Write Translational, Rotational, Scaling, Reflection, Shear Transforma

Question

Write Translational, Rotational, Scaling, Reflection, Shear Transformation matrix for 2D and 3D homogeneous system. Determine the final coordinates of a polygon ABCD, A (1, 4), B (-4, 1) C (-1, -1), D(2, -2) when it is scaled up to twice its size with respect to an arbitrary point P(1, 1).

16 Sep 2022

Answer :

Word Count : 807

Transformation matrices are used in computer graphics to transform or change the position, orientation, or size of objects in a 2D or 3D space. Here are the transformation matrices for some common transformations in both 2D and 3D homogeneous systems:

2D Transformation Matrices:

Translation:
| 1 0 tx |
| 0 1 ty |
| 0 0 1 |

Scaling:
| Sx 0 0 |
| 0 Sy 0 |
| 0 0 1 |

Reflection:
Reflection across the X-axis:
| 1 0 0 |
| 0 -1 0 |
| 0 0 1 |

Reflection across the Y-axis:
| -1 0 0 |
| 0 1 0 |
| 0 0 1 |

Shear:
Shear in the X direction:
| 1 Sx 0 |
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