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show that the b-spline does not begin at p0 but x0 is in conv p0 p1 p2 assuming that p0 p1 and p2 are affinely
a quartic beacutezier curve is determined by five control points p0 p1 p2 p3 and p4construct the quartic basis matrix
let xt and yt be segments of a b-spline as in exercise 6 show that the curve has c2 continuity as well as c1 continuity
the parametric vector form of a b-spline curve was defined in the practice problems asa show that for 0 le t le 1 xt is
suppose a beacutezier curve is translated to xt b that is for 0 le t le 1 the new curve isshow that this new curve is
let xt and yt be beacutezier curves from exercise 5 and suppose the combined curve has c2 continuity which includes c1
let x t and y t be cubic beacutezier curves with control points p0 p1 p2 p3 and p3 p4 p5 p6 respectively so that xt
let xt be a cubic beacutezier curve determined by points p0 p1 p2 and p3a compute the tangent vector x t determine
a b-spline is built out of b-spline segments described in exercise 2 let p0 p4 be control points for 0 le t le 1 let
the b in b-spline refers to the fact that a segment x t may be written in terms of a basis matrix ms in a form similar
mark each statement true or false justify each answera the essential properties of beacutezier curves are preserved
neveah has created the function fx the quantity of 2x plus 4 divided by 3 to represent the growth of her hair where x
given the function fx 23x section a is from x 0 to x 1 and section b is from x 2 to x 3find the average rate of
return on an investmenta business purchased for650000 in 2005 is sold in 2008 for 850000 what is the annual rate of
let a be an n x n matrix with n real eigenvalues counting multiplicities denoted by lambda1 lambdan it can be shown
suppose the columns of a are linearly independent determine what happens to the least-squares solutionof ax b when b
to make a trend analysis of six evenly spaced data points one can use orthogonal polynomials with respect to evaluation
find the least-squares line y szlig0 szlig1x that best fits the data -2 0 1 0 0 2 1 4 and 2 4 assuming that the first
suppose 5 out of 25 data points in a weighted least-squares problem have a y-measurement that is less reliable than the
fit a cubic trend function to the data in example 2 the orthogonal cubic polynomial isexample 2the simplest and most
the space is c 0 2pi with the inner product 6show that sin mt and sin nt are orthogonal when m ne
explain why an equation ax b has a solution if and only if b is orthogonal to all solutions of the equation a tx 0
the space is c 0 2pi with the inner product 6show that sin mt and cos nt are orthogonal for all positive integers m and
mark each statement true or false justify each answera every symmetric matrix is orthogonally diagonalizableb if b
the following statements refer to vectors in rn or rm with the standard inner product mark each statement true or false