Diverse Topologies for Evaluation of Geometric Similarity Metrics

A collection of 7 datasets with each set containing 3D shapes with varying topological complexity. The datasets can be used to compare different metrics of geometric dissimilarity. Two of the datasets have topologically complex shapes that resemble designs obtained from topology optimization, a widely used design optimization method for engineering structures.

We used this dataset for a related journal article with the following abstract: "In the early stages of engineering design, multitudes of feasible designs can be generated using structural optimization methods by varying the design requirements or user preferences for different performance objectives. Data mining such potentially large datasets is a challenging task. An unsupervised data-centric approach for exploring designs is to find clusters of similar designs and recommend only the cluster representatives for review. Design similarity can be defined not only on a purely functional level but also based on geometric properties, such as size, shape, and topology. While metrics such as chamfer distance measure the geometrical differences intuitively, it is more useful for design exploration to use metrics based on geometric features, which are extracted from high-dimensional 3D geometric data using dimensionality reduction techniques. If the Euclidean distance in the geometric features is meaningful, the features can be combined with performance attributes resulting in an aggregate feature vector that can potentially be useful in design exploration based on both geometry and performance. We propose a novel approach to evaluate such derived metrics by measuring their similarity with the metrics commonly used in 3D object classification. Furthermore, we measure clustering accuracy, which is a state-of-the-art unsupervised approach to evaluate metrics. For this purpose, we use a labeled, synthetic dataset with topologically complex designs. From our results, we conclude that Pointcloud Autoencoder is promising in encoding geometric features and developing a comprehensive design exploration method."

For each dataset, shapes/designs are saved as surface mesh files (extension: stl) and point cloud files (extension: ply) in the folders "stls" and "plys" respectively. A brief description of the 7 different datasets is in the following table. For each dataset, the designs are named using numbers starting from 0, e.g., “0.stl, 1.stl, …, 19.stl” in the folder for the surface mesh files. Some of the datasets are labeled, i.e., each design belongs to a class. In a labeled dataset, all classes have the same number of designs, and the designs are named in the order of their class. For example, a labeled dataset with 4 designs and 2 classes contains files whose names start with {0, 1, 2, 3} where the designs {0, 1} belong to class 1, and {2, 3} belong to class 2.

Dataset name
Directory name
Number of designs
Number of classes

Beam-rotation
"rotate_beam"
20
None

Beam-elongation
"elongate_beam"
20
None

Beam-translation
"move_beam"
20
None

Three cube trusses
"three_cube_truss"
150
6

Single cube trusses
"single_cube_truss"
275
11

Random topologies
"three_cube_truss_random"
1000
50

Topologically optimized designs
"cube_opt_shapes"
1500
None