oriented point on space

hi,

if we have a plane(3 points known) and a point in this plane

then we orient the 3 points or the plane some how to another location

how is it possible to know the location of the point oriented

this is using mathematics

not without grasshopper

is it possible ?

Replies to This Discussion

Permalink Reply by Chris Tietjen on September 9, 2011 at 4:47pm

This gives you the coordinates of the point at the new location.

Chris

Permalink Reply by Mohamed Naeim on September 9, 2011 at 10:39pm

Thanks Chris

but what i was looking for is not to use Grasshopper components

i mean is it possible by mathematics using these points x,x1,y,y1,z,z1,A to find B

lets say i like to do this in an excel file

Permalink Reply by David Rutten on September 10, 2011 at 1:17am

You need to write the point in plane-coordinates. I.e. rewrite it from World-XYZ coordinates into Plane-UVW coordinates. Then, you can evaluate any other plane at the same UVW coordinates to get new XYZ coordinates and it will look as though the point has been moved along with the plane.

Using the Rhino SDK this is quite easy because all that functionality is already available, but it is just a large collection of multiplications, subtractions and divisions.

Another possibility (which only works for coordinates coincident with the plane defined by your three points) is to express the location as a weighted average. You could say for example that

A = (1.2*x0 + 1.5*y0 + 0.8*z0) / (1.2 + 1.5 + 0.8)

The benefit of this approach is that it requires significantly less mathematics.

David Rutten

david@mcneel.com

Leusden, Holland

Permalink Reply by Mohamed Naeim on September 10, 2011 at 8:03am

thansk David

but what is the relastionship between the avarage and the points coordinates

i mean

if x= (1,4,3) etc

where does the average came from

Permalink Reply by Chris Tietjen on September 10, 2011 at 9:23am