Question

Let f = 4 be the focal length of a camera. Let p = (1, 2, 2) be a world point. Find the coordinate of the 2D point p when projecting it onto the image. Assume that the projection is done in camera coordinates so there is no need for a transformation between coordinate systems. Assume that the image is rotated so that the object does not appear inverted. Note that the point p is two dimensional and so has two coordinates. Add the coordinates of p and use this sum to mark the answer.

Answer 1

Using ray tracing and simple projection formulas, we determine that the 2D projected coordinates of the point (1, 2, 2) onto the image plane with a focal length of 4 are (2, 4). Adding these coordinates yields the number 6.

Step-by-step explanation:

To find the coordinates of the 2D point p when projecting it onto the image plane using a camera with a focal length f, we use the principles of ray tracing in optics. The point p=(1, 2, 2) in three-dimensional space needs to be projected onto a two-dimensional plane. Using the camera's focal length, we can apply the thin lens formula which is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

However, since we are seeking the 2D projection onto the image plane, we can use the simple projection formula x' = f * (x/z) and y' = f * (y/z). Using the given focal length f = 4 and the point p = (1, 2, 2), we can calculate:

• x' = 4 * (1/2) = 2
• y' = 4 * (2/2) = 4

Thus, the coordinates of the 2D point on the image plane are (2, 4). Adding these coordinates as per the instruction, we obtain 2 + 4 = 6, which would be used to mark the answer.