bool
lineIntersectsTriangle(Line3 const & line, Vector3 const & v0, Vector3 const & edge01, Vector3 const & edge02, Real * time)
{
// The code is taken from the ray-triangle intersection test in Dave Eberly's Wild Magic library, v5.3, released under the
// Boost license: http://www.boost.org/LICENSE_1_0.txt .
static Real const EPS = 1e-30f;
Vector3 diff = line.getPoint() - v0;
Vector3 normal = edge01.cross(edge02);
// Solve Q + t*D = b1*E1 + b2*E2 (Q = diff, D = line direction, E1 = edge01, E2 = edge02, N = Cross(E1,E2)) by
// |Dot(D,N)|*b1 = sign(Dot(D,N))*Dot(D,Cross(Q,E2))
// |Dot(D,N)|*b2 = sign(Dot(D,N))*Dot(D,Cross(E1,Q))
// |Dot(D,N)|*t = -sign(Dot(D,N))*Dot(Q,N)
Real DdN = line.getDirection().dot(normal);
int sign;
if (DdN > EPS)
sign = 1;
else if (DdN < -EPS)
{
sign = -1;
DdN = -DdN;
}
else
{
// Line and triangle are parallel, call it a "no intersection" even if the line does intersect
return false;
}
Real DdQxE2 = sign * line.getDirection().dot(diff.cross(edge02));
if (DdQxE2 >= 0)
{
Real DdE1xQ = sign * line.getDirection().dot(edge01.cross(diff));
if (DdE1xQ >= 0)
{
if (DdQxE2 + DdE1xQ <= DdN)
{
// Line intersects triangle
Real QdN = -sign * diff.dot(normal);
if (time) *time = QdN / DdN;
return true;
}
// else: b1 + b2 > 1, no intersection
}
// else: b2 < 0, no intersection
}
// else: b1 < 0, no intersection
return false;
}
Real
closestPtLineTriangle(Line3 const & line, Vector3 const & v0, Vector3 const & edge01, Vector3 const & edge02, Real & s,
Vector3 & c1, Vector3 & c2)
{
if (lineIntersectsTriangle(line, v0, edge01, edge02, &s))
{
c1 = c2 = line.getPoint() + s * line.getDirection();
return 0;
}
// Either (1) the line is not parallel to the triangle and the point of
// intersection of the line and the plane of the triangle is outside the
// triangle or (2) the line and triangle are parallel. Regardless, the
// closest point on the triangle is on an edge of the triangle. Compare
// the line to all three edges of the triangle.
Real min_sqdist = -1;
Vector3 v[3] = { v0, v0 + edge01, v0 + edge02 };
Vector3 tmp_c1, tmp_c2;
float tmp_s, t;
for (int i0 = 2, i1 = 0; i1 < 3; i0 = i1++)
{
Real sqdist = closestPtSegmentLine(v[i0], v[i1], line.getPoint(), line.getPoint() + line.getDirection(),
t, tmp_s, tmp_c2, tmp_c1);
if (min_sqdist < 0 || sqdist < min_sqdist)
{
min_sqdist = sqdist;
s = tmp_s;
c1 = tmp_c1;
c2 = tmp_c2;
}
}
return min_sqdist;
}