Taking 2D objects and mapping onto a 2D screen is pretty straightforward. The window is the same plane as the 2D world. Now we are taking 3D objects and mapping them onto a 2D screen. Here is where the advantage of separating the model world from its rendered image becomes more obvious. The easiest way to think about converting 3D world into 2D image is the way we do it in real life – with a camera. Lets say we have an object in the real world (e.g. the Sears Tower.) The tower sits there in its 3Dness. You can move around the tower, on the ground, on the water, in the air, and take pictures of it, converting it to a 2D image. Depending on where you put the camera and the settings on the camera, and other factors such as light levels, you get different looking images. In the computer we have a synthetic camera taking still or moving pictures of a synthetic environment. While this synthetic camera gives you a much wider range of options than a real camera, you will find it is VERY easy to take a picture of nothing at all. Albrecht Dürer, Daraughsman Drawing a Recumbent Woman (1525) Woodcut illusion from ‘The Teaching of Measurements.’ rays (projectors) projected from the center of projection pass through each point of the models and intersect projection plane. Since everything is synthetic, the projection plane can be in front of the models, inside the models, or behind the models. which type of projection is used depends on the needs of the user – whether the goal is the mathematically correct depiction of length and angles, or a realistic looking image of the object. since the View Plane (n=0) is infinite (as it is a plane) we need to declare a region of that plane to be our window. Perspective projections are categorized by the number of axes the view plane cuts (ie 1-point perspective, 2-point perspective or 3-point perspective) If the plane cuts the z axis only, then lines parallel to the z axis will meet at infinity, lines parallel to the x or y axis will not meet at infinity because they are parallel to the view plane. This is 1-point perspective. If the plane cuts the x and z axes, then lines parallel to the x axis or the z axis will meet at infinity, lines parallel to the y axis will not meet at infinity because they are parallel to the view plane. This is 2-point perspective. If the plane cuts the x, y, and z axis then lines parallel to the x, y, or z axis will meet at infinity. This is 3-point perspective. The front plane’s location is given by the front distance F relative to the VRP The back plane’s location is given by the back distance B relative to the VRP In both cases the positive direction is in the direction of the VPN Viewing volume has 6 clipping planes (left, right, top, bottom, near (hither), far (yon)) instead of the 4 clipping lines we had in the 2D case, so clipping is a bit more complicated perspective – viewing volume is a frustum of a 4-sided pyramid parallel – viewing volume is a rectangular parallelepiped (ie a box) In the red version of the Foley vanDam book see P.211-212. In the white version of the Foley vanDam book see P.250-252. Here are some examples using the same house as in the book (figure 6.18 in the red version of the Foley vanDam book, figure 6.24 in the white version of the Foley vanDam book, but using Andy Johnson’s solution to the former HW3 as the viewing program: For other examples, in the red version of the Foley vanDambook see P.206-211. In the white version of the Foley vanDam book see P.245-250. In the red version of the Foley vanDam book see P.212-213. In the white version of the Foley vanDam book see P.253. Source.