bool Intersects(const Ray2 &ray, const Circle &circle, float *distance)
{
const Vector2 &rayDir = ray.GetDirection();
// Adjust ray origin relative to circle center
const Vector2 &rayOrig = ray.GetOrigin() - circle.GetCentre();
float radius = circle.GetRadius();
// Check origin inside first
if (rayOrig.MagnitudeSquared() <= radius * radius)
{
SetPtrValue(distance, 0.0f);
return true;
}
// Mmm, quadratics
// Build coeffs which can be used with std quadratic solver
// ie t = (-b +/- sqrt(b * b + 4ac)) / 2a
float a = Vector2::DotProduct(rayDir, rayDir);
float b = 2 * Vector2::DotProduct(rayOrig, rayDir);
float c = Vector2::DotProduct(rayOrig, rayOrig) - radius * radius;
// Calc determinant
float d = (b * b) - (4 * a * c);
if (d < 0)
{
// No intersection
SetPtrValue(distance, 0.0f);
return false;
}
else
{
// BTW, if d=0 there is one intersection, if d > 0 there are 2
// But we only want the closest one, so that's ok, just use the
// '-' version of the solver
float negB(-b);
float sqrtD(Sqrt(d));
float twoA(2 * a);
float t = (negB - sqrtD) / twoA;
if (t < 0)
{
t = (negB + sqrtD) / twoA;
}
if (t > 0)
{
SetPtrValue(distance, t);
return true;
}
return false;
}
}
bool Intersects(const LineSegment2 &lineSegment, bool singleSided, const Ray2 &ray, float *distance)
{
if (singleSided && Vector2::DotProduct(ray.GetDirection(), lineSegment.GetNormal()) >= 0.0f)
{
// Ray is pointing in the same direction as the line normal
return false;
}
const Vector2 &P0 = ray.GetOrigin();
const Vector2 &D0 = ray.GetDirection();
const Vector2 &P1 = lineSegment.GetTail();
const Vector2 &D1 = lineSegment.GetVector();
Vector2 perpD0 = Perp(D0);
Vector2 perpD1 = Perp(D1);
if (Dot(perpD1, D0) != 0.0f)
{
Vector2 P1MinusP0 = P1 - P0;
float s = Dot(perpD1, P1MinusP0) / Dot(perpD1,D0);
float t = Dot(perpD0, P1MinusP0) / Dot(perpD1,D0);
bool intersects = s >= 0.0f && 0.0f <= t && t <= 1.0f;
if (intersects)
{
if (distance)
{
// We've probably already calculated the nearest point in terms of s & t but
// I can't figure it out.
*distance = s; // ((lineSegment.GetTail() + lineSegment.GetDirection() * t) - ray.GetOrigin()).Magnitude();
// *distance = (nearestPoint - ray.GetOrigin()).Magnitude();
}
return true;
}
}
return false;
}
//----------------------------------------------------------------------------
bool Mgc::FindIntersection (const Ray2& rkRay0, const Ray2& rkRay1,
int& riQuantity, Real afT[2])
{
Vector2 kDiff;
Real fD0SqrLen;
bool bIntersects = Find(rkRay0.Origin(),rkRay0.Direction(),
rkRay1.Origin(),rkRay1.Direction(),kDiff,fD0SqrLen,riQuantity,afT);
if ( bIntersects )
{
if ( riQuantity == 1 )
{
if ( afT[0] < 0.0f || afT[1] < 0.0f )
{
// lines intersect, but rays do not
riQuantity = 0;
}
}
else
{
// rays are on same line
Real fDot = kDiff.Dot(rkRay0.Direction());
if ( rkRay0.Direction().Dot(rkRay1.Direction()) > 0.0f )
{
// Rays point in same direction, get semiinfinite interval
// of intersection.
afT[0] = ( fDot >= 0.0f ? fDot/fD0SqrLen : 0.0f );
afT[1] = Math::MAX_REAL;
}
else
{
// test for overlap of opposite pointing rays
if ( fDot > 0.0f )
{
afT[0] = 0.0f;
afT[1] = fDot/fD0SqrLen;
}
else if ( fDot < 0.0f )
{
// no overlap
riQuantity = 0;
}
else
{
// rays have a common origin
riQuantity = 1;
afT[0] = 0.0f;
}
}
}
}
return riQuantity != 0;
}
//----------------------------------------------------------------------------
bool Mgc::FindIntersection (const Line2& rkLine, const Ray2& rkRay,
int& riQuantity, Real afT[2])
{
Vector2 kDiff;
Real fD0SqrLen;
bool bIntersects = Find(rkLine.Origin(),rkLine.Direction(),
rkRay.Origin(),rkRay.Direction(),kDiff,fD0SqrLen,riQuantity,afT);
if ( bIntersects )
{
if ( riQuantity == 1 )
{
if ( afT[1] < 0.0f )
{
// lines intersect, but ray does not intersect line
riQuantity = 0;
}
}
else
{
// ray is contained by line, adjust intersection interval
if ( rkLine.Direction().Dot(rkRay.Direction()) > 0.0f )
{
afT[0] = (kDiff.Dot(rkLine.Direction()))/fD0SqrLen;
afT[1] = Math::MAX_REAL;
}
else
{
afT[0] = -Math::MAX_REAL;
afT[1] = (kDiff.Dot(rkLine.Direction()))/fD0SqrLen;
}
}
}
return riQuantity != 0;
}
//=============================================================================
bool Ray2::intersectParam( const Ray2& ray1, const Ray2& ray2, double& parameter, bool onlyExistence)
{
double determinant = ray1.getDir().x()*ray2.getDir().y() - ray1.getDir().y()*ray2.getDir().x();
bool exists = true;
if ( ( determinant > -10e-12 ) && ( determinant < 10e-12 ) ) exists = false;
if (exists == false) return false;
if (onlyExistence) return exists;
Vector2F delta( ray2.origin_, ray1.origin_);
parameter = ( delta.y()*ray2.getDir().x() - delta.x()*ray2.getDir().y() ) / determinant;
return true;
}
//----------------------------------------------------------------------------
bool Mgc::FindIntersection (const Ray2& rkRay, const Segment2& rkSegment,
int& riQuantity, Real afT[2])
{
Vector2 kDiff;
Real fD0SqrLen;
bool bIntersects = Find(rkRay.Origin(),rkRay.Direction(),
rkSegment.Origin(),rkSegment.Direction(),kDiff,fD0SqrLen,riQuantity,
afT);
if ( bIntersects )
{
if ( riQuantity == 1 )
{
if ( afT[0] < 0.0f || afT[1] < 0.0f || afT[1] > 1.0f )
{
// lines intersect, but ray and segment do not
riQuantity = 0;
}
}
else
{
// ray and segment are on the same line
Real fDotRS = rkRay.Direction().Dot(rkSegment.Direction());
Real fDot0, fDot1;
if ( fDotRS > 0.0f )
{
fDot0 = kDiff.Dot(rkRay.Direction());
fDot1 = fDot0 + fDotRS;
}
else
{
fDot1 = kDiff.Dot(rkRay.Direction());
fDot0 = fDot1 + fDotRS;
}
// compute intersection of [t0,t1] and [0,+infinity]
if ( fDot0 >= 0.0f )
{
// complete overlap
Real fInvLen = 1.0f/fD0SqrLen;
afT[0] = fDot0*fInvLen;
afT[1] = fDot1*fInvLen;
}
else if ( fDot1 > 0.0f )
{
// partial overlap
afT[0] = 0.0f;
afT[1] = fDot1/fD0SqrLen;
}
else if ( fDot1 < 0.0f )
{
// no overlap
riQuantity = 0;
}
else
{
// overlap at a single end point
riQuantity = 1;
afT[0] = 0.0f;
}
}
}
return riQuantity != 0;
}
Vector2 operator*(const Ray2 &ray, float distance)
{
return Vector2(ray.GetOrigin() + ray.GetDirection() * distance);
}
// Ray Intersection
bool Intersects(const Ray2 &ray, const AARect &rect, float *distance)
{
if (rect.IsNull())
{
SetPtrValue(distance, 0.0f);
return false;
}
float lowt = 0.0f;
float t;
bool hit = false;
Vector2 hitpoint;
const Vector2 &rectMin = rect.GetMinimum();
const Vector2 &rectMax = rect.GetMaximum();
const Vector2 &rayOrig = ray.GetOrigin();
const Vector2 &rayDir = ray.GetDirection();
// Check origin inside first
if (rayOrig.x > rectMin.x && rayOrig.y > rectMin.y && rayOrig.x < rectMax.x && rayOrig.y < rectMax.y)
{
SetPtrValue(distance, 0.0f);
return true;
}
// Check each face in turn, only check closest 3
// Min x
if (rayOrig.x < rectMin.x && rayDir.x > 0)
{
t = (rectMin.x - rayOrig.x) / rayDir.x;
if (t > 0)
{
// Substitute t back into ray and check bounds and dist
hitpoint = rayOrig + rayDir * t;
if (hitpoint.y >= rectMin.y && hitpoint.y <= rectMax.y /* && (!hit || t < lowt) */)
{
if (distance == NULL)
{
return true;
}
hit = true;
lowt = t;
}
}
}
// Max x
if (rayOrig.x > rectMax.x && rayDir.x < 0)
{
t = (rectMax.x - rayOrig.x) / rayDir.x;
if (t > 0)
{
// Substitute t back into ray and check bounds and dist
hitpoint = rayOrig + rayDir * t;
if (hitpoint.y >= rectMin.y && hitpoint.y <= rectMax.y &&
(!hit || t < lowt))
{
if (distance == NULL)
{
return true;
}
hit = true;
lowt = t;
}
}
}
// Min y
if (rayOrig.y < rectMin.y && rayDir.y > 0)
{
t = (rectMin.y - rayOrig.y) / rayDir.y;
if (t > 0)
{
// Substitute t back into ray and check bounds and dist
hitpoint = rayOrig + rayDir * t;
if (hitpoint.x >= rectMin.x && hitpoint.x <= rectMax.x &&
(!hit || t < lowt))
{
if (distance == NULL)
{
return true;
}
hit = true;
lowt = t;
}
}
}
// Max y
if (rayOrig.y > rectMax.y && rayDir.y < 0)
{
t = (rectMax.y - rayOrig.y) / rayDir.y;
if (t > 0)
{
// Substitute t back into ray and check bounds and dist
hitpoint = rayOrig + rayDir * t;
if (hitpoint.x >= rectMin.x && hitpoint.x <= rectMax.x &&
(!hit || t < lowt))
{
if (distance == NULL)
{
return true;
}
hit = true;
lowt = t;
}
}
}
SetPtrValue(distance, lowt);
return hit;
}