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i was working in 3d geometry and i looking for know, if a point belongs to a triangle. I found this "Determine if projection of 3D point onto plane is within a triangle" but i doesn't know how resolve this operation. $$ γ=[(u⃗ × w⃗ )⋅n⃗ ]/n⃗ ² $$ On google i found how resolve

  • u × w
    • resulta.x = u.yw.z-u.zw.y;
    • resulta.y = u.zw.x-u.xw.z;
    • resulta.z = u.xw.y-u.yw.x;
  • u . w
    • resulta = (u.xw.x)+(u.yw.y)+(u.z*w.z);

But how resolve this : $$ [(u⃗ × w⃗ )⋅n⃗ ]/n⃗² $$

Community
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edelangh
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1 Answers1

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In these expressions that you copied (without great clarity), the "$n$" has an exponent of $2$ (one that's almost invisible on my system), so that it's $$ \gamma = [ (u \times w) \cdot n ] / n^2 . $$

That's a little sloppy; by $n^2$, the author means $n \cdot n$, i.e., $n_x^2 + n_y^2 + n_z^2$.

A further hint: to make life easier for the folks answering your questions, spend a minute learning how to use LaTeX to format your mathematics.

John Hughes
  • 93,729
  • thanks, this is my first question on Mathematics and i does know anything about Latex. – edelangh Sep 10 '14 at 13:13
  • Perhaps take a look at this tutorial: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – John Hughes Sep 10 '14 at 13:20