Orienting a new plane with 2 points and a vector

Hi,

As part of solving my Catenary by Height problem, I am trying to create a new plane at a point A where the y-axis aligns with the negative of an arbitrary vector (in this case, gravity), and the x-axis aligns with the horizontal component of the vector between two arbitrary points (A & B). If that doesn't make sense, then what I'm basically trying to do is nullify the component of the vector from A to B that aligns with the gravity vector and use that for the x-axis. I tried simply subtracting the unitized gravity vector from the A-to-B vector, but that didn't work. I also tried creating a new plane at point A normal to the cross-product of the A-to-B vector and the gravity vector (2nd image), but the y-axis was aligned with the gravity vector (not the opposite of the gravity vector) and the x-axis was also in the wrong direction, pointing away from point B instead of towards it (along the horizontal component of A-to-B anyway). I know there is something easy that I'm missing here...sorry for not understanding vectors & planes better.

Thanks!

Attachments:

vector_plane_1.png, 94 KB
vector_plane_2.png, 97 KB

Replies to This Discussion

Permalink Reply by Will McElwain on January 15, 2014 at 7:51pm

Figured it out...here's the VB code that worked for me:

[inputs: PtA, PtB, Grav (direction of gravity vector)]

Grav.Unitize
Dim line As New Line(PtA, PtB)
Dim v As Vector3d = line.Direction ' get the vector between A and B and unitize it
v.Unitize
Dim plane As New Plane(PtA, Grav, v) ' create the plane with the x-axis in the direction of Grav and the A-to-B vector (v) on the y-axis
Dim nV As Vector3d = Vector3d.CrossProduct(Grav, v) ' get cross product of Grav and v and unitize it
nV.Unitize
plane.Rotate(Math.PI / 2, nV) ' rotate the new plane 90 degrees around the axis of cross product vector so the y-axis is now aligned with the opposite (negative) of Grav

No doubt there's an easier way to do this, but it seemed to work for me.

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