Stitching Locally Fitted T-Splines for Fast Fitting of Large-Scale Freeform Point Clouds

Area of Science:

• Optical Engineering
• Computer-Aided Design (CAD)
• Computational Geometry

Background:

• Parametric splines, particularly T-splines, are essential for precision optical metrology of complex freeform surfaces.
• Existing T-spline fitting algorithms (global, local, split-connect) face computational efficiency challenges with large datasets and high accuracy demands.

Purpose of the Study:

• To develop a speed-improved algorithm for efficient, large-scale freeform point cloud fitting using T-splines.
• To enhance the computational performance of T-spline fitting for optical metrology applications.

Main Methods:

• A novel algorithm is proposed that stitches locally fitted T-splines using a series of localized operations.
• The method focuses on optimizing the fitting process for speed and scalability.

Main Results:

• The proposed algorithm demonstrates a 3-to-8-fold efficiency improvement over global and local fitting algorithms.
• It achieves a 2-to-4-fold improvement compared to the latest split-connect algorithm in high-accuracy, large-scale scenarios.
• A Lena image study confirmed the algorithm is at least twice as fast as the split-connect algorithm, using fewer control points.

Conclusions:

• The developed algorithm offers a significant advancement in the computational efficiency of T-spline fitting for freeform surfaces.
• This improved speed is crucial for handling large-scale data in precision optical metrology and other demanding applications.