Version 7 (modified by 7 years ago) ( diff ) | ,
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Goal is to integrate various functions along lines of sight which is constrained to be in the y-z plane and has components
and
is the tilt angle of the jet towards the observer
so
Each pixel in the resulting image will be given by the integral of the function along the path
where
corresponds to crossing of the planeand we have
andand
For 3D we just need to create the expressions in visit, create the lineouts, and then integrate the resulting query for each x_i and y_i
For 2.5D, we need to transform the integral along
(normally in the yz plane) into an integral in the plane.Since everything is axi-symmetric, the value at
can be inferred by rotating the corresponding solution at
by an angle
.
So our new path is in the xy plane and is given by
And we have
So our path integral becomes
Where
is the rotated vector through the angle .Now if
, this simplifies to
Now
is unchanged under rotations about the jet axis, however will be given by