HackerPoet/NonEuclidean
NonEuclidean
NonEuclidean is a graphics framework and rendering engine designed to compute and display three-dimensional scenes using non-standard spatial rules and geometries. It serves as a visualization tool for exploring complex mathematical spaces where traditional Euclidean laws of distance and angle do not apply.
The project implements custom rendering pipelines to visualize non-standard geometric projections and warped spatial logic. This includes the ability to map non-Euclidean coordinates to Poincaré disk or Klein models to render curved space on flat screens.
The system utilizes dynamic metric tensor calculations, manifold-based mesh deformation, and non-linear projection matrices to determine how objects and light bend. It further incorporates ray-marching distance estimation and vertex-shader coordinate warps to simulate spatial curvature based on camera distance.
Features
- Non-Euclidean Metric Projections - Computes and displays three dimensional scenes using non-standard spatial rules and geometries.
- Graphics Programming - Implements custom rendering pipelines to visualize complex mathematical spaces and non-standard geometric projections.
- Non-Euclidean Space Projections - Maps non-Euclidean coordinates to Poincaré disk or Klein models to render curved space on flat screens.
- Geometry Visualization Tools - Provides a tool for rendering and exploring complex mathematical spaces and non-Euclidean geometric shapes in real time.
- 3D Rendering Engines - Functions as a graphics engine that computes and displays three dimensional scenes using non-standard spatial rules.
- Non-Euclidean Graphics Frameworks - Provides a specialized framework for creating visual environments where traditional Euclidean laws of distance and angle do not apply.
- Metric Tensor Calculations - Implements dynamic metric tensor calculations to determine how light and objects bend in non-standard spaces.
- Experimental Spatial Design - Builds immersive environments with impossible architectural loops or warped spatial logic for surreal gameplay.
- Manifold-Based Deformations - Modifies geometric primitives in real-time to fit the topological constraints of non-Euclidean spatial manifolds.
- Coordinate Warping - Offsets 3D vertex positions in the GPU pipeline to simulate spatial curvature based on distance from the camera.
- Non-Linear Projection Matrices - Replaces standard perspective projections with custom matrices that account for non-constant spatial expansion.
- Signed Distance Fields - Calculates surface intersections by stepping through a curved spatial field using signed distance functions.
