How can I figure out and edit the Interpolation algorithm in 2D Contour plots?

[#1]

Hi everyone. I am recently started JMP user and I´m trying to generate 2D contour plots by using 2 different ways. The first way is from the graph builder menu and the second one is from the outside menu bar, as shown below: 

After generating results with both options for the same set of values, I got different output plots, with the highest difference at lowest value ranges, as shown below:  

I guess these differences are because they both use different interpolation Methods. Does anybody know which interpolation algorithm uses each one? If this information available in the help section? There is any option to modify the interpolation algorithm used, or a way to edit the script to do so? I appreciate so much if I can get some help on this, thanks in advance.  

[#2]

The right-hand picture suggests the data may be sparse...I'm guessing very sparse where the pictures diverge. Chances are there is some form of triangulation involved: converting the data points into a mesh of triangles without making them too long and skinny if possible. It only takes a few different choices about how to make the best mesh to get graphs that are that different. I think the older contour platform has some options for saving a table of the triangles it used, or gridding the data. It might be helpful to plot the points on top of the contours.

[#3]

Thang Mr Hales for your answer. Yes, In fact I follow your suggestion of plotting the point on top of contours and matches perfectly with the Option 1 graph (Left side). Moreover, I´ve been answered with a confirmation of what you told me before, is that  the JMP Contour Plot uses a triangulation algorithm, more specifically: Delaunay triangulation. However, it is not specified which contour plot is referred to (If the one from the Graph Builder(Option 1) or the one in the external menu (Option 2). 

In addition, I have faced a curious thing. With Option 1 plot (left graph - main graph builder), when I specify the z-values as ¨Interval¨ variable, it becomes instantaneously in Plot for Option 2 (right graph), but when clicking ¨done¨ it goes back to its original plot. It seems Option 2 is a variation of any setting from Option 1, but I´m not clear yet on it. Do you have an idea of what could be happening? Thanks again,  

[#4]

not sure, can you share your data and the scripts you are using to make the graphs?