Projecting a light onto a quad

Question

I need to project the light onto the quad and use its value for translating the vertices.

I'm currently having 6 vertices, two quads,
The points are A X C B Y D

Point X, Y are coming from two ray casting downwards.

C =  X + RightVector
D =  Y +  RightVector
A =  X - RightVector
B =  Y - RightVector

Now I want to translate the vertices based on lightDirectionVector, how would I do that ? I have a directional light, and that mesh of the two quads acting as a shadow quad.

    Vector3 lightDir = mDirectionalLight.transform.forward;
    Vector3 normLight = lightDir.normalized;
    normaLight.y = 0;

Answer 1

I am not sure if projection is actually the correct word for this, but I hope it is what you are looking for.

First you need the planes normal which is the cross product of the directions from one of your vertices to two of the others, which in case of your image could be C-A and B-A. (the three vertices may not lay in the same line, there is a simple mathematical term for it, but I guess I forgot it :( something with linearity...).

If you got the normal, you can calculate the closest distance of some arbitrary point of which your light direction is the position vector by building the dot product between your light direction and the normal.

Now you can calculate the position of that point within the plane by moving it along the normal towards the plane with the previously calculated distance: newdirection = direction - normal * dot(normal, direction)

But this will only give you the direction to the closest point on your plane to some arbitrary point defined by the light direction and I currently can´t get my head around if it really exactly is what you need or if it is only close.