Rays and Spheres: The MATH! // Ray Tracing series

Visit http://brilliant.org/TheCherno to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. AMAZING place to learn all the math you'll need for this series! Support on Patreon ► https://patreon.com/thecherno Discord (#raytracing-series) ► https://discord.gg/thecherno Source code ► https://github.com/TheCherno/RayTracing 🧭 FOLLOW ME Instagram ► https://instagram.com/thecherno Twitter ► https://twitter.com/thecherno Twitch ► https://twitch.tv/thecherno Learn C++ with my series ► https://www.youtube.com/watch?v=18c3MTX0PK0&list=PLlrATfBNZ98dudnM48yfGUldqGD0S4FFb 📚 RESOURCES (in order of complexity) 🟢 Ray Tracing in One Weekend series ► https://raytracing.github.io 🟡 Scratch a Pixel ► https://scratchapixel.com 🔴 Physically Based Rendering: From Theory to Implementation ► https://amzn.to/3y2bGK7 💾 SOFTWARE you'll need installed to follow this series Visual Studio 2022 ► https://visualstudio.microsoft.com Git ► https://git-scm.com/downloads Vulkan SDK ► https://vulkan.lunarg.com Welcome to the exciting new Ray Tracing Series! Ray tracing is very common technique for generating photo-realistic digital imagery, which is exactly what we'll be doing in this series. Aside from learning all about ray tracing and the math to goes into it, as well as how to implement it, we'll also be focusing on performance and optimization in C++ to make our renderer as efficient as possible. We'll eventually switch to using the GPU instead of the CPU (using Vulkan) to run our ray tracing algorithms, as this will be much faster that using the CPU. This will also be a great introduction to leveraging the power of the GPU in the software you write. All of the code episode-by-episode will be released, and if you need help check out the #raytracing-series channel on my Discord server. I'm really looking forward to this series and I hope you are too! ❤️ CHAPTERS 0:00 - Math and this episode 5:03 - Lines and rays 11:45 - Spheres and circles 17:23 - How this relates to ray tracing 19:23 - How do we find intersection points? 23:50 - Quadratic equations 28:22 - Solving the equation 29:16 - Using the discriminant to see if there are intersections 32:32 - Finding exact intersection points 35:53 - Validating our result 36:37 - Next steps and homework This video is sponsored by Brilliant. #RayTracing