BlurFunction

FunctionWithCachingFunction
[IoId("00000000-b1c0-4a10-9f21-0a1b2c3d4e5f")] public sealed class BlurFunction : FunctionWithCaching

A polyline (strictly increasing x) that is progressively blurred by repeated averaging of vertex y-values with their neighbours. In the joint limit of infinitely dense sampling and infinitely many averaging passes this is the one-dimensional heat equation on the vertex-x domain, so the blurred curve is the diffusion of the polyline towards its steady state.

The amount of blur is controlled by a second Function evaluated in x (default: a constant), clamped to 0 (no blur, the original polyline) .. 1 (full blur). The endpoint y-values are pinned (Dirichlet), so the full-blur steady state is the straight chord between the first and last vertex.

Evaluation is a closed-form eigenmode sum: the polyline is expanded once into a sine series and each mode decays as e^(-(nπ)²·τ), where τ is the dimensionless diffusion time mapped from the blur amount. No dense point cloud is ever materialised.

Constructors

BlurFunction

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public BlurFunction()
Create a default blur function: a small tent polyline with no blur.

BlurFunction

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public BlurFunction(IEnumerable<Point2d> points, Function blur)
Create a new blur function. The endpoint y-values are always pinned, so full blur converges to the straight chord between the first and last vertex.
Parameters:
points (IEnumerable<Point2d>)Polyline vertices. Sorted left to right internally.
blur (Function)Blur amount as a function of x (null -> no blur). Clamped to 0..1.

BlurFunction

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public BlurFunction(IReader reader)
Parameters:
reader (IReader)

Properties

Blur

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public Function Blur { get; }
Gets the blur-controlling function.

Derivative

public sealed override Function Derivative { get; }
Gets a function which is the derivative of this function. The returned function may be either analytic or approximate.
inherited fromFunctionWithCaching
Overrides: Function.Derivative

Integral

public sealed override Function Integral { get; }
Gets a function which is the indefinite integral of this function. The returned function may be analytic or approximate. Note that numeric approximation of indefinite integrals is a slow and not particularly high quality process.
inherited fromFunctionWithCaching
Overrides: Function.Integral

MaximumX

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public double MaximumX { get; }
Gets the highest vertex x-coordinate.

MinimumX

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public double MinimumX { get; }
Gets the lowest vertex x-coordinate.

Nomen

public sealed override Nomen Nomen { get; }
Gets a description of this function.
inherited fromFunctionWithCaching
Overrides: Function.Nomen

Notation

public override string Notation { get; }
Gets the notation for this function. Notation is aimed at humans and does not need to return a parseable string.
inherited fromFunctionWithCaching
Overrides: Function.Notation

Samples

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public Point2d[] Samples { get; }
Gets the polyline vertices, sorted left to right.

Ui

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public override FunctionUi Ui { get; }
Overrides: Function.Ui

Methods

Asymptotes

public virtual Line[] Asymptotes()
Returns an array of *all* the non-vertical asymptotes for this function. This property may return both null and empty arrays, implying no asymptotes. Due to the nature of non-vertical asymptotes, there can only be a finite amount of them.
inherited fromFunction

AutoCoDomain

protected void AutoCoDomain(double x0, double x1, out double y0, out double y1, int samples = 100)
Compute the automatic codomain for a given domain.
inherited fromFunction
Parameters:
x0 (double)Domain start.
x1 (double)Domain end.
y0 (out double)Lowest value in codomain.
y1 (out double)Highest value in codomain.
samples (int = 100)Samples.

DomainEstimate

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public override void DomainEstimate(out double x0, out double x1, out double y0, out double y1)
Parameters:
x0 (out double)
x1 (out double)
y0 (out double)
y1 (out double)
Overrides: Function.DomainEstimate

EmitDerivative

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protected override Function EmitDerivative()
Overrides: FunctionWithCaching.EmitDerivative

EmitIntegral

protected virtual Function EmitIntegral()
Override this method to provide an analytic indefinite integral.
inherited fromFunctionWithCaching

Holes

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public override Interval[] Holes(double x0, double x1)
Returns a collection of domains for which this function is not defined. This method may return null or an empty array, implying no undefined domains. This method may also return domains outside of the specified interval.
Parameters:
x0 (double)Lower limit of query domain.
x1 (double)Upper limit of query domain.
Overrides: Function.Holes

Integrate

public virtual double Integrate(double x0, double x1)
Evaluate the definite integral between two parameters. Unless a function specifically implements an analytic integral, this value will be approximate. Note to implementer: if you provide an analytic integral via the Function.Integral property, that function will be used to compute an analytic result. There is typically no reason to override this method.
inherited fromFunction
Parameters:
x0 (double)Integral start.
x1 (double)Integral end.
Returns: Definite integral from x0 to x1.

Poles

public virtual Pole[] Poles(double x0, double x1)
Returns an array of all the poles (i.e. vertical asymptotes) within a domain. This method may return both null and empty arrays, implying no poles. Furthermore this method may choose to return poles which fall outside of the given domain.
inherited fromFunction
Parameters:
x0 (double)Lower limit of query domain.
x1 (double)Upper limit of query domain.

Store

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public override void Store(IWriter writer)
Parameters:
writer (IWriter)
Overrides: FunctionWithCaching.Store

Y

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public override double Y(double x)
Parameters:
x (double)
Overrides: Function.Y

YYYY

public double[] YYYY(double[] x)
Evaluate a large amount of values. Functions may choose to use multiple threads to perform this calculation. This method should not throw, instead every failed evaluation will be represented by a NaN value.
inherited fromFunction
Parameters:
x (double[])Value to evaluate.
Returns: Evaluation results. Array will contain double.NaN entries for failed evaluations.