Visualizing model predictions in 3d

Here is a brief exploration of the misc3d package, which has some nice functions that can be used in conjunction with rgl. I am especially pleased with the output of contour3d which I have used to plot GAM predictions in 3d.
The example is a simple dataset of x, y, and z, data that were used to calculate a 4th variable "value" with the equation:

 value = -0.01x³ + -0.2*y² + -0.3*z²

 Fitting GAM model to this dataset resulted in the following spline terms.

Then, the fitted GAM model was used to predict values on a regular 3d grid for plotting with the rgl package. The following plot shows the original data, with value values colored (blue colors of the spectrum are low values, red colors are high values). Finally, the contour3d function is used to add the GAM predictions as colored contours.

I got some nice insight from the R code accompanying the book by Murcell (2011).

References:
Murrell, P., 2011. R graphics. CRC Press.


Example script:

A ridiculous proof of concept: xyz interpolation

Ridiculous Orb

This is really the last one on this theme for a while... I had alluded to a combination of methods regarding xyz interpolation at the end of my last post and wanted to demonstrate this in a final example.

The ridiculousness that you see above involved two interpolation steps. First, a thin plate spline interpolation ("Tps" function of the fields package) is applied to the original random xyz field of distance to Mecca. This fitted model is then used to predict values at a new grid of 2° resolution. Finally, in order to avoid plotting polygons for each grid (which can be slow for fine grids), I obtain their projected coordinates with the mapproject function. Using these projected coordinates and their respective z values, a second interpolation is done with the "interp" function of the akima package onto a relatively fine grid of 1000x1000 positions. The result is a smooth field that can then be overlayed on the map using the "image" function (very fast).

So you may ask - When is this even necessary? I would say that it really only makes sense for projecting a filled.contour-type plot for relatively sparse geographic data. Be warned - for large amounts of xyz data, the interpolation algorithms can take a long time.

A couple of functions, found within this blog, are needed to reproduce the plot (earth.dist, color.palette).

the code to reproduce the figure...

XYZ geographic data interpolation, part 3

This will be probably be a final posting on interpolation of xyz data as I believe I have come to some conclusions to my original issues. I show three methods of xyz interpolation:
1. The quick and dirty method of interpolating projected xyz points (bi-linear)
2. Interpolation using Cartesian coordinates (bi-linear)
3. Interpolation using spherical coordinates and geographic distances (thin plate spline)