Computer Graphics - Graphics Operations

21. The entire graph of the function f(x) = x2 + kx - x + 9 is strictly above the x-axis if and only if

  • Option : D
  • Explanation :
    y = x2 + (k- 1) x + 9 = (x + (k -1)/2)2 - ((k- 1)/2) + 9
    For the entire graph to lie above the x-axis. y should be greater than 0, for all x.
    So, 9 - ((k- 1)/2) 2 > 0 i.e., (k - 7) (k + 5) < 0 or - 5 < k < 7
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22. Perform window to viewport transformation for the point (20, 15). Assume that (Xwmin, Ywmin) is (0, 0) (Xwmax, Ywmax) is (100, 100); (Xvmin, Yvmin) is (5, 5); (Xvmax ,Yvmax) is (20, 20). The value of x and y in viewport is

CGGO Q

  • Option : C
  • Explanation :
    x(view port) = (XV max - XV min) (XW - XW min) / (XW max - XW min) + XVmin 
     y(viewport) = (YVmax - YVmin)( YW - YWmin) / (YWmax- YWmin ) + YVmin
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23. If (a, b, c) x (1, 3, 1) = (2, 1, 6), where x denotes the vector product, then (a, b, c) is given by

  • Option : D
  • Explanation :
    CGGO Q
    The determinant given above = (2, 1, 6)
    It gives the three equations, b - 3 c = 2; c - a = 1; 3a - b = 6.
    This system of equations, has no solution as using the second equation in the third gives b - 3c = -3, which contradicts the first.
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24. A Bezier cubic curve with control points Po, Pi' P2, P3 is defined by the equation

CGGO Q
B32 is

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