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get-implicit-form1-dd-with-running-error

function getImplicitForm1DdWithRunningError(ps: number[][]): object

Defined in implicit-form/double-double/get-implicit-form1-dd-with-running-error.ts:31

Returns a double-double precision implicit form of the given line segment and a coefficientwise error bound. Returned coefficients are subscripted to match their monomial's variables, e.g. vₓᵧ is the coefficient of the monomial vₓᵧxy

  • the implicit form is given by: vₓx + vᵧy + v = 0
  • intermediate calculations are done in double-double precision and this is reflected in the error bound
  • the error bound returned first needs to be scaled by γγ3 === (3*u*u) / (1 - 3*u*u) === 3.697785493223493e-32, where u === Number.EPSILON / 2 before use
  • adapted from Indrek Mandre
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Parameters:

NameTypeDescription
psnumber[][]a line segment given as an array of its control points, e.g. [[1,2],[3,4]]

Returns: object

NameType
coeffs{ vₓ: number[]; vᵧ: number[]; v: number[] }
errorBound{ v_: number }