Advanced Graphics with the Commodore 128 by M. M. Novak (auth.)

By M. M. Novak (auth.)

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We say that an operation is performed on a matrix through its elements. Then we can assert that two matrices are equal if all the corresponding elements are also equal. That is, matrices K and L are equal if Kii = Lii where i andj are subscripts. The transpose of a matrix K is a matrix KT that is obtained by writing the rows of the original matrix K as the columns of the new matrix KT. That is, KT is the transpose of K if ~ii = Kii Suppose now that we wish to add two matrices, K and L. The sum of these two matrices, here denoted by M, is again a matrix whose elements are equal to the sum of the corresponding elements of matrices K and L.

M. Novak, Advanced Graphics with the Commodore 128 © M. M. 1 where T x represents the number of units by which the coordinate is displaced in the x-direction and T y denotes the corresponding number of units in they-direction. The magnitude ofTx and T y can be either positive, negative or zero. In the last case, the transformed image coincides with the original one. Scaling The effect of this transformation is either to change the size or to alter the overall proportions of the original image. 2.

If both Sx and Sy are negative (and equal to - 1), then the transformed object forms a mirror image of the original. ReDection This transformation can be considered as a special case of scaling. Reflection is, in fact, a mirror image of the original. 3(c). 3 where both Sx and Sy are negative. If the factors Sx and Sy are set to - 1, then the transformed image is an undistorted reflection of the original; otherwise, a distortion is introduced. 52 Advanced Graphics with the Commodore 128 Rotation Application of this transformation creates an image that is rotated with respect to the original.

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