Dr. KID: Direct Remeshing and K-set Isometric Decomposition for Scalable Physicalization of Organic Shapes

TL;DR

Dr. KID tackles the problem of physically representing potato-shaped biological structures by decomposing their surfaces into a small number of isometric patch classes for reconfigurable 3D puzzles. The core approach maps each triangular face to a 3D feature space defined by edge lengths, then alternates between K-means clustering and remeshing to minimize within-class dissimilarity, guided by a threshold $T$ and energy $F_d(M_f)$. Key contributions include a new triangle-distance metric, a curvature-aware thickening and connector design, and an automatic patch-classification framework that supports both planar and curved patches, enabling scalable production via injection molding or 3D printing. The method produces accurate, perceptually faithful decompositions with workable puzzle pieces, demonstrated on virions, mitochondria, and nuclei, and shows favorable comparisons to related approaches in smoothness and speed, with implications for education, outreach, and research prototyping.

Abstract

Dr. KID is an algorithm that uses isometric decomposition for the physicalization of potato-shaped organic models in a puzzle fashion. The algorithm begins with creating a simple, regular triangular surface mesh of organic shapes, followed by iterative k-means clustering and remeshing. For clustering, we need similarity between triangles (segments) which is defined as a distance function. The distance function maps each triangle's shape to a single point in the virtual 3D space. Thus, the distance between the triangles indicates their degree of dissimilarity. K-means clustering uses this distance and sorts of segments into k classes. After this, remeshing is applied to minimize the distance between triangles within the same cluster by making their shapes identical. Clustering and remeshing are repeated until the distance between triangles in the same cluster reaches an acceptable threshold. We adopt a curvature-aware strategy to determine the surface thickness and finalize puzzle pieces for 3D printing. Identical hinges and holes are created for assembling the puzzle components. For smoother outcomes, we use triangle subdivision along with curvature-aware clustering, generating curved triangular patches for 3D printing. Our algorithm was evaluated using various models, and the 3D-printed results were analyzed. Findings indicate that our algorithm performs reliably on target organic shapes with minimal loss of input geometry.

Figures (15)

• Figure 1: The physicalization of potato-shaped biological structures with $k$ types of triangles. Back row: SARS-CoV-2 virion membrane (left) with $k=2$, SARS-CoV-2 virion membrane with smooth triangle patches (right), using $k=6$, and front row: cell nuclei membrane (left), using $k=5$, SARS-CoV-2 virion membrane (center), using $k=2$, mitochondria outer membrane (right), using $k=6$.
• Figure 2: The overview of the presented method illustrating inputs and outputs of the individual steps.
• Figure 3: Converting segmented volumetric data (left) to mesh representation using Marching Cubes (middle) and mesh refinement using cvt (right).
• Figure 4: Triangle distance metric based on the sorted lengths of individual edges.
• Figure 5: Pressure calculation for vertex translation. Left: three cases of pressure direction. The current edge length is increased/decreased/kept unchanged depending on the required edge length. Right: 1-ring neighborhood of a vertex $v_c$ and calculation of accumulative pressure.