3.4 Viewing Transformations

This section describes how to transform the models in the virtual world so that they appear on a virtual screen. The main purpose is to set the foundation for graphical rendering, which adds effects due to lighting, material properties, and quantization. Ultimately, the result appears on the physical display. One side effect of these transforms is that they also explain how cameras form images, at least the idealized mathematics of the process. Think of this section as describing a virtual camera that is placed in the virtual world. What should the virtual picture, taken by that camera, look like? To make VR work correctly, the ``camera'' should actually be one of two virtual human eyes that are placed into the virtual world. Thus, what should a virtual eye see, based on its position and orientation in the virtual world? Rather than determine precisely what would appear on the retina, which should become clear after Section 4.4, here we merely calculate where the model vertices would appear on a flat, rectangular screen in the virtual world. See Figure 3.13.

Figure 3.13: If we placed a virtual eye or camera into the virtual world, what would it see? Section 3.4 provides transformations that place objects from the virtual world onto a virtual screen, based on the particular viewpoint of a virtual eye. A flat rectangular shape is chosen for engineering and historical reasons, even though it does not match the shape of our retinas.

Figure 3.14: Consider an eye that is looking down the $ z$ axis in the negative direction. The origin of the model is the point at which light enters the eye.

Steven M LaValle 2020-01-06