Scientific theoretic and applied developments,
original discoveries and inventions:
- Refined theory and applied algorithms for linear systems equations (LAS) resolution called “sequential and parallel orthogonalization” (versus known basic methods of Gauss- Jordan and Cramer’s rule), improved “special” cases of square-root and conjugated gradients algorithms.
- Fourier analysis refinement, the best solutions for radix 2 Fast Fourier Transform (FFT), Fermat Number Transform (FNT), new 2D real FFT and 3D FFT;
- A new branch in Fourier analysis called “Fourier-splines” convolutional approximation based on finite spline functions as truncated Fourier series.
- The most productional FFT-structure algorithm of array ranking (sorting), totally in-place, N*log(N) complexity.
- New mathematical 3D model approximation methods based on Fourier-series and/or Fourier-splines.
- The development of a project for a new codec/decodec standard based on Fourier-splines for digital 1D audio- signals, 2D images, 3D tomography etc providing correct and more efficient compression versus jpeg/mpeg for HDTV/DVD etc.
- The original fast rendering 3D engine with new features (rendering without z-buffer, arbitrary polygons including non-convex and nested ones, universal transparency, textures compression with Fourier-splines).
- Full set of algorithmic solutions for medical and seismic tomography primarily refined methods “Marching Cubes” and “Ray Casting”.
- Cloud-to-mesh transform for regular 3D models (devices Microsoft Kinect, Apple iPhone LIDAR etc)
for applications of virtual web-suiting, interior restoration and dynamic moving objects registration.
- Efficient targets recognition and navigation algorithmic solution for IR-warheads, sports shooting, biological applications (i.e. DNA photos processing) etc.
- Gravitational orbits and atom electrons orbitals approximation on Fourier-series basis or equivalently Fourier-splines basis (just 5 spectral Fourier components).
- Generalization of classic physical laws:
- gravity (I. Newton, followed a proof of galaxies stability without so called “dark matter”),
- electrostatic (J.O. Coulomb), Van-der-Waals, currents (A.M. Ampere) etc based on spread masses/charges model,
- final resolution of singularity problem in zero.
- Stars (including the Sun) in Galaxies movement theory development as generalization of classic Newton’s solution for planets and satellites in Fourier-series based on spread masses integrals;
- Planck’s law parameters fast determination algorithms based on series for different wavelengths (frequencies).
Specialization: physical modelling developments, high productional computing (HPC), fast mathematical algorithms for digital technologies based on parallel GPU processing (GLSL, NVIDIA CUDA).
Programming:
Languages C/C++, assembler,
Platforms Windows/Linux,
Microsoft Visual C++ 2022,
Trolltech Qt 5.15/6.11,
Borland C++ Builder 6.0,
Embarcadero RAD Studio,
OpenGL/GLSL,
NVIDIA CUDA/cuDNN,
OpenCV,
multi-threading acceleration.