public abstract class QuaternionTools
extends java.lang.Object
| Modifier and Type | Field | Description |
|---|---|---|
(package private) static double |
EPS |
| Constructor | Description |
|---|---|
QuaternionTools() |
| Modifier and Type | Method | Description |
|---|---|---|
static void |
addTransform(QuaternionReadOnly quaternion,
Tuple3DReadOnly tupleOriginal,
Tuple3DBasics tupleTransformed) |
Transforms the tuple
tupleOriginal using quaternion and adds the result to
tupleTransformed . |
static void |
appendPitchRotation(QuaternionReadOnly quaternionOriginal,
double pitch,
QuaternionBasics quaternionToPack) |
Append a rotation about the y-axis to
quaternionOriginal and stores the result in
quaternionToPack . |
static void |
appendRollRotation(QuaternionReadOnly quaternionOriginal,
double roll,
QuaternionBasics quaternionToPack) |
Append a rotation about the x-axis to
quaternionOriginal and stores the result in
quaternionToPack . |
static void |
appendYawRotation(QuaternionReadOnly quaternionOriginal,
double yaw,
QuaternionBasics quaternionToPack) |
Append a rotation about the z-axis to
quaternionOriginal and stores the result in
quaternionToPack . |
static double |
distancePrecise(QuaternionReadOnly q1,
QuaternionReadOnly q2) |
Computes the distance between the two given quaternions.
|
static void |
inverseTransform(QuaternionReadOnly quaternion,
Matrix3DReadOnly matrixOriginal,
Matrix3D matrixTransformed) |
Performs the inverse of the transform of the matrix
matrixOriginal using
quaternion and stores the result in matrixTransformed . |
static void |
inverseTransform(QuaternionReadOnly quaternion,
RotationMatrixReadOnly rotationMatrixOriginal,
RotationMatrix rotationMatrixTransformed) |
Performs the inverse of the transform of the rotation matrix
rotationMatrixOriginal using
quaternion and stores the result in rotationMatrixTransformed . |
static void |
inverseTransform(QuaternionReadOnly quaternion,
Tuple2DReadOnly tupleOriginal,
Tuple2DBasics tupleTransformed,
boolean checkIfTransformInXYPlane) |
Performs the inverse of the transform of the tuple
tupleOriginal using quaternion
and stores the result in tupleTransformed . |
static void |
inverseTransform(QuaternionReadOnly quaternion,
Tuple3DReadOnly tupleOriginal,
Tuple3DBasics tupleTransformed) |
Performs the inverse of the transform of the tuple
tupleOriginal using quaternion
and stores the result in tupleTransformed . |
static void |
inverseTransform(QuaternionReadOnly quaternion,
QuaternionReadOnly quaternionOriginal,
QuaternionBasics quaternionTransformed) |
Performs the inverse of the transform of the quaternion
quaternionOriginal using
quaternion and stores the result in quaternionTransformed . |
static void |
inverseTransform(QuaternionReadOnly quaternion,
Vector4DReadOnly vectorOriginal,
Vector4DBasics vectorTransformed) |
Performs the inverse of the transform of the vector part of
vectorOriginal using
quaternion and stores the result in vectorTransformed . |
static void |
multiply(Orientation3DReadOnly orientation1,
boolean inverse1,
Orientation3DReadOnly orientation2,
boolean inverse2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
orientation1 and orientation2 and stores the
result in quaternionToPack . |
static void |
multiply(Orientation3DReadOnly orientation1,
boolean inverse1,
QuaternionReadOnly orientation2,
boolean inverse2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
orientation1 and orientation2 and stores the
result in quaternionToPack . |
static void |
multiply(QuaternionReadOnly orientation1,
boolean inverse1,
Orientation3DReadOnly orientation2,
boolean inverse2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
orientation1 and orientation2 and stores the
result in quaternionToPack . |
static void |
multiply(QuaternionReadOnly q1,
QuaternionReadOnly q2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
q1 and q2 and stores the result in
quaternionToPack . |
static void |
multiply(Tuple4DReadOnly t1,
Tuple4DReadOnly t2,
Vector4DBasics vectorToPack) |
Performs the multiplication, in the sense of quaternion multiplication, of
t1 and
t2 and stores the result in vectorToPack . |
static void |
multiplyConjugateBoth(QuaternionReadOnly q1,
QuaternionReadOnly q2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of the conjugate of
q1 and the conjugate of q2 and
stores the result in quaternionToPack . |
static void |
multiplyConjugateLeft(QuaternionReadOnly q1,
QuaternionReadOnly q2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
q1 conjugated and q2 and stores the result in
quaternionToPack . |
static void |
multiplyConjugateLeft(Tuple4DReadOnly t1,
Tuple4DReadOnly t2,
Vector4DBasics vectorToPack) |
Performs the multiplication, in the sense of quaternion multiplication, of
t1 conjugated
and t2 and stores the result in vectorToPack . |
static void |
multiplyConjugateRight(QuaternionReadOnly q1,
QuaternionReadOnly q2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
q1 and q2 conjugated and stores the result in
quaternionToPack . |
static void |
multiplyConjugateRight(Tuple4DReadOnly t1,
Tuple4DReadOnly t2,
Vector4DBasics vectorToPack) |
Performs the multiplication, in the sense of quaternion multiplication, of
t1 and
t2 conjugated and stores the result in vectorToPack . |
(package private) static void |
multiplyImpl(double q1x,
double q1y,
double q1z,
double q1s,
boolean conjugateQ1,
double q2x,
double q2y,
double q2z,
double q2s,
boolean conjugateQ2,
QuaternionBasics quaternionToPack) |
Performs the multiplication of
q1 and q2 and stores the result in
quaternionToPack . |
static void |
prependPitchRotation(double pitch,
QuaternionReadOnly quaternionOriginal,
QuaternionBasics quaternionToPack) |
Prepend a rotation about the y-axis to
quaternionOriginal and stores the result in
quaternionToPack . |
static void |
prependRollRotation(double roll,
QuaternionReadOnly quaternionOriginal,
QuaternionBasics quaternionToPack) |
Append a rotation about the x-axis to
quaternionOriginal and stores the result in
quaternionToPack . |
static void |
prependYawRotation(double yaw,
QuaternionReadOnly quaternionOriginal,
QuaternionBasics quaternionToPack) |
Prepend a rotation about the z-axis to
quaternionOriginal and stores the result in
quaternionToPack . |
static void |
subTransform(QuaternionReadOnly quaternion,
Tuple3DReadOnly tupleOriginal,
Tuple3DBasics tupleTransformed) |
Transforms the tuple
tupleOriginal using quaternion and subtracts the result to
tupleTransformed . |
static void |
transform(QuaternionReadOnly quaternion,
Matrix3DReadOnly matrixOriginal,
Matrix3D matrixTransformed) |
Transforms the matrix
matrixOriginal using quaternion and stores the result in
matrixTransformed . |
static void |
transform(QuaternionReadOnly quaternion,
RotationMatrixReadOnly rotationMatrixOriginal,
RotationMatrix rotationMatrixTransformed) |
Transforms the rotation matrix
rotationMatrixOriginal using quaternion and stores
the result in rotationMatrixTransformed . |
static void |
transform(QuaternionReadOnly quaternion,
Tuple2DReadOnly tupleOriginal,
Tuple2DBasics tupleTransformed,
boolean checkIfTransformInXYPlane) |
Transforms the tuple
tupleOriginal using quaternion and stores the result in
tupleTransformed . |
static void |
transform(QuaternionReadOnly quaternion,
Tuple3DReadOnly tupleOriginal,
Tuple3DBasics tupleTransformed) |
Transforms the tuple
tupleOriginal using quaternion and stores the result in
tupleTransformed . |
static void |
transform(QuaternionReadOnly quaternion,
QuaternionReadOnly quaternionOriginal,
QuaternionBasics quaternionTransformed) |
Transforms the quaternion
quaternionOriginal using quaternion and stores the
result in quaternionTransformed . |
static void |
transform(QuaternionReadOnly quaternion,
Vector4DReadOnly vectorOriginal,
Vector4DBasics vectorTransformed) |
Transforms the vector part of
vectorOriginal using quaternion and stores the
result in vectorTransformed . |
(package private) static void |
transformImpl(double qx,
double qy,
double qz,
double qs,
boolean conjugateQuaternion,
Matrix3DReadOnly matrixOriginal,
Matrix3D matrixTransformed) |
Transforms the matrix
matrixOriginal using quaternion and stores the result in
matrixTransformed . |
static final double EPS
public static void multiply(QuaternionReadOnly q1, QuaternionReadOnly q2, QuaternionBasics quaternionToPack)
q1
and q2
and stores the result in
quaternionToPack
.
quaternionToPack = q1 * q2
All three arguments can be the same object for in place operations.
q1
- the first quaternion in the multiplication. Not modified.q2
- the second quaternion in the multiplication. Not modified.quaternionToPack
- the quaternion in which the result is stores. Modified.public static void multiplyConjugateLeft(QuaternionReadOnly q1, QuaternionReadOnly q2, QuaternionBasics quaternionToPack)
q1
conjugated and q2
and stores the result in
quaternionToPack
.
quaternionToPack = q1* * q2
All three arguments can be the same object for in place operations.
q1
- the first quaternion in the multiplication. Not modified.q2
- the second quaternion in the multiplication. Not modified.quaternionToPack
- the quaternion in which the result is stores. Modified.public static void multiplyConjugateRight(QuaternionReadOnly q1, QuaternionReadOnly q2, QuaternionBasics quaternionToPack)
q1
and q2
conjugated and stores the result in
quaternionToPack
.
quaternionToPack = q1 * q2*
All three arguments can be the same object for in place operations.
q1
- the first quaternion in the multiplication. Not modified.q2
- the second quaternion in the multiplication. Not modified.quaternionToPack
- the quaternion in which the result is stores. Modified.public static void multiplyConjugateBoth(QuaternionReadOnly q1, QuaternionReadOnly q2, QuaternionBasics quaternionToPack)
q1
and the conjugate of q2
and
stores the result in quaternionToPack
.
quaternionToPack = q1* * q2*
All three arguments can be the same object for in place operations.
q1
- the first quaternion in the multiplication. Not modified.q2
- the second quaternion in the multiplication. Not modified.quaternionToPack
- the quaternion in which the result is stores. Modified.public static void multiply(Orientation3DReadOnly orientation1, boolean inverse1, Orientation3DReadOnly orientation2, boolean inverse2, QuaternionBasics quaternionToPack)
orientation1
and orientation2
and stores the
result in quaternionToPack
.
More precisely, orientation1
and orientation2
are first converted to quaternions,
then a quaternion multiplication is performed using the two first arguments as entry.
All three arguments can be the same object for in place operations.
orientation1
- the first orientation in the multiplication. Not modified.inverse1
- whether the first orientation should be inverted in the multiplication.orientation2
- the second orientation in the multiplication. Not modified.inverse2
- whether the second orientation should be inverted in the multiplication.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void multiply(Orientation3DReadOnly orientation1, boolean inverse1, QuaternionReadOnly orientation2, boolean inverse2, QuaternionBasics quaternionToPack)
orientation1
and orientation2
and stores the
result in quaternionToPack
.
More precisely, orientation1
is first converted to a quaternion, then a quaternion
multiplication is performed using the two first arguments as entry.
All three arguments can be the same object for in place operations.
orientation1
- the first orientation in the multiplication. Not modified.inverse1
- whether the first orientation should be inverted in the multiplication.orientation2
- the second orientation in the multiplication. Not modified.inverse2
- whether the second orientation should be inverted in the multiplication.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void multiply(QuaternionReadOnly orientation1, boolean inverse1, Orientation3DReadOnly orientation2, boolean inverse2, QuaternionBasics quaternionToPack)
orientation1
and orientation2
and stores the
result in quaternionToPack
.
More precisely, orientation2
is first converted to a quaternion, then a quaternion
multiplication is performed using the two first arguments as entry.
All three arguments can be the same object for in place operations.
orientation1
- the first orientation in the multiplication. Not modified.inverse1
- whether the first orientation should be inverted in the multiplication.orientation2
- the second orientation in the multiplication. Not modified.inverse2
- whether the second orientation should be inverted in the multiplication.quaternionToPack
- the quaternion in which the result is stored. Modified.static void multiplyImpl(double q1x, double q1y, double q1z, double q1s, boolean conjugateQ1, double q2x, double q2y, double q2z, double q2s, boolean conjugateQ2, QuaternionBasics quaternionToPack)
q1
and q2
and stores the result in
quaternionToPack
.
This method is for internal use only.
Provides the option to conjugate either quaternion when multiplying them.
All three arguments can be the same object for in place operations.
q1x
- the x-component of the first quaternion in the multiplication. Not modified.q1y
- the y-component of the first quaternion in the multiplication. Not modified.q1z
- the z-component of the first quaternion in the multiplication. Not modified.q1s
- the s-component of the first quaternion in the multiplication. Not modified.conjugateQ1
- whether to conjugate q1
or not.q2x
- the x-component of the second quaternion in the multiplication. Not modified.q2y
- the y-component of the second quaternion in the multiplication. Not modified.q2z
- the z-component of the second quaternion in the multiplication. Not modified.q2s
- the s-component of the second quaternion in the multiplication. Not modified.conjugateQ2
- whether to conjugate q2
or not.quaternionToPack
- the quaternion in which the result is stores. Modified.public static void multiply(Tuple4DReadOnly t1, Tuple4DReadOnly t2, Vector4DBasics vectorToPack)
t1
and
t2
and stores the result in vectorToPack
.
vectorToPack = t1 * t2
This
All three arguments can be the same object for in place operations.
t1
- the first tuple in the multiplication. Not modified.t2
- the second tuple in the multiplication. Not modified.vectorToPack
- the vector in which the result is stores. Modified.public static void multiplyConjugateLeft(Tuple4DReadOnly t1, Tuple4DReadOnly t2, Vector4DBasics vectorToPack)
t1
conjugated
and t2
and stores the result in vectorToPack
.
vectorToPack = t1* * t2
This
All three arguments can be the same object for in place operations.
t1
- the first tuple in the multiplication. Not modified.t2
- the second tuple in the multiplication. Not modified.vectorToPack
- the vector in which the result is stores. Modified.public static void multiplyConjugateRight(Tuple4DReadOnly t1, Tuple4DReadOnly t2, Vector4DBasics vectorToPack)
t1
and
t2
conjugated and stores the result in vectorToPack
.
vectorToPack = t1 * t2*
This
All three arguments can be the same object for in place operations.
t1
- the first tuple in the multiplication. Not modified.t2
- the second tuple in the multiplication. Not modified.vectorToPack
- the vector in which the result is stores. Modified.public static void transform(QuaternionReadOnly quaternion, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)
tupleOriginal
using quaternion
and stores the result in
tupleTransformed
.
Both tuples can be the same object for performing in place transformation.
tupleTransformed = quaternion * tupleOriginal * quaternion-1
quaternion
- the quaternion used to transform the tuple. Not modified.tupleOriginal
- the tuple to transform. Not modified.tupleTransformed
- the tuple in which the result is stored. Modified.public static void inverseTransform(QuaternionReadOnly quaternion, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)
tupleOriginal
using quaternion
and stores the result in tupleTransformed
.
This is equivalent to calling
transform(QuaternionReadOnly, Tuple3DReadOnly, Tuple3DBasics)
with the inverse of the
given quaternion.
Both tuples can be the same object for performing in place transformation.
tupleTransformed = quaternion-1 * tupleOriginal * quaternion
quaternion
- the quaternion used to transform the tuple. Not modified.tupleOriginal
- the tuple to transform. Not modified.tupleTransformed
- the tuple in which the result is stored. Modified.public static void addTransform(QuaternionReadOnly quaternion, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)
tupleOriginal
using quaternion
and adds the result to
tupleTransformed
.
Both tuples can be the same object for performing in place transformation.
tupleTransformed = tupleTransformed + quaternion * tupleOriginal * quaternion-1
quaternion
- the quaternion used to transform the tuple. Not modified.tupleOriginal
- the tuple to transform. Not modified.tupleTransformed
- the tuple in which the result is stored. Modified.public static void subTransform(QuaternionReadOnly quaternion, Tuple3DReadOnly tupleOriginal, Tuple3DBasics tupleTransformed)
tupleOriginal
using quaternion
and subtracts the result to
tupleTransformed
.
Both tuples can be the same object for performing in place transformation.
tupleTransformed = tupleTransformed - quaternion * tupleOriginal * quaternion-1
quaternion
- the quaternion used to transform the tuple. Not modified.tupleOriginal
- the tuple to transform. Not modified.tupleTransformed
- the tuple in which the result is stored. Modified.public static void transform(QuaternionReadOnly quaternion, Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed, boolean checkIfTransformInXYPlane)
tupleOriginal
using quaternion
and stores the result in
tupleTransformed
.
Both tuples can be the same object for performing in place transformation.
tupleTransformed = quaternion * tupleOriginal * quaternion-1
quaternion
- the quaternion used to transform the tuple. Not modified.tupleOriginal
- the tuple to transform. Not modified.tupleTransformed
- the tuple in which the result is stored. Modified.checkIfTransformInXYPlane
- whether this method should assert that the quaternion represents
a transformation in the XY plane.NotAMatrix2DException
- if checkIfTransformInXYPlane == true
and the quaternion
does not represent a transformation in the XY plane.public static void inverseTransform(QuaternionReadOnly quaternion, Tuple2DReadOnly tupleOriginal, Tuple2DBasics tupleTransformed, boolean checkIfTransformInXYPlane)
tupleOriginal
using quaternion
and stores the result in tupleTransformed
.
This is equivalent to calling
transform(QuaternionReadOnly, Tuple2DReadOnly, Tuple2DBasics, boolean)
with the inverse
of the given quaternion.
Both tuples can be the same object for performing in place transformation.
tupleTransformed = quaternion-1 * tupleOriginal * quaternion
quaternion
- the quaternion used to transform the tuple. Not modified.tupleOriginal
- the tuple to transform. Not modified.tupleTransformed
- the tuple in which the result is stored. Modified.checkIfTransformInXYPlane
- whether this method should assert that the quaternion represents
a transformation in the XY plane.NotAMatrix2DException
- if checkIfTransformInXYPlane == true
and the quaternion
does not represent a transformation in the XY plane.public static void transform(QuaternionReadOnly quaternion, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionTransformed)
quaternionOriginal
using quaternion
and stores the
result in quaternionTransformed
.
Both quaternionOriginal
and quaternionTransformed
can be the same object for
performing in place transformation.
quaternionTransformed = quaternion * quaternionOriginal
Note that this transformation is equivalent to concatenating the orientations of
quaternion
and quaternionOriginal
.
quaternion
- the quaternion used to transform the quaternion. Not modified.quaternionOriginal
- the quaternion to transform. Not modified.quaternionTransformed
- the quaternion in which the result is stored. Modified.public static void inverseTransform(QuaternionReadOnly quaternion, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionTransformed)
quaternionOriginal
using
quaternion
and stores the result in quaternionTransformed
.
This is equivalent to calling
transform(QuaternionReadOnly, QuaternionReadOnly, QuaternionBasics)
with the inverse of
the given quaternion.
Both quaternionOriginal
and quaternionTransformed
can be the same object for
performing in place transformation.
quaternionTransformed = quaternion-1 * quaternionOriginal
quaternion
- the quaternion used to transform the quaternion. Not modified.quaternionOriginal
- the quaternion to transform. Not modified.quaternionTransformed
- the quaternion in which the result is stored. Modified.public static void transform(QuaternionReadOnly quaternion, Vector4DReadOnly vectorOriginal, Vector4DBasics vectorTransformed)
vectorOriginal
using quaternion
and stores the
result in vectorTransformed
.
Both vectors can be the same object for performing in place transformation.
vectorTransformed.s = vecorOriginal.s
vectorTransformed.xyz = quaternion * vectorOriginal.xyz * quaternion-1
quaternion
- the quaternion used to transform the vector. Not modified.vectorOriginal
- the vector to transform. Not modified.vectorTransformed
- the vector in which the result is stored. Modified.public static void inverseTransform(QuaternionReadOnly quaternion, Vector4DReadOnly vectorOriginal, Vector4DBasics vectorTransformed)
vectorOriginal
using
quaternion
and stores the result in vectorTransformed
.
This is equivalent to calling
transform(QuaternionReadOnly, Tuple3DReadOnly, Tuple3DBasics)
with the inverse of the
given quaternion.
Both vectors can be the same object for performing in place transformation.
vectorTransformed.s = vecorOriginal.s
vectorTransformed.xyz = quaternion-1 * vectorOriginal.xyz * quaternion
quaternion
- the quaternion used to transform the vector. Not modified.vectorOriginal
- the vector to transform. Not modified.vectorTransformed
- the vector in which the result is stored. Modified.public static void transform(QuaternionReadOnly quaternion, Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)
matrixOriginal
using quaternion
and stores the result in
matrixTransformed
.
Both matrices can be the same object for performing in place transformation.
matrixTransformed = R(quaternion) * matrixOriginal * R(quaternion)-1
where R(quaternion) is the function to convert a quaternion into a 3-by-3 rotation matrix.
quaternion
- the quaternion used to transform the matrix. Not modified.matrixOriginal
- the matrix to transform. Not modified.matrixTransformed
- the matrix in which the result is stored. Modified.public static void inverseTransform(QuaternionReadOnly quaternion, Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)
matrixOriginal
using
quaternion
and stores the result in matrixTransformed
.
This is equivalent to calling transform(QuaternionReadOnly, Matrix3DReadOnly, Matrix3D)
with the inverse of the given quaternion.
Both matrices can be the same object for performing in place transformation.
matrixTransformed = R(quaternion)-1 * matrixOriginal * R(quaternion)
where R(quaternion) is the function to convert a quaternion into a 3-by-3 rotation matrix.
quaternion
- the quaternion used to transform the matrix. Not modified.matrixOriginal
- the matrix to transform. Not modified.matrixTransformed
- the matrix in which the result is stored. Modified.static void transformImpl(double qx, double qy, double qz, double qs, boolean conjugateQuaternion, Matrix3DReadOnly matrixOriginal, Matrix3D matrixTransformed)
matrixOriginal
using quaternion
and stores the result in
matrixTransformed
.
This method is for internal use only.
Both matrices can be the same object for performing in place transformation.
matrixTransformed = R(quaternion) * matrixOriginal * R(quaternion)-1
where R(quaternion) is the function to convert a quaternion into a 3-by-3 rotation matrix.
qx
- the x-component of the quaternion used to transform the matrix.qy
- the y-component of the quaternion used to transform the matrix.qz
- the z-component of the quaternion used to transform the matrix.qs
- the s-component of the quaternion used to transform the matrix.conjugateQuaternion
- whether to conjugate the quaternion or not.matrixOriginal
- the matrix to transform. Not modified.matrixTransformed
- the matrix in which the result is stored. Modified.public static void transform(QuaternionReadOnly quaternion, RotationMatrixReadOnly rotationMatrixOriginal, RotationMatrix rotationMatrixTransformed)
rotationMatrixOriginal
using quaternion
and stores
the result in rotationMatrixTransformed
.
Both rotation matrices can be the same object for performing in place transformation.
rotationMatrixTransformed = R(quaternion) * rotationMatrixOriginal
where R(quaternion) is the function to convert a quaternion into a 3-by-3 rotation matrix.
Note that this transformation is equivalent to concatenating the orientations of
quaternion
and rotationMatrixOriginal
.
quaternion
- the quaternion used to transform the rotation matrix. Not modified.rotationMatrixOriginal
- the rotation matrix to transform. Not modified.rotationMatrixTransformed
- the rotation matrix in which the result is stored. Modified.public static void inverseTransform(QuaternionReadOnly quaternion, RotationMatrixReadOnly rotationMatrixOriginal, RotationMatrix rotationMatrixTransformed)
rotationMatrixOriginal
using
quaternion
and stores the result in rotationMatrixTransformed
.
This is equivalent to calling
transform(QuaternionReadOnly, RotationMatrixReadOnly, RotationMatrix)
with the inverse
of the given quaternion.
Both rotation matrices can be the same object for performing in place transformation.
rotationMatrixTransformed = R(quaternion)-1 * rotationMatrixOriginal
where R(quaternion) is the function to convert a quaternion into a 3-by-3 rotation matrix.
Note that this transformation is equivalent to concatenating the orientations of
quaternion
and rotationMatrixOriginal
.
quaternion
- the quaternion used to transform the rotation matrix. Not modified.rotationMatrixOriginal
- the rotation matrix to transform. Not modified.rotationMatrixTransformed
- the rotation matrix in which the result is stored. Modified.public static void prependYawRotation(double yaw, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionToPack)
quaternionOriginal
and stores the result in
quaternionToPack
.
All the quaternions can be the same object.
/ qx = 0 \ quaternionToPack = | qy = 0 | * quaternionOriginal | qz = sin(yaw/2) | \ qs = cos(yaw/2) /
yaw
- the angle to rotate about the z-axis.quaternionOriginal
- the quaternion on which the yaw rotation is prepended. Not modified.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void appendYawRotation(QuaternionReadOnly quaternionOriginal, double yaw, QuaternionBasics quaternionToPack)
quaternionOriginal
and stores the result in
quaternionToPack
.
All the quaternions can be the same object.
/ qx = 0 \ quaternionToPack = quaternionOriginal * | qy = 0 | | qz = sin(yaw/2) | \ qs = cos(yaw/2) /
quaternionOriginal
- the quaternion on which the yaw rotation is appended. Not modified.yaw
- the angle to rotate about the z-axis.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void prependPitchRotation(double pitch, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionToPack)
quaternionOriginal
and stores the result in
quaternionToPack
.
All the quaternions can be the same object.
/ qx = 0 \ quaternionToPack = | qy = sin(pitch/2) | * quaternionOriginal | qz = 0 | \ qs = cos(pitch/2) /
pitch
- the angle to rotate about the y-axis.quaternionOriginal
- the quaternion on which the pitch rotation is prepended. Not modified.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void appendPitchRotation(QuaternionReadOnly quaternionOriginal, double pitch, QuaternionBasics quaternionToPack)
quaternionOriginal
and stores the result in
quaternionToPack
.
All the quaternions can be the same object.
/ qx = 0 \ quaternionToPack = quaternionOriginal * | qy = sin(pitch/2) | | qz = 0 | \ qs = cos(pitch/2) /
quaternionOriginal
- the quaternion on which the pitch rotation is appended. Not modified.pitch
- the angle to rotate about the y-axis.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void prependRollRotation(double roll, QuaternionReadOnly quaternionOriginal, QuaternionBasics quaternionToPack)
quaternionOriginal
and stores the result in
quaternionToPack
.
All the quaternions can be the same object.
/ qx = sin(roll/2) \ quaternionToPack = | qy = 0 | * quaternionOriginal | qz = 0 | \ qs = cos(roll/2) /
roll
- the angle to rotate about the x-axis.quaternionOriginal
- the quaternion on which the roll rotation is prepended. Not modified.quaternionToPack
- the quaternion in which the result is stored. Modified.public static void appendRollRotation(QuaternionReadOnly quaternionOriginal, double roll, QuaternionBasics quaternionToPack)
quaternionOriginal
and stores the result in
quaternionToPack
.
All the quaternions can be the same object.
/ qx = sin(roll/2) \ quaternionToPack = quaternionOriginal * | qy = 0 | | qz = 0 | \ qs = cos(roll/2) /
quaternionOriginal
- the quaternion on which the roll rotation is appended. Not modified.roll
- the angle to rotate about the x-axis.quaternionToPack
- the quaternion in which the result is stored. Modified.public static double distancePrecise(QuaternionReadOnly q1, QuaternionReadOnly q2)
q1
- the quaternion to be used in the comparison. Not modified.q2
- the quaternion to be used in the comparison. Not modified.


11
A Final Plague Threatened
1 The LORD said to Moses, “Yet one plague more I will bring upon Pharaoh and upon Egypt. Afterward he will let you go from here. When he lets you go, he will drive you away completely.
2 Speak now in the hearing of the people, that they ask, every man of his neighbor and every woman of her neighbor, for silver and gold jewelry.”
3 And the LORD gave the people favor in the sight of the Egyptians. Moreover, the man Moses was very great in the land of Egypt, in the sight of Pharaoh's servants and in the sight of the people.
4 So Moses said, “Thus says the LORD: About midnight I will go out in the midst of Egypt,
5 and every firstborn in the land of Egypt shall die, from the firstborn of Pharaoh who sits on his throne, even to the firstborn of the slave girl who is behind the handmill, and all the firstborn of the cattle.
6 There shall be a great cry throughout all the land of Egypt, such as there has never been, nor ever will be again.
7 But not a dog shall growl against any of the people of Israel, either man or beast, that you may know that the LORD makes a distinction between Egypt and Israel.
8 And all these your servants shall come down to me and bow down to me, saying, ‘Get out, you and all the people who follow you.’ And after that I will go out.” And he went out from Pharaoh in hot anger.
9 Then the LORD said to Moses, “Pharaoh will not listen to you, that my wonders may be multiplied in the land of Egypt.”
10 Moses and Aaron did all these wonders before Pharaoh, and the LORD hardened Pharaoh's heart, and he did not let the people of Israel go out of his land.