edge-edge-distance

Compute the distance between two edges (line segments) in a 3D space robustly.

Known Issues

This implementation can have larger errors for intersecting edges.

Usage

The core function is ee_closest_point(x0, x1, x2, x3, t0, t1, parallel_sin_sq_tol) in lib/Distance.h. It takes two edges $(x_0, x_1), (x_2, x_3)$ as input, and returns the type of the closest points on the two edges. It also writes into t0 and t1, so that the closest points can be computed as x0 + t0 * (x1 - x0) and x2 + t1 * (x3 - x2).

We also provide an example executable to read the user input and compute the distance (see "Example"), and some utility scripts to test the function (see "Test").

Build

mkdir build
cd build
cmake ..
make

Example

./example/example

Sample input:

(1.648724e-01 5.538958e-01 9.169785e-01) (4.051462e-01 1.222591e-01 8.325946e-01) (1.026980e-01 1.108083e-01 4.213850e-01) (2.735318e-01 -1.960839e-01 3.613884e-01)

Sample Output:

type: 5
t0: 1
t1: 0.184954
h0: (4.051462e-01 1.222591e-01 8.325946e-01)
h1: (1.342945e-01 5.404726e-02 4.102884e-01)
dist: 0.506316

Test

Use tests/testgen to generate test cases in 3 different categories: random, parallel, and coplanar.

./tests/testgen 

Use tests/testscript to run the test cases in a .txt file.

./tests/testscript testdata_random.txt
./tests/testscript testdata_parallel.txt
./tests/testscript testdata_coplanar.txt

You can also use tests/testscript to test your own test cases.