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You work for a computer graphics company and you are the chief developer of visual effects and computer animated applications.You have beentasked with the writing of a computerprogram that manipulate s two-dimensional objectsthat are specified by a collection of cornerpoints.

(a) Find the 2 x 2 transformation matrix A that scales agiven object by a factor of ? in the horizontal direction(x-axis) and by a factor of ? inthe vertical direction (y-axis).

(b)  Find the 2 x 2 transformation matrix Bthat rotates the object about the origin by anangle of ? in the clockwise sense.

(c)  LetC1 be the 2 x 2 matrix that represents the combined transformation "first scale, thenrotate". Let C2 bethe matrix thatperformsthe combined transformation in reverse order. Find C1 andC2.

(d) Explain why C1? C2.

(e)  Find the 2 x 2 matrices that undo the operations performed by C1 and C2.

(t)  A triangle with verticesat (0, 0), (4, 0), and (0, 1) undergoes scaling by a factor of 0.5 in the horizontal direction and by a factor of 3 inthe vertical direction, followedby a clockwise rotation of 90° about the origin. Determinethe new coordinates of the triangle as a result of thistransformation.

Electrical & Electronics, Engineering

  • Category:- Electrical & Electronics
  • Reference No.:- M9847809

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