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Quaternion

Quaternion struct

Represents the four coefficient values in a quaternion. The first value a is the real part, while the rest multiplies i, j and k, that are imaginary. quaternion = a + bi + cj + dk

Derived Classes:

Namespace: Rhino.Geometry
Quaternion: references

Constructors (1)

Quaternion(double a, double b, double c, double d)

Initializes a new quaternion with the provided coefficients.

Properties (19)

A

Gets or sets the real part of the quaternion.

B

Gets or sets the first imaginary coefficient of the quaternion.

C

Gets or sets the second imaginary coefficient of the quaternion.

Conjugate

Gets a new quaternion that is the conjugate of this quaternion.
This is (a,-b,-c,-d)

D

Gets or sets the third imaginary coefficient of the quaternion.

I

Returns the (0,1,0,0) quaternion.

Identity

Returns the (1,0,0,0) quaternion.

Inverse

Computes a new inverted quaternion,
(a/L2, -b/L2, -c/L2, -d/L2),
where L2 = length squared = (a*a + b*b + c*c + d*d). This is the multiplicative inverse, i.e., (a,b,c,d)*(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0). If this is the zero quaternion, then the zero quaternion is returned.

IsScalar

True if b, c, and d are all zero.

IsValid

Determines if the four coefficients are valid numbers within RhinoCommon.
See .

IsVector

True if a = 0 and at least one of b, c, or d is not zero.

IsZero

True if a, b, c, and d are all zero.

J

Returns the (0,0,1,0) quaternion.

K

Returns the (0,0,0,1) quaternion.

Length

Returns the length or norm of the quaternion.

LengthSquared

Gets the result of (a^2 + b^2 + c^2 + d^2).

Scalar

The real (scalar) part of the quaternion
This is .

Vector

The imaginary part of the quaternion
(B,C,D)

Zero

Returns the default quaternion, where all coefficients are 0.

Methods (28)

CreateFromRotationZYX(double yaw, double pitch, double roll)

Constructs a quaternion defined by Tait-Byran angles, also loosely known as Euler angles.

CreateFromRotationZYZ(double alpha, double beta, double gamma)

Constructs a quaternion defined by Euler angles.

CrossProduct(Quaternion p, Quaternion q)

Computes the vector cross product of p and q = (0,x,y,z),
where (x,y,z) = CrossProduct(p.Vector,q.Vector).
This is not the same as the quaternion product p*q.

Distance(Quaternion p, Quaternion q)

Returns the distance or norm of the difference between two quaternions.

DistanceTo(Quaternion q)

Computes the distance or norm of the difference between this and another quaternion.

EpsilonEquals(Quaternion other, double epsilon)

Check that all values in other are within epsilon of the values in this

Equals(object obj)

Determines whether an object is a quaternion and has the same value of this quaternion.

Equals(Quaternion other)

Determines whether this quaternion has the same value of another quaternion.

GetEulerZYZ(out double alpha, out double beta, out double gamma)

Find the Euler angles for a rotation transformation.

GetHashCode()

Gets a non-unique but repeatable hashing code for this quaternion.

GetRotation(out double angle, out Vector3d axis)

Returns the rotation defined by the quaternion.

GetRotation(out Plane plane)

Returns the frame created by applying the quaternion's rotation to the canonical world frame (1,0,0),(0,1,0),(0,0,1).

GetRotation(out Transform xform)

Returns a transformation matrix that performs the rotation defined by the quaternion. The transformation returned by this method has the property that xform * V = q.Rotate(V). If the quaternion is not unitized, the rotation of its unitized form is returned.

GetYawPitchRoll(out double yaw, out double pitch, out double roll)

Find sthe Tait-Byran angles, also loosely called Euler angles, for this quaternion.

Invert()

Modifies this quaternion to become
(a/L2, -b/L2, -c/L2, -d/L2),
where L2 = length squared = (a*a + b*b + c*c + d*d).
This is the multiplicative inverse, i.e., (a,b,c,d)*(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0).

Lerp(Quaternion a, Quaternion b, double t)

Interpolates between two quaternions, using linear interpolation.

MatrixForm()

Returns 4x4 real valued matrix form of the quaternion a b c d -b a -d c -c d a -b -d -c b a which has the same arithmetic properties as the quaternion.

Product(Quaternion p, Quaternion q)

The quaternion product of p and q. This is the same value as p*q.

Rotate(Vector3d v)

Rotates a 3d vector. This operation is also called conjugation, because the result is the same as (q.Conjugate()*(0,x,y,x)*q/q.LengthSquared).Vector.

RotateTowards(Quaternion a, Quaternion b, double maxRadians)

Returns the quaternion obtained by rotating a towards b, limiting the rotation by MaxRadians.

Rotation(double angle, Vector3d axisOfRotation)

Returns the unit quaternion cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z where (x,y,z) is the unit vector parallel to axis. This is the unit quaternion that represents the rotation of angle about axis.

Rotation(Plane plane0, Plane plane1)

Returns the unit quaternion that represents the rotation that maps plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and plane0.zaxis to plane1.zaxis.

Set(double a, double b, double c, double d)

Sets all coefficients of the quaternion.

SetRotation(double angle, Vector3d axisOfRotation)

Sets the quaternion to cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z where (x,y,z) is the unit vector parallel to axis. This is the unit quaternion that represents the rotation of angle about axis.

SetRotation(Plane plane0, Plane plane1)

Sets the quaternion to the unit quaternion which rotates plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and plane0.zaxis to plane1.zaxis.

Slerp(Quaternion a, Quaternion b, double t)

Interpolates between two quaternions, using spherical linear interpolation.

ToString()

Returns a string representation of this Quaternion.

Unitize()

Scales the quaternion's coordinates so that a*a + b*b + c*c + d*d = 1.

Operators (9)

!=

Determines whether two quaternions have different values.

==

Determines whether two quaternions have the same value.

operator-

Subtracts a quaternion from another one.
This computes the difference of each quaternion coefficient with its correspondent and returns a new result quaternion.

operator*

Multiplies a quaternion with another one.
Quaternion multiplication (Hamilton product) is not commutative.

operator*

Multiplies (scales) all quaternion coefficients by a factor and returns a new quaternion with the result.

operator*

Multiplies (scales) all quaternion coefficients by a factor and returns a new quaternion with the result.

operator*

Multiplies (scales) all quaternion coefficients by a factor and returns a new quaternion with the result.

operator/

Divides all quaternion coefficients by a factor and returns a new quaternion with the result.

operator+

Adds two quaternions.
This sums each quaternion coefficient with its correspondent and returns a new result quaternion.

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