Weeks of 6/11/2014 - 6/24/2014

• Work plans

After talking to Charles, we agreed to implement the following 3D functinalities:

  * Transformation (move x y z)
  * Rotation (rotate n degrees in the x, m in y, c in z)
  * Scaling (make the thing .5 times it's current size in the z axis)
  * Textures (apply this image to all the surface on the object) 
 

• Transformation

Suppose we are looking at the stage on the X-Y plane from point A at (z_eye, 0), point C at (z_obj, h_obj) is projected as point B on the stage as follows:

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We can apply the same idea on the X-Axis too. So if we can implement this idea perfectly, then object movements on the Z-axis look naturally. However, what I have implemented so far is not perfect -- when moving an object in the Z direction, I only change the size of the object, but keep the x and y coordinates the same. This is illustrated in the following example:

The center of the object does not change and is always at (x, y) = (100, 100) -- logically and physically. In this example, the viewpoint is at (x, y, z) = (0, 0, 200), so following the idea presented above, the projected X and Y coordinates on the stage should be:

• For (x, y, z) = (100, 100, -100): (x_proj, y_proj) = (66.67, 66.67)
• For (x, y, z) = (100, 100, 100) : (x_proj, y_proj) = (200, 200) 

To implement this correctly, 3D objects need to have logical coordinates as well as physical coordinates on the stage, but it causes a major change to the existing 2D system. So, it might be less problematic if we keep the 3D system as it is currently implemented.