This example is ported from the demos in https://github.com/danshapero/predicates. These provide nice visualizations of the robustness of the predicates in this crate, as well as the non-robustness of a naive implementation of these predicates.
The example computes the predicates in this crate, over a 2D grid of values for one of the inputs, while keeping the rest of the inputs at fixed values.
For example, we compute the orient2d predicate on (12.0, 12.0), (c[i], c[j]), (24.0, 24.0); where i, j varies
in 0..256, and c[i] is the ith float after 0.5. In
other words, c[i] is obtained by starting at 0.5, and
calling
nextafter
i times.
The inputs are set up so that, if the predicates are
calculated exactly, the output is a png with gray values on
the main diagonal, black on the lower-left, and white on
the upper-right side of it. However, the naive versions show
that the predicate is not robust: it switches values on both
sides of the main diagonals, indicating the round-off errors.
cargo run --example predicate-map naive incircle naive-incircle.png
cargo run --example predicate-map naive orient2d naive-orient2d.png
cargo run --example predicate-map robust incircle robust-incircle.png
cargo run --example predicate-map robust orient2d robust-orient2d.png