49 lignes
1.4 KiB
Go
49 lignes
1.4 KiB
Go
package vector
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import (
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"errors"
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"fmt"
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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: ts[]{0, 1/3, 2/3}, extrapolate to 1.
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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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// Implements Neville's Algorithm for a slice of points (P) at parameter
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// values(ts), to parameter value (t). Returns the point and an error
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func Neville(P []Point2d, ts []float64, t float64) (*Point2d, error) {
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if len(P) != len(ts) {
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return nil, errors.New(
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fmt.Sprintf(
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"Incompatable slice lengths len(P): %d != len(ts): %d",
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len(P),
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len(ts),
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),
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)
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}
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Q := []Point2d(P)
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order := len(P) - 1
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for i := 0; i < order; i++ {
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for j := 0; j < order-i; j++ {
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tLeft := ts[i+j+1] - t
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tRight := t - ts[j]
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Q[j] = Q[j].ToVector().Scale(tLeft).ToPoint().Add(P[j+1].ToVector().Scale(tRight))
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Q[j] = Q[j].ToVector().Scale(1.0 / (ts[i+j+1] - ts[j])).ToPoint()
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}
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}
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return &Q[0], nil
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}
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