Surface Reconstruction

ShapeWorks reconstructs dense surface meshes from sparse correspondence particles. Since correspondence particles are placed sparsely across the surface, a dense mesh must be generated for visualization and downstream analysis. ShapeWorks does this by deforming a reference (template) mesh to match each shape's particle positions.

Reconstruction Methods

Three surface reconstruction methods are available in the Analysis module, depending on your data:

Method	Requirements	Description
Mesh Warping	Meshes or distance transforms	Deforms a template mesh using correspondence particles as control points. Recommended for most workflows.
Distance Transform	Distance transforms	Reconstructs surfaces from distance transforms. Requires groomed distance transforms in the project.
Legacy	Particles only	Fallback method for older XML projects that only contain particle files.

The reconstruction method can be selected from the radio buttons in the Surface Reconstruction panel.

Below is an example of the difference between reconstruction methods.

Mesh Warping

Mesh warping is the default and recommended reconstruction method. It works by:

1. Selecting a template shape (typically the median) from the population.
2. Embedding the template's correspondence particles as vertices in its mesh (splitting triangles as needed).
3. Deforming the enriched template mesh so that the embedded particle vertices move to each target shape's particle positions, dragging the rest of the mesh along smoothly.

This produces a dense mesh for every shape in the population that shares the same connectivity (triangle topology), which is useful for computing point-to-point correspondences across the full surface.

Template Selection

The template shape serves as the reference mesh that gets deformed to reconstruct all other shapes. You can choose the template using the options in the Mesh Warp panel:

• Median -- Automatically selects the shape closest to the population median. This is the default and generally works well.
• Template Sample -- Manually select a specific shape index to use as the template.

After changing the template or warp method, click Run Mesh Warp to regenerate the reconstructions.

Warp Methods

Two warp methods are available for deforming the template mesh. The method can be selected from the Warp Method dropdown in the Mesh Warp options. The warp method is saved per project. The default for new projects can be changed in Edit > Preferences under the Mesh Optimization section.

Biharmonic (Default)

Biharmonic deformation computes a weight matrix that expresses every mesh vertex as a weighted combination of the particle positions. Once computed, each per-shape warp is a single matrix multiplication. This is the default and works well for most cases.

Laplacian

Laplacian surface deformation preserves the local curvature of the reference mesh during warping. Vertices far from any particle maintain their original surface shape, which can reduce artificial thinning in regions with sparse particle coverage.

Both methods use libigl for the underlying geometry processing (biharmonic weights and cotangent Laplacian respectively).

Laplacian may produce better results when particles are unevenly distributed or on thin structures. Biharmonic is a good default for most datasets.

Biharmonic	Laplacian

Python API

The warp method can also be set programmatically using the Python API:

import shapeworks

warper = shapeworks.MeshWarper()

# Set warp method (default is Biharmonic)
warper.setWarpMethod(shapeworks.WarpMethod.Laplacian)
# or
warper.setWarpMethod(shapeworks.WarpMethod.Biharmonic)

# Set up and run warping
warper.generateWarp(reference_mesh, reference_particles)
warped_mesh = warper.buildMesh(target_particles)