MTMatrix53

Class MTMatrix53 inherits from class MTMatrix (4.2).

This matrix is composed of a matrix describing a rotation, a vector for translation, plus a vector to be applied before rotation (usually the translation back to the origin).

$RT=\left[\begin{array}{ccc} r1 & r2 & r3\\ r4 & r5 & r6\\ r7 & r8 & r9\\ ox & oy & oz\\ tx & ty & tz\end{array}\right]$

$\mathbf{v}'=R*(\mathbf{v}-\mathbf{o})+\mathbf{t}$

Methods:

-(MTMatrix53*)invert	inverts the rotation part of the 5x3 matrix (4.4) and the origin part
* getter
-(MTCoordinates*)getOrigin	returns the coordinates (3.9) of the origin part
-(MTMatrix44*)getRotation	returns the rotation part (4.3)
-(MTMatrix44*)getTranslation	returns the translation part as a 4x4 matrix (4.3) (useful for subsequent matrix multiplication)
* creation
+(MTMatrix53*)matrixFromString:(NSString*)str	creates a new 5x3 matrix (4.4) with values from parsing string str
+(id)matrixIdentity	creates a new 5x3 matrix with values:
+(MTMatrix53*)transformation3By3: (MTMatrix44*)first and: (MTMatrix44*)second	computes the transformation (4.4) which matches three points in second onto first. The coordinates are encoded in matrices: