Parametric surface reconstruction from 3D point data using partial differential equation and bilinearly blended Coons patch

Existing methods for parametric surface reconstruction from 3D point data typically segment the points into multiple subsets, each fitted with a parametric surface patch. These methods face two primary issues. First, they fail to achieve positional continuity between adjacent patches, resulting in gaps or overlaps. Second, parameterizing the data within each subset is a challenging task. In this paper, we address these problems by proposing a novel surface reconstruction method based on Partial differential equation (PDE) deformation surfaces and bilinearly blended Coons patches. Our approach involves first extracting four boundaries for each subset. Next, we generate a bilinearly blended Coons patch from these boundaries. Any errors between the points in the subset and their corresponding points on the Coons patch are minimized or eliminated using a PDE deformation surface, which employs as many unknown constants as necessary to achieve this goal. The proposed method offers several advantages. Firstly, it ensures good positional continuity between adjacent patches, as they share common boundaries. Secondly, reconstruction errors can be easily controlled by adjusting the hyper-parameters in the PDE deformation equation, thereby changing the number of unknown constants as needed. Thirdly, the challenge of point parameterization within each subset is effectively addressed by using the bilinearly blended Coons patch. We validate our method on various datasets of differing complexities and shapes, with results demonstrating the effectiveness and advantages of our approach.