com.io7m.jtensors

Class QuaternionI4D

java.lang.Object

com.io7m.jtensors.QuaternionI4D

All Implemented Interfaces:

QuaternionReadable4DType, VectorReadable2DType, VectorReadable3DType, VectorReadable4DType

public class QuaternionI4D
extends Object
implements QuaternionReadable4DType

A four-dimensional immutable quaternion type with double precision elements.

Values of this type are immutable and can therefore be safely accessed from multiple threads.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	QuaternionI4D.Context The Context type contains the minimum storage required for all of the functions of the QuaternionI4D class.

Field Summary

Fields

Modifier and Type	Field and Description
static QuaternionI4D	IDENTITY The "identity" quaternion, [0.0 0.0 0.0 1.0]

Constructor Summary

Constructors

Constructor and Description
QuaternionI4D() Default constructor, initializing the quaternion with values [0.0, 0.0, 0.0, 1.0]
QuaternionI4D(double in_x, double in_y, double in_z, double in_w) Construct a quaternion initialized with the given values.
QuaternionI4D(QuaternionReadable4DType q) Construct a quaternion initialized with the values contained in q.

Method Summary

Modifier and Type	Method and Description
static QuaternionI4D	add(QuaternionReadable4DType q0, QuaternionReadable4DType q1) Calculate the element-wise sum of the quaternions q0 and q1.
static boolean	almostEqual(com.io7m.jequality.AlmostEqualDouble.ContextRelative context, QuaternionReadable4DType qa, QuaternionReadable4DType qb) Determine whether or not the quaternions qa and qb are equal to within the degree of error given in context.
static QuaternionI4D	conjugate(QuaternionReadable4DType q) Calculate the conjugate of the input quaternion q.
static double	dotProduct(QuaternionReadable4DType q0, QuaternionReadable4DType q1) Calculate the scalar product of the quaternions q0 and q1.
boolean	equals(Object obj)
double	getWD()
double	getXD()
double	getYD()
double	getZD()
int	hashCode()
static QuaternionI4D	interpolateLinear(QuaternionReadable4DType q0, QuaternionReadable4DType q1, double alpha) Linearly interpolate between q0 and q1 by the amount alpha, such that: interpolateLinear(q0, q1, 0.0) = q0 interpolateLinear(q0, q1, 1.0) = q1
static boolean	isNegationOf(com.io7m.jequality.AlmostEqualDouble.ContextRelative context, QuaternionReadable4DType qa, QuaternionReadable4DType qb) Return true iff qa is the negation of qb.
static QuaternionI4D	lookAtWithContext(QuaternionI4D.Context context, VectorReadable3DType origin, VectorReadable3DType target, VectorReadable3DType up) Produce a quaternion that represents a rotation that "looks at" the point at target assuming the viewer is at origin, using up as the "up" vector.
static double	magnitude(QuaternionReadable4DType q) Calculate the magnitude of the quaternion q.
static double	magnitudeSquared(QuaternionReadable4DType q) Calculate the squared magnitude of the quaternion q.
static QuaternionI4D	makeFromAxisAngle(VectorReadable3DType axis, double angle) Produce a quaternion that represents a rotation of angle degrees around the axis specified by axis.
static QuaternionI4D	makeFromRotationMatrix3x3(MatrixReadable3x3DType m) Produce a quaternion equivalent to the rotation matrix m.
static QuaternionI4D	makeFromRotationMatrix4x4(MatrixReadable4x4DType m) Produce a quaternion equivalent to the rotation matrix m, writing the result to out.
static MatrixM3x3D	makeRotationMatrix3x3(QuaternionReadable4DType q, MatrixM3x3D m) Produce a rotation matrix from the quaternion q, saving the result to m.
static MatrixM4x4D	makeRotationMatrix4x4(QuaternionReadable4DType q, MatrixM4x4D m) Produce a rotation matrix from the quaternion q, saving the result to m.
static QuaternionI4D	multiply(QuaternionReadable4DType q0, QuaternionReadable4DType q1) Multiply the quaternion q0 by the quaternion q1 .
static QuaternionI4D	negate(QuaternionReadable4DType q) Negate the elements of q.
static QuaternionI4D	normalize(QuaternionReadable4DType q) Normalize the quaternion q, preserqing its direction but reducing it to unit length.
static QuaternionI4D	scale(QuaternionReadable4DType q, double r) Scale the quaternion q by the scalar r.
static QuaternionI4D	subtract(QuaternionReadable4DType q0, QuaternionReadable4DType q1) Subtract the quaternion q0 from the quaternion q1.
String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

IDENTITY

public static final QuaternionI4D IDENTITY

The "identity" quaternion, [0.0 0.0 0.0 1.0]

Constructor Detail

QuaternionI4D

public QuaternionI4D()

Default constructor, initializing the quaternion with values [0.0, 0.0, 0.0, 1.0]

QuaternionI4D

public QuaternionI4D(double in_x,
                     double in_y,
                     double in_z,
                     double in_w)

Construct a quaternion initialized with the given values.

Parameters:

in_x - The x value

in_y - The y value

in_z - The z value

in_w - The w value

QuaternionI4D

public QuaternionI4D(QuaternionReadable4DType q)

Construct a quaternion initialized with the values contained in q.

Parameters:

q - The source quaternion

Method Detail

add

public static final QuaternionI4D add(QuaternionReadable4DType q0,
                                      QuaternionReadable4DType q1)

Calculate the element-wise sum of the quaternions q0 and q1.

Parameters:

q0 - The left input quaternion

q1 - The right input quaternion

Returns:

(q0.x + q1.x, q0.y + q1.y, q0.z + q1.z, q0.w + q1.w)

almostEqual

public static final boolean almostEqual(com.io7m.jequality.AlmostEqualDouble.ContextRelative context,
                                        QuaternionReadable4DType qa,
                                        QuaternionReadable4DType qb)

Determine whether or not the quaternions qa and qb are equal to within the degree of error given in context.

Parameters:

context - The equality context

qa - The left input quaternion

qb - The right input quaternion

Returns:

true if the quaternions are almost equal

Since:

5.0.0

See Also:

AlmostEqualDouble.almostEqual(ContextRelative, double, double)

conjugate

public static final QuaternionI4D conjugate(QuaternionReadable4DType q)

Calculate the conjugate of the input quaternion q.

Parameters:

q - The input quaternion

Returns:

The conjugate of the input quaternion

dotProduct

public static final double dotProduct(QuaternionReadable4DType q0,
                                      QuaternionReadable4DType q1)

Calculate the scalar product of the quaternions q0 and q1.

Parameters:

q0 - The left input quaternion

q1 - The right input quaternion

Returns:

The scalar product of the two quaternions

interpolateLinear

public static final QuaternionI4D interpolateLinear(QuaternionReadable4DType q0,
                                                    QuaternionReadable4DType q1,
                                                    double alpha)

Linearly interpolate between q0 and q1 by the amount alpha, such that:

• interpolateLinear(q0, q1, 0.0) = q0
• interpolateLinear(q0, q1, 1.0) = q1

Parameters:

q0 - The left input quaternion

q1 - The right input quaternion

alpha - The interpolation value, between 0.0 and 1.0

Returns:

(1 - alpha) * q0 + alpha * q1

isNegationOf

public static final boolean isNegationOf(com.io7m.jequality.AlmostEqualDouble.ContextRelative context,
                                         QuaternionReadable4DType qa,
                                         QuaternionReadable4DType qb)

Return true iff qa is the negation of qb.

Each element is compared with AlmostEqualDouble.almostEqual(ContextRelative, double, double).

Parameters:

context - The equality context

qa - The left quaternion

qb - The right quaternion

Returns:

true iff qa is the negation of qb

Since:

5.0.0

lookAtWithContext

public static final QuaternionI4D lookAtWithContext(QuaternionI4D.Context context,
                                                    VectorReadable3DType origin,
                                                    VectorReadable3DType target,
                                                    VectorReadable3DType up)

Produce a quaternion that represents a rotation that "looks at" the point at target assuming the viewer is at origin, using up as the "up" vector.

The function uses storage preallocated in context to avoid any new allocations.

Parameters:

context - Preallocated storage

origin - The origin point

target - The target point

up - The up vector

Returns:

A quaternion looking at the target

Since:

5.0.0

magnitude

public static final double magnitude(QuaternionReadable4DType q)

Calculate the magnitude of the quaternion q. Correspondingly, magnitude(normalize(q)) == 1.0.

Parameters:

q - The input quaternion

Returns:

The magnitude of the input quaternion

magnitudeSquared

public static final double magnitudeSquared(QuaternionReadable4DType q)

Calculate the squared magnitude of the quaternion q.

Parameters:

q - The input quaternion

Returns:

The squared magnitude of the input quaternion

makeFromAxisAngle

public static final QuaternionI4D makeFromAxisAngle(VectorReadable3DType axis,
                                                    double angle)

Produce a quaternion that represents a rotation of angle degrees around the axis specified by axis. axis is assumed to be of unit length.

Parameters:

axis - The normalized vector representing the axis

angle - The angle to rotate, in radians

Returns:

A quaternion representing the rotation

See Also:

VectorI3D.normalize(VectorReadable3DType), VectorI4D.normalize(VectorReadable4DType)

makeFromRotationMatrix3x3

public static final QuaternionI4D makeFromRotationMatrix3x3(MatrixReadable3x3DType m)

Produce a quaternion equivalent to the rotation matrix m.

Parameters:

m - The rotation matrix

Returns:

A quaternion representing the rotation matrix

Since:

5.0.0

makeFromRotationMatrix4x4

public static final QuaternionI4D makeFromRotationMatrix4x4(MatrixReadable4x4DType m)

Produce a quaternion equivalent to the rotation matrix m, writing the result to out.

Parameters:

m - The rotation matrix

Returns:

A quaternion representing the rotation matrix

Since:

5.0.0

makeRotationMatrix3x3

public static final MatrixM3x3D makeRotationMatrix3x3(QuaternionReadable4DType q,
                                                      MatrixM3x3D m)

Produce a rotation matrix from the quaternion q, saving the result to m.

Parameters:

q - The input quaternion

m - The output matrix

Returns:

m

Since:

5.0.0

makeRotationMatrix4x4

public static final MatrixM4x4D makeRotationMatrix4x4(QuaternionReadable4DType q,
                                                      MatrixM4x4D m)

Produce a rotation matrix from the quaternion q, saving the result to m.

Parameters:

q - The input quaternion

m - The output matrix

Returns:

m

Since:

5.0.0

multiply

public static final QuaternionI4D multiply(QuaternionReadable4DType q0,
                                           QuaternionReadable4DType q1)

Multiply the quaternion q0 by the quaternion q1 .

Note that this operation is not commutative.

The function is most often used to concatenate quaternions to combine rotations. As an example, assuming that:

• qx represents some rotation around the X axis
• qy represents some rotation around the Y axis
• qz represents some rotation around the Z axis

The following code produces a quaternion qr1 that represents a rotation around the X axis, followed by a rotation around the Y axis, followed by a rotation around the Z axis:

qr0 = QuaternionI4D.multiply(qy, qx); qr1 = QuaternionI4D.multiply(qz, qy);

Parameters:

q0 - The left input quaternion

q1 - The right input quaternion

Returns:

The multiplication of the input quaternions

negate

public static final QuaternionI4D negate(QuaternionReadable4DType q)

Negate the elements of q.

Parameters:

q - The source quaternion

Returns:

The negation of q

Since:

5.0.0

normalize

public static final QuaternionI4D normalize(QuaternionReadable4DType q)

Normalize the quaternion q, preserqing its direction but reducing it to unit length.

Parameters:

q - The input quaternion

Returns:

A quaternion with the same orientation as q but with magnitude equal to 1.0

scale

public static final QuaternionI4D scale(QuaternionReadable4DType q,
                                        double r)

Scale the quaternion q by the scalar r.

Parameters:

q - The input quaternion

r - The scaling value

Returns:

(q.x * r, q.y * r, q.z * r, q.w * r)

subtract

public static final QuaternionI4D subtract(QuaternionReadable4DType q0,
                                           QuaternionReadable4DType q1)

Subtract the quaternion q0 from the quaternion q1.

Parameters:

q0 - The left input quaternion

q1 - The right input quaternion

Returns:

(q0.x - q1.x, q0.y - q1.y, q0.z - q1.z)

equals

public final boolean equals(@Nullable
                            Object obj)

Overrides:

equals in class Object

getWD

public final double getWD()

Specified by:

getWD in interface VectorReadable4DType

Returns:

The W value of the given vector.

getXD

public final double getXD()

Specified by:

getXD in interface VectorReadable2DType

Returns:

The X value of the given vector.

getYD

public final double getYD()

Specified by:

getYD in interface VectorReadable2DType

Returns:

The Y value of the given vector.

getZD

public final double getZD()

Specified by:

getZD in interface VectorReadable3DType

Returns:

The Z value of the given vector.

hashCode

public final int hashCode()

Overrides:

hashCode in class Object

toString

public final String toString()

Overrides:

toString in class Object