Augmented and Virtual Reality Systems - pág.18

In addition to serving as the most commonly utilized approach for mathematically mapping actual, theoretical, and creative virtual spaces, the Cartesian system is also used to define a user´s position and viewpoint within that space.

Spherical Polar Coordinates

Although the positions of points, lines, planes, and complete objects within a virtual space will typically be defined using standard Cartesian coordinates, the location of objects and features relative to the user´s position, such as that of a virtual sound source, or in the mapping of spherical video (also known as 360^o video) will often be defined using a different system known as spherical polar coordinates. As shown in Figure 2.4, this coordinate system is based on fundamental planes bisecting a sphere and is composed of three elements: azimuth, elevation, and the distance (magnitude or range). This system and its application in the localization of sound sources are covered in additional detail in Chapter 7, «The Mechanics of Hearing.»

Figure 2.4 A diagram of spherical coordinates, defining a point (P) by azimuth (?), distance/range (?), and elevation (?).

Cylindrical Coordinates

The third coordinate system commonly applied within virtual reality applications, and a holdover from Apple´s QuickTime VR of the 1990´s, is the cylindrical method. Used extensively in the creation of still image mosaics for 360^o × 180^o «immersive» panoramas or 360^o video backgrounds, the mathematical techniques enabled by this coordinate system allow for the precise mapping and alignment of multiple images for overlap and edge stitching, with all points being the same distance from a central reference axis.

As shown in Figure 2.5, this central reference axis (L), also called the cylindrical or longitudinal axis, serves as the origin (O) for defining a radial distance (?).