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Computational Geometry Reconstruction of 3D Irregular Multi-Leaf Masonry with Generated Internal Blocks and Lumped Joints

par Hermans, Yahroun Fei ;Ehab Moustafa Kamel, Karim ;Milani, Gabriele;Massart, Thierry Jacques
Référence International Masonry Conference (IMC2026)(11: 12/7/2026-15/76/2026: Lubeck, Germany), Proceedings of the 11th International Masonry Conference
Publication Publié, 2026-07-15

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Recent advances in image-based reconstruction have significantly improved our ability to investigate masonry mechanics, particularly in combination with kinematic Limit Analysis approaches. Nevertheless, most applications to date remain restricted to planar or quasi-2D frameworks, relying primarily on visible wall surfaces and idealised internal representations. For historical masonry, this leads to geometric simplifications that neglect the hidden heterogeneity of rubble cores or multi-leaf arrangements. The present contribution introduces a methodology that enables the construction of fully three-dimensional computational geometries of blocky masonry directly from segmented image data, where visible masonry leaves are reconstructed from observations and inaccessible internal regions are populated with generated blocks that resemble stone rubble. The approach yields explicit block–joint representations suitable for subsequent structural modelling and block-based Limit Analysis, thus bridging the gap between image-driven reconstruction and realistic 3D simulation of masonry.The process begins with segmentation of masonry images obtained through photogrammetry or LiDAR scanning. From these data, the outer stones are delineated through segmentation techniques. This information then serves as input for a 2D watershed-based expansion, representing mortar joints as zero-thickness interfaces between adjacent blocks and ensuring that neighbouring stone boundaries touch, resulting in a coherent tessellation of the visible surface. These segmented outer leaves are subsequently extruded in the direction normal to the façade surface, reconstructing the visible masonry in depth and providing an approximate thickness measurement.This operation defines delimiting outer shells for both external leaves, separating regions where geometry is directly captured from those lacking measurement, namely the core infill of the wall. To reconstruct the interior, a synthetic block generation procedure is initiated by seeding points throughout the unobserved domain. A packing constraint is enforced through exclusion zones, ensuring a minimum separation between seed points and thereby controlling the effective block size distribution. These seeds are used to generate a constrained Voronoï tessellation [3], providing a first volumetric subdivision that outlines the rubble core.The tessellation cells act as delimiting domains for the generation of representative rubble blocks that are irregular and potentially non-convex.The signed distance field of each tessellation cell is computed, after which geometric irregularity is introduced through the synthesis of procedural noise fields. Inspired by stone-cutting patterns and quarry surface textures, several noise families are superimposed. Worley–Manhattan noise reproduces sharp planar partitions characteristic of tool-cut surfaces, while Open Simplex and Perlin noise introduce long-wavelength undulations and micro-pitting. The combination of these fields disrupts smooth Voronoï faces, creating local bulging, indentations, and fracture-like features. By summing the cell distance field with weighted noise perturbations and subsequently thresholding the result, non-convex rubble-like inclusions emerge that preserve the general proportions of the original cells while reflecting realistic stone textures. At this stage, a global signed distance field is computed over the entire masonry volume to quantify spatial relationships between inclusions and identify nearest neighbours. This field is used to inform a 3D watershed procedure. By incorporating the global distance information, noisy joints, where neighbouring expanded blocks might otherwise interpenetrate, are avoided. The resulting geometry exhibits contacting blocks that approximate stone-to-stone fitting without resorting to oversimplified planar joint assumptions. Once a consistent assembly is obtained, explicit identification of block interfaces becomes necessary to facilitate discretisation. The outer voxel layer of each processed block is extracted and analysed for adjacency relationships. Neighbourhood relations are defined using 26-connectivity, meaning that each voxel is consideredadjacent to all voxels sharing a face (6 neighbours), an edge (12 neighbours), or a corner (8 neighbours) within a 3×3×3 neighbourhood. For each voxel, the number of distinct block labels present in this neighbourhood is computed. Voxels belonging to regions where four or more blocks meet are classified as vertices, those associated with three-block adjacency as edges, and those adjacent to exactly two blocks as faces. This classification enables a robust geometric abstraction of the masonry interface network, capturing topological features independently of voxel orientation or local interface curvature. The vertex and edge groups serve as input for a graph-based edge reconstruction. Each edge extremity is associated with a vertex group, for which a representative point is determined. Through geodesic path evaluation, nodes are uniformly distributed along the edges. Voxelised faces are then sampled and combined with the corresponding edge nodes to construct triangulated surface meshes. These meshes define watertight block geometries with explicit zero-thickness joint surfaces. The availability of closed surface meshes further enables a straightforward extension to finite element simulations through the generation of tetrahedral elements.The capabilities of the proposed framework are illustrated through a kinematic Limit Analysis of a fully threedimensional masonry structure reconstructed directly from image data. The resulting block assembly is employed to investigate collapse mechanisms and failure kinematics, demonstrating the influence of irregular block shapes, non-planar interfaces, and inferred rubble-core configurations on structural response. Overall, the framework enables the systematic derivation of fully three-dimensional masonry geometries from image data, extending traditional segmentation approaches beyond the visible façade. By explicitly representing irregular and non-convex stone geometries together with inferred internal heterogeneity, it supports block mechanics simulations that incorporate realistic discontinuities rather than idealised planar interfaces. By bridging image-based reconstruction, geometric synthesis, and computational mechanics, the methodology supports fullscale analysis of low- to mid-sized historical stone masonry structures and ruins.