by \(F(z \,|\, m)\) the incomplete elliptic function of first kind, the function \[ \varphi(z) = -\sqrt{i} \, F\bigl(i \sinh^{-1}(\sqrt{i} \, z) \,|\, -1 \bigr). \] is a conformal mappi... [Read more...]

There’s a kind of error in the previous post. In this formula: \[ \exp\Bigl(-\frac{{(i/n-0.5)}^2 + {(j/n-0.5)}^2}{0.025^2} \Bigr), \] the indices \(i\) and \(j\) should range from ... [Read more...]

I found such an algorithm on Paul Bourke’s website: take a random matrix \(M\) of size \(n \times n\) (we’ll take \(n=400\)), real or complex; ... [Read more...]