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- Q4: Write the parametric equation of revolution surface in matrix form only which generated by rotate a Bezier curve defined by the coefficient parameter in one plane only, for the x-axis [0,5, 10,4], y-axis [1,4,2,2] respectively, for u-0.5 and 9=7/4. Note: [the rotation about y-axis].(a) Draw an undirected graph G1 represented by the following adjacency matrix: 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 Does G1 contain a Hamiltonian cycle? Explain (b) Determine which pairs of graphs G1 in part (a) and G2 and G3 shown below are isomorphic and which are not, and explain your answer. If you use any invariant property in your argument, explain why this property is an invariant. Tex our answer. t 2 G2 G3 5. 7 8.A quadratic Bézier curve is determined by 3 control points Po, P1, and p2. The equation is x(t) = (1 - t)ʻPo + 2t(1 - t)p, +tp2. Construct the quadratic Bézier basis matrix Mp for x(t). 1 1 O A. - 2 1 1 - 2 1 В. 2 - 2 1 1 0 1 OC. 0 1 1 0 0 1 1 2 2 0 2 -2 0 0 1
- Q1: Consider a surface of revolution generated by a Bezier curve defined by the four control points P(0,0,0), (2,1,2), P₂ (3,3,0) P, (2,2,3) respectively, rotating about the X-axis. Calculate the point on the surface at u = 0.25, 0= π/2.6. For every set S of grid-points in the 3-D orthogonal grid, either (1) two points in S are non-coplanar, or (2) at least [2S/31 grid-points are in a single grid-plane.Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. (a) the characteristic equation - 1 = 0 (b) the eigenvalues (Enter your answers from smallest to largest.) 1 (22, 22) =| 2 2 a basis for each of the corresponding eigenspaces X, = X, = 1
- 9. If p(x) = 4x – 2 and q(x) = -x + 3, as a function of x, find: (a) (p o q)(x) and determine its domain and range. (b) (q • p)(x) and determine its domain and range.1. Give solution, graph and if the point ( 3, y) is equidistant from ( 4, -2 ) and ( -1, 4)llowing function on the axes provided. f(x)={(-2 for x<=-4),(2x+1 for x>0):}
- Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. 3 -1 1 2 (a) the characteristic equation P (b) the eigenvalues (Enter your answers from smallest to largest.) 1 1 - 2 a basis for each of the corresponding eigenspaces 1 X, = 1 3 X2 1Reduce this term into normal from, if it exists (show your working):(λx.((λz.zwz)(((λxyx.y)(λx.y)(λy.x))((λx.xx)(λy.yyy)))))tUsing K-map obtain the minimal sum of product and minimal product of sums of the function. f (A, B, C, D) = Em (1, 2, 3, 5, 6, 7, 8, 13) Good Luck