Question

How can I programmatically detect whether or not two triangles touch each other, given their vertices on a 2D coordinate plane? This includes touching points or edges, as well as if one triangle is completely inside the other one.

Answer 1

Use Line Line intersection

https://www.topcoder.com/community/data-science/data-science-tutorials/geometry-concepts-line-intersection-and-its-applications/#line_line_intersection

Also consider the possibility that some vertex might be touching one of the sides of the other triangle.

http://www.blackpawn.com/texts/pointinpoly/default.html

function SameSide(p1,p2, a,b)
    cp1 = CrossProduct(b-a, p1-a)
    cp2 = CrossProduct(b-a, p2-a)
    if DotProduct(cp1, cp2) >= 0 then return true
    else return false

function PointInTriangle(p, a,b,c)
    if SameSide(p,a, b,c) and SameSide(p,b, a,c)
        and SameSide(p,c, a,b) then return true
    else return false

Or look at this link and scroll down

http://compsci.ca/v3/viewtopic.php?t=6034