Ch11oddslns - Angel Interactive Computer Graphics Fourth Edition Chapter 11 Solutions 11.1(m 1)3 a 11.3 As u varies over(a b v = ua varies over(0 1

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Angel: Interactive Computer Graphics, Fourth Edition Chapter 11 Solutions 11.1 ( m +1) 3 11.3 As u varies over ( a, b ), v = u a b a varies over (0 , 1). Substituting into the polynomial p ( u )= n k =0 c k u k ,wehave q ( v )= v i =0 d i v i = n k =0 c k (( b a ) v + a ) k . We can expand the products on the right and match powers of v to obtain { d i } . 11.5 Consider the Bernstein polynomial b kd ( u )= d k ! u k (1 u ) d k . For k =0or k = d , the maximum value of 1 is at one end of the interval (0,1) and the minimum is at the other because all the zeros are at 1 or 0. For other values of k , the polynomial is 0 at both ends of the interval and we can di±erentiate to ²nd that the maximum is at u = k/d. Substituting into the polynomial, the maximum value is d ! d d k k k ! ( d k ) d k ( d k )! which is always between 0 and 1. 11.7 Proceeding as in the text, we have the interpolating control point array q and can form the interpolating polynomial
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This note was uploaded on 01/25/2011 for the course CSCI 6821 taught by Professor Alxe during the Spring '10 term at Georgia Southwestern.

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Ch11oddslns - Angel Interactive Computer Graphics Fourth Edition Chapter 11 Solutions 11.1(m 1)3 a 11.3 As u varies over(a b v = ua varies over(0 1

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