Matlab griddata equivalent in C++ - c++

Question

I am looking for a C++ equivalent to Matlab's griddata function, or any 2D global interpolation method.
I have a C++ code that uses Eigen 3. I will have an Eigen Vector that will contain x,y, and z values, and two Eigen matrices equivalent to those produced by Meshgrid in Matlab. I would like to interpolate the z values from the Vectors onto the grid points defined by the Meshgrid equivalents (which will extend past the outside of the original points a bit, so minor extrapolation is required).
I'm not too bothered by accuracy--it doesn't need to be perfect. However, I cannot accept NaN as a solution--the interpolation must be computed everywhere on the mesh regardless of data gaps. In other words, staying inside the convex hull is not an option.
I would prefer not to write an interpolation from scratch, but if someone wants to point me to pretty good (and explicit) recipe I'll give it a shot. It's not the most hateful thing to write (at least in an algorithmic sense), but I don't want to reinvent the wheel.
Effectively what I have is scattered terrain locations, and I wish to define a rectilinear mesh that nominally follows some distance beneath the topography for use later. Once I have the node points, I will be good.
My research so far:
The question asked here: MATLAB functions in C++ produced a close answer, but unfortunately the suggestion was not free (SciMath).
I have tried understanding the interpolation function used in Generic Mapping Tools, and was rewarded with a headache.
I briefly looked into the Grid Algorithms library (GrAL). If anyone has commentary I would appreciate it.
Eigen has an unsupported interpolation package, but it seems to just be for curves (not surfaces).
Edit: VTK has a matplotlib functionality. Presumably there must be an interpolation used somewhere in that for display purposes. Does anyone know if that's accessible and usable?
Thank you.

Answer 1

This is probably a little late, but hopefully it helps someone.
Method 1.) Octave: If you're coming from Matlab, one way is to embed the gnu Matlab clone Octave directly into the c++ program. I don't have much experience with it, but you can call the octave library functions directly from a cpp file.
See here, for instance. http://www.gnu.org/software/octave/doc/interpreter/Standalone-Programs.html#Standalone-Programs
griddata is included in octave's geometry package.
Method 2.) PCL: They way I do it is to use the point cloud library (http://www.pointclouds.org) and VoxelGrid. You can set x, and y bin sizes as you please, then set a really large z bin size, which gets you one z value for each x,y bin. The catch is that x,y, and z values are the centroid for the points averaged into the bin, not the bin centers (which is also why it works for this). So you need to massage the x,y values when you're done:
Ex:
//read in a list of comma separated values (x,y,z)
FILE * fp;
fp = fopen("points.xyz","r");
//store them in PCL's point cloud format
pcl::PointCloud<pcl::PointXYZ>::Ptr basic_cloud_ptr (new pcl::PointCloud<pcl::PointXYZ>);
int numpts=0;
double x,y,z;
while(fscanf(fp, "%lg, %lg, %lg", &x, &y, &z)!=EOF)
{
pcl::PointXYZ basic_point;
basic_point.x = x; basic_point.y = y; basic_point.z = z;
basic_cloud_ptr->points.push_back(basic_point);
}
fclose(fp);
basic_cloud_ptr->width = (int) basic_cloud_ptr->points.size ();
basic_cloud_ptr->height = 1;
// create object for result
pcl::PointCloud<pcl::PointXYZ>::Ptr cloud_filtered(new pcl::PointCloud<pcl::PointXYZ>());
// create filtering object and process
pcl::VoxelGrid<pcl::PointXYZ> sor;
sor.setInputCloud (basic_cloud_ptr);
//set the bin sizes here. (dx,dy,dz). for 2d results, make one of the bins larger
//than the data set span in that axis
sor.setLeafSize (0.1, 0.1, 1000);
sor.filter (*cloud_filtered);
So that cloud_filtered is now a point cloud that contains one point for each bin. Then I just make a 2-d matrix and go through the point cloud assigning points to their x,y bins if I want an image, etc. as would be produced by griddata. It works pretty well, and it's much faster than matlab's griddata for large datasets.