Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000 points. The transformation is composed of 8 matrices (call them M¡ through Mg), so for each point (x, y, z) in the object, the following operation is performed. JI M1 M2 M3 M7 M8 Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions, for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48 additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about 4 x 4 matrix multiplication.) The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M, by M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of the 3000 points. How many arithmetic operations would this require for transforming one point? How many would it require in total for transforming all 3000 points?

Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000 points. The transformation is composed of 8 matrices (call them M¡ through Mg), so for each point (x, y, z) in the object, the following operation is performed. JI M1 M2 M3 M7 M8 Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions, for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48 additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about 4 x 4 matrix multiplication.) The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M, by M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of the 3000 points. How many arithmetic operations would this require for transforming one point? How many would it require in total for transforming all 3000 points?

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

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