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Explain the steps used in rotation of 2D object about an arbitrary axis and derive the matrix for the same.OR Discuss all the steps used in reflection of an object about an arbitrary line with example
written 6.9 years ago by gravatar for prof.vaibhavbadbe prof.vaibhavbadbe • 1.7k modified 4.6 years ago by gravatar for sanketshingote sanketshingote • 100
computer graphics
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written 6.8 years ago by gravatar for prof.vaibhavbadbe prof.vaibhavbadbe • 1.7k

Rotation about an Arbitrary Point:-

To rotate an object about an arbitrary point, (Xp ,Yp) we have to carry out three steps:

  1. Translate point (Xp, Yp) to the origin.

  2. Rotate it about the origin and,

  3. Finally, translate the center of rotation back where it belongs (See figure 1.).

we have already seen that matrix multiplication is not commutative, i.e. multiplying matrix A by matrix B will not always yield the same result as multiplying matrix B by matrix A. Therefore, in obtaining composite transformation matrix, we must be careful to order the matrices so that they correspond to the order of the transformations on the object. Let us find the transformation matrices to carry out individual steps.

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