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# Project Camera View onto plane through Matrix

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Hi, I'm trying to project a 3D camera's view onto a plane. I currently have this working by:

1. Find normalized viewport position (-1 to 1)

2. Project this coordinate into 3d using the inverse of the cameras View and Projection matrices

3. Find the direction of this coordinate relative to the camera view

4. Find intersection of this direction onto plane.

I'm doing this inside a shader but wondering if I could simplify it by constructing some sort of matrix that finds the plane intersection for a normalized viewpoint.

Not sure if that's even possible. Here's a picture that might better explain:

What I currently have:

float4 unproject(float x, float y, float z)
{
// unproject the point
// _ProjMatrix is the inverse of a cameras view and projection matrices
// _ProjMatrix = inverse(cam.projectionMatrix * cam.viewMatrix)

float4 pos = mul(_ProjMatrix, float4(x, y, z, 1));

return pos * (1.0 / pos.w);
}

v2f vert (appdata v)
{
v2f o;

//convert the mesh vertex into local viewport space

float4 vp = v.vertex;
float x = vp.x / _Size;
float y = vp.z / _Size;

//unproject into the near and far clipping planes of the camera

float4 p1 = unproject(x, y, -1);
float4 p2 = unproject(x, y, 1);

//find the direction of this viewport point

float4 dir = normalize(p2 - p1);

//project this viewport direction onto the world plane

float distanceOfVertex = mul(_WorldMatrix, p1.xyz).y;
float lengthOfLightDirectionInY = mul(_WorldMatrix, dir.xyz).y;

dir = dir * (distanceOfVertex / -lengthOfLightDirectionInY);

//output vertex

o.vertex = mul(UNITY_MATRIX_VP, p1 + dir);
}


As you can see there's lots of multiplication here. First I have to find the near and far projections, find the normal between them, find the projection of that normal on the plane.

Wondering if this could be simplified if I could just take that viewport position and multiply by the camera projection and view + some plane intersection matrix.

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