24 lines
734 B
Go
24 lines
734 B
Go
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package govector
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import (
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"errors"
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)
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// explicitly implements Neville's algorithm for three points at very
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// particular parameter values.
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// TODO: update this to take an arbitrary parameter value, and arbitrary slice
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// of Point2d
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func Extrapolate(P []Point2d) (*Point2d, error) {
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if len(P) != 3 {
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return nil, errors.New("only works for len(P) == 3")
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}
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// P_{01} = -2 * P_0 + 3 * P_1
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p01 := P[0].ToVector().Scale(-2.0).ToPoint().Add(P[1].ToVector().Scale(3.0))
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// P_{12} = -1 * P_1 + 2 * P_2
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p12 := P[1].ToVector().Scale(-1.0).ToPoint().Add(P[2].ToVector().Scale(2.0))
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// P_{012} = 1/2 * P_{01} + 3/2 * P_{12}
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p012 := p01.ToVector().Scale(-1.0 / 2.0).ToPoint().Add(p12.ToVector().Scale(3.0 / 2.0))
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return &p012, nil
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}
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