//------------------------------------------------------------------------------
bool Plane::Intersect( const Ray& _ray, Intersection& o_intersection) const
{
float rayParameter = ( m_distance - m_normal.Dot( _ray.Origin() ) ) / m_normal.Dot( _ray.Direction() );
if (rayParameter < 0.0f)
return false;
Vector position = _ray.Origin() + _ray.Direction() * rayParameter;
o_intersection = Intersection( position, m_normal,Vector2D(0,0), rayParameter, m_pMaterial );
return true;
}
// Light's Functions
void AreaLight::AccumulateIlluminationAtSurface(
const Ray &ray,
const Vector<float> &surfaceNormal,
const float &surfaceRoughness,
const Scene &scene,
Color &diffuse,
Color &specular ) const
{
if( _positions.empty() )
return;
Color areaLightDiffuse( 0 );
Color areaLightSpecular( 0 );
// Accumulate the illumination from all the positions
for(VectorList::const_iterator itr = _positions.begin(); itr != _positions.end(); ++itr )
{
const Vector<float> &lightPosition = (*itr);
Vector<float> lightRayDirection = lightPosition - ray.Origin();
const float lightRayLength = lightRayDirection.Normalize();
// If the light is out of range of the surface
if( lightRayLength > _range )
continue;
// The illumination from this light
const Ray lightRay( ray.Origin(), lightRayDirection, ray );
const Color illuminationFromLight = Illumination( lightRay, lightRayLength, scene );
if( illuminationFromLight.Magnitude2() < Maths::Tolerance )
continue;
// Calculate the illumination at the point on the surface
const Color illumination = illuminationFromLight * ( 1 - lightRayLength * _oneOverRange );
// Accumulate the diffuse
areaLightDiffuse += illumination * Maths::Max<float>(0, surfaceNormal.Dot( lightRayDirection ));
// Accumulate the specular
areaLightSpecular += illuminationFromLight * powf( Maths::Max<float>(0, ray.Direction().Dot( lightRayDirection.Reflect( surfaceNormal ) ) ), surfaceRoughness );
}
diffuse += areaLightDiffuse * (1.0f / _positions.size());
specular += areaLightSpecular * (1.0f / _positions.size());
}
bool Plane::Intersects(const Ray& r,float& result) const
{
float VD=Vector3::Dot(normal,r.Dir());
if(VD==0)
return false;
float V0=-(Vector3::Dot(normal,r.Origin())+distance);
result=V0/VD;
if(result<EPSILON) //role of EPSILON is explained in "common.h"
return false;
return true;
}
Ray Shape::Reflect(const Point& rReflectFrom, const Ray& rIncidentRay) const
{
Ray result; // the reflected ray
Vector result_direction; // the reflected direction vector
Vector incident_unit = rIncidentRay.Direction().Normalize();
Vector normal = this->Normal(rReflectFrom, rIncidentRay.Origin() );
if ( !normal.IsSameDirection(incident_unit) )
normal.ReverseDirection(); // we want the normal in the same direction of the incident ray.
result.Origin(rReflectFrom);
result.Direction( normal*2.0*normal.Dot(incident_unit) - incident_unit );
/*
if ( normal.Dot(rIncidentRay.Direction().Normalize()) < 0.0 )
normal.ReverseDirection();
result.Origin(rReflectFrom);
result.Direction((normal*2.0) - rIncidentRay.Direction().Normalize());
*/
return result;
}
//------------------------------------------------------------------------------
bool Sphere::Intersect( const Ray& _ray, Intersection& o_intersection ) const
{
Vector p = Position() - _ray.Origin();
float pDotRayDir = p.Dot( _ray.Direction() );
// ray pointing away from sphere
if(( pDotRayDir )<0 )
return false;
/* pDotRayDir distance between origin and P's projection on Ray
p.Dot( p ) magnitude sqaured of p
O, O,
|\ |\
| \ | \
R. \ p R. \ p
| \ ,-- | \ ,--
| '\ | '\
| ' \ | ' \
|'_____. |___'______ .
Q ' r P Q ' r P
'
figure 1 ) figure 2 )
1 ) rSquared + RSquared = PSquared
2 ) rSquared + RSquared < PSquared
*/
float temp = m_radiusSquared + pDotRayDir * pDotRayDir - p.Dot( p );
// no intersection
if ( temp < 0.0f )
{
return false;
}
//rayParameter = pDotRayDir - sqrtf( temp );
float rayParameter;
// if ray origin is inside sphere
if ( ( pDotRayDir - sqrtf( temp ) ) < 0.0f )
{
rayParameter = pDotRayDir + sqrtf( temp );
Vector intersectionPos= _ray.GetPosition( rayParameter );
Vector normal = ( intersectionPos - Position() ).Normalise();
o_intersection = Intersection( intersectionPos, normal, Vector2D(0,0), rayParameter, g_air );
//intersection inside sphere;
return true;
}
rayParameter = pDotRayDir - sqrtf( temp );
Vector intersectionPos = _ray.GetPosition( rayParameter );
Vector normal = ( intersectionPos - Position() ).Normalise();
o_intersection = Intersection( intersectionPos, normal, Vector2D(0,0), rayParameter, m_pMaterial );
return true;
}
bool Plane::Intersect(const Ray& ray, Intersection& intersection, void* additional_data) const
{
float dir_norm = ray.Direction().DotProduct(m_Orientation);
if (abs(dir_norm) < std::numeric_limits<float>::epsilon())
return false;
float t = (m_Center - ray.Origin()).DotProduct(m_Orientation) / dir_norm;
Range<float> range = ray.EffectRange();
if (Math::Contain(t, range))
{
intersection.SetDistance(t);
intersection.SetIntersectObject((IIntersectTarget*)this);
intersection.SetTestObject(&ray);
return true;
}
return false;
}
bool AABB::Intersect(const Ray& ray, Intersection& intersection, void* additional_data) const
{
++Profiler::numRayVolumeTestsPerFrame;
Vector3 origin = ray.Origin();
Vector3 inversed_dir = ray.InvDirection();
Range<float> t, t_y, t_z;
if (inversed_dir.X() >= 0)
{
t.Max = (m_MaxExtent.X() - origin.X()) * inversed_dir.X();
t.Min = (m_MinExtent.X() - origin.X()) * inversed_dir.X();
}
else
{
t.Min = (m_MaxExtent.X() - origin.X()) * inversed_dir.X();
t.Max = (m_MinExtent.X() - origin.X()) * inversed_dir.X();
}
if (inversed_dir.Y() >= 0)
{
t_y.Max = (m_MaxExtent.Y() - origin.Y()) * inversed_dir.Y();
t_y.Min = (m_MinExtent.Y() - origin.Y()) * inversed_dir.Y();
}
else
{
t_y.Min = (m_MaxExtent.Y() - origin.Y()) * inversed_dir.Y();
t_y.Max = (m_MinExtent.Y() - origin.Y()) * inversed_dir.Y();
}
if (t.Min > t_y.Max || t_y.Min > t.Max)
return false;
if (t.Min < t_y.Min)
t.Min = t_y.Min;
if (t.Max > t_y.Max)
t.Max = t_y.Max;
if (inversed_dir.Z() >= 0)
{
t_z.Max = (m_MaxExtent.Z() - origin.Z()) * inversed_dir.Z();
t_z.Min = (m_MinExtent.Z() - origin.Z()) * inversed_dir.Z();
}
else
{
t_z.Min = (m_MaxExtent.Z() - origin.Z()) * inversed_dir.Z();
t_z.Max = (m_MinExtent.Z() - origin.Z()) * inversed_dir.Z();
}
if (t.Min > t_z.Max || t_z.Min > t.Max)
return false;
if (t.Min < t_z.Min)
t.Min = t_z.Min;
if (t.Max > t_z.Max)
t.Max = t_z.Max;
Range<float> range = ray.EffectRange();
if (Math::Contain(t.Min, range))
intersection.SetDistance(t.Min);
else if (Math::Contain(t.Max, range))
intersection.SetDistance(0.f);
else if (range.Min > t.Min && range.Max < t.Max)
intersection.SetDistance(0.f);
else
return false;
intersection.SetIntersectObject((IIntersectTarget*)this);
intersection.SetTestObject(&ray);
return true;
}
//------------------------------------------------------------------------
Ray operator * ( const Matrix& _transform, const Ray& _ray )
{
return Ray( _transform * _ray.Origin(), _transform * _ray.Direction(), _ray.GetMaterial() );
}
bool Kdtree::intersect(Ray &r, HitInfo* pHitInfo )
{
pHitInfo->bHasInfo = false;
pHitInfo->hitTime = INFINITY;
Point3 invDir(1.f/r.Direction().X(), 1.f/r.Direction().Y(), 1.f/r.Direction().Z());
float tmin = 0;
float tmax = 0;
// intersect bounding box
if(!m_Bounds.Intersect(r, tmin, tmax))
{
return false;
}
bool done = false;
list<TODO> todo;
BSPNode *current = &m_pTree[0];
while(!done)
{
if(pHitInfo->hitTime < tmin)
{
break;
}
if(!current->isLeaf())
{
int axis = current->splitAxis();
float split = current->SplitPos();
split = (split > -EPSILON && split < EPSILON) ? 0 : split;
float tplane = (split - r.Origin()[axis]) * invDir[axis];
BSPNode *first, *second;
// decide which child to check first
int below = r.Origin()[axis] <= split;
if(below)
{
first = &m_pTree[current->leftChild];
second = &m_pTree[current->leftChild+1];
}
else
{
second = &m_pTree[current->leftChild];
first = &m_pTree[current->leftChild+1];
}
if(tplane == 0)//(tplane > -EPS && tplane < EPS)
{
if(invDir[axis] > 0)
current = second;
else
current = first;
}
else if(tplane >= tmax || tplane < 0)
current = first;
else if(tplane <= tmin)
current = second;
else
{
TODO temp;
temp.node = second;
temp.tmax = tmax;
temp.tmin = tplane;
todo.push_front(temp);
current = first;
tmax = tplane;
}
}
else
{
// check all intersect in this leaf
std::list<IPrimitive*>::const_iterator it;
if(current->m_pPrimList)
{
for(int i = 0; i < current->nTriangle(); i++)
{
HitInfo thisHit;
current->m_pPrimList[i]->intersect( r, &thisHit);
if( thisHit.hitTime < pHitInfo->hitTime )
{
*pHitInfo = thisHit;
}
} // end checking all Primitives in this leaf
}
if(!todo.empty())
{
TODO temp = (*todo.begin());
current = temp.node;
tmin = temp.tmin;
tmax = temp.tmax;
todo.pop_front();
}
else
{
done = true;
}
} // end check leaf
} // end while loop
return pHitInfo->bHasInfo;
}
Vector3D RecursiveTraceStrategy::operator ()(const Ray &tracer, const int depth, const double refrIndex) const
{
double usableEpsilion = std::numeric_limits<float>::epsilon(); // Epsilon for a float will always produce a usable delta for doubles (this is a little bit of a bad idea)
//begin traversing the world
//
double closestDist = std::numeric_limits<double>::infinity();
std::shared_ptr<Shape> closest;
for(std::shared_ptr<Shape> s : _Shapes)
{
//find the distance from the origin to the point of intersection
//
double dist = s->Intersect(tracer);
if(dist > 0)
{
if(dist > closestDist)
continue;
closestDist = dist;
closest = s;
}
}
if(closest == nullptr)
return {0.0, 0.0, 0.0};
Vector3D compositeColor = {0.0, 0.0, 0.0};
//calculate the position vector of the point of intersection using the line along the current ray
//
Vector3D intersectPoint = tracer.Origin() + (tracer.Direction() * closestDist);
//get the unit normal at the point of intersection to apply shading
Vector3D unitNormal = closest->Normal(intersectPoint);
// Get the material of the shape
std::shared_ptr<const Material> shapeMat = closest->SurfaceMaterial();
//traverse the world again looking for lights
//
for(std::shared_ptr<Light> l : _Lights)
{
//retrieve the position vector of the light source (treated as a uniform pointline source)
Vector3D lightCenter = l->Position();
//create a vector from the intersect point to the light source
Vector3D toLight = (lightCenter - intersectPoint).Normalize();
//calculate occlusion (for a pointlike source this is boolean)
// Note that I'm adding a small offset in the direction we want to go so that we don't
// intersect with the current shape
Ray occlRay(intersectPoint + (usableEpsilion * toLight), toLight);
double visibility = 1.0; // occlusion = 1 - visibility
for(std::shared_ptr<Shape> o : _Shapes)
{
double d = o->Intersect(occlRay);
if(d > 0)
{
visibility = 0.0;
break;
}
}
if(visibility > 0)
{
//apply lighting function
//
double radianceDist = shapeMat->Brdf(tracer.Direction(), toLight, unitNormal);
std::shared_ptr<const Material> lightMat = l->LightMaterial();
compositeColor += shapeMat->Color().Weight(lightMat->Color() * radianceDist * visibility);
}
}
//apply reflections
//
double refl = shapeMat->Reflectance();
double refr = shapeMat->Refractance();
double rindex = shapeMat->IndexOfRefraction();
if(refl > 0.0 && depth < _MaxTraceIterations)
{
Vector3D reflectionDir;
reflectionDir = tracer.Direction() - 2.0 * (tracer.Direction() * unitNormal) * unitNormal;
Ray reflected(intersectPoint + (usableEpsilion * reflectionDir), reflectionDir);
Vector3D reflCol = (*this)(reflected, depth + 1, refrIndex);
compositeColor += shapeMat->Color().Weight(refl * reflCol);
}
//apply refractions
//
if(refr > 0.0 && depth < _MaxTraceIterations)
{
// This is basically Snell's law
double relIndex = refrIndex / rindex;
Vector3D refractionNormal = unitNormal;
// The cosine between the incident ray's direction and the unit normal should be non-positive (e.g. angle in [PI/2, PI]), otherwise normals need to be reversed
if(refractionNormal * tracer.Direction() > 0)
refractionNormal *= -1;
double cosI = - (refractionNormal * tracer.Direction());
double cosT2 = 1.0 - (relIndex * relIndex) * (1.0 - (cosI * cosI));
if(cosT2 > 0.0)
{
Vector3D refractedDir = (relIndex * tracer.Direction()) + (relIndex * cosI - sqrt(cosT2)) * refractionNormal;
Ray refracted(intersectPoint + (usableEpsilion * refractedDir), refractedDir);
Vector3D refrCol = (*this)(refracted, depth + 1, rindex);
compositeColor += shapeMat->Color().Weight(refr * refrCol);
}
}
return compositeColor;
}
//------------------------------------------------------------------------------
//from[http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_7_Kd-Trees_and_More_Speed.shtml]
bool Triangle::Intersect( const Ray& _ray, Intersection& o_intersection ) const
{
/* v0
/\
b / \c
v1/_____\ v2
a
*/
Vector b = m_vertex[1] - m_vertex[0];
Vector c = m_vertex[2] - m_vertex[0];
Vector normal = b.Cross (c);
//triangle is a line
if( RealCompare( normal.Dot(normal), 0.0f, 0.0000000001 ) )
return false;
Normalise(normal);
//ray-plane intersection
float rayParameter = normal.Dot ( m_vertex[0] - _ray.Origin () ) / normal.Dot ( _ray.Direction () );
//no intersection on the plane
if ( rayParameter < 0.0f )
{
return false;
}
//if on the plane
//solve the problem on 2d
//get dominant axis of normal
uint8_t axis = normal.DominantAxis();
// p = p1*v1 + p2*v2 + p3*v3
// p1+ p2+ p3 =1
// p2 ( v2 - v1 ) + p3 ( v3 - v1 ) = intersection - v1
Vector intersectionPos = _ray.Origin () + rayParameter * _ray.Direction ();
Vector diff = intersectionPos - m_vertex[0];
float bU, bV, cU, cV, diffU, diffV;
uint8_t axisU = ( axis + 1 )%3;
uint8_t axisV = ( axis + 2 )%3;
diffU = diff[axisU];
diffV = diff[axisV];
bU = b[axisU];
bV = b[axisV];
cU = c[axisU];
cV = c[axisV];
float tmp = bU * cV - bV * cU ;
float p2 = ( cV * diffU - cU * diffV ) / tmp;
if ( p2<0.0 )
{
return false;
}
float p3 = ( bU * diffV - bV * diffU ) / tmp;
if ( p3<0.0 )
{
return false;
}
if ( p2+ p3> 1.0 )
{
return false;
}
float p1 = 1.0 - p2 - p3;
Vector averageNormal = p1 * m_normal[0] + p2 * m_normal[1] + p3 * m_normal[2];
Vector2D averageTexCoord = p1 * m_texture[0] + p2 * m_texture[1] + p3 * m_texture[2];
Normalise(averageNormal);
if( averageNormal.Dot( _ray.Direction() ) > 0 )
{
return false;
}
if( m_pMaterial->kf() > 0 && _ray.Direction().Dot( averageNormal ) > 0 )
{
//when calculating refraction for the ray inside object
o_intersection = Intersection ( intersectionPos, averageNormal, averageTexCoord, rayParameter, g_air );
}
else if( m_pMaterial->kf()==0 && _ray.Direction().Dot(averageNormal ) > 0)
{
printf("back face\n");
o_intersection = Intersection ( intersectionPos, averageNormal, averageTexCoord, rayParameter, m_pMaterial );
}
else
o_intersection = Intersection ( intersectionPos, averageNormal, averageTexCoord, rayParameter, m_pMaterial );
return true;
}