get-implicit-form1-error-counters
function getImplicitForm1ErrorCounters(ps: number[][]): object
Defined in implicit-form/get-error-counters/get-implicit-form1-error-counters.ts:45
Returns a representation of the error (from which an absolute error bound can be calculated) when calculating the implicit form of the given bezier curve (using getImplicitForm1 or getImplicitForm1Dd).
- returned coefficients are subscripted to match their monomial's variables,
e.g.
vₓᵧ
is the coefficient of the monomialvₓᵧxy
- the implicit form is given by:
vₓx + vᵧy + v
- The returned error representation needs to be multiplied with
Stewart error counters¹
and an appropriate error function,
γ
, depending on the precision used (e.g. double or double-double). This is explained in more detail below. See also Higham 2002 p. 68 near the bottom.
(1) G. W. Stewart. Introduction to Matrix Computations. Academic Press, New York, 1973. xiii+441 pp. ISBN 0-12-670350-7
The absolute erros below can be calculated as follows (where <E>
are the
error counters as indicated in the comments of the return value below):
- double precision:
<E> * (γ(1)) * result_
- double-double precision:
<E> * (2*γγ(3)) * result_
where [[γ]] and [[γγ]] are the usual error functions (provided in this library
as functions with the same name) with γ(1) === 1.1102230246251568e-16
and γγ(3) === 3.697785493223493e-32
.
return {
vₓ_, // <1>
vᵧ_, // <1>
v_ // <3>
}
Parameters:
Name | Type | Description |
---|---|---|
ps | number[][] |
Returns: object
Name | Type |
---|---|
vₓ_ | number |
vᵧ_ | number |
v_ | number |