Converting coordinates placed on 360texture plane to spherical

I have a 360 spherical video. I use this video as a texture on a sphere in Unity. Inside the sphere is a camera and this functions as the setup for my Virtual Reality experience. Pretty basic.

I am trying to write a bit of code on the web where people can upload 360 images and videos, place a marker/hotspot on the 360 spherical image/video, and then apply the image/video-texture on the sphere in Unity3D. If I overlay a simple x/y coordinate grid on the 360 video/image-texture, put in some x/y-coordinates to place the marker/hotspot, and put the texture back on the sphere, Unity will not interpret this correctly since we are now in 3D space and we are looking at the texture from within the sphere mapped onto the plane with all the distortion happening.

My question is, how do I convert these x and y coordinates on the 2D plane of the 360 video texture to coordinates that can be understood in 3D within Unity3D?

My first thought was to use 2-dimensional cartesian coordinates and convert these into spherical coordinates, but I seem to be missing a z-axis in the cartesian coordinates to make this work.

Is the z-axis simply 0 or is it the radius from center of the sphere to the x/y-coordinate? What does the z-axis represent? Is there maybe two coordinate systems. One that is coordinates on a plane and one that is from the centre of the sphere?

This is the conversion code that I have so far:

public static void CartesianToSpherical(Vector3 cartCoords, out float outRadius, out float outPolar, out float outElevation){
    if (cartCoords.x == 0)
        cartCoords.x = Mathf.Epsilon;
    outRadius = Mathf.Sqrt((cartCoords.x * cartCoords.x)
                    + (cartCoords.y * cartCoords.y)
                    + (cartCoords.z * cartCoords.z));
    outPolar = Mathf.Atan(cartCoords.z / cartCoords.x);
    if (cartCoords.x < 0)
        outPolar += Mathf.PI;
    outElevation = Mathf.Asin(cartCoords.y / outRadius);
}

This is my very first post so please excuse me if I am doing anything wrong and let me know how to improve.

Answers


Spherical co-ordinates are different from 2d or 3d co-ordinates as you need to measure them in radians. It is usually measured from the center of the sphere and XY axis. It marks a rectangular area on the surface of the sphere. Please refer to this link for spherical co-ordinates in unity - https://blog.nobel-joergensen.com/2010/10/22/spherical-coordinates-in-unity/


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