public static double GetMinValue(IReadOnlyList <IGraphAnchor> anchors)
{
var customExtrema = anchors.Any(o =>
o.Interpolator.GetType().GetCustomAttribute <CustomExtremaAttribute>() != null);
if (!customExtrema)
{
// It suffices to find the smallest Y value of the anchors, because the interpolated parts never stick out above or below the anchors.
return(anchors.Min(o => o.Pos.Y));
}
IGraphAnchor previousAnchor = null;
double minValue = double.PositiveInfinity;
foreach (var anchor in anchors)
{
if (previousAnchor != null)
{
var p1 = previousAnchor.Pos;
var p2 = anchor.Pos;
var difference = p2 - p1;
IEnumerable <double> values;
// If the interpolator has a CustomExtremaAttribute than we check the min/max value for all the specified locations
var customExtremaAttribute =
anchor.Interpolator.GetType().GetCustomAttribute <CustomExtremaAttribute>();
if (customExtremaAttribute != null)
{
// Update the interpolator with the tension of the anchor. This doesn't happen automatically
anchor.Interpolator.P = anchor.Tension;
values = customExtremaAttribute.ExtremaPositions
.Select(o => p1.Y + difference.Y * anchor.Interpolator.GetInterpolation(o));
}
else
{
values = new[] { p1.Y, p2.Y };
}
var localMinValue = values.Min();
if (localMinValue < minValue)
{
minValue = localMinValue;
}
}
previousAnchor = anchor;
}
return(minValue);
}
public static double GetMinDerivative(IReadOnlyList <IGraphAnchor> anchors)
{
IGraphAnchor previousAnchor = null;
double minValue = double.PositiveInfinity;
foreach (var anchor in anchors)
{
if (previousAnchor != null)
{
var p1 = previousAnchor.Pos;
var p2 = anchor.Pos;
var difference = p2 - p1;
// Update the interpolator with the tension of the anchor. This doesn't happen automatically
anchor.Interpolator.P = anchor.Tension;
IEnumerable <double> values;
if (anchor.Interpolator is IDerivableInterpolator derivableInterpolator)
{
// If the interpolator has a CustomDerivativeExtremaAttribute than we check the min/max derivative for all the specified locations
var customExtremaAttribute =
anchor.Interpolator.GetType().GetCustomAttribute <CustomDerivativeExtremaAttribute>();
if (customExtremaAttribute != null)
{
values = customExtremaAttribute.ExtremaPositions
.Select(o => derivableInterpolator.GetDerivative(o) * difference.Y / difference.X);
}
else
{
values = new[] { 0, 1 }
.Select(o => derivableInterpolator.GetDerivative(o) * difference.Y / difference.X);
}
}
else
{
values = new[] { difference.Y / difference.X };
}
var localMinValue = values.Min();
if (localMinValue < minValue)
{
minValue = localMinValue;
}
}
previousAnchor = anchor;
}
return(minValue);
}
public static double GetIntegral(double t1, double t2, IReadOnlyList <IGraphAnchor> anchors)
{
double height = 0;
IGraphAnchor previousAnchor = null;
foreach (var anchor in anchors)
{
if (previousAnchor != null)
{
var p1 = previousAnchor.Pos;
var p2 = anchor.Pos;
var p1C = new Vector2(MathHelper.Clamp(p1.X, t1, t2), p1.Y);
var p2C = new Vector2(MathHelper.Clamp(p2.X, t1, t2), p2.Y);
if (p2.X < t1 || p1.X > t2)
{
previousAnchor = anchor;
continue;
}
var difference = p2 - p1;
var differenceC = p2C - p1C;
if (differenceC.X < Precision.DOUBLE_EPSILON)
{
previousAnchor = anchor;
continue;
}
// Update the interpolator with the tension of the anchor. This doesn't happen automatically
anchor.Interpolator.P = anchor.Tension;
double integral;
if (anchor.Interpolator is IIntegrableInterpolator integrableInterpolator)
{
integral = integrableInterpolator.GetIntegral((p1C.X - p1.X) / difference.X,
(p2C.X - p1.X) / difference.X);
}
else
{
integral = 0.5 * Math.Pow((p2C.X - p1.X) / difference.X, 2) - 0.5 * Math.Pow((p1C.X - p1.X) / difference.X, 2);
}
height += integral * difference.X * difference.Y + differenceC.X * p1.Y;
}
previousAnchor = anchor;
}
return(height);
}
// Note: This method is not accurate for segments passing through zero
public double GetIntegralDistanceTraveled()
{
double distance = 0;
IGraphAnchor previousAnchor = null;
foreach (var anchor in this)
{
if (previousAnchor != null)
{
distance += Math.Abs(GetIntegral(previousAnchor.Pos.X, anchor.Pos.X));
}
previousAnchor = anchor;
}
return(distance);
}
public static double GetMinIntegral(IReadOnlyList <IGraphAnchor> anchors)
{
double height = 0;
double minValue = double.PositiveInfinity;
IGraphAnchor previousAnchor = null;
foreach (var anchor in anchors)
{
if (previousAnchor != null)
{
var p1 = previousAnchor.Pos;
var p2 = anchor.Pos;
var difference = p2 - p1;
if (difference.X < Precision.DOUBLE_EPSILON)
{
previousAnchor = anchor;
continue;
}
// Update the interpolator with the tension of the anchor. This doesn't happen automatically
anchor.Interpolator.P = anchor.Tension;
double minIntegral;
double endIntegral;
if (anchor.Interpolator is IIntegrableInterpolator integrableInterpolator)
{
endIntegral = integrableInterpolator.GetIntegral(0, 1) * difference.X * difference.Y +
difference.X * p1.Y;
// If the interpolator has a CustomIntegralExtremaAttribute than we check the min/max integral for all the specified locations
var customExtremaAttribute =
anchor.Interpolator.GetType().GetCustomAttribute <CustomIntegralExtremaAttribute>();
if (customExtremaAttribute != null)
{
minIntegral = customExtremaAttribute.ExtremaPositions
.Select(o => integrableInterpolator.GetIntegral(0, o) * difference.X * difference.Y + o * difference.X * p1.Y).Min();
}
else
{
minIntegral = integrableInterpolator.GetIntegral(0, 1)
* difference.X * difference.Y + difference.X * p1.Y;
}
// Check if the interpolation passes through 0
if (difference.Y * p1.Y < 0)
{
// Possibility of max/min not at endpoints. Need to calculate the hard way
double newMinIntegral;
if (integrableInterpolator is IInvertibleInterpolator invertibleInterpolator)
{
// Calculate all the zeros of the interpolation
var zeros = invertibleInterpolator.GetInverse(-p1.Y / difference.Y).Where(o => o <= 1 && o >= 0).ToArray();
if (zeros.Length > 0)
{
newMinIntegral = zeros.Select(z =>
integrableInterpolator.GetIntegral(0, z) * difference.X * difference.Y +
z * difference.X * p1.Y).Min();
}
else
{
newMinIntegral = double.PositiveInfinity;
}
}
else
{
double newMinIntegralPosition = GradientDescentUtil.GradientDescent(
d => integrableInterpolator.GetIntegral(0, d) * difference.X * difference.Y + d * difference.X * p1.Y,
0, 1, 0.1);
newMinIntegral = integrableInterpolator.GetIntegral(0, newMinIntegralPosition) * difference.X * difference.Y +
newMinIntegralPosition * difference.X * p1.Y;
}
if (newMinIntegral < minIntegral)
{
minIntegral = newMinIntegral;
}
}
}
else
{
endIntegral = 0.5 * difference.X * difference.Y + difference.X * p1.Y;
minIntegral = endIntegral;
// Check if the interpolation passes through 0
if (difference.Y * p1.Y < 0)
{
// Possibility of max/min not at endpoints. For a linear interpolator this is possible to solve algebraically
var x = -p1.Y / difference.Y;
if (x >= 0 && x <= 1)
{
double newMinIntegral = 0.5 * Math.Pow(x, 2)
* difference.X * difference.Y + x * difference.X * p1.Y;
if (newMinIntegral > minIntegral)
{
minIntegral = newMinIntegral;
}
}
}
}
var possibleMinValue = height + minIntegral;
if (possibleMinValue < minValue)
{
minValue = possibleMinValue;
}
height += endIntegral;
}
previousAnchor = anchor;
}
return(minValue);
}
