Lookup table for a two-dimensional function. Created with lookupTable2.

Specification of a discrete grid, used for sampling contour lines.

Subdivide the unit square with 50 squares (51 steps!) in x direction, and 30 (31 steps!) in y direction:

Grid (Vec2 0 0, Vec2 1 1) (50, 30)

Build a 2D lookup table, suitable for caching function calls. Values are initialized lazily, so that only repeated computations are sped up.

Example: lookup table for \(f(x,y) = x\cdot y\)

grid = Grid (Vec2 (-10) (-10), Vec2 10 10), (100, 100)
f (Vec2 x y) = x*y
table = createLookupTable2 grid f

Nearest neigbour lookup in a two-dimensional lookup table. Lookup outside of the lookup table’s domain is clamped to the table’s edges.

Compared to lookupBilinear this function works on types that don’t support arithmetic on them, and is faster. The downside is of course that only the values on the grid points are accessible, without any interpolation.

Bilinear lookup in a two-dimensional lookup table. Lookup outside of the lookup table’s domain is clamped to the table’s edges, so while it will not make the program crash, the values are not useful.

This lookup approximates a function in the sense that

lookupBilinear (createLookupTable2 grid f) x ≈ f x

Perform an action for each entry in the lookup table. Can be handy for plotting its contents.

grid = Grid (Vec2 0 0, Vec2 100, 100) (100, 100)
f (Vec2 x y) = x + sin y
table = createLookupTable2 grid f

forLookupTable2_ table $ val pos _ ->
    moveToVec pos
    showTextAligned HCenter VCenter (show val)

Discrete Vec2. Useful as coordinate in a Vector (Vector a).

Continuous version of IVec2. Type-wise the same as Vec2, but it shows fractional grid coodrdinates, so we can express the fact that our lookup might be »between i and i+1« and we can interpolate.

Round a »continuous integral« coordinate to a »proper integral« coordinate.

Map a coordinate from the discrete grid to continuous space.

A raw value table, filled (lazily) by a function applied to the underlying Grid.

We first index by i and then j, so that vec!i!j has the intuitive meaning of »go in ix direction and then in jy. The drawback is that this makes the table look like downward columns of y values, indexed by x. The more common picture for at least me is to have line numbers and then rows in each line.