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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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closed as unclear what you're asking by Daniel Lichtblau, m_goldberg, Henrik Schumacher, Coolwater, LCarvalho Feb 8 '18 at 19:35

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 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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