Class lsst::afw::math::Chebyshev1Function2

template<typename ReturnT>
class Chebyshev1Function2 : public lsst::afw::math::BasePolynomialFunction2<ReturnT>

2-dimensional weighted sum of Chebyshev polynomials of the first kind.

f(x,y) = c0 T0(x’) T0(y’) # order 0

• c1 T1(x’) T0(y’) + c2 T0(x’) T1(y’) # order 1

• c3 T2(x’) T0(y’) + c4 T1(x’) T1(y’) + c5 T0(x’) T2(y’) # order 2

• …

= c0 # order 0

• c1 T1(x’) + c2 T1(y’) # order 1

• c3 T2(x’) + c4 T1(x’) T1(y’) + c5 T2(y’) # order 2

• …

where:

• Tn(x) is the nth Chebyshev function of the first kind: T0(x) = 1 T1(x) = x Tn+1(x) = 2xTn(x) + Tn-1(x)

• x’ is x offset and scaled to range [-1, 1] as x ranges over [minX, maxX]

• y’ is y offset and scaled to range [-1, 1] as y ranges over [minY, maxY]

Return value is incorrect if function arguments are not in the range [minX, maxX], [minY, maxY].