Added general Neville's Algorithm

interp.go

@@ -6,9 +6,7 @@ import (
 )
 
 // 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
+// particular parameter values: ts[]{0, 1/3, 2/3}, extrapolate to 1.
 func Extrapolate(P []Point2d) (*Point2d, error) {
 	if len(P) != 3 {
 		return nil, errors.New("only works for len(P) == 3")
@@ -23,6 +21,8 @@ func Extrapolate(P []Point2d) (*Point2d, error) {
 	return &p012, nil
 }
 
+// Implements Neville's Algorithm for a slice of points (P) at parameter
+// values(ts), to parameter value (t). Returns the point and an error
 func Neville(P []Point2d, ts []float64, t float64) (*Point2d, error) {
 	if len(P) != len(ts) {
 		return nil, errors.New(
@@ -33,5 +33,16 @@ func Neville(P []Point2d, ts []float64, t float64) (*Point2d, error) {
 			),
 		)
 	}
-	return nil, errors.New("smb")
+	Q := []Point2d(P)
+	order := len(P) - 1
+	for i := 0; i < order; i++ {
+		for j := 0; j < order-i; j++ {
+			var tLeft float32 = float32(ts[i+j+1] - t)
+			var tRight float32 = float32(t - ts[j])
+			Q[j] = Q[j].ToVector().Scale(tLeft).ToPoint().Add(P[j+1].ToVector().Scale(tRight))
+			Q[j] = Q[j].ToVector().Scale(float32(1.0 / (ts[i+j+1] - ts[j]))).ToPoint()
+
+		}
+	}
+	return &Q[0], nil
 }