Delaunay Triangulation - A Tale of Triangles

In this video, I explain Delaunay Triangulation, why triangles are so important in computer graphics, how to generate triangles for a set of points, and 2 Delaunay triangulation algorithms - In a well animated, and step by step process.
It also answers the question, What is Overshading? and explains the inaccuracy of Finite Element Analysis when performed with poorly triangulated meshes.

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Resources
• https://en.wikipedia.org/wiki/Delaunay_triangulation
• https://en.wikipedia.org/wiki/Direct_stiffness_method
• http://fragmentbuffer.com/gpu-performance-for-game-artists/
• https://jeesunkim.com/notes/graphics/quads/
• https://stackoverflow.com/questions/16365385/explanation-of-dfdx
• https://developer.arm.com/documentation/101897/0304/Tessellation--
geometry-shading--and-tiling/Tiling-and-effective-triangulation
• An introduction to shader derivative functions - A Clockwork Berry - https://www.aclockworkberry.com/shader-derivative-functions/
• Learning DirectX 12, Lesson 4(Textures) - 3D Game Engine Programming - https://www.3dgep.com/learning-directx-12-4/

#computergraphics #gamedev #rendering #triangulation #proceduralmodeling #maths

Chapters
00:00 Intro - The Need for Normal vectors
00:24 Deriving Normal vector from triangle
00:54 Why Triangles
01:25 Opening Theme
01:48 Game dev tools
03:24 Difficulty of Triangulation
04:01 A Naive triangulation method
04:50 Problem with naive triangulation - Needle triangles
05:23 Problem with naive triangulation - Finite Element Analysis
06:29 Problem with naive triangulation - Overshading
07:31 Delaunay Triangulation - Intro
07:59 Delaunay Triangulation
08:45 Delaunay Condition on naive triangulation
09:14 Delaunay Algorithm 1 - Converting Naive triangulation to Delaunay
10:18 Delaunay Algorithm 2 - Bowyer - Watson Algorithm
12:21 Triangulation timelapse using Bowyer - Watson algo
13:38 Extra
13:56 Outro

Видео Delaunay Triangulation - A Tale of Triangles канала Diphiniti