Package org.apache.commons.numbers.quaternion

Class Slerp

java.lang.Object

org.apache.commons.numbers.quaternion.Slerp

All Implemented Interfaces:

DoubleFunction<Quaternion>

public class Slerp
extends Object
implements DoubleFunction<Quaternion>

Perform spherical linear interpolation (Slerp). The Slerp algorithm is designed to interpolate smoothly between two rotations/orientations, producing a constant-speed motion along an arc. The original purpose of this algorithm was to animate 3D rotations. All output quaternions are in positive polar form, meaning a unit quaternion with a positive scalar component.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private final class	Slerp.Linear	Linear interpolation, used when the quaternions are too closely aligned.
private final class	Slerp.Spherical	Spherical interpolation, used when the quaternions are too closely aligned.

Field Summary

Fields

Modifier and Type	Field	Description
private final DoubleFunction<Quaternion>	algo	Linear or spherical interpolation algorithm.
private final Quaternion	end	End of the interpolation.
private static final double	MAX_DOT_THRESHOLD	Threshold max value for the dot product.
private final Quaternion	start	Start of the interpolation.

Constructor Summary

Constructors

Constructor	Description
Slerp(Quaternion start, Quaternion end)	Create an instance.

Method Summary

Modifier and Type	Method	Description
Quaternion	apply(double t)	Performs the interpolation.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

MAX_DOT_THRESHOLD

private static final double MAX_DOT_THRESHOLD

Threshold max value for the dot product. If the quaternion dot product is greater than this value (i.e. the quaternions are very close to each other), then the quaternions are linearly interpolated instead of spherically interpolated.

See Also:

• Constant Field Values

start

private final Quaternion start

Start of the interpolation.

end

private final Quaternion end

End of the interpolation.

algo

private final DoubleFunction<Quaternion> algo

Linear or spherical interpolation algorithm.

Constructor Details

Slerp

public Slerp(Quaternion start,
 Quaternion end)

Create an instance.

Parameters:

start - Start of the interpolation.

end - End of the interpolation.

Method Details

apply

public Quaternion apply(double t)

Performs the interpolation. The rotation returned by this method is controlled by the interpolation parameter, t. All other values are interpolated (or extrapolated if t is outside of the [0, 1] range). The returned quaternion is in positive polar form, meaning that it is a unit quaternion with a positive scalar component.

Specified by:

apply in interface DoubleFunction<Quaternion>

Parameters:

t - Interpolation control parameter. When t = 0, a rotation equal to the start instance is returned. When t = 1, a rotation equal to the end instance is returned.

Returns:

an interpolated quaternion in positive polar form.