Surface Explorer

Surface Explorer is a high-performance visualizer for intricate mathematical surfaces, 2D manifolds embedded in three- or four-dimensional space, bringing abstract geometry to life with real-time GPU rendering. KEY FEATURES • Ray Marching Engine — real-time rendering of implicit surfaces and signed-distance fields, with procedural displacement, transparency, and multi-layer field surfaces. • Geodesic Flow — explore intrinsic geometry on curved manifolds (S³, H²×R, SL(2,R) and more), integrating geodesics from initial conditions. • 4D Spatial Exploration — dedicated controls for hyperspatial rotation (Omega, Phi, Psi) and projection. • 4D Lighting Models — Directional, Observer, and Slice lighting designed for hyperspace. • Dynamic GLSL Scripting — write custom shaders for procedural textures and surface logic in the built-in editor. • Audio-Visual Synthesis — synchronize geometric parameters with a mathematical sound synthesizer. • Video Recording — capture your explorations directly in the app and save them to your device. A library of ready-made presets ships with the app, from classic parametric surfaces to black-hole ergospheres and curved-space tori. Built with Qt and Metal for smooth, native performance on iPhone and iPad.