/// Returns the distance of the given ray to this line.
/// @param d [out] Receives the distance along this line that specifies the closest point on this line to the given point.
/// @param d2 [out] Receives the distance along the other line that specifies the closest point on that line to this line.
float Ray::Distance(const Ray &other, float *d, float *d2) const
{
float u2;
float3 c = ClosestPoint(other, d, &u2);
if (d2) *d2 = u2;
return c.Distance(other.GetPoint(u2));
}
bool Polygon::Intersects(const Ray &ray) const
{
float d;
if (!PlaneCCW().Intersects(ray, &d))
return false;
return Contains(ray.GetPoint(d));
}
bool Circle::IntersectsDisc(const Ray &ray) const
{
float d;
bool intersectsPlane = ray.Intersects(ContainingPlane(), &d);
if (intersectsPlane)
return false;
return ray.GetPoint(d).DistanceSq(pos) <= r*r;
}
int Plane::Intersect(Ray& ray, IntersectResult* result) {
Normal3dF normal(0, 1, 0);
float dotA = ray.d.Dot(normal);
if (dotA >= 0) {
result = &IntersectResult::NoHit;
return 0;
}
float dotB = normal.Dot(ray.o - position);
float distance = -dotB / dotA;
*result = IntersectResult(this, distance, ray.GetPoint(distance), normal);
return 0;
}
bool Triangle::Intersects(const Ray &r, float *d, float3 *intersectionPoint) const
{
float u, v, t;
bool success = IntersectLineTri(r.pos, r.dir, a, b, c, u, v, t);
if (!success || t <= 0.f)
return false;
if (d)
*d = t;
if (intersectionPoint)
*intersectionPoint = r.GetPoint(t);
return success;
}
bool Triangle::Intersects(const Ray &r, float *d, float3 *intersectionPoint) const
{
float u, v;
float t = IntersectLineTri(r.pos, r.dir, a, b, c, u, v);
bool success = (t >= 0 && t != FLOAT_INF);
if (!success)
return false;
if (d)
*d = t;
if (intersectionPoint)
*intersectionPoint = r.GetPoint(t);
return success;
}
//http://www.qiujiawei.com/triangle-intersect/
int Triangle::Intersect(Ray& ray, IntersectResult* result) {
const VectorArray& vertices = mesh->vertices;
const Vector3dF& p0 = vertices[indexes[0]];
const Vector3dF& p1 = vertices[indexes[1]];
const Vector3dF& p2 = vertices[indexes[2]];
const Vector3dF&& e1 = p1 - p0;
const Vector3dF&& e2 = p2 - p0;
if (mesh->normals[tri_idx].isEmpty()) {
mesh->normals[tri_idx] = (e1.Cross(e2)).Normalize();
if (mesh->reverse) {
mesh->normals[tri_idx] = -mesh->normals[tri_idx];
}
}
const Normal3dF& normal = mesh->normals[tri_idx];
float nDotRay = normal.Dot(ray.d);
if (mesh->face == 0) { //only front face
if (nDotRay >= 0) {
return 0;
}
}
else if (mesh->face == 1) { //only back face
if (nDotRay <= 0) {
return 0;
}
}
//printf("nDotRay %.1f ray.d: %.2f,%.2f,%.2f len:%.1f n: %.1f,%.1f,%.1f\n", nDotRay, ray.d.x, ray.d.y, ray.d.z, ray.d.Length(), normal.x, normal.y, normal.z);
const Vector3dF& s = ray.o - p0;
const Vector3dF& s1 = ray.d.Cross(e2);
Real d = s1.Dot(e1);
if (almost_equal(d, Real(0), 2))
return 0;
d = 1. / d;
const Vector3dF& s2 = s.Cross(e1);
const Real& r1 = s2.Dot(e2);
const Real& r2 = s1.Dot(s);
const Real& r3 = s2.Dot(ray.d);
const Real& t = r1 * d;
const Real& b1 = r2 * d;
if (b1 < 0. || b1 > 1.)
return 0;
const Real& b2 = r3 * d;
if (b2 < 0. || b1 + b2 > 1.)
return 0;
const Vector3dF&& position = ray.GetPoint(t);
*result = IntersectResult(mesh, t, std::forward<const Vector3dF>(position), normal);
return 0;
}
vec Plane::ClosestPoint(const Ray &ray) const
{
assume(ray.IsFinite());
assume(!IsDegenerate());
// The plane and a ray have three configurations:
// 1) the ray and the plane don't intersect: the closest point is the ray origin point.
// 2) the ray and the plane do intersect: the closest point is the intersection point.
// 3) the ray is parallel to the plane: any point on the ray projected to the plane is a closest point.
float denom = Dot(normal, ray.dir);
if (denom == 0.f)
return Project(ray.pos); // case 3)
float t = (d - Dot(normal, ray.pos)) / denom;
if (t >= 0.f && t < 1e6f) // Numerical stability check: Instead of checking denom against epsilon, check the resulting t for very large values.
return ray.GetPoint(t); // case 2)
else
return Project(ray.pos); // case 1)
}
bool operator()(KdTree<Triangle> &tree, const KdTreeNode &leaf, const Ray &ray, float tNear, float tFar)
{
u32 *bucket = tree.Bucket(leaf.bucketIndex);
assert(bucket);
while(*bucket != KdTree<Triangle>::BUCKET_SENTINEL)
{
const Triangle &tri = tree.Object(*bucket);
float u, v, t;
t = Triangle::IntersectLineTri(ray.pos, ray.dir, tri.a, tri.b, tri.c, u, v);
bool intersects = t < std::numeric_limits<float>::infinity();
if (intersects && t >= tNear && t <= tFar && t < result.t)
{
result.t = t;
result.pos = ray.GetPoint(t);
result.triangleIndex = *bucket;
result.submeshIndex = (u32)-1;
result.barycentricUV = float2(u,v);
}
++bucket;
}
return result.t < std::numeric_limits<float>::infinity(); // If we hit a triangle, no need to visit any farther nodes, since we are only interested in the nearest hit.
}
float Ray::Distance(const Ray &other, float &d, float &d2) const
{
vec c = ClosestPoint(other, d, d2);
return c.Distance(other.GetPoint(d2));
}
Color trace(const Scene& scene, Ray ray, int depth)
{
const Color background(0,0,0);
const int maxDepth = 3;
if (depth >= maxDepth)
return background;
Color color(0,0,0);
double distance = 0;
const Primitive* prim = NULL;
int intersectionType = 0;
findNearsetIntersection(scene, ray, &prim, &distance, &intersectionType);
if (prim != NULL)
{
if (prim->IsIlluminative())
{
return prim->GetMaterial().GetColor();
}
const Vector3 intersectionPoint = ray.GetPoint(distance);
const Vector3 n = prim->GetNormal(intersectionPoint);
if (prim->GetMaterial().GetDiffuse() > 0)
{
for (Scene::ConstIterator it = scene.Begin(); it != scene.End(); it++)
{
const double intensive = getIntensity((*it), intersectionPoint, n, scene);
if (intensive != .0)
{
Vector3 x = (prim->GetMaterial().GetColor());
Vector3 y = ((*it)->GetMaterial().GetColor());
color = color + (intensive * prim->GetMaterial().GetDiffuse()) * x * y;
}
}
}
//refraction
{
const Vector3 x = ray.GetDirection();
const Vector3 y = intersectionType * (-n);
double n;
if (intersectionType == IntersectOutside)
n = 1.0 / prim->GetMaterial().GetRefractionRate();
else
n = prim->GetMaterial().GetRefractionRate();
const double sin_1 = sqrt(1 - Dot(x,y));
const double sin_2 = n * sin_1;
if (sin_2 < 1)
{
const double cos_2 = sqrt(1 - sin_2);
Vector3 xPerpendicular = x - Dot(x,y)*y;
Vector3 z = cos_2 * y + sin_2 * xPerpendicular;
z.Normalize();
if (prim->GetMaterial().GetRefraction() > 0)
{
if (intersectionType == IntersectInside)
{
color = color +
prim->GetMaterial().GetRefraction() *
exp(-prim->GetMaterial().GetAbsorptionRate()*distance) *
trace(scene, Ray(intersectionPoint, z), depth + 1);
}
else
color = color +
prim->GetMaterial().GetRefraction() * trace(scene, Ray(intersectionPoint, z), depth + 1);
}
}
}
//reflection
if (prim->GetMaterial().GetReflection() > 0)
{
const Vector3 a = ray.GetDirection();
Vector3 newA = a - 2 * (Dot(a,n)) * n;
color = color + prim->GetMaterial().GetReflection() * trace(scene, Ray(intersectionPoint, newA), depth + 1);
}
}
return color;
}