How to draw text on a 3d sphere?

Question

I am facing a problem in mapping 3d co-ordinate to screen co-ord . I require it because i want to draw text on the model . model is drawn at the 3d-cordinate, so if i know the position of that co-ord on the screen i can draw text at that position.

my view is on z axis test position is on x axis

In the follwing code I did what i said above but the transformation is not happening the way it should i.e, text should appear on the model

float aspectRatio = graphics.GraphicsDevice.Viewport.AspectRatio;
Vector2 screenOrigin = new Vector2(GraphicsDevice.Viewport.Width / 2, GraphicsDevice.Viewport.Height / 2);
Vector3 testPosition = new Vector(10,0,0);
Vector3 cameraPosition = new vector(0,0,50),

Matrix world = Matrix.Identity;
Matrix view = Matrix.CreateLookAt(cameraPosition,Vector3.Zero, Vector3.Up);
Matrix projection = Matrix.CreatePerspectiveFieldOfView(MathHelper.ToRadians(45.0f), aspectRatio, 1.0f, 10000.0f);

Matrix totalEffect = world * view * projection;

Vector2 spritePos = getXYPosition(vecAndMatMultiplication(testPosition, totalEffect))+screenOrigin;

Where vecAndMatMultiplication() multiplies vector with the matrix and getXYpostion() should be fairly obvious.

Answer 1

Short Answer

Use the Viewport.Project method that already does the work for you (link to documentation):

Viewport viewport = GraphicsDevice.Viewport;
Vector3 screenPosition = viewport.Project(worldPosition, projection, view, world);
Vector2 spritePosition = new Vector2(screenPosition.X, screenPosition.Y);

So, just call it with the correct matrices, and ignore the Z value of the result.

Long Answer

If you want to understand what you are doing wrong in your example, it's basically because the correct procedure is not just to multiply the position by the WorldViewProjection matrix and add the screen origin. There's a little bit more to it than that.

The actual procedure is to:

• Expand position into a Vector4 such as (x,y,z,1)
• Multiply that Vector4 by the WorldViewProjection matrix.
• Homogenize the result back into a Vector3 by doing (x/w, y/w, z/w)

• Apply the viewport transformation to map from (-1,-1,1,1) range to the the viewport and flip the Y axis so that it runs top-bottom instead of bottom-up:

  screenX = viewportX + viewportW * (x + 1.0) * 0.5
  screenY = viewportY + viewportH * (1.0 - y) * 0.5
  

I have not tested the following bit of code, but I think the implementation should be something like this:

public static Vector2 ConvertWorldToScreen(Vector3 source, Matrix world, Matrix view, Matrix projection, Viewport viewport)
{
    Vector4 result = Vector4.Transform(new Vector4(source, 1), world * view * projection);
    result /= result.W;
    float screenX = (float)viewport.X + (float)viewport.Width * (result.X + 1.0f) * 0.5f;
    float screenY = (float)viewport.Y + (float)viewport.Height * (1.0f - result.Y) * 0.5f;
    return new Vector2(screenX, screenY);
}