  We present a set of rules to guide the design of GPU algorithms. These rules
are grounded on the principle of reducing waste in GPU utility to achieve good
speed up. In accordance to these rules, we propose GPU algorithms for 2D
constrained, 3D constrained and 3D Restricted Delaunay refinement problems
respectively. Our algorithms take a 2D planar straight line graph (PSLG) or 3D
piecewise linear complex (PLC) $\mathcal{G}$ as input, and generate quality
meshes conforming or approximating to $\mathcal{G}$. The implementation of our
algorithms shows that they are the first to run an order of magnitude faster
than current state-of-the-art counterparts in sequential and parallel manners
while using similar numbers of Steiner points to produce triangulations of
comparable qualities. It thus reduces the computing time of mesh refinement
from possibly hours to a few seconds or minutes for possible use in interactive
graphics applications.
