Calculate vector3 global point projecting it in local space using Unity and C#?

Question

How to project a vector 3 locally ? Unity has a special function for this?

For example, if a has a GameObject that contains 2 children Vector A (transform) "My A Arrow" and Vector C (transform) "My C arrow projection".

I wish a C# solution script for "C" vector (transform) so that it can be used in Unity Game engine.

Just for example: My game object "A" is child moving and rotating locally. I wish to make the projection locally. "B" is my world forward in case is needed. "C" is a simple projection of "A" to the plane in local axis.

Is simple to get the vector in world global axis, just taking x (x = 0f). But I fail locally, since my parent GameObject is rotating.

Attempted solution. public Vector3 vector_A, projection_C;

vector_A= new Vector3(4f, 5f, 11f);

void FixedUpdate() 
{
    projection_C = transform.TransformPoint(vector_A);
}

I try using transform, rotation, vector3 unity functions and quaternion. My skill was not at the level to understand wich function to choose for the task reference: https://docs.unity3d.com/ScriptReference/Vector3.html

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I was able to get the solution but was so complex that I was thinking that Unity has a function that makes the local projection.

This is my attempt to describe the process:

First you need to make a clone of the game object, rotate it to world global and move it to origine 000. The child vector will folow the perent game object. Now you can make the projection of "A" taking out x. The result "C" must be rotated and move by the original game object rotation and position.

Answer 1

Let's say you have a trasnformed coordinate system defined by a quaternion rotation, and vector3 position. For example, the transformed coordinate system may represent the orientation and position of an object in your game.

You can use Matrix.TRS to get a transformation matrix that represents this coordinate system. It would be done as follows:

Matrix4x4 m = Matrix4x4.TRS(position, rotation, new Vector3(1, 1, 1));

Note: new Vector3(1, 1, 1) is the identity scaling vector, it means no scaling is applied.

Once you have the matrix, you can use it to convert points from the transformated coordinate system to wolrd coordinates:

Vector3 trasnformedPoint = m.MultiplyPoint3x4(point);

You may convert from world to the trasnformed coordinate system by using the inverse of the matrix:

Vector3 point = m.inverse.MultiplyPoint3x4(trasnformedPoint);

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Alternatively, if you are using an scene object, you can use its Transform to get the same results.

Vector3 trasnformedPoint = transform.TransformPoint(point);

And in the opposite direction:

Vector3 point = transform.InverseTransformPoint(trasnformedPoint);

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Once you have the point represented in the coordinate system you need it, you can proceed to manipulate it any way you need, and you can transform it back to the coordinate system you had it to begin with.

For example, we can transform a point, remove a component, and transform it back:

Transform transform = gameObject.transform;

// ...

Vector3 trasnformedPoint = transform.TransformPoint(point);
trasnformedPoint.x = 0;
Vector3 newPoint = transform.InverseTransformPoint(trasnformedPoint);