In[]:=
a=-
3
π
;b=
3
π
;r=
2
x
+
2
y
;
In[]:=
DensityPlot[ar+b,{x,y}∈Disk[],Frame->False]
Out[]=
constrain[{x_,y_}]:={Piecewise[{{0,x<0},{x,0<=x<=1},{1,x>1}}],0};
In[]:=
DynamicModule[{pt={0.5,0}},​​Graphics[{​​{Thick,Circle[]},​​Line[{{0,0},Dynamic[pt]}],​​Locator[Dynamic[pt,(pt=constrain[#])&],None],​​{EdgeForm[Thin],Opacity[0.05],Disk[{0,0},Dynamic[pt[[1]]]]},​​{PointSize->0.018,Point[Dynamic[pt]]}​​},PlotRange->1.1]]
Out[]=