Densityplot with two argument function

Question

I want to plot the heat map of a two-variable function which has two arguments, but the function is continuous on the transition line.

However, the densityplot put no color on the transition line.

Here is an example

r[x_, y_] = If[x^2 + y^2 <= 1, x^2 + y^2, If[x^2 + y^2 >= 1, 1]]
DensityPlot[r[x, y], {x, -2, 2}, {y, -2, 2}, PlotRange -> All]

This gives the following image

I want the white circle to be coloured as 1.

Answer 1

r[x_, y_] = If[x^2 + y^2 <= 1, x^2 + y^2, If[x^2 + y^2 >= 1, 1]];
DensityPlot[r[x, y], {x, -2, 2}, {y, -2, 2}, PlotRange -> All, 
 Exclusions -> None, PlotPoints -> 100]