i am programming voxelizing algorithm in unity. and now it turns out that i need some fansy intersection checking between cube and polygon.
actually i have a code here.
public static bool Intersects(Triangle tri, Bounds aabb)
{
float p0, p1, p2, r;
Vector3 extents = aabb.max - aabb.center;
Vector3 v0 = tri.a - aabb.center,
v1 = tri.b - aabb.center,
v2 = tri.c - aabb.center;
Vector3 f0 = v1 - v0,
f1 = v2 - v1,
f2 = v0 - v2;
Vector3 a00 = new Vector3(0, -f0.z, f0.y),
a01 = new Vector3(0, -f1.z, f1.y),
a02 = new Vector3(0, -f2.z, f2.y),
a10 = new Vector3(f0.z, 0, -f0.x),
a11 = new Vector3(f1.z, 0, -f1.x),
a12 = new Vector3(f2.z, 0, -f2.x),
a20 = new Vector3(-f0.y, f0.x, 0),
a21 = new Vector3(-f1.y, f1.x, 0),
a22 = new Vector3(-f2.y, f2.x, 0);
// Test axis a00
p0 = Vector3.Dot(v0, a00);
p1 = Vector3.Dot(v1, a00);
p2 = Vector3.Dot(v2, a00);
r = extents.y * Mathf.Abs(f0.z) + extents.z * Mathf.Abs(f0.y);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a01
p0 = Vector3.Dot(v0, a01);
p1 = Vector3.Dot(v1, a01);
p2 = Vector3.Dot(v2, a01);
r = extents.y * Mathf.Abs(f1.z) + extents.z * Mathf.Abs(f1.y);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a02
p0 = Vector3.Dot(v0, a02);
p1 = Vector3.Dot(v1, a02);
p2 = Vector3.Dot(v2, a02);
r = extents.y * Mathf.Abs(f2.z) + extents.z * Mathf.Abs(f2.y);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a10
p0 = Vector3.Dot(v0, a10);
p1 = Vector3.Dot(v1, a10);
p2 = Vector3.Dot(v2, a10);
r = extents.x * Mathf.Abs(f0.z) + extents.z * Mathf.Abs(f0.x);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a11
p0 = Vector3.Dot(v0, a11);
p1 = Vector3.Dot(v1, a11);
p2 = Vector3.Dot(v2, a11);
r = extents.x * Mathf.Abs(f1.z) + extents.z * Mathf.Abs(f1.x);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a12
p0 = Vector3.Dot(v0, a12);
p1 = Vector3.Dot(v1, a12);
p2 = Vector3.Dot(v2, a12);
r = extents.x * Mathf.Abs(f2.z) + extents.z * Mathf.Abs(f2.x);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a20
p0 = Vector3.Dot(v0, a20);
p1 = Vector3.Dot(v1, a20);
p2 = Vector3.Dot(v2, a20);
r = extents.x * Mathf.Abs(f0.y) + extents.y * Mathf.Abs(f0.x);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a21
p0 = Vector3.Dot(v0, a21);
p1 = Vector3.Dot(v1, a21);
p2 = Vector3.Dot(v2, a21);
r = extents.x * Mathf.Abs(f1.y) + extents.y * Mathf.Abs(f1.x);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
// Test axis a22
p0 = Vector3.Dot(v0, a22);
p1 = Vector3.Dot(v1, a22);
p2 = Vector3.Dot(v2, a22);
r = extents.x * Mathf.Abs(f2.y) + extents.y * Mathf.Abs(f2.x);
if (Mathf.Max(-Mathf.Max(p0, p1, p2), Mathf.Min(p0, p1, p2)) > r)
{
return false;
}
if (Mathf.Max(v0.x, v1.x, v2.x) < -extents.x || Mathf.Min(v0.x, v1.x, v2.x) > extents.x)
{
return false;
}
if (Mathf.Max(v0.y, v1.y, v2.y) < -extents.y || Mathf.Min(v0.y, v1.y, v2.y) > extents.y)
{
return false;
}
if (Mathf.Max(v0.z, v1.z, v2.z) < -extents.z || Mathf.Min(v0.z, v1.z, v2.z) > extents.z)
{
return false;
}
var normal = Vector3.Cross(f1, f0).normalized;
var pl = new Plane(normal, Vector3.Dot(normal, tri.a));
return Intersects(pl, aabb);
}
public static bool Intersects(Plane pl, Bounds aabb)
{
Vector3 center = aabb.center;
var extents = aabb.max - center;
var r = extents.x * Mathf.Abs(pl.normal.x) + extents.y * Mathf.Abs(pl.normal.y) + extents.z * Mathf.Abs(pl.normal.z);
var s = Vector3.Dot(pl.normal, center) - pl.distance;
return Mathf.Abs(s) <= r;
}
but it is just very hard to understand the process and why it works... so it would be very appreciated if there's short explaining on this code or another short algorithm. cheers
