3D updating of solid models based on local geometrical meshes applied to the reconstruction of ancient monumental structures

Abstract

We introduce a novel methodology for locally updating an existing 3D solid model of a complex monumental structure with the geometric information provided by a 3D mesh (point cloud) extracted from the digital survey of a specific sector of a monument. Solid models are fundamental for engineering analysis and conservation of monumental structures of the cultural heritage. Finite elements analysis (FEA), the most versatile and commonly used tool for the numerical simulation of the static and dynamic response of large structures, requires 3D solids which accurately represent the outside as well as the inside geometry and topology of the domain to be analyzed. However, the structural changes introduced during the lifetime of the monument and the damage caused by anthropogenic and natural factors contribute to producing complex geometrical configurations that may not be generated with the desired accuracy in standard CAD solid modeling software. On the other hand, the development of digital techniques for surveying historical buildings and cultural monuments, such as laser scanning and photogrammetric reconstruction, has made possible the creation of accurate 3D mesh models describing the geometry of those structures for multiple applications in heritage documentation, preservation, and archaeological interpretations. The proposed methodology consists of a series of procedures which utilize image processing, computer vision, and computational geometry algorithms operating on entities defined in the Solid Modeling space and the Mesh space. The operand solid model is defined as the existing solid model to be updated. The 3D mesh model containing new surface information is first aligned to the operand solid model via 3D registration and, subsequently, segmented and converted to a provisional solid model incorporating the features to be added or subtracted. Finally, provisional and operand models are combined and data is transferred through regularized Boolean operations performed in a standard CAD environment. We test the procedure on the Main Platform of the Huaca de la Luna, Trujillo, Peru, one of the most important massive earthen structures of the Moche civilization. Solid models are defined in AutoCAD while 3D meshes are recorded with a Faro Focus laser scanner. The results indicate that the proposed methodology is effective at transferring complex geometrical and topological features from the mesh to the solid modeling space. The methodology preserves, as much as possible, the initial accuracy of meshes on the geometry of the resultant solid model which would be highly difficult and time consuming using manual approaches.