SMath Documentation

Geometry, statistics and combinatorics for .NET, written against generic math. Every formula is generic over the numeric type, so the same call site works for double, float, decimal or Half without overloads or casting.

Design Principles

  • Generic over the number type: Constraints express the mathematics rather than a concrete type: a formula needing a square root asks for IRootFunctions<N>, one needing only addition asks for INumberBase<N>. Passing a type that cannot support the operation is a compile error.
  • Static and allocation free: There are no wrapper structs for points or vectors. Coordinates are plain tuples such as (N X, N Y), so values stay on the stack and interoperate with any other library. All entry points are static.
  • Names that read as the formula: Types are nested by the quantity being computed and the input it comes from, giving call sites like Circle.Region.Area.FromRadius(r) or Line.Segment.Length.FromTwoPoints(a, b).
  • Functions describe themselves: A function of one variable reports its parity, continuity, domain, image and plain text formula next to Eval and DerivativeEval, so a caller can reason about the function without hard coding its properties.
  • Span overloads on the hot paths: Statistics and grid traversal accept ReadOnlySpan<T> next to IEnumerable<T>, avoiding enumerator allocation and interface dispatch per element. Coordinate generators additionally offer buffer filling overloads, so a caller can size a buffer with the matching count helper and reuse or stackalloc it.

Installation

Install the NuGet package:

dotnet add package SMath

Quick Navigation

  • API Reference - Full reference documentation for all namespaces, types, and mathematical formulas.
  • GitHub Repository - Source code, issues, and discussions.

Overview of Modules

Area Types & Capabilities
Geometry 1D LineSegment
Geometry 2D Point2, Line (ray, segment, projection, intersection), Circle (arc, chord, sector, segment, tangents, distance, intersection), Ellipse, Hyperbola, Parabola, Polygon (shoelace area, centroid, containment), Triangle, Rectangle, Square, Rhombus, RegularHexagon, GeometricVector2 (polar/cartesian, normals, rotation, reflection, dot/cross product), Function1Geometry
Geometry 3D Point3 (distances, neighbors, grid traversal), Sphere, SphereCap, BallCap, SphericalShell, Ellipsoid, Cuboid
Statistics ArithmeticMean (also weighted), GeometricMean, HarmonicMean, QuadraticMean, CubicMean, GeneralizedMean, Median, Mode, Variance, StandardDeviation, Moment, Skewness, Kurtosis, Covariance, PearsonCorrelation (cross, auto, weighted), SpearmanRankCorrelation, KendallCorrelation, CramerCorrelation, Histogram
Combinatorics Permutations, PermutationsWithRepetition, Combinations, CombinationsWithRepetition
Sequences ArithmeticSequence, GeometricSequence, FibonacciSequence, GeneralisedFibonacciSequence, CollatzConjecture
Series ArithmeticSeries, GeometricSeries
Expansions BinomialCoefficient, PascalsTriangle
Functions (1D) Identity, Sine, Cosine, Tangent, Cotangent, Power2 to Power8, Root2 to Root8, Reciprocal, Exponential, NaturalExponential, Logarithm, Polynomial, SigmoidFunction, BipolarSigmoid, LogisticFunction, GaussianFunction, SignFunction, StepFunction, UnitStepFunction
Functions (2D & nD) AckleyFunction, BoothFunction, RastriginFunction, RosenbrockFunction
Distances (nD) EuclideanDistance, ManhattanDistance, ChebyshevDistance, HammingDistance
General & Extensions BinaryIntegerExtension (Hamming distance, Gray code, GCD, Pow), Factorial, Determinant, PythagorasTheorem, Summation
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