Improve nurbs surface fitting efficiency with Eigen sparse matrix solver

[ZhuLingfeng1993]

Compared to the existing Eigen dense solver, using the Eigen sparse solver significantly reduces solution time and memory usage, without relying on UMFPACK/SuiteSparse libraries that are based on the GPL open source license.

[mvieth]

Thank you for your pull request.
Can you give some performance measurement, how much faster your proposed new solver is, compared to the existing dense solver? (Ideally also compared to the SuiteSparse solver)
Do you know if there already is a test (e.g. in test/surface/...) that covers your new code?

[ZhuLingfeng1993]

Efficiency test result of pcl::on_nurbs::FittingSurface:

Scene number	ROI(m)	input point number	nurbs refinement(XxY)	Time with dense solver(s)	Memory with dense solver(MB)	Time with sparse solver(s)	Time of sparse solve function(s)	Memory with sparse solver(MB)
1	120x120	6051	5x5	3.9	300	1.24	0.03	306
2	220x194	19094	6x6	182.6	1771	11.8	0.08	521
3	260x154	25313	7x6	1062.6	4871	30.1	0.22	618
4	430x130	27990	7x6	1321.2	5115	28.7	0.15	1030

Note of the table:

1. dense solver: solve with Eigen::CompleteOrthogonalDecomposition
2. sparse solver: solve with Eigen::SparseLU
3. Time of sparse solve function: time of NurbsSolve::solve() using Eigen::SparseLU

Sinces the time of sparse solve funtion is small, I think no need to compare to SuiteSparse solver.

And I find there is no tests for on_nurbs in test/surface, I just test my commit by my own private application code.

[larshg]

It works well with the nurbs fitting example and when run on the bun0.pcd (small cloud) the performance increase is still nice, from about 5 secs to about 800ms.
It would be nice to be able to swap between them, without having to recompile PCL, but that would require more work.
For now its fine for me to merge - it at least gives the option.

[mvieth]

@larshg Could it make sense to convert the nurbs fitting example to a test? Since the new sparse solver is used by default, I think it is important to have at least some kind of test to make sure it works correctly.

[larshg]

The unittest from #6407 also passes with this new sparse solver. But we can merge the unittest first and then rebase this afterwards?

[larshg]

@ZhuLingfeng1993 can you rebase this on main, thanks.

[ZhuLingfeng1993]

@larshg I have rebase this on main

[mvieth]

Thanks for the rebase. Looks good otherwise, just a question regarding this commented-out code: Is there a reason to keep this, or can it be removed?

[larshg]

Suggested change

	#include <iostream>
	/*
	* SPDX-License-Identifier: BSD-3-Clause
	*
	* Point Cloud Library (PCL) - www.pointclouds.org
	* Copyright (c) 2025-, Open Perception Inc.
	*
	* All rights reserved
	*/
	#include <iostream>