Computer Programming (TKK-2144) 13/14 Semester 1 Instructor: Rama Oktavian Office Hr.: M.13-15, W. 13-15 Th. 13-15, F. 13-15.

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Computer Programming (TKK-2144) 13/14 Semester 1 Instructor: Rama Oktavian Office Hr.: M.13-15, W Th , F

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Computer Programming (TKK-2144) 13/14 Semester 1 Instructor: Rama Oktavian Office Hr.: M.13-15, W Th , F

Outlines 1. Quadratic Interpolation 2. Cubic Interpolation 3. Spline Interpolation 4. Example in chem.eng

Quadratic interpolation We want to find a polynomial which satisfies for for given data points (x0,y0),(x1,y1),(x2,y2).

Quadratic interpolation 4 The upward velocity of a rocket is given as a function of time in Table 2. Find the velocity at t=16 seconds using the direct method for quadratic interpolation Table 1 Velocity as a function of time. Figure 1Velocity vs. time data for the rocket example

Quadratic interpolation Solving the above three equations gives Figure 2 Quadratic interpolation.

Quadratic interpolation Figure 2 Quadratic interpolation.

Cubic Interpolation Figure 3 Cubic interpolation.

Cubic Interpolation Figure 3 Cubic interpolation.

Spline Interpolation  Spline:  In Mathematics, a spline is a special function defined piecewise by polynomials;  In Computer Science, the term spline more frequently refers to a piecewise polynomial (parametric) curve.  Simple construction, ease and accuracy of evaluation, capacity to approximate complex shapes through curve fitting and interactive curve design.

Spline Interpolation  Spline Interpolation:  Linear spline  Quadratic spline  Cubic spline

Spline Interpolation  Linear Spline Interpolation:

Spline Interpolation  Linear Spline Interpolation:

Spline Interpolation  Quadratic Spline Interpolation:

Spline Interpolation  Quadratic Spline Interpolation:

Spline Interpolation  Quadratic Spline Interpolation: