Transform Screen Point to Transform extension

Questions & Answers
1

I have a problem I had a couple of times now and need a universal solution to it.
Basically the question is: How do I get the red vector to touch the blue one, no matter the length?

88148-vectorproblem.png

The picture shows a camera and it’s view frustum. The first orthogonal line is the near clipping plane. The red vector Indicates a point on screen transformed into world space on the plane. What I need is the position at the tip of the red vector.
The thick black bar is the plane/ Vector I want to cross with that arrow, in this case it’s the forward vector (blue) of the green sphere. I know how to get the pink point just by transforming the screen position to that depth, but I have no idea how to get to the tip of the vector.
I don’t want to use a raycast, because it’s not just moving a character on a flat floor around but several places I need to do this. Like transforming a touch into the 2D movement plane of a spaceship. It works as long as camera looks perfectly straight at the plane, but at an angle I don’t know how to do that.

Trying to use Project didn’t help much because no matter how I put it I always the the shorter vector.

2

I pretty much came up with a solution myself:

public Vector3 GetPointOnPlane(Vector3 planeCenter, Vector3 planeNormal, Vector3 origin, Vector3 direction){
		var p = new Plane(planeNormal, planeCenter);
		float pointToPlaneDistance = p.GetDistanceToPoint (origin);
		float partTowardsPlane = Vector3.Dot (direction, -planeNormal);
		float scalar = pointToPlaneDistance / partTowardsPlane;
		return origin + direction * scalar;
	}

Parameters:

  • planeCenter: some point in space that goes through the imaginative plane
  • planeNormal: the normalised direction the plane faces
  • origin: another point in space from where the direction and distance to plane are measured
  • direction: a direction vector of which the tip should finally end on the plane