Fint2d(X, Ws, s, method = c("round", "bilinear", "bicubic"), derivs = FALSE, ...)Interpolation of a function, say H, is achieved by the following formula (cf. Gilleland et al 2010, sec. 3), where r and s represent the fractional part of their respective coordinate. that is, r = x - g( x ) and s = y - g( y ), where g( x ) is the greatest integer less than x.
sum_k sum_l b_k( r ) * b_l( s ) * H(g( x ) + l, g( y ) + k).
The specific choices for the values of b_l and b_k and their ranges depends on the type of interpolation. For bilinear interpolation, they both range from 0 to 1, and are given by: b_0( x ) = 1 - x and b_1( x ) = x. for bicubic interpolation, they both range from -1 to 2 and are given by:
b_{-1}( t ) = (2 * t^2 - t^3 - t) / 2
b_0( t ) = (3 * t^3 - 5 * t^2 + 2) / 2
b_1( t ) = (4 * t^2 - 3 * t^3 + t) / 2
b_2( t ) = ((t - 1) * t^2) / 2.
rigider, rigidTransform