Dividing a triangle into equal parts

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UW
UW 2012-11-14
Hi Guys,
Can anyone tell me how can i divide a triangle into 'n' equal triangles?
I have a triangle set by 3 points P1, P2, P3. And can anyone help me with solving this problem?
  2 个评论
Matt Fig
Matt Fig 2012-11-14
Show the code you have written so far.
Anton Semechko
Anton Semechko 2012-11-14
When you say equal, do you mean the triangles should have equal areas?

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回答（2 个）

Image Analyst
Image Analyst 2012-11-14
Can't you use polyarea() to get the area of P1P2P3, and then, with a P4 inside the triangle, use polyarea() again to get the area of the 3 interior triangles. Then use fzero() to minimize 3*totalArea - area1-area2-area3?
Is this a homework problem?
Anton Semechko
Anton Semechko 2012-11-14
编辑：Anton Semechko 2012-11-14
Suppose you have a triangle defined by the vertices A, B and C. To subdivide this triangle into n triangles of equal area you can do the following:
1) Insert n-1 points along the edge AB
2) Connect new points to C to form n new triangles
3) Use the fact that the desired of area of each triangle is area(ABC)/n to adjust the positions of newly inserted points. Note that contrary to the suggestion given by Image Analyst, no optimization is required to compute new positions.
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Walter Roberson
Walter Roberson 2012-11-14
My recollection is that equally spaced points gives the desired solution, but an immediate proof of that is not coming to mind.
Image Analyst
Image Analyst 2012-11-14
Well if one point is fixed, and you divide the base by 3 then the area will be 1/3 the original area since the area is base*height/2 and the height is the same and the base is 1/3 the original base.

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