Documentation

Find the iso lines of a function (= where the function has the same height, like e.g. height lines on a map) within a certain Grid (which unifies size and resolution).

This function can be partially applied to cache the function values when drawing iso lines, which is especially useful if repeatedly sampling the function is expensive:

-- BAD! Recalculates the values of f across the grid for each invocation
isosBad = [isoLines grid f isoHeight | isoHeight <- [1..10]]

-- Good: Calculates the value table only once
isosGood = let iso = isoLines grid f
             in [iso isoHeight | isoHeight [1..10]]

This is also the reason why the contour threshold is not implitly zero but an explicit parameter: if we used the family of functions \(f_h(x) = f(x)-h\) to calculate the iso lines at height \(h\), we would have to recreate the value table for each invocation.

Concrete example

circle p = \x -> normSquare (x -. p)

grid :: Grid
grid = Grid (Vec2 (-10) (-10), Vec2 10 10) (100, 100)

circleTrajectory :: Double -> [Vec2]
circleTrajectory =
    let iso = isoLines grid (circle zero)
    in \r -> head (iso (r^2)) -- NB head is safe here because each of our functions has exactly one iso line at a certain height

manyCircles :: [[Vec2]]
manyCircles = map circleTrajectory [1..9]

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)