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Math Help - Parametric Cubic Curve Points and Coordinates

  1. #1
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    Oct 2009
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    Parametric Cubic Curve Points and Coordinates

    Hey, I am having trouble to the solution for this problem.

    Determine the new coordinates of a point B: [1,2,1]T
    a)if it is first rotated -30 degrees around the x axis and then translated by 1 unit along the y axis

    b)if the order of transformations is reversed.

    If any help, would be greatly appreciated. Thanks
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  2. #2
    Senior Member
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    Apr 2009
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    Atlanta, GA
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    409

    Standard Operations

    "Rotate counterclockwise about the x-axis" is multiplication by the standard rotation matrix R_x(\theta)=\left[\begin{matrix}0 & 0 & 0 \\ 0 & \cos\theta & -\sin\theta \\ 0 & \sin\theta & \cos\theta \end{matrix}\right]
    "Translate by one unit up the y-axis" is an addition by (0,1,0)

    So (a) is B_{new}=(1,2,1)R_x(-30^\circ)+(0,1,0)

    And (b) is B_{new}=((1,2,1)+(0,1,0))R_x(-30^\circ)
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