Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
import 'dart:math';
import 'dart:ui';
import 'package:meta/meta.dart';
@immutable
class MonotoneInterpolator {
const MonotoneInterpolator._(this.points, this._c1s, this._c2s, this._c3s);
final List<Offset> points;
final List<double> _c1s;
final List<double> _c2s;
final List<double> _c3s;
factory MonotoneInterpolator.fromPoints(List<Offset> points) {
assert(points.isNotEmpty);
final n = points.length;
final dxs = <double>[];
final dys = <double>[];
final ms = <double>[];
// calculate differences and slopes
for (var i = 0; i < n - 1; i++) {
final dx = points[i + 1].dx - points[i].dx;
final dy = points[i + 1].dy - points[i].dy;
dxs.add(dx);
dys.add(dy);
ms.add(dy / dx);
}
// degrees 1, 2, and 3 coefficients
final c1s = <double>[ms[0]];
final c2s = <double>[];
final c3s = <double>[];
// calculate degree 1 coefficients
for (var i = 0; i < dxs.length - 1; i++) {
var m = ms[i];
var mNext = ms[i + 1];
if (m * mNext <= 0) {
c1s.add(0.0);
} else {
var dx = dxs[i];
var dxNext = dxs[i + 1];
var common = dx + dxNext;
c1s.add(3 * common / ((common + dxNext) / m + (common + dx) / mNext));
}
}
c1s.add(ms[ms.length - 1]);
// calculate degrees 2 and 3 coefficients
for (var i = 0; i < c1s.length - 1; i++) {
var c1 = c1s[i];
var m = ms[i];
var invDx = 1 / dxs[i];
var common_ = c1 + c1s[i + 1] - m - m;
c2s.add((m - c1 - common_) * invDx);
c3s.add(common_ * invDx * invDx);
}
return new MonotoneInterpolator._(points, c1s, c2s, c3s);
}
double interpolate(double x) {
// The rightmost point in the dataset should give an exact result
var i = points.length - 1;
if (x == points[i].dx) {
return points[i].dy;
}
// Search for the interval x is in, returning the corresponding y if x is one of the original xs
var low = 0;
int mid;
int high = _c3s.length - 1;
while (low <= high) {
mid = (0.5 * (low + high)).floor();
var xHere = points[mid].dx;
if (xHere < x) {
low = mid + 1;
} else if (xHere > x) {
high = mid - 1;
} else {
return points[mid].dy;
}
}
i = max(0, high);
// Interpolate
var diff = x - points[i].dx, diffSq = diff * diff;
return points[i].dy +
_c1s[i] * diff +
_c2s[i] * diffSq +
_c3s[i] * diff * diffSq;
}
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.