Dividing a triangle into equal parts

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?

[Matt Fig]

Show the code you have written so far.

[Anton Semechko]

When you say equal, do you mean the triangles should have equal areas?

Answer 1

[Image Analyst]

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?

Answer 2

[Anton Semechko]

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.

[Image Analyst]

Good point. I didn't think of it like that. I was thinking that the original sides would each be the base of a triangle and the vertex would be somewhere inside the original triangle, but your way is an alternate way of chopping up the triangle into parts that is easier to solve.

[Walter Roberson]

My recollection is that equally spaced points gives the desired solution, but an immediate proof of that is not coming to mind.

[Image Analyst]

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.