#7 Amazing Morphing Wave Functions: Sine, Grid, 3D, Perspective, Rotate скачать в хорошем качестве

#7 Amazing Morphing Wave Functions: Sine, Grid, 3D, Perspective, Rotate

August 3, 2024. This video showcases the same equations as the prior, except the result is not rendered as a graph where the solution is zero. Instead, the actual result is converted into a prismatic color spectrum approximately covering all values from -1 to +1, where it fades to black beyond that range. While it's harder to see the beauty in the equation solutions, it does show a nice color gradient of possible values, and has some nice transitions. Although, if I were to solely showcase the color gamut, I would have chosen different equations. In this case, it's nice to compare against the original video to see the differences and similarities. I added a few more intro and outro equations in the mix, including the classic y = x equation to showcase the basics of the rainbow optical spectrum, from which to understand the rest. The color mapping I used is taken from Ken Silverman's EvalDraw program: R = exp((v - 0.75)^2 * -8) G = exp((v - 0.50)^2 * -8) B = exp((v - 0.25)^2 * -8) It makes for a nice smooth flow of colors since the changes in R, G, and B are not abrupt and linear like they are in the classic color wheel, or when converting HSV to RGB. I have similar examples in a ShaderToy demo: https://shadertoy.com/view/4dVXWW 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) intro y - x y - pow(x, 2) (y*y+x*x - 2) y - x 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) sin(x * 5.0 / abs(y)) * sin((5.0 / abs(y)) + t * 8.0) sin(xrot(x,y,t) * 5.0 / abs(yrot(x,y,t))) * sin((5.0 / abs(yrot(x,y,t))) + t * 8.0) outro y - x (y*y+x*x - 2) y - pow(x, 2) y - x 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