Question

For Computer Graphics

Given a canonical view volume, what do we need to do to project our points to the viewing window?

Answer 1

Answer:-

Perspective projections are used to produce images which look natural. When we view scenes in everyday life far away items appear small relative to nearer items. This is called perspective foreshortening. A side effect of perspective foreshortening is that parallel lines appear to converge on a vanishing point. An important feature of perspective projections is that it preserves straight lines, this allows us to project only the end-points of 3D lines and then draw a 2D line between the projected endpoints.

Objects in the real world appear smaller as they move further away.

Perspective projection depends on the relative position of the eye and the viewplane. In the usual arrangement the eye lies on the z-axis and the viewplane is the xy plane. To determine the projection of a 3D point connect the point and the eye by a straight line, where the line intersects the viewplane. This intersection point is the projected point.

Perspective projections, while providing a realistic view of an object, are rather restrictive. They require that the eye to lie on a coordinate axis and that the viewplane must coincide with a coordinate plane. If we wish to view an object from a different point of view, we must rotate the model of an object. This causes an awkward mix of modelling (describing the objects to be viewed) and viewing (rendering a picture of the object). We will develop a flexible method for viewing that is completely separate from modling, this method is called the synthetic camera. A synthetic camera is a way to describe a camera (or eye) positioned and oriented in 3D space.