T_Rhino_Geometry_Quaternion - mcneel/rhinocommon-api-docs GitHub Wiki
Represents the four coefficient values in a quaternion. The first value a is the real part, while the rest multipies i, j and k, that are imaginary.
quaternion = a + bi + cj + dk
Namespace: Rhino.Geometry
Assembly: RhinoCommon (in RhinoCommon.dll) Version: Rhino 6.0
C#
[SerializableAttribute]
public struct Quaternion : IEquatable<Quaternion>VB
<SerializableAttribute>
Public Structure Quaternion
Implements IEquatable(Of Quaternion)The Quaternion type exposes the following members.
| Name | Description | |
|---|---|---|
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Quaternion | Initializes a new quaternion with the provided coefficients. |
| Name | Description | |
|---|---|---|
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A | Gets or sets the real part of the quaternion. |
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B | Gets or sets the first imaginary coefficient of the quaternion. |
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C | Gets or sets the second imaginary coefficient of the quaternion. |
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Conjugate | Gets a new quaternion that is the conjugate of this quaternion. This is (a,-b,-c,-d) |
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D | Gets or sets the third imaginary coefficient of the quaternion. |
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I | Returns the (0,1,0,0) quaternion. |
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Identity | Returns the (1,0,0,0) quaternion. |
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Inverse |
Computes a new inverted quaternion,
(a/L2, -b/L2, -c/L2, -d/L2),
where L2 = length squared = (aa + bb + cc + dd). 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. |
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IsScalar | true if b, c, and d are all zero. |
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IsValid | Determines if the four coefficients are valid numbers within RhinoCommon. See IsValidDouble(Double). |
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IsVector | true if a = 0 and at least one of b, c, or d is not zero. |
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IsZero | true if a, b, c, and d are all zero. |
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J | Returns the (0,0,1,0) quaternion. |
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K | Returns the (0,0,0,1) quaternion. |
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Length | Returns the length or norm of the quaternion. |
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LengthSquared | Gets the result of (a^2 + b^2 + c^2 + d^2). |
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Scalar | The real (scalar) part of the quaternion This is A. |
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Vector | The imaginary part of the quaternion (B,C,D) |
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Zero | Returns the dafault quaternion, where all coefficients are 0. |
| Name | Description | |
|---|---|---|
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CrossProduct |
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. |
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Distance | Returns the distance or norm of the difference between two quaternions. |
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DistanceTo | Computes the distance or norm of the difference between this and another quaternion. |
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EpsilonEquals | Check that all values in other are within epsilon of the values in this |
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Equals(Object) | Determines whether an object is a quaternion and has the same value of this quaternion. (Overrides ValueType.Equals(Object).) |
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Equals(Quaternion) | Determines whether this quaternion has the same value of another quaternion. |
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GetHashCode | Gets a non-unique but repeatable hashing code for this quaternion. (Overrides ValueType.GetHashCode().) |
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GetRotation(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). |
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GetRotation(Double, Vector3d) | Returns the rotation defined by the quaternion. |
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GetType | Gets the Type of the current instance. (Inherited from Object.) |
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Invert |
Modifies this quaternion to become
(a/L2, -b/L2, -c/L2, -d/L2),
where L2 = length squared = (aa + bb + cc + dd). This is the multiplicative inverse, i.e., (a,b,c,d)(a/L2, -b/L2, -c/L2, -d/L2) = (1,0,0,0). |
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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. |
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Product | The quaternion product of p and q. This is the same value as pq. |
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Rotate | 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. |
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Rotation(Double, Vector3d) | 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. |
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Rotation(Plane, Plane) | Returns the unit quaternion that represents the the rotation that maps plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and plane0.zaxis to plane1.zaxis. |
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Set | Sets all coefficients of the quaternion. |
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SetRotation(Double, Vector3d) | 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. |
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SetRotation(Plane, Plane) | 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. |
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ToString | Returns the fully qualified type name of this instance. (Inherited from ValueType.) |
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Unitize | Scales the quaternion's coordinates so that aa + bb + cc + dd = 1. |
| Name | Description | |
|---|---|---|
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Addition | Adds two quaternions. This sums each quaternion coefficient with its correspondant and returns a new result quaternion. |
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Division | Divides all quaternion coefficients by a factor and returns a new quaternion with the result. |
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Equality | Determines whether two quaternions have the same value. |
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Inequality | Determines whether two quaternions have different values. |
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Multiply(Quaternion, Quaternion) | Multiplies a quaternion with another one. Quaternion multiplication (Hamilton product) is not commutative. |
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Multiply(Quaternion, Double) | Multiplies (scales) all quaternion coefficients by a factor and returns a new quaternion with the result. |
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Multiply(Quaternion, Int32) | Multiplies (scales) all quaternion coefficients by a factor and returns a new quaternion with the result. |
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Multiply(Quaternion, Single) | Multiplies (scales) all quaternion coefficients by a factor and returns a new quaternion with the result. |
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Subtraction | Subtracts a quaternion from another one. This computes the difference of each quaternion coefficient with its correspondant and returns a new result quaternion. |
Supported in: 6.0.16224.21491, 5D58w