Inside Macintosh: 3D Graphics Programming With QuickDraw 3D /

Chapter 4 - Geometric Objects / Geometric Objects Reference

Data Structures

Polar and Spherical Points

QuickDraw 3D defines polar and spherical points in the usual way. A polar point is a point in a plane described using polar coordinates. As illustrated in Figure 4-7, a polar point is uniquely determined by a distance r along a ray (the radius vector) that forms a given angle q with a polar axis. Polar points are defined by the TQ3PolarPoint data type.

Note

Given a fixed polar origin and polar axis, a polar point can be described by infinitely many polar coordinates. For example, the polar point (5, p) is the same as the polar point (5, 3p).

Figure 4-7 A planar point described with polar coordinates

typedef struct TQ3PolarPoint {
   float       r;
   float       theta;
} TQ3PolarPoint;

Field Description

r

The distance along the radius vector from the polar origin to the polar point.

theta

The angle, in radians, between the polar axis and the radius vector.

A spherical point is a point in space described using spherical coordinates. As illustrated in Figure 4-8, a spherical point is uniquely determined by a distance r along a ray (the radius vector) that forms a given angle q with the x axis and another given angle f with the z axis. Spherical points are defined by the TQ3SphericalPoint data type.

Figure 4-8 A spatial point described with spherical coordinates

typedef struct TQ3SphericalPoint {
   float       rho;
   float       theta;
   float       phi;
} TQ3SphericalPoint;

Field Description

rho

The distance along the radius vector from the polar origin to the spherical point.

theta

The angle, in radians, between the x axis and the projection of the radius vector onto the xy plane.

phi

The angle, in radians, between the z axis and the radius vector.