Gorilla.Utils.Quaternions

Records

• record TQuaternion

Constants

• const QuatIdentityRot : TQuaternion = ;

Functions / Procedures

• public function QuatFromAxisAngle  ( const  Axis :  TPoint3D; const  AngleRad :  Single; const  NormalizeAxis :  Boolean  =  False )  : TQuaternion ;  overload;

  Calculate unit quaternion representing rotation around Axis by AngleRad angle (in radians). Axis must be normalized, or you have to pass NormalizeAxis = true (then we'll normalize it ourselves inside). Otherwise you will get non-normalized quaternion that doesn't represent rotation, and is usually useless for us.

• public function QuatFromAxisAngle  ( const  AxisAngle :  TVector3D; const  NormalizeAxis :  Boolean  =  False )  : TQuaternion ;  overload;

  Calculate unit quaternion representing rotation around Axis by AngleRad angle (in radians). Axis must be normalized, or you have to pass NormalizeAxis = true (then we'll normalize it ourselves inside). Otherwise you will get non-normalized quaternion that doesn't represent rotation, and is usually useless for us.

• public function SLerp  ( const  A :  Single; const  Q1 :  TQuaternion; const  Q2 :  TQuaternion )  : TQuaternion ;  overload;

  Interpolate between two rotations, along the shortest path on the unit sphere, with constant speed. The overloaded version that works with TVector4Single takes a rotation (not a quaternion) expressed as an axis (first 3 elements) and angle (in radians, 4th element). Axis does not have to be normalized (we'll normalize it). This is nice e.g. to interpolate VRML/X3D rotations.

• public function SLerp  ( const  A :  Single; const  Rot1 :  TVector3D; const  Rot2 :  TVector3D )  : TVector3D ;  overload;

  Interpolate between two rotations, along the shortest path on the unit sphere, with constant speed. The overloaded version that works with TVector4Single takes a rotation (not a quaternion) expressed as an axis (first 3 elements) and angle (in radians, 4th element). Axis does not have to be normalized (we'll normalize it). This is nice e.g. to interpolate VRML/X3D rotations.

• public function NLerp  ( const  A :  Single; const  Q1 :  TQuaternion; const  Q2 :  TQuaternion; const  ForceShortestPath :  Boolean  =  True )  : TQuaternion ;  overload;

  Interpolate between two rotations, along the straightest path on the unit sphere. This is faster than SLerp, but does not guarantee the interpolated result travels with constant speed. Often it's not a noticeable / important problem (see http://number-none.com/product/Understanding%%20Slerp,%%20Then%%20Not%%20Using%%20It/) When ForceShortestPath = @false, this doesn't guarantee choosing the shortest path. Although it goes through the @italic(straightest) path, there are two such paths, it may go through the shorter or longer one. Use ForceShortestPath = @true if you want to interpolate through the shortest. The overloaded version that works with TVector4Single takes a rotation (not a quaternion) expressed as an axis (first 3 elements) and angle (in radians, 4th element). Axis does not have to be normalized (we'll normalize it). This is nice e.g. to interpolate VRML/X3D rotations.

• public function NLerp  ( const  A :  Single; const  Rot1 :  TVector3D; const  Rot2 :  TVector3D; const  ForceShortestPath :  Boolean  =  True )  : TVector3D ;  overload;

  Interpolate between two rotations, along the straightest path on the unit sphere. This is faster than SLerp, but does not guarantee the interpolated result travels with constant speed. Often it's not a noticeable / important problem (see http://number-none.com/product/Understanding%%20Slerp,%%20Then%%20Not%%20Using%%20It/) When ForceShortestPath = @false, this doesn't guarantee choosing the shortest path. Although it goes through the @italic(straightest) path, there are two such paths, it may go through the shorter or longer one. Use ForceShortestPath = @true if you want to interpolate through the shortest. The overloaded version that works with TVector4Single takes a rotation (not a quaternion) expressed as an axis (first 3 elements) and angle (in radians, 4th element). Axis does not have to be normalized (we'll normalize it). This is nice e.g. to interpolate VRML/X3D rotations.