# How to solve for points in a region of a plane? [closed]

I have three points in 3D Cartesian space:

A = {-0.154, -0.246, -0.439};

B ={-0.0055, -0.3945, -0.3895};

C= {-0.154, -0.444, -0.241};


that all lie on the plane with the equation: 1x + 1.5y + 1.5z = -1.1815

The region of interest is bounded by the vectors AB, AC, BC.

I'd like to generate a list of coordinates that lie both on the plane and that fall within this bounded region.

Any help is greatly appreciated on how to approach this problem!

• What do you mean by "a list of coordinates"? – David G. Stork Feb 6 '18 at 0:47
• There are an uncountable infinity of points inside a triangle. How do you want to select a finite set of them? – m_goldberg Feb 6 '18 at 1:45
• Ever heard about barycentric coordinates? If not, you might give it a shot... – Henrik Schumacher Feb 6 '18 at 10:42

RandomPoint[