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Find triangles half of surface, and tetrahedron half of volume

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triv.png

on pic you see that blue color has the same area as red one  (and they are not sliced)

 

i need to find new base and new h that  it will have half of original tri area [to be more precise for triangle i need the point ].And for tetrahedron thing i think i will have to start from that tip of pyramid, otherwise it will break my calculations  :x

 

for thetrahedron it seems it has the same base * height  problem, anyway i need to find the point that lies on new base if i find new h for that base, so it will have half volume of original one, i will be able to easily claculate the point for it

 

 

all triangle vertices are known, (for thetrahedron base and h is known too). triangle can be any triangle.

Edited by WiredCat

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For cutting a triangle in half, based on your image, the dimensions of the cut are like so: 

 

WLlkGWb.png

 

The same thing goes for pyramid with a triangle base, otherwise known as a 3-simplex. Multiply the height of the triangle by sqrt(2)/2 and that's how far down from the tip you have to go before you can cut perpendicularly to get a 3-simplex with half the volume

Edited by CulDeChu

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i think that wont work for tris and tetrahedrons liek this. base is uknnown and i pick it as the first side of triangle, thus the height is easy one (modified closestpointonline)

 

tris2.png

 

what i actually have is the base and height of tetrahedron, verts etc.

 

for triangles i start with 3 vertices only

 

 

edit.

 

after some research i think my solution to all problem is easy: geometric center.:)

Edited by WiredCat

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