Task: Determine if two triangles overlap




Go: package main

import "fmt"

type point struct {
    x, y float64
}

func (p point) String() string {
    return fmt.Sprintf("(%.1f, %.1f)", p.x, p.y)
}

type triangle struct {
    p1, p2, p3 point
}

func (t *triangle) String() string {
    return fmt.Sprintf("Triangle %s, %s, %s", t.p1, t.p2, t.p3)
}

func (t *triangle) det2D() float64 {
    return t.p1.x * (t.p2.y - t.p3.y) +
           t.p2.x * (t.p3.y - t.p1.y) +
           t.p3.x * (t.p1.y - t.p2.y) 
}

func (t *triangle) checkTriWinding(allowReversed bool) {
    detTri := t.det2D()
    if detTri < 0.0 {
        if allowReversed {
            a := t.p3
            t.p3 = t.p2
            t.p2 = a
        } else {
            panic("Triangle has wrong winding direction.")
        }
    }
}

func boundaryCollideChk(t *triangle, eps float64) bool {
    return t.det2D() < eps
}

func boundaryDoesntCollideChk(t *triangle, eps float64) bool {
    return t.det2D() <= eps
}

func triTri2D(t1, t2 *triangle, eps float64, allowReversed, onBoundary bool) bool {
    
    t1.checkTriWinding(allowReversed)
    t2.checkTriWinding(allowReversed)

    
    var chkEdge func (*triangle, float64) bool
    if onBoundary {
        chkEdge = boundaryCollideChk
    } else {
        chkEdge = boundaryDoesntCollideChk
    }
    lp1 := [3]point{t1.p1, t1.p2, t1.p3}
    lp2 := [3]point{t2.p1, t2.p2, t2.p3}

    
    for i := 0; i < 3; i++ {
        j := (i + 1) % 3
        
        
        tri1 := &triangle{lp1[i], lp1[j], lp2[0]}
        tri2 := &triangle{lp1[i], lp1[j], lp2[1]}
        tri3 := &triangle{lp1[i], lp1[j], lp2[2]}
        if chkEdge(tri1, eps) && chkEdge(tri2, eps) && chkEdge(tri3, eps) {
            return false
        }
    }

    
    for i := 0; i < 3; i++ {
        j := (i + 1) % 3
        
        
        tri1 := &triangle{lp2[i], lp2[j], lp1[0]}
        tri2 := &triangle{lp2[i], lp2[j], lp1[1]}
        tri3 := &triangle{lp2[i], lp2[j], lp1[2]}
        if chkEdge(tri1, eps) && chkEdge(tri2, eps) && chkEdge(tri3, eps) {
            return false
        }
    }

    
    return true
}

func iff(cond bool, s1, s2 string) string {
    if cond {
        return s1
    }
    return s2
}

func main() {
    t1 := &triangle{point{0.0, 0.0}, point{5.0, 0.0}, point{0.0, 5.0}}
    t2 := &triangle{point{0.0, 0.0}, point{5.0, 0.0}, point{0.0, 6.0}}
    fmt.Printf("%s and\n%s\n", t1, t2)
    overlapping := triTri2D(t1, t2, 0.0, false, true)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))

    
    t1 = &triangle{point{0.0, 0.0}, point{0.0, 5.0}, point{5.0, 0.0}}
    t2 = t1
    fmt.Printf("\n%s and\n%s\n", t1, t2)
    overlapping = triTri2D(t1, t2, 0.0, true, true)
    fmt.Println(iff(overlapping, "overlap (reversed)", "do not overlap"))

    t1 = &triangle{point{0.0, 0.0}, point{5.0, 0.0}, point{0.0, 5.0}}
    t2 = &triangle{point{-10.0, 0.0}, point{-5.0, 0.0}, point{-1.0, 6.0}}
    fmt.Printf("\n%s and\n%s\n", t1, t2)
    overlapping = triTri2D(t1, t2, 0.0, false, true)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))

    t1.p3 = point{2.5, 5.0}
    t2 = &triangle{point{0.0, 4.0}, point{2.5, -1.0}, point{5.0, 4.0}}
    fmt.Printf("\n%s and\n%s\n", t1, t2)
    overlapping = triTri2D(t1, t2, 0.0, false, true)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))

    t1 = &triangle{point{0.0, 0.0}, point{1.0, 1.0}, point{0.0, 2.0}}
    t2 = &triangle{point{2.0, 1.0}, point{3.0, 0.0}, point{3.0, 2.0}}
    fmt.Printf("\n%s and\n%s\n", t1, t2)
    overlapping = triTri2D(t1, t2, 0.0, false, true)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))

    t2 = &triangle{point{2.0, 1.0}, point{3.0, -2.0}, point{3.0, 4.0}}
    fmt.Printf("\n%s and\n%s\n", t1, t2)
    overlapping = triTri2D(t1, t2, 0.0, false, true)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))

    t1 = &triangle{point{0.0, 0.0}, point{1.0, 0.0}, point{0.0, 1.0}}
    t2 = &triangle{point{1.0, 0.0}, point{2.0, 0.0}, point{1.0, 1.1}}
    fmt.Printf("\n%s and\n%s\n", t1, t2)
    println("which have only a single corner in contact, if boundary points collide")
    overlapping = triTri2D(t1, t2, 0.0, false, true)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))

    fmt.Printf("\n%s and\n%s\n", t1, t2)
    fmt.Println("which have only a single corner in contact, if boundary points do not collide")
    overlapping = triTri2D(t1, t2, 0.0, false, false)
    fmt.Println(iff(overlapping, "overlap", "do not overlap"))
}




Python: from __future__ import print_function
import numpy as np

def CheckTriWinding(tri, allowReversed):
	trisq = np.ones((3,3))
	trisq[:,0:2] = np.array(tri)
	detTri = np.linalg.det(trisq)
	if detTri < 0.0:
		if allowReversed:
			a = trisq[2,:].copy()
			trisq[2,:] = trisq[1,:]
			trisq[1,:] = a
		else: raise ValueError("triangle has wrong winding direction")
	return trisq

def TriTri2D(t1, t2, eps = 0.0, allowReversed = False, onBoundary = True):
	
	t1s = CheckTriWinding(t1, allowReversed)
	t2s = CheckTriWinding(t2, allowReversed)

	if onBoundary:
		
		chkEdge = lambda x: np.linalg.det(x) < eps
	else:
		
		chkEdge = lambda x: np.linalg.det(x) <= eps

	
	for i in range(3):
		edge = np.roll(t1s, i, axis=0)[:2,:]

		
		
		if (chkEdge(np.vstack((edge, t2s[0]))) and
			chkEdge(np.vstack((edge, t2s[1]))) and  
			chkEdge(np.vstack((edge, t2s[2])))):
			return False

	
	for i in range(3):
		edge = np.roll(t2s, i, axis=0)[:2,:]

		
		
		if (chkEdge(np.vstack((edge, t1s[0]))) and
			chkEdge(np.vstack((edge, t1s[1]))) and  
			chkEdge(np.vstack((edge, t1s[2])))):
			return False

	
	return True

if __name__=="__main__":
	t1 = [[0,0],[5,0],[0,5]]
	t2 = [[0,0],[5,0],[0,6]]
	print (TriTri2D(t1, t2), True)

	t1 = [[0,0],[0,5],[5,0]]
	t2 = [[0,0],[0,6],[5,0]]
	print (TriTri2D(t1, t2, allowReversed = True), True)

	t1 = [[0,0],[5,0],[0,5]]
	t2 = [[-10,0],[-5,0],[-1,6]]
	print (TriTri2D(t1, t2), False)

	t1 = [[0,0],[5,0],[2.5,5]]
	t2 = [[0,4],[2.5,-1],[5,4]]
	print (TriTri2D(t1, t2), True)

	t1 = [[0,0],[1,1],[0,2]]
	t2 = [[2,1],[3,0],[3,2]]
	print (TriTri2D(t1, t2), False)

	t1 = [[0,0],[1,1],[0,2]]
	t2 = [[2,1],[3,-2],[3,4]]
	print (TriTri2D(t1, t2), False)

	
	t1 = [[0,0],[1,0],[0,1]]
	t2 = [[1,0],[2,0],[1,1]]
	print (TriTri2D(t1, t2, onBoundary = True), True)

	
	t1 = [[0,0],[1,0],[0,1]]
	t2 = [[1,0],[2,0],[1,1]]
	print (TriTri2D(t1, t2, onBoundary = False), False)