Error-Bounded Unstructured T-spline Surface Fitting With Low Distortion

With the development of 3D acquisition technology,a large number of 3D discrete geometric models came into being.However,these models can rarely be directly edited in computer modeling design.In computer-aided design,we generally describe spline surfaces as parametric equations.This representation method has higher order continuity and more compact properties,making it more conducive to the description and editing of smooth shapes in modeling design.Therefore,we need to perform spline surface fitting on the input discrete data to obtain a spline surface that is easy to edit.This paper focuses on how to fit discrete triangular meshes.The goal is to make the error between the fitting spline surface and the input mesh bounded,the spline function has low distortion,and the number of control vertices is small.This paper presents a new method for calculating fitting spline surfaces:given a triangular mesh fitting domain of any complex topology,a low distortion unstructured Tspline fitting surface with bounded error is obtained.The key of this method is to adopt a step-by-step solution strategy to meet the three objectives of low distortion,fitting error threshold and fewer control points.In order to solve a mapping suitable for obtaining spline surfaces with low fitting error,we generate a polycube structures with the same topology as the fitting domain as the parameter domain,and optimize the corresponding relationship between the surface to be fitted and the parameter domain through multiple re-parameterization processes to obtain a low distortion mapping.At the same time,we use the local subdivision property of unstructured T-spline,the region that does not meet the fitting error is adaptively subdivided,and the low distortion spline surface that meets the fitting error is obtained.Next,in order to obtain the fitting surface with less control vertices,we present a fitting surface simplification strategy that removes redundant control vertices.The redundant control vertices are deleted on the basis of satisfying the fitting error threshold and low distortion.The effectiveness of this methodis proved on various complex models.Compared with the latest methods,this method could attain lower parametric distortion with fewer control vertices.