Moving along a flat plane with accordance to camera view

Question

I'm making a 3D game, and I'm stuck on a little experiment.

I currently have a flat plane with a free camera running around, and a sphere (really, a light approximated as a sphere) that rests above the surface of the plane at, say, 50 units up. I'm trying to move the sphere, and I can do this easily by simply adding to the position in the X and Z direction. However, I got a bit messed up because when I move the camera, pressing the left arrow might move the sphere to the right, because of the coordinates. So I'm trying to move the sphere along the X and Z dependant on where my camera is looking.

For example, if I was looking at it from behind, down on an angle, I expect the sphere to move to the camera's left along the plane, or move down towards the camera, still along the plane.

I have seemed to get left and right working with a.Position -= Vector3.Cross(((FreeCamera)camera).Forward, ((FreeCamera)camera).Up); but trying to move the sphere using just the camera's forward causes the sphere to move into or out of the plane, depending on the angle of the camera (this makes sense, because the camera's forward may be pointing into the plane).

My question is, how do I move an object left or right along a plane (remaining 50 units above the Y axis) in accordance to the camera's direction? For example, viewing the plane from its left facing towards the center, moving left should make it move towards the top of the plane if viewed from the back or to the camera's local left.

Here's two screenshots showing what I mean:

When viewing the red light from here: Pressing right should give me this. Notice how the red sphere has moved (disregard the fact the camera angle changed slightly):

Answer 1

Your Camera class generates a View matrix right? Multiplying a position in world space by the view matrix results in that same position being transformed into view space. Conversely, if you multiply a position in view space by the inverse of your view matrix, you'll get your position back in world space. On to your question.

Part 1) Moving light in relation to the camera

So you'd like to move the light position according to the camera's current orientation. An easy way to do this is simply to apply the transformation in view space (as opposed to world space). As an example:

Vector3 viewLightPosition = Vector3.Transform(light.Position, camera.ViewMatrix);
if(keystate.IsKeyDown(Keys.Right)) viewLightPosition += Vector3.Right * moveSpeed * dt;
light.Position = Vector3.Transform(viewLightPosition, Matrix.Invert(camera.ViewMatrix));

That takes care of the problem where movement should always be relative to the camera.

Part 2) Clamping the light back onto the correct plane

In step 1 the light was moved according to the camera, but disregarding the plane. Now it's time to fix that, i.e. you need to validate the light position to ensure that it remains at the same distance from the plane. The first thing that occurs to me would be:

1. Project your light position into the plane.
2. Then move it out of the plane by the desired amount along the plane's normal.

I'm not sure but I think XNA's Matrix.CreateShadow could be leveraged to simplify the first step. Once again, example:

Matrix projectionMatrix = Matrix.CreateShadow(plane.Normal, plane);
light.Position = Vector3.Transform(light.Position, projectionMatrix);
light.Position += plane.Normal * distance;

Note) Calculating the correct plane for your wall

Of course part 2 only works if you're using the correct plane. Since the Plane is usually stored as a Normal and Distance from the origin, it might be hard to come up with the correct values to fit a specific object in the world.

Luckily the Plane class also has a constructor that makes this task easy - you only need to pass it three points that lie on the plane. So to create a plane for your wall, all you'd have to do is:

Plane plane = new Plane(wall.Vertices[0], wall.Vertices[1], wall.Vertices[2]);

Answer 2

Figure out the camera's rotation around the Y axis and use that with trig functions to calculate the X and Z distances:

x = cos(angle) * speed

z = sin(angle) * speed

btw an answer I gave to a different question described the same math for a slightly different situation https://gamedev.stackexchange.com/a/18395/6588