From Point Clouds to 3D Simulations of Marble Sulfation

In this chapter we present a complete workflow for the prediction of the marble sulfation of a work of art. The computations are based on a mathematical model of the physical-chemical phenomenon of penetration of a pollutant gas in the pores of the stone, its reaction with the pristine material and the consequent change of porosity and speed of diffusion of the gas. The computations are performed in three space dimensions and the geometry of the object is described by a levelset function, which in turn is computed from a cloud of points belonging to the surface of the object, without using any information on the connectivity among the points. We consider a synthetic and a real object. On the first an exact levelset is also known and we study the convergence of the levelset algorithms and compare the solutions computed on the exact and on the approximated geometry. The second one is a point cloud acquired by laser scanning a real stone object representing a frog.