about PFrames

perhaps is a basic question,

i tried to find the explanation but i can´t.

what is the explanation of the plane rotation using PFrames component?

why the normal plane rotates relative to the osculator plane.

thanks

Replies to This Discussion

Permalink Reply by TheChosenOne on January 17, 2012 at 9:54am

http://www.grasshopper3d.com/forum/topics/chenge-axis-flipplane

Permalink Reply by paco g on January 17, 2012 at 3:23pm

yes, i know the way to change the orientation,

but i would like to understand the reason the plane is rotated,

the relationship between the rotation of the plane and the geometry of the curve,

i suppose

thanks anyway,

pretty custom component

Permalink Reply by TheChosenOne on January 17, 2012 at 6:40pm

Permalink Reply by Chris Tietjen on January 17, 2012 at 10:10pm

I've been trying to figure this one out too. At first I thought that it might have something to do with the binormal vector or the curve's torsion but now I'm wondering if it isn't just an averaging of position between first and last frames so as to maintain minimum rotation...but I don't really know.

Permalink Reply by TheChosenOne on January 18, 2012 at 2:06am

I do not understand what you here do not understand, there are two vectors, one at a tangent, the other to the center of the circle of curvature of the curve, and between a point and two vectors constructed plane, the X-axis to the center of curvature or the Z-axis to the direction of the tangent.

Permalink Reply by TheChosenOne on January 18, 2012 at 2:38am

Oh, apparently, still have some algorithm for orientation, for it is up and running "Swp1". The first planes of the same, and the subsequent attempt to preserve the relative orientation to the world ...

Permalink Reply by TheChosenOne on January 18, 2012 at 2:48am

Permalink Reply by paco g on January 18, 2012 at 7:56am

i don´t understand the relationship between the rotation of the normal plane (obtained by PFrames ) at each point of the curve and the geometry of the own curve?

this rotation occurs when the curve is not a plane curve.

TheChosenone, as you say, i get the osculator plane (red in the image) and perpendicular to this plane the normal plane (magenta).

if i get the normal plane (green) to the curve using Pframes the plane is the same plane obviously but is rotated in relation to the previous plane.

Chris, I also suspect that It had to do with the binormal
but i cannot find this relationship.

thanks

Permalink Reply by TheChosenOne on January 18, 2012 at 9:22am

Permalink Reply by Chris Tietjen on January 18, 2012 at 11:34am

A lot of interesting graphics but the question still remains what are the pframes oriented to. They rotate in their own plane according to what? It's not been made obvious by looking at pictures.

Chris

Permalink Reply by TheChosenOne on January 18, 2012 at 9:32am

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