R help - Oct 2006 - function used to smooth the scatter plot and generate a density map

Dear R-helpers,

I want to smooth a scatter plot (or 2d histogram) to generate the density
map using a squared Euclidean kernel function, with each data point
contributing a density of 1/(r*r + k) to each cell on the heatmap, where
r*r?was the squared Euclidean distance between the coordinates of the cell
and the coordinates of the point, and k was a constant smoothing factor.
There is figure to demonstrate the process in the attachment.

I don?t know if there function in some package can do this. I have used many
keywords to search the R help files and the R project web but did not get
the answer. Can anybody help me? Thank very much.

Sincerely
?Honglin zhou
?
College of Life Sciences
Beijing Normal University
Beijing, 100875
P. R. China