website articles
These are written articles on the techniques I develop for my computer graphics experiments, demos, shadertoys and movies. For video tutorials, code and other useful resources visit the landing page. All computer graphics and most of the maths here are self-taught, and similarly, all the content in this site is mostly written casually rather than in an academic form. I am a big fun of discovering and inventing things by myself, it's my little hobbie. Still, if you happen to base your academic research paper in any of this content, it would be fair to give proper credit, right...? Lastly, since I write these articles whenever I happen to have a little bit of spare time (mostly late at night), and as a non-native english speaker, I usually do lots of grammar mistakes in my writing. I always correct when a reader's emails me about them. Actually, thanks so much for reading guys!

 31 Dec 2018rational rendering and floating bar numbers 12 Sep 2018intersectors 07 Sep 20182D SDF functions 22 Aug 2018numerical normals for SDFs 22 Jun 2017gradient noise derivatives 03 Jun 2017raymarching SDFs If you want to help me allocate official time for more and better content, now you can become my patron on Patreon! Become a patron

118 articles, lots of grammatical and spelling errors, but hopefully some interesting math and code

 useful maths 2018. bezier bounding box 2017. inverse smoothstep 2016. disk/cylinder bounding box 2015. sphere density 2014. distance to triangle 2014. sphere projection 2011. distance estimation to implicits 2011. useful little functions 2010. inverse bilinear interpolation 2010. trigonometric tricks 2009. distance to an ellipse 2008. fourier series 2008. patched sphere 2008. sphere visibility 2008. on fm synthesis 2006. working with ellipses 2006. sphere ambient occlusion 2006. thinking with quaternions fractals/complex dynamics 2007. continuous iteration count 2006. area of M1 in the Mandelbrot set 2006. M2 bulb in the Mandelbrot set 2006. the M1 bulb of the Mandelbrot set 2006. the symmetry of the Mandelbrot set 2002. introduction to the Mandelbrot set fractals rendering algorithms 2011. iterative shapes 2009. mandelbulb fractal 2006. 3d orbit traps for fractals 2006. experimental 3d fractals 2004. distance rendering for fractals 2002. procedural traps for fractals 2002. bitmaps traps for fractals 2002. budhabrot fractals 2002. ifs fractals 2001. lyapunov fractals 2001. 3d julia set fractals 1999. geometric traps for fractals compression 2010. genetic algorithm 2007. mesh compression 2007. wavelet compression 2005. introduction to 3d models storage rendering techniques 2016. basic VR 2015. texture repetition 2015. texturing and raymarching 2015. numerical normals for SDFs 2015. sphere functions 2014. sphere soft shadow 2013. directional derivative 2013. filtering procedural textures 2013. smooth minimum 2006. volumetric sort 2005. modern raytracing 2002. terrain marching 2002. simple point clouds 2001. a basic raytracer 2000. simple voxel index of primitives, intersectors and bounding boxes 2017. intersectors 2015. sphere functions 2015. box functions 2013. 2D SDF functions 2008. 3D SDF functions lighting 2014. box occlusion 2013. outdoors lighting 2012. multires ambient occlusion 2012. simple pathtracing 2010. penumbra shadows 2010. better fog 2007. screen space ambient occlusion 2005. per vertex ao 2004. simple global ilumination procedural content 2017. filterable procedurals 2017. improved analytic checkers pattern filtering 2017. analytic checkers pattern filtering 2017. gradient noise derivatives 2008. raymarching SDFs 2015. modeling with SDFs 2008. value noise derivatives 2014. voronoise 2012. smooth voronoi 2012. voronoi edges 2002. domain warping 2002. icon images 1999. popcorn images explorations 2018. rational rendering and floating bar coding tricks 2016. stereo rendering 2015. gamma correct blurring 2013. tunnel artifact 2013. improved hardware interpolation 2013. fixing frustum culling 2013. avoiding trigonometry 2010. zbuffer for raymarching 2010. minimal frustum culling 2009. improved bilinear filtering 2008. tile rendering 2008. normal/areas for polygons 2005. float and random 2005. begining with sse coding 2004. clever normalization of a mesh 2003. how to render a cube in qbasic 2003. minimal spline code 2002. compiling small 1999. simple color palettes simple effects 2013. voxel lines and occlusion 2005. 2d dynamic clouds 2005. simple gpu raytracing 2004. simple water 2002. cellular effect 2002. feedback effect 1999. plane deformations 1998. the game of life coding hacks 2008. gm.dls textures 2008. how to store floats in 4k 2008. opening a file in 4k presentations 2009. Function 09 - Behind Elevated 2008. Function 08 - Living Characters in 4 kilobytes 2008. NVScene 08 - Rendering Worlds With Two Triangles 2007. Siggraph 07 - Massive Model Visualization 2007. Breakpoint 07 - Techniques for 64k demos 2006. ICM 06 - Mathematics in Movement