M3ROTATE

M3ROTATE BYREF M, angle [, x, y]

Multiply the 2D transformation matrix M by a rotation matrix with an angle angle and a rotation center x,y. M is a 3x3 matrix.

If x = 0 and y = 0 the rotation matrix has the form:

       | cos(angle) -sin(angle)  0 |
MRot = | sin(angle)  cos(angle)  0 |
       | 0           0           1 |

else:

       | cos(angle) -sin(angle)  (1 - cos(angle))*x + sin(angle) * y |
MRot = | sin(angle)  cos(angle)  (1 - cos(angle))*y - sin(angle) * x |
       | 0           0           1 |

Example

DIM M(2,2)

Rectangle = [-1,-1, 1,-1, 1,1, -1,1, -1,-1]  ' Create a rectangular polygon

M3IDENT M                                    ' Create Identity Matrix

M3Trans M, 100,100                           ' Move rectangle to position (100,100) 
M3SCALE M, 0, 0, 50, 50                      ' Scale rectangle by factor 50 in x and y
M3ROTATE M, 45*pi/180                        ' Rotate by 45°

M3APPLY M, Rectangle                         ' Transform the rectangle

DRAWPOLY Rectangle

M3TRANS, M3SCALE and M3ROTATE perform a matrix multiplication. When performing matrix multiplication, then last matrix is applied first. In the example above, the rectangle is first rotated, then scaled and in the last step translated. If the order is changed, the outcome might be different.

ABS ABSMAX ABSMIN ACOS ACOSH ACOT ACOTH ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATAN2 ATANH ATN CEIL COS COSH COT COTH CSC CSCH DEG DERIV DETERM DIFFEQN EXP EXPRSEQ FIX FLOOR FRAC INT INTERSECT INVERSE LINEQN LOG LOG10 M3APPLY M3IDENT M3ROTATE M3SCALE M3TRANS MAX MIN POLYAREA POLYCENT POLYEXT POW PTDISTLN PTDISTSEG PTSIGN RAD RND ROOT ROUND SEC SECH SEGCOS SEGLEN SEGSIN SEQ SGN SIN SINH SQR STATMEAN STATMEANDEV STATMEDIAN STATSPREADP STATSPREADS STATSTD SUM SUMSQ TAN TANH

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M3ROTATE

Example