Creating a Transparent Hemisphere with Rotation Capability in MATLAB

This MATLAB program enables you to generate a transparent hemisphere that can be freely rotated in 3D space for comprehensive viewing from all angles. The implementation utilizes parametric equations to define the hemispherical surface, where the x, y, and z coordinates are calculated using spherical coordinates with theta ranging from 0 to pi (latitude) and phi from 0 to pi (azimuth). Key functions employed include: - meshgrid: Creates the coordinate matrices for the spherical surface - surf: Renders the transparent surface with 'FaceAlpha' property set to 0.5 for transparency - rotate3d: Enables interactive rotation of the plot for dynamic visualization The program structure allows straightforward modification to create a full sphere by extending the phi range from 0 to 2*pi. This implementation provides valuable visual insights into spherical geometry and serves as an excellent educational tool for mathematics and physics instruction. Additional enhancements could incorporate texture mapping, custom color schemes using colormap functions, or surface pattern generation through mathematical functions. These extensions would demonstrate advanced MATLAB graphics capabilities while maintaining the core rotational and transparency features. The program exemplifies effective use of MATLAB's 3D visualization tools for both academic and research applications.