Surface Explorer

Surface Explorer is a high-performance visualizer for intricate mathematical surfaces — 2D manifolds embedded in three- or four-dimensional space, and 3D slices of four-dimensional hypersurfaces — bringing abstract geometry to life with real-time GPU rendering.

KEY FEATURES
• Cross Section — slice four-dimensional hypersurfaces and watch their 3D sections change shape as you rotate them in 4D or slide the cutting plane along the fourth axis, even along a 4D camera path.
• Ray Marching Engine — real-time rendering of implicit surfaces and signed-distance fields, with procedural displacement, transparency, adjustable shells, and a precise mode for high-degree equations.
• Multi-Mesh Surfaces — build figures from several independent grids, set with a single field or a script, each with its own color, transparency, texture, image and domain.
• Solid Curve — write a curve in 3D or 4D and see the tube drawn around it, with adjustable thickness; several tubes from a script.
• Surface Borders — add a tube along the edges of a parametric surface, with its own color, texture and thickness.
• 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), projection, and 3D and 4D camera paths.
• 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.
• Backgrounds — images and procedural effects, fixed on screen or wrapped around the scene as a sphere, cylinder or cube.
• 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, curved-space tori and slices of the 3-torus, together with a searchable built-in manual.

Built with Qt and Metal for smooth, native performance on iPhone and iPad.