#6 Amazing Morphing Equations: 3D Perspective, Grid, Rotate, Complex Sine скачать в хорошем качестве

#6 Amazing Morphing Equations: 3D Perspective, Grid, Rotate, Complex Sine

July 28, 2024. Showcasing an array of fascinating equations, each morphing into the next. I lined up the equations to be mostly incremental changes from prior to produce a flow and also make interesting morphing patterns. The finale is my invention of the 3D formula which makes all 3D graphics on a 2D screen possible -- the Holy Grail of 3D graphics -- changed into a 2D equation. Many of the equations have a T variable which is the passage of time in seconds, though this can and is adjusted in real-time. Enjoy! Showcases: --------------------- smooth transition equation morphing 3D formulas rotation, via the xrot() and yrot() functions, which are simply the 2D rotation matrix: xrot(x, y, t) = x * sin(t) + y * cos(t) yrot(x, y, t) = x * cos(t) - y * sin(t) T animation speed adjustment Equations: ------------------ (In order, and grouped by category / pattern) patterns that eventually make a grid (sin(y * x) * cos(x * y)) - (cos(y - x) * sin(x - y)) (sin(y * x * x) * cos(x * y * y)) - (cos(y - x) * sin(x - y)) (sin(y * x * x + t) * cos(x * y * y - t)) - (cos(y - x + t) * sin(x - y - t)) (sin(y * x / t) * cos(x * y / t)) - (cos(y - x * t) * sin(x - y * t)) pixelated circle y*y + x*x - t (y - sin(y * t)) * (y + sin(y * t)) + (x - sin(x * t)) * (x + sin(x * t)) - t, void circles sin(x + y) + cos(y - x) - sin(x * y) sin(x + y + t) + cos(y - x + t) - sin(x * y) (sin(y * t * x) * cos(x * t * y)) - (cos(y - t) * sin(x - t)) wavy grid (sin(x + t) + cos(y - t)) - (sin(y - t) * cos(x + t)) (sin(x + t) + cos(y - t)) - (sin(y - t) * cos(x * t)) bubbly y - (sin(x * x) + cos(y * y) + sin(x * y) + cos(x * y)) y - (sin(x * x + t) + cos(y * y + t) + sin(x * y + t) + cos(x * y + t)) funky (cos(x) * y) - (sin(x + y * x) - y) (cos(x + t) * y) - (sin(x + y * x - t) - y) (cos(x+y) * (y-t)) - (sin((x-t) + (y-t) * (x-t)) - (y*t)) 2D grid sin(x) sin(y) sin(x) * sin(y) sin(xrot(x,y,t)) * sin(yrot(x,y,t)) 3D perspective sin(x * 5.0 / y) sin(5.0 / y) sin(x * 5.0 / y) * sin(5.0 / y) sin(x * 5.0 / y) * sin((5.0 / y) + t * 8.0) sin(xrot(x,y,t) * 5.0 / yrot(x,y,t)) * sin((5.0 / yrot(x,y,t)) + t * 8.0) Hardware / Processing: --------------------------------------- Rendering is entirely on the CPU! No GPU used except to upload the already rendered software buffer. Alienware m18 R2 NVIDIA GeForce RTX 4090 16GB GDDR6 (laptop version) 14th Gen Intel Core i9 14900HX (24-Core, 36MB L3 Cache, up to 5.8GHz Max Turbo Frequency) (16 E-Cores, and 8 P-Cores hyperthreaded = 32 V-Cores total) 64 GB: 2 x 32 GB, DDR5, 5200 MT/s, non-ECC, dual-channel 18" FHD+ (1920 x 1200) 480Hz, 3ms, ComfortView Plus, NVIDIA G-SYNC + DDS, 100% DCI-P3, FHD IR Camera AlienFX RGB backlit Alienware CherryMX ultra low-profile mechanical keyboard 4 TB, M.2, PCIe NVMe, SSD Playlists: -------------- Xona System 8:    • Game Dev Engine #1. A New Beginning.   Voxel:    • Voxel Engine #8 - Correct Peripheral ...   Ray Cast:    • 3D Ray Casting Engine: #4 (Global Gam...   Graph-All:    • #1 Graph-All Equation Renderer - Mult...   Scroll Shmup:    • The First Pixel: Devlog #9 - Enemies,...   Road:    • Pseudo 3D Road #8 - infinite vegetati...   Arena Shmup:    • Arena Shmup Demo #3 - Object Pool Opt...   Wave Function:    • A.I. Texture Generation, High Res (Wa...   3D Polygon:    • 3D Polygon Engine #9 - Multiple Mater...   GW-BASIC:    • GW-BASIC - Escape From Monster Cavern...   Websites: --------------- GitHub: https://github.com/JDoucette Blog: http://thefirstpixel.com Studio: http://xona.com