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Concise Plane Arrangements for Low-Poly Surface and Volume Modelling

Raphael Sulzer, Florent Lafarge

TL;DR

The paper tackles the scalability bottleneck of plane-arrangement-based 3D modelling by introducing a concise, adaptive plane arrangement framework driven by a dynamic plane–cell ordering and inlier-point based intersection tests. This approach, built on a BSP-tree, also integrates a remeshing and simplification pipeline to produce lightweight surface meshes and convex decompositions of volumes from point clouds. Empirical results across plane-assembly, surface simplification, and volume decomposition show state-of-the-art efficiency and competitive accuracy against both learning-based and traditional methods on datasets like Thingi10k and ShapeNet. The method handles thousands of planes, yields watertight and intersection-free representations, and offers practical benefits for storage, analysis, and downstream applications in low-poly modelling. Code is publicly available, enabling broad adoption and further research in concise 3D representations.

Abstract

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire scenes: (i) an ordering scheme for the plane insertion and (ii) the direct use of input points during arrangement construction. Both ingredients reduce the number of unwanted splits, resulting in improved scalability of the construction mechanism by up to two orders of magnitude compared to existing algorithms. We further introduce a remeshing and simplification technique that allows us to extract low-polygon surface meshes and lightweight convex decompositions of volumes from the arrangement. We show that our approach leads to state-of-the-art results for the aforementioned tasks by comparing it to learning-based and traditional approaches on various different datasets. Our implementation is available at https://github.com/raphaelsulzer/compod .

Concise Plane Arrangements for Low-Poly Surface and Volume Modelling

TL;DR

The paper tackles the scalability bottleneck of plane-arrangement-based 3D modelling by introducing a concise, adaptive plane arrangement framework driven by a dynamic plane–cell ordering and inlier-point based intersection tests. This approach, built on a BSP-tree, also integrates a remeshing and simplification pipeline to produce lightweight surface meshes and convex decompositions of volumes from point clouds. Empirical results across plane-assembly, surface simplification, and volume decomposition show state-of-the-art efficiency and competitive accuracy against both learning-based and traditional methods on datasets like Thingi10k and ShapeNet. The method handles thousands of planes, yields watertight and intersection-free representations, and offers practical benefits for storage, analysis, and downstream applications in low-poly modelling. Code is publicly available, enabling broad adoption and further research in concise 3D representations.

Abstract

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire scenes: (i) an ordering scheme for the plane insertion and (ii) the direct use of input points during arrangement construction. Both ingredients reduce the number of unwanted splits, resulting in improved scalability of the construction mechanism by up to two orders of magnitude compared to existing algorithms. We further introduce a remeshing and simplification technique that allows us to extract low-polygon surface meshes and lightweight convex decompositions of volumes from the arrangement. We show that our approach leads to state-of-the-art results for the aforementioned tasks by comparing it to learning-based and traditional approaches on various different datasets. Our implementation is available at https://github.com/raphaelsulzer/compod .
Paper Structure (30 sections, 1 equation, 11 figures, 2 tables)

This paper contains 30 sections, 1 equation, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Concise Surface Reconstruction.
  4. Plane Arrangement.
  5. Volumetric Decomposition of 3D shapes.
  6. Algorithm
  7. Background on Adaptive Plane Arrangement
  8. Our Concise and Scalable Plane Arrangement
  9. Ordering of Splitting Operations.
  10. Fast Intersection Tests with Inlier Points.
  11. Practical Description.
  12. Remeshing and Simplification
  13. Aggregation of Convex Facets.
  14. Aggregation of Convex Cells.
  15. Experiments
  16. ...and 15 more sections

Figures (11)

  • Figure 1: Our representation of the Meeting Room tanksandtemples as a watertight and intersection-free surface mesh with 90k polygonal facets (center) or as a simplified volume mesh with 2500 convex polyhedra (right). Our method inputs 40k planes (middle left) detected from a LiDAR scan of the scene (top left). For comparison, a Screened Poisson screened_poisson reconstruction consists of over 6M triangles (bottom left).
  • Figure 2: Pipeline. Our method processes a set of planes with their corresponding inlier points \ref{['subfig:pipeline_b']} detected from a point cloud \ref{['subfig:pipeline_a']} into a compact plane arrangement \ref{['subfig:pipeline_c']}. From this arrangement we extract either a watertight and intersection-free surface mesh \ref{['subfig:pipeline_d']} or a volume mesh with intersection-free convexes \ref{['subfig:pipeline_e']}. The surface mesh can optionally be remeshed to represent each planar region with only one facet, and with Delaunay triangles for regions with holes \ref{['subfig:pipeline_f']}. The remeshed surface is still watertight and intersection-free. The volume mesh can be simplified by merging groups of convex volumes and potentially allowing them to intersect \ref{['subfig:pipeline_g']}.
  • Figure 3: Comparison with Plane Arrangements. Our algoritm builds a more concise plane arrangement than existing mechanisms (top row), leading to a polyon mesh with fewer facets (bottom row).
  • Figure 4: Scalability. Average runtime (left) and memory peak (right) in function of the number of input planar shapes for different construction mechanisms. The transparent band around each curve indicates the minimal and maximal values measured on various models. Our algorithm offers the best performance and can process 10k planar shapes in around 30 minutes without exceeding the memory consumption of a standard computer. It also exhibits a better stability than other methods whose variation bands are thicker.
  • Figure 5: Surface Mesh Simplification. We compare RLPM and our pipeline on models from Thingi10k. We triangulate our output and perform edge collapse based on QEM s.t. OursTri and RLPM have the same number of triangles. \ref{['subfig:robust_a']} The runtimes of the methods, number of vertices $|V_S|$ and facets $|F_S|$ of the surface meshes (i.e. triangles for RLPM and OursTri, and polygons for Ours), and Chamfer (CD) and Hausdorff distance (HD) and normal consistency (NC) between ground truth and reconstruction. \ref{['subfig:robust_b']} The reconstructions of the Tower of Pi from the dataset. Note how both, our polygon and our triangle mesh is much more detailed compare to the one of RLPM.
  • ...and 6 more figures