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Thread: spline cubic interpolation

  1. #1
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    spline cubic interpolation

    hello everyone, I need help with problem 4 getting started. I posted earlier and rcvd help from Chiro for problem 3 and in route to completing

    Prob 4 just doesn't make sense, Can anyone help me get started.

    problem is attachedspline cubic interpolation-midterm.jpg
    Last edited by Paragandhi; Feb 23rd 2017 at 10:32 PM.
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  2. #2
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    Re: spline cubic interpolation

    Hey Paragandhi.

    Can you provide the definition for a clamped cubic spline?
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  3. #3
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    Re: spline cubic interpolation

    do u want the definition or the rule we are using to solve?
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    Re: spline cubic interpolation

    its the third level order using derivatives. I'm really drawing a blank on this problem.. because this has to be entered through MAple soft its very confusing. Each problem is taking more than 5 hours to solve. nd I don't know how to approach this one. If you can help me get started in the right direction with the formula input it would highly appreciated
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  5. #5
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    Re: spline cubic interpolation

    A "cubic spline" is a piecewise cubic function. A "clamped" cubic spline has both values and derivatives given at the endpoints. Here were are given the values (distance) and derivative (speed) at every point.

    Any cubic can be written in the form f_0(t)= a_0t^3+ b_0t^2+ c_0t+ d_0. At the first point, t= 0, we are given f_0(0)= d_0= 0 and f'(0)= c_0= 75. At the second point, t= 3, we are given f_0(3)= 27a_0+ 9b_0+ 3c_0+ d_0= 225 and f_0'(3)= 27a_0+ 6b_0+ c_0= 77. We have four equations to solve for the four coefficients.

    Between t= 3 and t= 5 we may have a different cubic which we can write as f_1(t)= a_1t^3+ b_1t^2+ c_1t+ d_1. At t= 3, we have f_1(3)=27a_1+ 9b_1+ 3c_1+ d_1= 225 and f_1'(3)= 27a_1+ 6b_1+ c_1= f_1'(3)= 77. At t= 5 we have f_1(5)= 125a_1+ 25b_1+ 5c_1+ d_1= 383 and f_1'(5)= 75a_1+ 10b_1+ c_1= 83, again four equations to solve for the four coefficients.

    Continue that over the intervals from t= 5 to 8 and from t= 8 to 13.
    Last edited by HallsofIvy; Feb 24th 2017 at 04:13 AM.
    Thanks from Paragandhi
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    Re: spline cubic interpolation

    Super, Thank YOU!!!
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