/// <summary>
/// Builds a list of <see cref="Bezier"/> from a list of <see cref="Point"/> for
/// the specified error tolerance.
/// </summary>
/// <param name="points">
/// A list of <see cref="Point"/> to build from.
/// </param>
/// <param name="tolerance">
/// The error tolerance value between 4 to 20 inclusive.
/// </param>
/// <returns>
/// A list of <see cref="Bezier"/> from a list of <see cref="Point"/> for
/// the specified error tolerance.
/// </returns>
public static ReadOnlyCollection <Bezier> Build(
IEnumerable <Point> points,
double tolerance = DefaultError)
{
if (points == null)
{
throw new ArgumentNullException("points");
}
if (!tolerance.IsBetween(MinimumError, MaximumError))
{
throw new ArgumentOutOfRangeException(
string.Format(
"The error tolerance must be between {0} and {1} inclusive.",
MinimumError,
MaximumError),
"tolerance");
}
List <Point> list = points.Filter(MinimumDistance);
if (list.Count < 2)
{
throw new ArgumentException("There must be at least two distinct points in the list.", "points");
}
List <Bezier> bezierList = new List <Bezier>();
ReadOnlyCollection <Point> bezierPoints = list.AsReadOnly();
Vector leftTangent = bezierPoints.LeftTangent();
Vector rightTangent = bezierPoints.RightTangent();
BezierBuilder bezierBuilder = new BezierBuilder(
bezierPoints,
leftTangent,
rightTangent,
tolerance);
bezierBuilder.Build(bezierList);
return(bezierList.AsReadOnly());
}
private void Build(List <Bezier> bezierList)
{
// Use heuristic if region only has two points in it
if (points.Count == 2)
{
Point p0 = points.First();
Point p3 = points.Last();
double distance = p0.DistanceTo(p3) / 3.0;
Point p1 = p0 + leftTangent * distance;
Point p2 = p3 + rightTangent * distance;
bezierList.Add(new Bezier(p0, p1, p2, p3));
return;
}
// Parameterize points, and attempt to fit curve
parameterizedLength = points.Parameterize();
Bezier bezier = Bezier.Create(this);
// Find max deviation of points to fitted curve
int index;
double maximumDistanceError = bezier.CalculateMaximumDistance(this, out index);
if (maximumDistanceError < tolerance)
{
bezierList.Add(bezier);
return;
}
// If error not too large, try some reparameterization and iteration
double iterationError = tolerance * tolerance;
if (maximumDistanceError < iterationError)
{
for (int i = 0; i < MaximumIterationCount; i++)
{
parameterizedLength = bezier.Reparameterize(this);
bezier = Bezier.Create(this);
maximumDistanceError = bezier.CalculateMaximumDistance(this, out index);
if (maximumDistanceError < tolerance)
{
bezierList.Add(bezier);
return;
}
}
}
// Fitting failed -- split at max error point and fit recursively
Vector centerTangent = points.CenterTangent(index);
BezierBuilder builder = new BezierBuilder(
points
.Take(index + 1)
.ToList()
.AsReadOnly(),
leftTangent,
centerTangent,
tolerance);
builder.Build(bezierList);
centerTangent.Negate();
builder = new BezierBuilder(
points
.Skip(index + 1)
.ToList()
.AsReadOnly(),
centerTangent,
rightTangent,
tolerance);
builder.Build(bezierList);
}
