3D Surface Reconstruction from Surface Normals with Implementation Details

This documentation package contains four specialized MATLAB functions for 3D surface reconstruction and analysis. The primary function, shapeletsurf.m, implements surface reconstruction from normal vectors by employing shapelet decomposition techniques that represent surface orientations in frequency domain. The frankotchellappa.m function specifically addresses the integrability constraint problem in surface reconstruction using Frankot and Chellappa's Fourier domain algorithm, which projects non-integrable gradient fields onto the nearest integrable solution through spectral processing. The grad2slanttilt.m function performs mathematical conversions from gradient values (p,q) to slant (surface inclination) and tilt (surface orientation) angles using inverse tangent operations and quadrant-aware calculations. Conversely, slanttilt2grad.m implements the reverse transformation, computing gradient components from angular representations through trigonometric relationships. Each function includes error handling and validation for input parameters. For complete implementation details, parameter specifications, and usage examples, please refer to the comprehensive documentation included in the compressed file.