# how is zooming done in computer graphics

Since a projection plane and a center of projection is used for achieving perspective projection, the shape of the view frustum doesn't change changing the focal length(which is the distance from the center of projection to the plane of projection i.e. the screen or buffer)

Then how is zooming done in computer graphics? It is mentioned in my textbook that this is done by changing the size of the view frustum and that the relationship that field of view is inversely proportional to the zoom holds(somehow I don't know) but looks to me more like a bit conterintuitive, e.g.:

• Your virtual camera film becomes smaller, but your screen remains the same size, meaning that a smaller region of the world is projected on the same area of the screen - that is a zoomed in region. Feb 17 '20 at 11:26
• @lightxbulb , does focal distance and focal length refer to the same thing in CG? It seems to be different in photography , because in my textbook it is mentioned that when you change the focal distance you also change the frustum, but that doesn't change if you change the plane of projection. Do you instead change the center of projection to change the focal distance(or is it focal length), could you please explain a bit about these? Feb 17 '20 at 11:41
• In this model, you can imagine the virtual film changing size on a fixed plane of projection (which changes the view frustum) or the focal length changing with a fixed virtual film size (also changing the view frustum). When you do the math to project a point on to the film, as a fraction of the size of the film, it works out to be the same, e.g. halving the size of the virtual film or doubling the focal length. Feb 17 '20 at 16:50
• @DanielMGessel , I think the mistake I was making in understand the entire textbook was that I was assuming the plane of projection is the one that is changed, but to increase or decrease d, also the center of projection can be changed, which one is usually changed? Feb 18 '20 at 2:53
• i think of the center of projection as the location of the camera, so to zoom, I imagine moving the plane of projection. However, once you turn it all into matrices, zooming becomes a scale of the projected coordinates and that can be thought of as changing the angles of the frustum! I had to work through the math a few times before it started to sink in. Feb 18 '20 at 4:51