Quaternion Structure

Initializes a new quaternion with the provided coefficients.

Gets or sets the real part of the quaternion.

Gets or sets the first imaginary coefficient of the quaternion.

Gets or sets the second imaginary coefficient of the quaternion.

Gets a new quaternion that is the conjugate of this quaternion.

This is (a,-b,-c,-d)

Gets or sets the third imaginary coefficient of the quaternion.

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

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

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.

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

Determines if the four coefficients are valid numbers within RhinoCommon.

See IsValidDouble(Double).

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

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

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

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

Returns the length or norm of the quaternion.

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

The real (scalar) part of the quaternion

This is A.

The imaginary part of the quaternion

(B,C,D)

Returns the default quaternion, where all coefficients are 0.

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

Constructs a quaternion defined by Euler angles.

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.

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

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

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

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

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

Find the Euler angles for a rotation transformation.

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

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

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.

Returns the rotation defined by the quaternion.

Gets the Type of the current instance.

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

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).

Interpolates between two quaternions, using linear interpolation.

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.

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

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.

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

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.

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.

Sets all coefficients of the quaternion.

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.

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.

Interpolates between two quaternions, using spherical linear interpolation.

Returns a string representation of this Quaternion.

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

Adds two quaternions.

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

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

Determines whether two quaternions have the same value.

Determines whether two quaternions have different values.

Multiplies a quaternion with another one.

Quaternion multiplication (Hamilton product) is not commutative.

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

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

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

Subtracts a quaternion from another one.

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