Added Neville extrapolation from 3 points

interp.go

@@ -0,0 +1,23 @@
+package govector
+
+import (
+	"errors"
+)
+
+// explicitly implements Neville's algorithm for three points at very
+// particular parameter values.
+// TODO: update this to take an arbitrary parameter value, and arbitrary slice
+// of Point2d
+func Extrapolate(P []Point2d) (*Point2d, error) {
+	if len(P) != 3 {
+		return nil, errors.New("only works for len(P) == 3")
+	}
+
+	// P_{01} = -2 * P_0 + 3 * P_1
+	p01 := P[0].ToVector().Scale(-2.0).ToPoint().Add(P[1].ToVector().Scale(3.0))
+	// P_{12} = -1 * P_1 + 2 * P_2
+	p12 := P[1].ToVector().Scale(-1.0).ToPoint().Add(P[2].ToVector().Scale(2.0))
+	// P_{012} = 1/2 * P_{01} + 3/2 * P_{12}
+	p012 := p01.ToVector().Scale(-1.0 / 2.0).ToPoint().Add(p12.ToVector().Scale(3.0 / 2.0))
+	return &p012, nil
+}