Geometric planning for masonry wall construction with natural stones using discrete convolution

Using unprocessed materials in construction is a promising approach to reducing energy and material consumption in the building industry. This paper presents a geometric planning algorithm for constructing multi-leaf masonry walls using natural stones. Our method combines hierarchical filtering with combinatorial optimization to determine the optimal arrangement of stones. The novelty of the approach lies in employing discrete convolution between landscape tensors and stone tensors for the rapid computation of geometric indices, which replicate traditional masonry expertise. This results in a stone stacking algorithm capable of generating densely packed masonry walls without restrictions on wall dimensions, stock size, or stone shapes. The generated walls are compared to those built by skilled masons, demonstrating comparable performance in terms of filling ratio, vertical joint interlocking, course horizontality and shear strength. Moreover, the algorithm exhibits robustness to variations in the stone sampling sequence and the number of stone orientations, while the number of candidate stones and the interlocking threshold significantly influence the metrics of the generated wall.