Feature: mesh deformation with RBFs (TPS and CPC2) by Lena-Richter · Pull Request #2470 · DLR-AMR/t8code

Lena-Richter · 2026-10-05T13:42:21Z

Describe your changes here:
This PR introduces an RBF-based mesh deformation, using OpenCASCADE and Eigen. It implements support for the compactly supported (CPC2) and globally supported (TPS) basis functions to compute the deformation for the inner nodes from the displacement of the boundary nodes. Additionally, for CPC2, a dynamic radius is implemented as well as a grading factor. The deformed geometry needs to have the same parametrization as the input geometry, otherwise the deformation will not work.

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…o the rbf_node struct and the interpolate function. add some minor changes to the mesh deformation to include the rbf_node struct to save the node data.

…th eigen next

codecov · 2026-10-06T11:57:57Z

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 83.11%. Comparing base (9d755d4) to head (6458bf3).
⚠️ Report is 4 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
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+ Coverage   82.76%   83.11%   +0.34%     
==========================================
  Files         139      138       -1     
  Lines       21593    21504      -89     
==========================================
  Hits        17872    17872              
+ Misses       3721     3632      -89

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ole-alb

Thank you for this very cool contribution and implementation. I have a couple general remarks.
Can you check if ervything that can be const is const?

Please add tests for your functionality as it is not tested yet. Please also test the new dependecy on the newly added thirdparty library Eigen.
After the PR is merged, please keep in mind to update the wiki accordingly (Eigen, CMake,..).

Also I thought if there could be the option to use a system Eigen like it is for SC and p4est?

And last but not least, I coudn't find you in the CITATION.cff and in doc/auther_. Please add yourself here.

ole-alb · 2026-10-07T06:20:00Z

+      /** Calculate the distance between the current pair of boundary nodes. */
+      const double distance = t8_dist (boundary_nodes[row].position, boundary_nodes[col].position);
+      /** Evaluate the radial basis function for the current distance and write the value to the matrix A. */
+      A (row, col) = rbf_function->evaluate (distance, 0.0);


Is it possible to solve that with a default value? As tps doesn't have a radius, adding 0 could be misunterstood.

ole-alb · 2026-10-07T06:24:02Z

+    double r = distance / radius;
+    if (r < 1.0) {
+      double d = 1.0 - r;
+      return (d * d * d * d) * (4.0 * r + 1.0);
+    }
+    return 0.0;


In genearal, the use of variables consisting of only one letter is stronlgy discouraged in t8code. For me this could be an exemption, as it's only four lines and just math, but maybe you can come up with a better way.

Okay renamed r to normalized_distance and removed d by using std::pow

ole-alb · 2026-10-07T06:31:32Z

-std::unordered_map<t8_gloidx_t, t8_3D_vec>
-t8_cmesh_mesh_deformation::calculate_displacement_surface_vertices (const t8_cad_handle *cad)
+static double
+calculate_local_support_radius (t8_cmesh_t cmesh, const std::vector<std::pair<t8_locidx_t, int>> &tree_list,


This function is specific to RBF, why is it here and not in t8_rbf.cxx? Also please add documentation and a "t8_" prefix to the function name.

ole-alb · 2026-10-07T06:39:22Z

-t8_cmesh_mesh_deformation::calculate_displacement_surface_vertices (const t8_cad_handle *cad)
+static double
+calculate_local_support_radius (t8_cmesh_t cmesh, const std::vector<std::pair<t8_locidx_t, int>> &tree_list,
+                                int current_global_vertex_id, const t8_3D_vec &displacements)


This is an int here, but in the usage a t8_gloidx_t is used a input. So I'd suggest to make this also a t8_gloidx_t

ole-alb · 2026-10-07T06:44:36Z

+      }
+    }
+    /* If the boundary node can not be found in the list of boundary nodes.*/
+    t8_errorf ("ERROR: The boundary node %ld is missing in the boundary node list.\n", global_id);


Suggested change

t8_errorf ("ERROR: The boundary node %ld is missing in the boundary node list.\n", global_id);

t8_errorf ("ERROR: The boundary node % " T8_GLOIDX_FORMAT " is missing in the boundary node list.\n", global_id);

ole-alb · 2026-10-07T12:02:55Z

+
+  double displacement_magnitude = std::sqrt (displacements[0] * displacements[0] + displacements[1] * displacements[1]
+                                             + displacements[2] * displacements[2]);
+  /** Get the first tree where this vertex exists. */


Which vertex?

ole-alb · 2026-10-07T12:15:18Z

+    }
+  }
+  /** Fill the sparse matrix A with the triplets. */
+  Eigen::SparseMatrix<double> A (num_boundary_nodes, num_boundary_nodes);


A might not be the best name.

ole-alb · 2026-10-07T12:23:50Z

+  A.setFromTriplets (coefficients.begin (), coefficients.end ());
+  /** Solve the linear system using the conjugate gradient method. */
+  Eigen::BiCGSTAB<Eigen::SparseMatrix<double>> solver;
+  solver.setTolerance (1e-10);


Is that an experimental value?

ole-alb · 2026-10-07T12:26:38Z

+    /** Because of the symmetric property of the distance between nodes, we only need to compute the upper triangular part of the matrix 
+       * and can mirror the values to the lower triangular part. */


Do you really do that?

ole-alb · 2026-10-07T12:33:14Z

 option( T8CODE_ENABLE_MPI "Enable t8code's features which rely on MPI" ON )
 option( T8CODE_ENABLE_VTK "Enable t8code's features which rely on VTK" OFF )
 option( T8CODE_ENABLE_OCC "Enable t8code's features which rely on OpenCASCADE" OFF )
+option( T8CODE_ENABLE_EIGEN "Enable t8code's features which rely on eigen" OFF )


Suggested change

option( T8CODE_ENABLE_EIGEN "Enable t8code's features which rely on eigen" OFF )

option( T8CODE_ENABLE_EIGEN "Enable t8code's features which rely on Eigen" OFF )

…on.cxx Co-authored-by: Ole Albers <122293607+ole-alb@users.noreply.github.com>

Lena-Richter and others added 13 commits March 26, 2026 14:34

include mesh deformation example (commit 78fd6b2)

0eead4d

import other mesh deformation logic as well

8759747

first steps for RBF implementation

0884867

add basis RBF function class and the CPC^2 and TPS functions. add als…

17f7cbd

…o the rbf_node struct and the interpolate function. add some minor changes to the mesh deformation to include the rbf_node struct to save the node data.

add more functionalities to the RBF class and implement the solver wi…

cf17193

…th eigen next

include eigen library and add a little test to try if it works

2542283

add solve function

19f1799

Merge branch 'main' into feature-RBF_CPC2

19df7af

add eigen as fetch content

64df1b1

first deformation with inner nodes

b0fcde7

updating the TPS calculation and fix some minor issuses

f2d1315

load mesh deformation .brep files in example dynamical

984da6c

clean up and fix some typos

d52a348

Lena-Richter changed the title ~~Feature rbf cpc2~~ Feature mesh deformation with RBFs (TPS and CPC2) Oct 5, 2026

Lena-Richter changed the title ~~Feature mesh deformation with RBFs (TPS and CPC2)~~ Feature: mesh deformation with RBFs (TPS and CPC2) Oct 5, 2026

fix doxygen errors and missing parameter documentation

d05a2e2

Lena-Richter force-pushed the feature-RBF_CPC2 branch from bbfd954 to d05a2e2 Compare October 6, 2026 10:01

Merge branch 'main' into feature-RBF_CPC2

d9ca696

Lena-Richter marked this pull request as ready for review October 6, 2026 11:05

build mesh deformation only with OCC and Eigen enabled

257f2e9

Lena-Richter assigned Lena-Richter and ole-alb and unassigned Lena-Richter Oct 6, 2026

ole-alb self-requested a review October 6, 2026 13:10

ole-alb reviewed Oct 7, 2026

View reviewed changes

ole-alb assigned Lena-Richter and unassigned ole-alb Oct 7, 2026

ole-alb requested changes Oct 7, 2026

View reviewed changes

Update src/t8_cmesh/t8_cmesh_mesh_deformation/t8_cmesh_mesh_deformati…

6458bf3

…on.cxx Co-authored-by: Ole Albers <122293607+ole-alb@users.noreply.github.com>

	t8_errorf ("ERROR: The boundary node %ld is missing in the boundary node list.\n", global_id);
	t8_errorf ("ERROR: The boundary node % " T8_GLOIDX_FORMAT " is missing in the boundary node list.\n", global_id);

		/** Because of the symmetric property of the distance between nodes, we only need to compute the upper triangular part of the matrix
		* and can mirror the values to the lower triangular part. */

	option( T8CODE_ENABLE_EIGEN "Enable t8code's features which rely on eigen" OFF )
	option( T8CODE_ENABLE_EIGEN "Enable t8code's features which rely on Eigen" OFF )

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Lena-Richter commented Oct 5, 2026 •

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