SmallBASIC Guide

2D & 3D graphics transformations

2D & 3D graphics transformations can represented as matrices. (c=cosè, s=sinè)
Command: M3IDENT BYREF m3x3 Resets matrix (Identity)

|  1  0  0 |
|  0  1  0 |
|  0  0  1 |

Command: M3ROTATE BYREF m3x3, angle [, x, y] Rotate by angle with center x,y

|  c  s  0 |
| -s  c  0 |
|  *  *  1 |

Command: M3SCALE BYREF m3x3, x, y, Sx, Sy Scaling

| Sx  0  0 |
|  0 Sy  0 |
|  *  *  1 |

Command: M3TRANS BYREF m3x3, Tx, Ty Translation

|  1  0  0 |
|  0  1  0 |
| Tx Ty  1 |

Command: M3APPLY m3x3, BYREF poly Apply matrice to poly-line Additional information:

|  1  0  0 |
|  0 -1  0 | = reflection on x
|  0  0  1 |

| -1  0  0 |
|  0  1  0 | = reflection on y
|  0  0  1 |

3D-Graphics Matrices:

|  1  0  0 Tx |
|  0  1  0 Ty | = translation
|  0  0  1 Tz |
|  0  0  0  1 |

| Sx  0  0  0 |
|  0 Sy  0  0 | = scaling
|  0  0 Sz  0 |
|  0  0  0  1 |

|  1  0  0  0 |
|  0  c -s  0 | = rotation on x
|  0  s  c  0 |
|  0  0  0  1 |

|  c  0  s  0 |
|  0  1  0  0 | = rotation on y
| -s  0  c  0 |
|  0  0  0  1 |

|  c -s  0  0 |
|  s  c  0  0 | = rotation on z
|  0  0  1  0 |
|  0  0  0  1 |

Any change to matrix will combined with its previous value.

DIM poly(24)
DIM M(2,2)
...
M3IDENT M
M3ROTATE M, pi/2, 0, 0
M3SCALE M, 0, 0, 1.24, 1.24
...
' Draw the original polyline
DRAWPOLY poly
...
' Draw the polyline
' rotated by pi/2 from 0,0 and scaled by 1.24
M3APPLY M, poly
DRAWPOLY poly

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