# Coordinate Transformations Question

• mjb
In summary, the goal of coordinate transformations is to get the aircraft and target locations in the same "plane" so that the vector between them is in a straight line.
mjb
Hi there. This isn't so much a math question as it is a conceptual question. I can't seem to wrap my head around the need for coordinate transformations. *Why* do they need to be done? I think I really need a picture for this, so this might not be the right place to ask, but if you can describe the "why" rather than the "how" that I find in all the papers/books I've found, that would be great.
Basically, the problem that I'm working on is a plane with a camera on a motorized gimbal. This gimbal needs to point to a spot on the ground and remain pointed to that spot as the plane flies through space. So, the first step is to convert the Lat/Lon into ECEF coordinates to get cartesian math. Get that part, no problem. My question is, why can't I just calculate the vector between these two points and call it a day? From everything I've read, I need to rotate the plane's coordinate system to align with the Earth's coordinate system using matrix transformations. But then, if the plane is now "tipped" to be on the same "axes" as the target, and I calculate the vector, it still won't be correct because the plane isn't really tipped! Please forgive me if I'm being rather obtuse here, but any insight that you can give me would be much appreciated.
thanks!

I've done this very thing in a computer program I made. Essentially you should simply create a matrix using an eye vector and then you have to create an "up" vector. You can
create a matrix using an eye vector and use the z axis as your up vector and then reorthonormalize the matrix, using the calculated binormal and the lookat vector.

There are tonnes of examples on the internet but essentially its going to result in
normalizing the lookat vector, taking a cross product between y-axis and lookat
vector and then calculating the up vector from the binormal and the lookat vector.

Hope that helps

Well, in thinking about it more I think I may have figured it out. Forgive me while I think "aloud". After converting the aircraft and target locations to ECEF coordinates, you subtract them to get the vector between them. BUT that vector is only the straight line distance between the two points. It doesn't take into account the orientation of the aircraft, which may very well be pitch up 25 degrees and banked 10 degrees. Therefore to get the new "coordinates" of the target, with respect to the planes' attitude, the transformation needs to be done to get them in the same "plane" (no pun intended ;P ). Any confirmation or correction of this thought is appreciated. thanks.

## 1. What is a coordinate transformation?

A coordinate transformation is a mathematical process used to convert coordinates from one reference system to another. This is often necessary in scientific research, engineering, and navigation.

## 2. Why are coordinate transformations important?

Coordinate transformations are important because they allow us to accurately describe and measure objects or locations in different reference systems. This is crucial for comparing data or locations from different sources or for navigating in different coordinate systems.

## 3. What are some common types of coordinate transformations?

Some common types of coordinate transformations include translation, rotation, scaling, and projection. These transformations can be applied to 2D or 3D coordinates and are used in a variety of fields, such as cartography, computer graphics, and robotics.

## 4. How are coordinate transformations calculated?

Coordinate transformations are typically calculated using mathematical formulas or algorithms. The specific method used depends on the type of transformation and the coordinate systems involved. In some cases, specialized software or programming languages may be used to perform the calculations.

## 5. Can coordinate transformations introduce errors?

Yes, coordinate transformations can introduce errors if they are not performed accurately or if there are inconsistencies between the reference systems being used. It is important to carefully consider the methods and parameters used in a transformation to minimize potential errors.

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