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---File: gp_Quaternion.cdl
---Created: Tue May 11 12:09:38 2010
---Author: Kirill GAVRILOV
---Copyright: Open CASCADE SAS 2010
class Quaternion from gp
---Purpose: Represents operation of rotation in 3d space as queternion
-- and implements operations with rotations basing on
-- quaternion mathematics.
--
-- In addition, provides methods for conversion to and from other
-- representatons of rotation (3*3 matrix, vector and
-- angle, Euler angles)
uses
Vec from gp,
Mat from gp,
EulerSequence from gp
is
Create returns Quaternion from gp;
---Purpose: Creates an identity quaternion
---C++: inline
Create (x, y, z, w: Real)
returns Quaternion from gp;
---Purpose: Creates quaternion directly from component values
Create (theToCopy: Quaternion from gp)
returns Quaternion from gp;
---Purpose: Creates copy of another quaternion
Create (theVecFrom, theVecTo: Vec from gp)
returns Quaternion from gp;
---Purpose: Creates quaternion representing shortest-arc rotation
-- operator producing vector theVecTo from vector theVecFrom.
Create (theVecFrom, theVecTo, theHelpCrossVec: Vec from gp)
returns Quaternion from gp;
---Purpose: Creates quaternion representing shortest-arc rotation
-- operator producing vector theVecTo from vector theVecFrom.
-- Additional vector theHelpCrossVec defines preferred direction for
-- rotation and is used when theVecTo and theVecFrom are directed
-- oppositely.
Create (theAxis: Vec from gp; theAngle: Real)
returns Quaternion from gp;
---Purpose: Creates quaternion representing rotation on angle
-- theAngle around vector theAxis
Create (theMat: Mat from gp)
returns Quaternion from gp;
---Purpose: Creates quaternion from rotation matrix 3*3
-- (which should be orthonormal skew-symmetric matrix)
IsEqual (me; theOther: Quaternion from gp) returns Boolean;
---Purpose: Simple equal test without precision
SetRotation (me: in out; theVecFrom, theVecTo: Vec from gp);
---Purpose: Sets quaternion to shortest-arc rotation producing
-- vector theVecTo from vector theVecFrom.
-- If vectors theVecFrom and theVecTo are opposite then rotation
-- axis is computed as theVecFrom ^ (1,0,0) or theVecFrom ^ (0,0,1).
SetRotation (me: in out; theVecFrom, theVecTo, theHelpCrossVec: Vec from gp);
---Purpose: Sets quaternion to shortest-arc rotation producing
-- vector theVecTo from vector theVecFrom.
-- If vectors theVecFrom and theVecTo are opposite then rotation
-- axis is computed as theVecFrom ^ theHelpCrossVec.
SetVectorAndAngle (me: in out; theAxis: Vec from gp; theAngle: Real);
---Purpose: Create a unit quaternion from Axis+Angle representation
GetVectorAndAngle (me; theAxis: out Vec from gp; theAngle: out Real);
---Purpose: Convert a quaternion to Axis+Angle representation,
-- preserve the axis direction and angle from -PI to +PI
SetMatrix (me: in out; theMat: Mat from gp);
---Purpose: Create a unit quaternion by rotation matrix
-- matrix must contain only rotation (not scale or shear)
--
-- For numerical stability we find first the greatest component of quaternion
-- and than search others from this one
GetMatrix (me) returns Mat from gp;
---Purpose: Returns rotation operation as 3*3 matrix
SetEulerAngles (me: in out; theOrder: EulerSequence from gp;
theAlpha, theBeta, theGamma: Real);
---Purpose: Create a unit quaternion representing rotation defined
-- by generalized Euler angles
GetEulerAngles (me; theOrder: EulerSequence from gp;
theAlpha, theBeta, theGamma: out Real);
---Purpose: Returns Euler angles describing current rotation
Set (me: in out; x, y, z, w: Real);
Set (me: in out; theQuaternion: Quaternion from gp);
X (me) returns Real;
Y (me) returns Real;
Z (me) returns Real;
W (me) returns Real;
SetIdent (me: in out);
---Purpose: Make identity quaternion (zero-rotation)
Reverse (me: in out);
---Purpose: Reverse direction of rotation (conjugate quaternion)
Reversed (me) returns Quaternion from gp;
---Purpose: Return rotation with reversed direction (conjugated quaternion)
Invert (me: in out);
---Purpose: Inverts quaternion (both rotation direction and norm)
Inverted (me) returns Quaternion from gp;
---Purpose: Return inversed quaternion q^-1
SquareNorm (me) returns Real;
---Purpose: Returns square norm of quaternion
Norm (me) returns Real;
---Purpose: Returns norm of quaternion
Scale (me: in out; theScale: Real);
---Purpose: Scale all components by quaternion by theScale; note that
-- rotation is not changed by this operation (except 0-scaling)
---C++: alias operator *=
Scaled (me; theScale: Real) returns Quaternion from gp;
---Purpose: Returns scaled quaternion
---C++: alias operator *
StabilizeLength (me: in out);
---Purpose: Stabilize quaternion length within 1 - 1/4.
-- This operation is a lot faster than normalization
-- and preserve length goes to 0 or infinity
Normalize (me: in out);
---Purpose: Scale quaternion that its norm goes to 1.
-- The appearing of 0 magnitude or near is a error,
-- so we can be sure that can divide by magnitude
Normalized (me) returns Quaternion from gp;
---Purpose: Returns quaternion scaled so that its norm goes to 1.
Negated (me) returns Quaternion from gp;
---Purpose: Returns quaternion with all components negated.
-- Note that this operation does not affect neither
-- rotation operator defined by quaternion nor its norm.
---C++: alias operator -
Added (me; theOther: Quaternion from gp) returns Quaternion from gp;
---Purpose: Makes sum of quaternion components; result is "rotations mix"
---C++: alias operator +
Subtracted (me; theOther: Quaternion from gp) returns Quaternion from gp;
---Purpose: Makes difference of quaternion components; result is "rotations mix"
---C++: alias operator -
Multiplied (me; theOther: Quaternion from gp) returns Quaternion from gp;
---Purpose: Multiply function - work the same as Matrices multiplying.
-- qq' = (cross(v,v') + wv' + w'v, ww' - dot(v,v'))
-- Result is rotation combination: q' than q (here q=this, q'=theQ).
-- Notices than:
-- qq' != q'q;
-- qq^-1 = q;
---C++: alias operator *
Add (me: in out; theOther: Quaternion from gp);
---Purpose: Adds componnets of other quaternion; result is "rotations mix"
---C++: alias operator +=
Subtract (me: in out; theOther: Quaternion from gp);
---Purpose: Subtracts componnets of other quaternion; result is "rotations mix"
---C++: alias operator -=
Multiply (me: in out; theOther: Quaternion from gp);
---Purpose: Adds rotation by multiplication
---C++: alias operator *=
Dot (me; theOther: Quaternion from gp) returns Real;
---Purpose: Computes inner product / scalar product / Dot
GetRotationAngle (me) returns Real;
---Purpose: Return rotation angle from -PI to PI
Multiply (me; theVec: Vec from gp) returns Vec from gp;
---Purpose: Rotates vector by quaternion as rotation operator
---C++: alias operator *
fields
x: Real;
y: Real;
z: Real;
w: Real;
end;
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