Problem 1: The indecisive artist An indecisive graphic artist has just applied a single transformation T in Adobe Illustrator to the two-dimensional initial shape described by the vector of points x in order to create the new shape described by the vector of points X'. Here T may denote any one of the operations described in Sections 2.2, 2.3, 2.4, or 2.6 of the course reader. The artist wants to undo this operation by pressing Ctrl+Z. 1. Write down in terms of x, X', and T the initial operation applied by the artist as well as the requested undo operation. 2. Suppose the initial shape is a polygon defined by n sides (n > 3) and assume homogenous coordinates. How many elements do x, X', and T contain? 3. In order for for the undo operation to be possible, what property is required of T? Does T have this property for each of the transformations described in the sections noted above? Briefly explain your reasoning for each case. (assume Sx, Sy, tx, and ty are all finite valued and nonzero) 4. The indecisive artist has now applied the scaled rotation M = STB RTF about the arbitrary point (Xo, Yo) to the initial point (x,y) and is once again pressing "Ctrl+Z (S is the scaling matrix in eq.(2.2) of the course reader). Write down (assuming homogenous coordinates) the single matrix that will fulfill the artist's undo request in terms of S, Sy, Xo, Yo, and 0. Will this operation be well defined? (i.e., does M have the previously noted property?) Briefly explain your reasoning. (assume Sx, Sy, Xo, and Yo are all finite valued and nonzero) Problem 1: The indecisive artist An indecisive graphic artist has just applied a single transformation T in Adobe Illustrator to the two-dimensional initial shape described by the vector of points x in order to create the new shape described by the vector of points X'. Here T may denote any one of the operations described in Sections 2.2, 2.3, 2.4, or 2.6 of the course reader. The artist wants to undo this operation by pressing Ctrl+Z. 1. Write down in terms of x, X', and T the initial operation applied by the artist as well as the requested undo operation. 2. Suppose the initial shape is a polygon defined by n sides (n > 3) and assume homogenous coordinates. How many elements do x, X', and T contain? 3. In order for for the undo operation to be possible, what property is required of T? Does T have this property for each of the transformations described in the sections noted above? Briefly explain your reasoning for each case. (assume Sx, Sy, tx, and ty are all finite valued and nonzero) 4. The indecisive artist has now applied the scaled rotation M = STB RTF about the arbitrary point (Xo, Yo) to the initial point (x,y) and is once again pressing "Ctrl+Z (S is the scaling matrix in eq.(2.2) of the course reader). Write down (assuming homogenous coordinates) the single matrix that will fulfill the artist's undo request in terms of S, Sy, Xo, Yo, and 0. Will this operation be well defined? (i.e., does M have the previously noted property?) Briefly explain your reasoning. (assume Sx, Sy, Xo, and Yo are all finite valued and nonzero)
