# Grasshopper2.Types.Functions.Standard namespace

Assembly: [Grasshopper2](https://developer.rhino3d.com/api/gh2/assembly/grasshopper2.md)

## Classes

- [AbsoluteFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.absolutefunction.md): The absolute value of a function.
- [AdditionFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.additionfunction.md): Addition of two functions.
- [AverageFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.averagefunction.md): The average of two functions.
- [BernsteinBasisFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.bernsteinbasisfunction.md): Represents an immutable bernstein polynomial basis function on the unit domain.
- [BlendFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.blendfunction.md): Represents an immutable interpolated equation.
- [BlockWaveFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.blockwavefunction.md): Block wave function in the form y = frac(x, [A,B)) < E ? C : D
- [BlurFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.blurfunction.md): 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](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.function.md) 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.
- [BumpFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.bumpfunction.md): A function with manually placed bumps in a variety of shapes.
- [ChainFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.chainfunction.md): It's a function inside another function.
- [ClipFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.clipfunction.md): A function clipped to two extreme functions.
- [ConicFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.conicfunction.md): conic section curve represented by a 3-point degree=2 nurbs curve with a weighted centre point. The corners can be filleted.
- [ConstantFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.constantfunction.md): Represents a constant value function.
- [CosineFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.cosinefunction.md): Cosine function in the form y = A·cos(D·x-B) + C
- [CrossRatioFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.crossratiofunction.md): Cross-ratio of four functions.
- [CumulativeDensityFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.cumulativedensityfunction.md): Represents an immutable cumulative density function.
- [CurveFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.curvefunction.md): Represents an immutable Rhino curve equation.
- [DecayFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.decayfunction.md): Represents an immutable function for various types of falloff curves.
- [DecayFunction.DecayDerivative](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.decayfunction.decayderivative.md)
- [DerivativeFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.derivativefunction.md): The derivative of a function.
- [DivisionFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.divisionfunction.md): Ratio of two functions.
- [DomainFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.domainfunction.md): A unary function which limits the existence of an underlying function to a given [Region1](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.numeric.region1.md).
- [ExponentiationFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.exponentiationfunction.md): One function raised to another function.
- [ExpressionFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.expressionfunction.md): Represents an immutable expression equation. This equation specifically doesn't allow for custom variable resolvers as the results are cached.
- [FourierFrequency](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.fourierfrequency.md): A single element in a Fourier frequency space.
- [FourierFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.fourierfunction.md): Provides a fourier transform interpolation of an equally spaced set of time samples.
- [GaussianFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.gaussianfunction.md): Represents an immutable gaussian equation.
- [HyperbolaFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.hyperbolafunction.md): Represents an immutable hyperbolic function in the form y = (ax + b) + (d/(x - c))
- [IntegralFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.integralfunction.md): The integral of a function.
- [InterpolationFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.interpolationfunction.md): Represents an immutable interpolated equation.
- [LimitFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.limitfunction.md): A function limited to two extreme functions.
- [LinearFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.linearfunction.md): Linear function in the form y = Ax+B
- [LinearMapFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.linearmapfunction.md): A linear transformation of another function.
- [LogarithmFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.logarithmfunction.md): Represents an immutable logarithm equation in the form y = logₐ(x-b) + c
- [LogisticMapFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.logisticmapfunction.md): A map from a function to the logistic function.
- [MaximumFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.maximumfunction.md): Maximum of two functions.
- [MinimumFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.minimumfunction.md): Minimum of two functions.
- [MirrorFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.mirrorfunction.md): A function which horizontally mirrors another function.
- [MoveFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.movefunction.md): A linear transformation of another function.
- [MultipleFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.multiplefunction.md): An operator function which counts the number of multiples of one function which fit into another. Use this instead of the [RoundingFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.roundingfunction.md) if you want to round to increments other than a fixed number of decimals.
- [MultiplicationFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.multiplicationfunction.md): Product of two functions.
- [NegativeFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.negativefunction.md): A unary operator function for limiting a function to only negative values.
- [ParabolaFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.parabolafunction.md): Represents an immutable parabolic equation in the form y = A(x-B)² + C
- [PolynomialFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.polynomialfunction.md): Represents an immutable polynomial equation in the form y = a + bx² + cx³ + ...
- [PositiveFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.positivefunction.md): A unary operator function for limiting a function to only positive values.
- [ProbabilityDensityFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.probabilitydensityfunction.md): Represents an immutable probability density function.
- [ReciprocalFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.reciprocalfunction.md): Represents an immutable reciprocal equation in the form y = 1/((x - b)^p) + c, however with fixed signs to allow for fractional exponents and negative numbers.
- [RoundingFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.roundingfunction.md): A unary operator function for rounding another function.
- [SawToothFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sawtoothfunction.md): Sawtooth function in the form y = norm(x, [A,B)) * (D-C) + C
- [SequenceFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sequencefunction.md): Defines a sequence of functions on consecutive numeric domains.
- [SigmoidFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sigmoidfunction.md): A bounded, monotonic sigmoid (S-curve) transitioning from a low asymptote to a high asymptote. The curve is antisymmetric about its inflection point, which sits at the mid-level halfway between the two asymptotes. The steepness is given by the slope at the inflection. A negative slope produces a falling sigmoid. Every [SigmoidKind](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sigmoidkind.md) shares the same asymptotes, inflection and inflection-slope for a given set of parameters, so switching variants keeps those anchors fixed and changes only the tail behaviour.
- [SignFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.signfunction.md): The sign of a function.
- [SimplexNoise](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.simplexnoise.md): Implementation of the Perlin simplex noise, an improved Perlin noise algorithm. Based loosely on SimplexNoise1234 by Stefan Gustavson http://staffwww.itn.liu.se/~stegu/aqsis/aqsis-newnoise/
- [SincFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sincfunction.md): Sinc (Sinus Cardinalis) function in the form y = A(sin(Dx-B))/x)+C
- [SineFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sinefunction.md): Cosine function in the form y = A*sin(Dx-B) + (Ex+C)
- [SmoothMaximumFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.smoothmaximumfunction.md): The smooth maximum of two functions.
- [SmoothMinimumFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.smoothminimumfunction.md): The smooth minimum of two functions.
- [SNoiseFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.snoisefunction.md): Represents a one-dimensional Simplex noise function.
- [SplineFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.splinefunction.md): Represents an immutable sequence of cubic grips.
- [SplineHandle](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.splinehandle.md): Represents a single grip in a two-dimensional bezier curve chain.
- [StudentTFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.studenttfunction.md): Represents an immutable Student-T distribution.
- [SubtractionFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.subtractionfunction.md): Subtraction of two functions.
- [TangentFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.tangentfunction.md): Tangent function in the form y = A*tan(Dx-B)) + C. The tangent function does not currently have a UI defined for it.
- [ThresholdFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.thresholdfunction.md): A function which jumps from zero to some constant at a threshold.
- [TransitionFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.transitionfunction.md): Transition from one function to another.
- [TriangleFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.trianglefunction.md): Triangle wave function.
- [UnaryArithmeticFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.unaryarithmeticfunction.md): Utility function for applying standard arithmetic to functions.
- [WaveletFunction](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.waveletfunction.md): A sinusoidal wavelet with a gaussian decay.

## Enums

- [BlendFunction.Kind](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.blendfunction.kind.md): Enumerates the possible interpolations to use for the BlendEquation.
- [BumpFunction.BumpShape](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.bumpfunction.bumpshape.md): Enumerates the possible bump shapes.
- [HandleType](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.handletype.md): Enumerates the possible types of cubic handles.
- [InterpolationAlgorithm](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.interpolationalgorithm.md): Enumerates the possible interpolation algorithms.
- [SigmoidKind](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.sigmoidkind.md): The family of common sigmoid (S-shaped) curves. All variants share the same anchors — an inflection point and a tangent slope — and differ only in how quickly they saturate towards their asymptotes (their tail behaviour).

## Structs

- [Bump](https://developer.rhino3d.com/api/gh2/type/grasshopper2.types.functions.standard.bump.md): A single bump.