Triangle Point Picking -- from Wolfram MathWorld
Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by x=a_1v_1+(1-a_1)a_2v_2, (1) where A_1 and A_2 are uniform variates in the interval [0,1]. However, as can be seen in the plot above, this samples the triangle nonuniformly, concentrating points in the v_1 corner. Randomly picking each of the trilinear coordinates from a uniform distribution [0,1] also does not produce a uniform
Considering a plane in 3D space with a triangle in it and a random point anywhere on that plane, what formula will tell me if the point is inside the triangle?
![](https://arxiv.org/html/2304.14388v3/x26.png)
Entropy and chirality in sphinx tilings
![](https://www.wikihow.com/images/thumb/9/90/Find-the-Area-of-an-Isosceles-Triangle-Step-1-Version-3.jpg/v4-460px-Find-the-Area-of-an-Isosceles-Triangle-Step-1-Version-3.jpg.webp)
How to Find the Area of an Isosceles Triangle (with Pictures)
![](https://cdn.serc.carleton.edu/images/mathyouneed/geomajors/ternary/teranry_all_1687539251625964187_744.webp)
Ternary Diagrams
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![](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Triangle_illustration.svg/640px-Triangle_illustration.svg.png&w=640&q=50)
Triangle - Wikiwand
![](https://devforum-uploads.s3.dualstack.us-east-2.amazonaws.com/uploads/original/4X/f/7/5/f756e915717b52e609a8733337d9399ff7dac13b.png)
Can someone help me get a value from this function - Scripting Support - Developer Forum
![](https://static.miraheze.org/rosettacodewiki/thumb/4/4e/SierpinskiTriangle-turtle.png/300px-SierpinskiTriangle-turtle.png)
Sierpinski triangle/Graphical - Rosetta Code
![](https://content.wolfram.com/sites/19/2015/06/Durrani_PlacedGraphics_2.gif)
Computing Exact Closed-Form Distance Distributions in Arbitrarily
![](https://img.yumpu.com/62571378/1/500x640/the-cosmic-game.jpg)
The Cosmic Game
![](https://www.robertdickau.com/thomsen3.png)
Thomsen's Figure - Robert Dickau
![](https://www.grc.nasa.gov/www/k-12/airplane/Images/coords.jpg)
Rectangular and Polar Coordinates
![](https://mathworld.wolfram.com/images/gifs/IsoscelesRightTriangleLinePicking.gif)
Triangle Line Picking -- from Wolfram MathWorld