I need to translate a point (
P1) in 3D a certain amount, call it
stepSize, along a vector described by a heading composed of three angles (basically pitch, roll and yaw). I know that in homogeneous coordinates the following translation matrix would be used
and I can multiply my existing point by
Tv to get the new point. However, I need something slightly different. I have
P1 and want the new point,
P2 to be separated by
stepSize so I need to recover
Vz as given in the matrix above (from Wikipedia). Any general suggestions about how to go about that? I will do this in
R once I know what to do.
EDIT: Here is some additional information. I am trying to do 3D Turtle Graphics which are very much analogous to aircraft position and headings. Specifically, I am writing code to implement the 3D L-systems described here. This figure from the book gives the coordinate system used in that field (rather non-standard if you ask me).
So I have my 'turtle' at the origin of this system, I have a given standard
stepSize, and I have saved the most recent headings, which are the angles around each of the axes H, L and U. I want to move the turtle forward by
stepSize. In the graphics system I am using, I have the current Cartesian coordinates of the turtle, and I need to compute the offset in the x, y and z directions to be added to the current position to get the new position (then repeat ...). A small (?) complication is that the graphics drawing system I am using has the (+)ive x/L axis going to the right, not left as in the book figure. H in the figure corresponds to the (+)-ive y-axis, and U to the (+)-ive z axis. Ugh.