Tori

A torus is a three-dimensional object formed by the rotation of an ellipse about an axis in the plane of the ellipse that does not cut the ellipse. The major radius is the distance of the center of the ellipse from that axis. A torus is defined by the TQ3TorusData data type. See "Creating and Editing Tori" for a description of the routines you can use to create and edit tori. Figure 35 shows a torus.

Figure 35 A torus

Figure 36 shows the standard surface parameterization of a torus.

Figure 36 The standard surface parameterization of a torus



 
typedef struct TQ3TorusData {

    TQ3Point3D                          origin;

    TQ3Vector3D                         orientation;

    TQ3Vector3D                         majorRadius;

    TQ3Vector3D                         minorRadius;

    float                               ratio;

    float                               uMin, uMax, vMin, vMax;

    TQ3EndCap                           caps;

    TQ3AttributeSet                     interiorAttributeSet;

    TQ3AttributeSet                     torusAttributeSet;

} TQ3TorusData;

origin: The center of the torus. This is the closest point on the axis of rotation to the rotated ellipse.
orientation: The orientation of the torus. This field specifies the axis of rotation and the half-thickness of the torus. The orientation must be orthogonal to both the major and minor radii.
majorRadius: The major radius of the torus.
minorRadius: The minor radius of the torus.
ratio: The ratio of the major radius of the rotated ellipse to the length of the orientation vector. In Figure 35 , this is r /length( orientation ).
uMin: The minimum value in the u parametric direction of the torus. This value should be greater than or equal to 0.0 and less than or equal to 1.0.
uMax: The maximum value in the u parametric direction of the torus. This value should be greater than or equal to 0.0 and less than or equal to 1.0.
vMin: The minimum value in the v parametric direction of the torus. This value should be greater than or equal to 0.0 and less than or equal to 1.0.
vMax: The maximum value in the v parametric direction of the torus. This value should be greater than or equal to 0.0 and less than or equal to 1.0.
caps: The style of cap to be used on the torus. See "End Caps Masks" for a description of the masks you can use to specify a value for this field.
interiorAttributeSet: A set of torus interior attributes.
torusAttributeSet: A set of attributes for the torus. The value in this field is NULL if no torus attributes are defined.