Results and Conclusions

The results generated by the graded triangulation routine implemented in ANSI C can be seen here. The routine is integrated with the IITZeus environment which facilitates the input and output of the data. Each result of the graded triangulation routine is compared with the AFM routine already implemented earlier.

For all the results obtained by the graded triangulation shown here, the same gradation function $L = (\alpha L_1 + \beta L_2 + \gamma L_3)/3$ is used. It can be clearly seen from these results that the triangulation obtained is somewhat dense around the specified boundary and relatively sparse away from the boundary and this gradation occurs much more smoothly than the corresponding AFM triangulation.

The time comparison between graded triangulation and AFM is not shown as it greatly depends on the number of triangles generated which is different for both the methods even for the same test data depending on the gradation function. However, in the case of same number of triangles in the output, the time difference between the two is small, AFM being only slightly faster.

It can be further concluded that the user now has a much better control over the triangulation generated by means of the gradation function to be specified, which is absent in both AFM and Delaunay triangulation.

**Figure:** Graded triangulation - Test data $% latex2html id marker 731 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/turbineblade.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 733 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/turbineblade.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 735 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/airfoil.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 737 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/airfoil.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 739 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/india.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 741 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/india.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 743 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/heart.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 745 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/heart.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 747 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/circle.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 749 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/circle.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 751 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/anirudh.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 753 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/anirudh.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 755 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/hexagon.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 757 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/hexagon.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 759 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/club.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 761 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/club.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 763 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/square.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 765 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/square.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 767 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/square2.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 769 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/square2.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Graded triangulation - Test data $% latex2html id marker 771 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=graded/fail1.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$

**Figure:** Advancing front triangulation - Test data $% latex2html id marker 773 $\arabic{fignum}$$
$\begin{figure} \centerline{ \psfig {figure=advfrnt/fail1.ps,angle=-90,height=9cm,width=10cm} } \end{figure}$