Version 5 (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 we can write the integral as
$\int F(x'(s)
and we have
which under the substitution gives
Assume jet is oriented along
and that we are integrating along the directionwhere
is the angle of inclination.We are interested in calculating the integral of
, , and whereIf
this is just , , andIf
then we have to tilt the integral and calculate using the expression above.