Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces

Area of Science:

• Computational electromagnetics
• Geometric optics
• Numerical analysis

Background:

• Calculating creeping ray paths on complex surfaces is challenging.
• Geodesic paths on nonuniform rational B-splines (NURBS) surfaces require numerical solutions.
• Modeling realistic objects often involves multiple connected NURBS patches, complicating path computation.

Purpose of the Study:

• To present an accurate creeping ray-tracing algorithm for arbitrarily shaped free-form parametric surfaces.
• To address the difficulty in determining geodesic paths on nonuniform rational B-splines (NURBS) surfaces.
• To enable the computation of creeping ray paths on complex objects composed of multiple NURBS patches.

Main Methods:

• Creeping ray tracing on individual NURBS patches solved using geodesic equations and a Runge-Kutta method.
• A novel transition method developed to handle creeping ray propagation across the borders of connected NURBS patches.
• Algorithm applied to complex objects modeled as unions of NURBS surface patches.

Main Results:

• The algorithm accurately determines the tracks of creeping rays on complex NURBS surfaces.
• The method successfully computes geodesic paths across connected NURBS patches.
• Numerical results validate the algorithm's accuracy and usefulness.

Conclusions:

• The developed creeping ray-tracing algorithm is practical for complex shapes.
• The algorithm enhances the applicability of NURBS surfaces in electromagnetic and optical fields.
• This work provides a robust method for analyzing surface diffracted fields on complex geometries.