Rotation Class Reference

Encapsulates a rotation of a point about an axis. More...

#include <rotation.h>

Public Member Functions
const Quaternion &	start (void) const
	Return the start point of the rotation.
const Quaternion &	axis (void) const
	Return the axis of rotation.
	Rotation (const Quaternion start, const Quaternion axis)
	Create a rotation. More...
double	intersection (const Quaternion &normal, const Quaternion &pole) const
	Determine whether a point will be rotated across a meridian. More...
double	intersection (const Quaternion &normal, const float h) const
	Determine whether a point will be rotated across a plane bounded by a small circle. More...

Detailed Description

Encapsulates a rotation of a point about an axis.

It mostly exists to support the two intersection methods.

Constructor & Destructor Documentation

Rotation::Rotation	(	const Quaternion	start,
		const Quaternion	axis
	)

Create a rotation.

Parameters

start	the point which is rotated
axis	the axis about which the point is rotated

Member Function Documentation

double Rotation::intersection	(	const Quaternion &	normal,
		const Quaternion &	pole
	)		const

Determine whether a point will be rotated across a meridian.

The point start is rotated around an axis axis. At what point does it cross a plane which is perpendicular to normal? We are interested in the meridian which is the intersection of this plane and the half-great-circle obtained by rotating pole by pi clockwise about normal.

Returns tan(theta/2), where theta is the angle by which start must be rotated to intersect the meridian. Negative values should be interpreted as theta/2 being in the second quadrant rather than the fourth (that is, theta is in the third or fourth quadrants).

See quaternion-pointing notes, section meridians.

Returns

tan(theta/2), as noted above; or return 0.0 if the rotation would not intersect the meridian at all

double Rotation::intersection	(	const Quaternion &	normal,
		const float	h
	)		const

Determine whether a point will be rotated across a plane bounded by a small circle.

The point start is rotated around an axis axis. At what point does it cross a plane which is perpendicular to normal and which cuts the vector normal at a distance h from the origin?

Returns tan(theta/2), where theta is the angle by which A must be rotated to intersect the plane. Negative values should be interpreted as theta/2 being in the second quadrant rather than the fourth (that is, theta is in the third or fourth quadrants). We return the value of tan(theta/2) corresponding to the smaller value of theta (that is, the first intersection of the rotation with the plane).

See quaternion-pointing notes, section meridians.

Returns

tan(theta/2), as noted above; or return 0.0 if the rotation would not intersect the meridian at all

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The documentation for this class was generated from the following files:

• rotation.h
• rotation.cpp