Segment-Segment intersection

[TheBlek]

Description

Ability to calculate intersection point of two line segments. Recently needed to hand-roll it, so I wonder if its a useful addition

Solution

Method intersectLine on Line3. Interface and behavior could be the same as Plane's intersectLine

Alternatives

I wrote it myself with guidance of https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection

Additional context

I could create a PR if the feature it deemed useful

[Mugen87]

May I ask for what use case you need line intersection in 3D?

When I remember correctly a good way to implement this is to compute the shortest distance between two line segments and if it is 0 or smaller than a tolerance/epsilon value, they are considered as intersecting.

[Mugen87]

@WestLangley Do you think it's worth implementing something like Line3.closestDistanceToLine()?

[TheBlek]

I recently implemented a new version of triangle-triangle intersection which handled all corner cases correctly here. And one of the corner cases is two triangles that degenerated into segments hence segment-segment intersection.

When I remember correctly a good way to implement this is to compute the shortest distance between two line segments and if it is 0 or smaller than a tolerance/epsilon value, they are considered as intersecting.

I'm not sure if that would be the fastest way to do the intersection. However distance between two segments seems more applicable. I'm imagining some puzzle game with lazer things where if you cross rays something bad will happen.

It is a slippery slope, as there are so many 3D and 2D (screen space) methods, and time-dependent CPA methods, involving points, lines, rays, line segments, and triangles.

Yes, I understand you wouldn't want every mathematical algorithm in the project. Since there are already some simple intersection algos like Plane-line I just thought that it would be something helpful. Maybe not the intersection, but distance?

[Mugen87]

Maybe not the intersection, but distance?

I would support such a method in Line3 if it is compacted enough. The complexity of similar methods in the math directory is a good guidance.