Non-Uniform B-Spline Surface Fitting from Unordered 3D Point Clouds for As-Built Modeling

The three-dimensional mapping of the built environment is of particular importance for engineering applications such as monitoring work-in-progress and energy performance simulation. The state-of-the-art methods for fitting primitives, non-uniform B-Spline surface (NURBS) and solid geometry to point clouds still fail to account for all the topological variations or struggle with mapping of physical space to parameter space given unordered, incomplete, and noisy point clouds. Assuming an input of points that can be described by a single non-self-intersecting NURBS, this article presents a new method that leverages segmented point clouds and outputs NURBS surfaces. It starts by successively fitting uniform B-Spline curves in two-dimensional as planar cross-sectional cuts on each surface. An intermediate B-Spline surface is then computed by globally optimizing and lofting over the cross-sections. This surface is used to parameterize the points and perform final refinement to a NURBS. For cylindrical segments such as pipes, a new supervised method is also introduced to string the fitted segments, identify connection types, standardize the connections, and then refine them using NURBS optimization. Experimental results show the applicability of the proposed methods for as-built modeling purposes.