Grasshopper

generative modeling for Rhino

# if a triangle's area will stay the same, by changing one of the point, how to let GH automatically update the position of the rest points?

here is my situation: I'm defining a triangle by three points (A,B,C), and now I want to move one of them (A point) up and down along the z-axis, at the same time, I hope the total area of this triangle will stay the same, how to let GH move the rest of the two points accordingly to maintain the area value?

to be specifically, let's say:
A point: moves up and down, so only z-value will be changed, x-value and y-value will stay intact.
B point: only moves in the YZ Plane, the x-value will not be changed.
C point: moves anywhere when needed, totally free point.

please check out the attachment for clearance.

any clue?

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### Replies to This Discussion

Just move B and C upwards with the same amount as A and your triangle will stay the same. Not just the same area, but the same shape even.

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David Rutten
david@mcneel.com
Seattle, WA
I don't want the same shape, in fact I want different shapes by moving three points, and all different triangle shapes will be the same area.
Well, then you'll have to tell me how you want them to differ.

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David Rutten
david@mcneel.com
Seattle, WA
for example, simplify my question a little bit, I have a triangle in XY Plane
A point is 0,0,0
B point is 10,0,0
C point is 10,10,0

it has an area of 50.

now, let's say A point is fixed at 0,0,0, and I drag B point along x-axis, how to let GH make C point move along the y-axis only to keep the area the same (50)
Ok, that is a properly constrained problem (in 2D anyway). See attached definition.

I construct a Plane from the 3 base points, then adjust the (uv) location of C based on the formula for triangle area.

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David Rutten
david@mcneel.com
Seattle, WA
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Hi guys,

A nice way to use the gala block.

Saluti Renzo
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Hi

I have a quite similar problem. I have several moving points on a line (maybe randomly).
But how can I connect the points to a single triangle an after to a surface (with extrude point?)
Thanks a lot!
Ferdinand
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Definition
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Hi Ferdinand,

this is the first version, with separated start- and endpoints.

Ciao Renzo

ps. Grüss mir Zürich.
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Hi Ferdinand,

This is a solution for your specific problem.

Grüsse Renzo
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Hi Renzo

Great:-) Thanks a lot for your help and the solution!

Viele Grüsse in das Tessin,
Ferdinand

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