Math Viewer Just for fun with mathematics and stuff Contents File types Rendering GPU CPU Algorithms 2-space Spaces with arbitrary number of dimensions Technical details Images 3-manifold reconstruction and path tracing in 4-space 4D Cornell box Real-time rendering 3D models 4D polytope File types OBJ and STL files with objects in 3-space Extended OBJ and STL files with objects in n-space Text files with the coordinates of points in n-space Rendering GPU Triangle meshes (rasterization) Volumes (ray marching) Isosurfaces (ray marching) Shadows (ray tracing, ray marching, shadow mapping) Order-independent transparency (lists of fragments) CPU Bidirectional path tracing with multiple importance sampling (n-1)-simplex meshes in n-space on (n-1)-dimensional screen n-dimensional microfacet BRDF Spectral rendering Algorithms 2-space C++ and GLSL Subject Algorithms Discrete Fourier transform for arbitrary sizes Bluestein's algorithm and radix-2 fast Fourier transform Optical flow Pyramidal Lucas-Kanade Convex hull Divide et impera Spaces with arbitrary number of dimensions C++ Subject Algorithms Convex hull Randomized incremental Delaunay triangulation Convex hull of paraboloid Voronoi diagram The Delaunay triangulation Manifold reconstruction Cocone Manifold reconstruction with boundary detection BoundCocone Euclidean minimum spanning tree Kruskal’s algorithm and the Delaunay triangulation Intersection of hyperplanes Gaussian elimination Intersection of convex polytopes The simplex algorithm Ray intersection acceleration using spatial subdivision 2 d -trees Ray intersection acceleration using object subdivision Bounding volume hierarchies and the surface area heuristic Eigenvalues and eigenvectors of symmetric matrices Jacobi method Least squares fitting a plane to points Principal component analysis State estimation The Kalman filter The extended Kalman filter (EKF) The unscented Kalman filter (UKF) The H ∞ filter Technical details Property Value Programming languages C++23, GLSL 4.60 C++ compilers GCC 13, Clang 18 Platforms Linux Graphics and compute APIs Vulkan 1.3 with ray tracing extensions Frameworks Qt 6 Libraries FreeType, GMP Optional libraries cuFFT (for DFT tests), FFTW (for DFT tests) Build systems CMake Images 3-manifold reconstruction and path tracing in 4-space 2D images of a 3D image of the 3-manifold reconstructed from the points on the 3-torus T 3 (S 1 ×S 1 ×S 1 ) 5-space The convex hull 4-simplex facets 4-space 3-simplex mesh without boundary 4-parallelotope hierarchy 4-dimensional microfacet BRDF 3-ball light source 4-dimensional soft shadows Parallel projection onto 3D screen Volumetric rendering 4D Cornell box 2D images of a 3D image of the 4-dimensional Cornell box Seven 3-parallelotopes (the sides of the box) One 3-parallelotope light source One 3-simplex mesh without boundary (3-sphere) One 4-parallelotope 4-dimensional microfacet BRDF 4-dimensional soft shadows Perspective projection onto 3D screen Real-time rendering Semitransparent objects Triangle mesh (green) and its ray tracing shadows Isosurface (blue) and its ray marching shadows 3D models Spectral rendering Blackbody 2500 K Daylight 4000 K Daylight D65 Blackbody 12000 K 4D polytope 4-dimensional cross-polytope v -11 0 0 0 v 0 -12 0 0 v 0 0 -13 0 v 0 0 0 -14 v 0 0 0 15 v 0 0 16 0 v 0 17 0 0 v 18 0 0 0 f 1 2 3 4 f 1 2 3 5 f 1 2 6 4 f 1 2 6 5 f 1 7 3 4 f 1 7 3 5 f 1 7 6 4 f 1 7 6 5 f 8 2 3 4 f 8 2 3 5 f 8 2 6 4 f 8 2 6 5 f 8 7 3 4 f 8 7 3 5 f 8 7 6 4 f 8 7 6 5
