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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!

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

RandomPoint[
    Triangle[{{-.154,-.246,-.439},{-.0055,-.3945,-.3895},{-.154,-.444,-.241}}],
    10
]

{{-0.113334, -0.366351, -0.34576}, {-0.142944, -0.361738, -0.330633}, \ {-0.117064, -0.338707, -0.370917}, {-0.0205711, -0.396208, -0.377744}, \ {-0.14849, -0.390776, -0.297898}, {-0.120295, -0.292451, -0.415019}, \ {-0.13287, -0.402038, -0.297049}, {-0.132239, -0.354835, -0.344672}, \ {-0.125268, -0.283741, -0.420414}, {-0.114952, -0.36908, -0.341952}}

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