Research Topics on Parametric Modeling and Scan-to-BIM for Historical Vault Geometry
The shift from traditional craftsmanship to digital reconstruction has created a new frontier for heritage documentation. As builders of the past shaped vaults directly around existing surfaces, today’s BIM operators face the challenge of translating these irregular geometries into accurate digital models. Modern approaches rely on mathematical descriptions, point-cloud processing, and parametric thinking to bridge this gap.
Challenges in Digitizing Historical Vault Geometry
Historical vaults rarely present uniform or idealized shapes, which complicates their capture and representation. Surface deformations, construction tolerances, and geometric irregularities require advanced scanning, segmentation, and modeling strategies to achieve BIM-ready outputs. Understanding these constraints is key to advancing reliable Scan-to-BIM workflows.
Role of Mathematical Descriptors in Parametric Vault Modeling
A descriptive mathematical framework allows researchers to abstract irregular vault shapes into manageable parameters. By defining governing variables, both simple and complex vault models can be replicated digitally. This structured representation supports consistency, repeatability, and adaptability across vault typologies.
Integrating Clustering, Optimization, and Fourier Analysis
Advanced computational tools provide a deeper reading of geometric variation. Clustering algorithms group similar vault sections, optimization refines parametric variables, and Fourier frequency analysis uncovers hidden geometric patterns. Together, these methods strengthen the accuracy of geometric reconstruction.
Kriging Interpolation for Surface Prediction in Scan-to-BIM
Ordinary Kriging offers a statistical approach to estimate and smooth irregular vault surfaces. By predicting spatial patterns within point clouds, it enhances surface continuity and reduces noise. Its integration into parametric workflows supports the development of more reliable vault models for heritage structures.
Validation of Simple and Complex Parametric Vault Models
Evaluating BIM models against segmented point clouds ensures that geometric replicas match physical conditions. The reported standard deviations (±0.0085 m and ±0.0066 m) demonstrate high precision across models. The minimal variation between simple and complex models proves the stability and robustness of the proposed mathematical approach.
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