As mesh refinement becomes a necessity in improving the quality of rad
iosity rendering, we must efficiently subdivide increasingly complex m
eshes. In triangulation (often the method chosen), each step may invol
ve numerous proximity node searches, edge selections, additions, and d
eletions. In this context we show two variations of an efficient trian
gulation mechanism based on the advancing front paradigm. We point out
where the computational bottlenecks occur and give the characteristic
s of the domain for which each method excels. While we have applied th
e advancing front mesh generation for the first time to radiosity rend
ering, the algorithms are general enough to be of interest in other do
mains of application.