New FT transform about the tank's auto aim function, and it was based on Euler's vector transform.

Some details about the formula:

Course about the Euler transform

Above from the image, you can see there are 3 matrix each about: Heading, Pitch and Roll.
Let's just from the first matrix about "Heading" to introduce:
when you change cockpit heading from 0 degree(attention, North in SimplePlanes is 0 degree) to a new degree called "v", enemy target's vector Z is still keep steady. But the vector x and y become changed. And now you just use Polar coordinates to build this processing:
{x0=Radiu×sin(R)}
{y0=Radiu×cos(R)}
And the variable R changed into: (R+v)
So the new x and y is:
{x=Radiu×sin(R+v)}
{y=Radiu×cos(R+v)}
And resultion above equation:
x=Radiu×(sinR×cosv+cosR×sinv)
y=Radiu×(cosR×cosv-sinR×sinv)
Simply we can put x0 and y0 into above is:
The new x=x0×cosv+y0×sinv
The new y=-x0×sinv+y0×cosv
And the matrix about the Heading is
[cosv sinv 0]
[-sinv cosv 0]
[0 0 1]
Similarly, we can gain the matrix about the Pitch and Roll on above image.
And then, we should let matrix Roll multiply matrix Pitch and multiply Heading, and then we can get a new matrix of relation below(above image is Heading multiply Pitch and multiply Roll. In fact that's because it's a matrix about gesture control which was used on my previous works, not the auto aim function we need! ):
[c(H)·c(R)-s(H)·s(P)·s(R) -s(H)·c(R)-c(H)·s(P)·s(R) c(P)·s(R)]
[s(H)·c(P) c(H)·c(P) s(P)]
[-c(H)·s(R)-s(H)·s(P)·c(R) s(H)·s(R)-c(H)·s(P)·c(R) c(P)·c(R)]
Above "c()" means "cos()", "s()" means "sin()". And most importantly, "H" means "-Heading", "P" means "-PitchAngle", "R" means "-RollAngle"!
And now you can use this new matrix to multiply the column vector:
[Target Longitude - Your Longitude]
[Target Latitude - Your Latitude]
[Target Altitude - Your Altitude]
And then, you will gain a new column vector:
[real X]
[real Y]
[real Z]
And the "real heading" about your horizontal rotator should write down :
arctan(real X / real Y)
And the "real elevation" about your vertical rotator should write down :
arctan(real Z/ sqrt((real X)×(real X)+(real Y)×(real Y)))
And now you will gain an anti-terrian auto aim tank:

Previous work:

Click here to download RheinMetall Main Battle Tank Revolution.

Click here to download ZTQ 15 Light Battle Tank.

Have fun!