RayIntersection SpatialList::rayIntersection(Ray ray) const {
if (objectsVector.empty() || (boundingBox && !boundingBox->rayIntersection(ray).intersects))
return RayIntersection();
RayIntersection first_intersection = RayIntersection();
for (unsigned int i = 0; i < objectsVector.size(); i++) {
RayIntersection intersection = objectsVector[i]->rayIntersection(ray);
if (intersection.intersects && (!first_intersection.intersects || intersection < first_intersection)) {
first_intersection = intersection;
}
}
return first_intersection;
}
RayIntersection Sphere::intersectWithRay(const Ray &ray) const {
// Solve square equation x^2 + b * x + c = 0
Vector cameraToRayOrigin = ray.getOriginPosition() - mCenter;
float b = ray.getDirection().dotProduct(cameraToRayOrigin);
float c = cameraToRayOrigin.dotProduct(cameraToRayOrigin) - mRadius * mRadius;
float descriminant = b * b - c;
if (descriminant < 0) {
return RayIntersection();
}
descriminant = sqrt(descriminant);
std::vector<float> intersectionDistances;
float closestRoot = -1.f;
// Get closest root
float root = -b - descriminant;
float rayExit = -1.f;
if (root >= 0.f) {
closestRoot = root;
intersectionDistances.push_back(root);
}
root = -b + descriminant;
if (root >= 0.f) {
intersectionDistances.push_back(root);
if (closestRoot < 0.f) {
closestRoot = root;
} else if (root < closestRoot) {
rayExit = closestRoot;
closestRoot = root;
} else {
rayExit = root;
}
}
if (closestRoot > 0.f) {
if (rayExit < 0.f) {
intersectionDistances.insert(intersectionDistances.begin(), 0.f);
}
SpherePointer pointer = SpherePointer(new Sphere(*this));
return RayIntersection(true, pointer, closestRoot, getNormal(ray, closestRoot), intersectionDistances);
}
return RayIntersection();
}
std::vector<RayIntersection> FastArc::RayIntersects(gp_Pnt p)
{
std::vector<RayIntersection> ret;
double y = p.Y() - C.Y();
if(fabs(y) > rad)
return ret;
double x1 = sqrt(rad*rad - y*y);
double x2 = x1+C.X();
x1 = C.X()-x1;
if(x1 < p.X())
ret.push_back(RayIntersection(GetU(x1,p.Y()),gp_Pnt(x1,p.Y(),0),false,false));
if(x2 < p.X())
ret.push_back(RayIntersection(GetU(x2,p.Y()),gp_Pnt(x2,p.Y(),0),false,false));
return ret;
}
RayIntersection Plane::intersectWithRay(const Ray &ray) const {
float cosineRayNormal = mNormal.dotProduct(ray.getDirection());
if (fabs(cosineRayNormal) < FLOAT_ZERO)
{
return RayIntersection();
}
float distance = -(ray.getOriginPosition().dotProduct(mNormal) + mDistance) / cosineRayNormal;
if (distance > 0.0)
{
PlanePointer pointer = PlanePointer(new Plane(*this));
std::vector<float> intersectionDistances;
intersectionDistances.push_back(distance);
return RayIntersection(true, pointer, distance, getNormal(ray, distance), intersectionDistances);
}
return RayIntersection();
}
RayIntersection TrianglePatch::intersectWithRay(const Ray &ray) const {
Vector rayOrigin = ray.getOriginPosition();
Vector rayDirection = ray.getDirection();
Vector e1 = mVertex1->getCoordinates() - mVertex0->getCoordinates();
Vector e2 = mVertex2->getCoordinates() - mVertex0->getCoordinates();
Vector pvector = rayDirection.crossProduct(e2);
float determinant = e1.dotProduct(pvector);
if (fabs(determinant) < FLOAT_ZERO) {
return RayIntersection();
}
const float invertedDeterminant = 1.0f / determinant;
Vector tvec = rayOrigin - mVertex0->getCoordinates();
float lambda = tvec.dotProduct(pvector);
lambda *= invertedDeterminant;
if (lambda < 0.0f || lambda > 1.0f) {
return RayIntersection();
}
Vector qvec = tvec.crossProduct(e1);
float mue = rayDirection.dotProduct(qvec);
mue *= invertedDeterminant;
if (mue < 0.0f || mue + lambda > 1.0f) {
return RayIntersection();
}
float f = e2.dotProduct(qvec);
f = f * invertedDeterminant - FLOAT_ZERO;
if (f < FLOAT_ZERO) {
return RayIntersection();
}
TrianglePatchPointer pointer = TrianglePatchPointer(new TrianglePatch(*this));
return RayIntersection(true, pointer, f, lambda, mue);
}
bool
Sphere::closestIntersectionModel(const Ray &ray, double maxLambda, RayIntersection& intersection) const
{
// Implicit sphere: (x-c)^2-r^2 = 0
// r = 1, c=0
// x^2 = 1
// Ray: x = o+t*d
// Solve: 0=(o+t*d)^2 -1
// 0 = t^2*(d*d) + t*(2*o*d) + (o*o-1)
// Then, these are the 2 possible solutions
// t0 = 0.5*(-b-sqrt(b*b - 4*a))
// simplify
// t01 = -o.d +- sqrt( (o.d)^2 - o.o + 1)
const Vec3d &d = ray.direction();
const Vec3d &o = ray.origin();
double b = dot(o,d);
double c = o.lengthSquared() - 1;
double ds = b*b - c;
//discriminant is negative, no intersection
if(ds < 0)
return false;
double dssqr = sqrt(ds);
double t0 = -b-dssqr;
double t1 = -b+dssqr;
double lambda = t0;
//ray starts inside sphere, discard first hit
if(t0 < 0)
lambda = t1;
if(lambda < 0 || lambda > maxLambda)
return false;
// Compute intersection point
const Vec3d p = ray.pointOnRay(lambda);
// Compute parameterization of intersection point
const double theta = std::atan2(p[1], p[0]);
const double phi = std::acos (p[2]);
const Vec3d uvw(theta,phi,double(0));
intersection = RayIntersection(ray,shared_from_this(),lambda,ray.pointOnRay(lambda),uvw);
return true;
}
bool IndexedTriangleMesh::closestIntersectionModel(const Ray &ray, double maxLambda, RayIntersection& intersection) const
{
double closestLambda = maxLambda;
Vec3d closestbary;
int closestTri = -1;
Vec3d bary;
double lambda;
// Loop over all stored triangles to find a possible intersection between ray
// and any triangle
for (size_t i=0;i<mIndices.size();i+=3)
{
const int i0 = mIndices[i+0];
const int i1 = mIndices[i+1];
const int i2 = mIndices[i+2];
if (Intersection::lineTriangle(ray,mVertexPosition[i0],mVertexPosition[i1],mVertexPosition[i2],bary,lambda) &&
lambda > 0 && lambda < closestLambda)
{
closestLambda = lambda;
closestbary = bary;
closestTri = (int)i;
}
}
// If an intersection occurred, compute the normal and the uv coordinates based
// on the barycentric coordinates of the hit point
if (closestTri >= 0)
{
const int i0 = mIndices[closestTri+0];
const int i1 = mIndices[closestTri+1];
const int i2 = mIndices[closestTri+2];
Vec3d n;
if(mVertexNormal.empty())
n = cross(mVertexPosition[i1]-mVertexPosition[i0],mVertexPosition[i2]-mVertexPosition[i0]).normalize();
else
n = (mVertexNormal[i0]*closestbary[0]+
mVertexNormal[i1]*closestbary[1]+
mVertexNormal[i2]*closestbary[2]).normalize();
Vec3d uvw(0,0,0);
if(!mVertexTextureCoordinate.empty())
uvw = (mVertexTextureCoordinate[i0]*closestbary[0]+
mVertexTextureCoordinate[i1]*closestbary[1]+
mVertexTextureCoordinate[i2]*closestbary[2]);
intersection=RayIntersection(ray,shared_from_this(),closestLambda,n,uvw);
return true;
}
return false;
}
bool
CollisionGeometry::closestIntersectionModel(const Ray &ray, float maxLambda, RayIntersection& intersection) const
{
const BVTree &collisionTree = mInstance ? mInstance->mCollisionTree : mCollisionTree;
const std::vector<Vec3f> &collisionPositions = mInstance ? mInstance->mCollisionPositions : mCollisionPositions;
const std::vector<Vec3f> &collisionNormals = mInstance ? mInstance->mCollisionNormals : mCollisionNormals;
const std::vector<Vec3i> &collisionIndices = mInstance ? mInstance->mCollisionIndices : mCollisionIndices;
const std::vector<int> &intersectionCandidates = collisionTree.intersectBoundingBoxes(ray,maxLambda);
float closestLambda = maxLambda;
Vec3f closestbary;
int closestTri = -1;
Vec3f bary;
float lambda;
for(size_t i=0;i<intersectionCandidates.size();++i)
{
const int triangleIndex = intersectionCandidates[i];
const int idx0 = collisionIndices[triangleIndex][0];
const int idx1 = collisionIndices[triangleIndex][1];
const int idx2 = collisionIndices[triangleIndex][2];
const Vec3f &p0 = collisionPositions[idx0];
const Vec3f &p1 = collisionPositions[idx1];
const Vec3f &p2 = collisionPositions[idx2];
if (Intersection::lineTriangle(ray,p0,p1,p2,bary,lambda) &&
lambda > 0 && lambda < closestLambda)
{
closestLambda = lambda;
closestbary = bary;
closestTri = triangleIndex;
}
}
if (closestTri >= 0)
{
const int i0 = collisionIndices[closestTri][0];
const int i1 = collisionIndices[closestTri][1];
const int i2 = collisionIndices[closestTri][2];
Vec3f n = collisionNormals[i0]*closestbary[0]+
collisionNormals[i1]*closestbary[1]+
collisionNormals[i2]*closestbary[2];
intersection = RayIntersection(ray,closestLambda,n);
return true;
}
return false;
}
bool
Sphere::closestIntersectionModel(const Ray &ray, double maxLambda, RayIntersection& intersection) const
{
/*
A ray and a sphere intersect if and only if
(o + lambda * d - c)^2 = r^2
where
o is the origin of the ray
d is the direction vector of the ray
c is the center of the sphere
r is the radius of the sphere
Since o and d are known, c = O and r = 1, we have
a quadratic equation in lambda. We solve it using calcRoots()
which is a slightly modified version of the classical
quadratic formula (as described in [1]).
[1] http://wiki.delphigl.com/index.php/Tutorial_Raytracing_-_Grundlagen_I#Quadratische_Gleichungen
*/
// a, b and c are the constants in
// a * lambda^2 + b * lambda + c = 0.
double a = dot(ray.direction(), ray.direction());
double b = 2 * dot(ray.direction(), ray.origin());
double c = dot(ray.origin(), ray.origin()) - 1;
// t1 and t2 are the solutions of our quadratic equation.
// W.l.o.g. t1 <= t2 (calcRoots takes care of that)
// calcRoots return the number of roots it found (zero, one or two).
double t1, t2;
int roots = calcRoots(a, b, c, t1, t2);
bool doIntersect = false;
if (roots > 0) {
// There is a solution, we just need the (smallest) positve one.
double lambda = t1 >= 0 ? t1 : t2;
if (lambda >= 0.0 && lambda < maxLambda) {
doIntersect = true;
intersection = RayIntersection(ray, shared_from_this(), lambda, ray.pointOnRay(lambda), Vec3d(0,0,0));
}
}
return doIntersect;
}
bool
Triangle::closestIntersectionModel(const Ray &ray, double maxLambda, RayIntersection& intersection) const
{
Vec3d bary;
double lambda;
if(!Intersection::lineTriangle(ray,mVertices[0],mVertices[1],mVertices[2],bary,lambda))
return false;
// Intersection is inside triangle if 0<=u,v,w<=1
if(lambda<0 || lambda>maxLambda)
return false;
const Vec3d normal = cross(mVertices[1]-mVertices[0],mVertices[2]-mVertices[0]).normalize();
const Vec3d uvw = mUVW[0]*bary[0]+mUVW[1]*bary[1]+mUVW[2]*bary[2];
intersection = RayIntersection(ray,shared_from_this(),lambda,normal,uvw);
return true;
}
std::vector<RayIntersection> FastLine::RayIntersects(gp_Pnt pnt)
{
std::vector<RayIntersection> ret;
//If this line is significantly horizontal, there is nothing good
//we can do here
if(B.Y() < A.Y() + TOLERANCE/4 && B.Y() > A.Y() - TOLERANCE/4)
return ret;
if((pnt.Y() < B.Y() + TOLERANCE && pnt.Y() > A.Y() - TOLERANCE)||
(pnt.Y() > B.Y() - TOLERANCE && pnt.Y() < A.Y() + TOLERANCE))
{
if(fabs(A.Y() - B.Y()) < TOLERANCE)
return ret;
double u = (pnt.Y() - A.Y())/(B.Y()-A.Y());
double x = GetXatU(u);
if(x < pnt.X())
ret.push_back(RayIntersection(u,gp_Pnt(x,pnt.Y(),0),false,false));
}
return ret;
}
bool
Plane::closestIntersectionModel(const Ray &ray, double maxLambda, RayIntersection &intersection) const {
// Solve linear equation for lambda
// see also http://en.wikipedia.org/wiki/Line-plane_intersection
double a = dot((-ray.origin()), (mNormal));
double d = dot(ray.direction(), (mNormal));
// No intersection if ray is (almost) parallel to plane
if (fabs(d) < Math::safetyEps())
return false;
double lambda = a / d;
// Only intersections in [0,1] range are valid.
if (lambda < 0.0 || lambda > maxLambda)
return false;
const Vec3d p = ray.pointOnRay(lambda);
const Vec3d uvw(dot(p, mTangent), dot(p, mBitangent), double(0));
intersection = RayIntersection(ray, shared_from_this(), lambda, mNormal, uvw);
return true;
}
RayIntersection Cone::intersectWithRay(const Ray &ray) const {
Vector coneAxis = (mBottomCenter - mTop);
coneAxis.normalize();
Vector rayOriginPosition = ray.getOriginPosition();
Vector rayDirection = ray.getDirection();
Vector bottomCenterToRayOrigin = rayOriginPosition - mTop;
float rayDirectionDotAxis = rayDirection.dotProduct(coneAxis);
float bottomCenterToRayOriginDotAxis = bottomCenterToRayOrigin.dotProduct(coneAxis);
float radiansPerHeight = mRadius / (mBottomCenter - mTop).length();
Vector u = rayDirection + coneAxis * (-rayDirectionDotAxis);
Vector v = bottomCenterToRayOrigin + coneAxis * (-bottomCenterToRayOriginDotAxis);
float w = bottomCenterToRayOriginDotAxis * radiansPerHeight;
float radiansPerDirection = rayDirectionDotAxis * radiansPerHeight;
// Solve square equation a * x^2 + b * x + c = 0
float a = u.dotProduct(u) - radiansPerDirection * radiansPerDirection;
float closestRoot = -1.f;
float rayExit = -1.f;
float root = 0.f;
std::vector<float> intersectionDistances;
if (fabs(a) > FLOAT_ZERO) {
float b = 2 * (u.dotProduct(v) - w * radiansPerDirection);
float c = v.dotProduct(v) - w * w;
float discriminant = b * b - 4 * a * c;
if (discriminant < 0.0) {
return RayIntersection();
}
discriminant = sqrtf(discriminant);
float denominator = 1.0 / (2.0 * a);
root = (-b - discriminant) * denominator;
if (root > 0.0) {
Vector point = ray.getPointAt(root);
Vector bottomCenterToPoint = point - mTop;
Vector topToPoint = point - mBottomCenter;
if (coneAxis.dotProduct(bottomCenterToPoint) > 0.0 && (-coneAxis).dotProduct(topToPoint) > 0.0) {
intersectionDistances.push_back(root);
closestRoot = root;
}
}
root = (-b + discriminant) * denominator;
if (root > 0.0) {
Vector point = ray.getPointAt(root);
Vector bottomCenterToPoint = point - mTop;
Vector topToPoint = point - mBottomCenter;
if (coneAxis.dotProduct(bottomCenterToPoint) > 0.0 && (-coneAxis).dotProduct(topToPoint) > 0.0) {
intersectionDistances.push_back(root);
if (closestRoot < 0.0) {
closestRoot = root;
} else if (root < closestRoot) {
rayExit = closestRoot;
closestRoot = root;
} else {
rayExit = root;
}
}
}
}
// Intersection with bottom
if (fabs(rayDirectionDotAxis) < FLOAT_ZERO) {
if (closestRoot > 0.0) {
if (rayExit < 0.f) {
intersectionDistances.insert(intersectionDistances.begin(), 0.f);
}
ConePointer pointer = ConePointer(new Cone(*this));
return RayIntersection(true, pointer, closestRoot, getNormal(ray, closestRoot), intersectionDistances);
}
return RayIntersection();
}
// Intersection with top and bottom points
root = (-coneAxis).dotProduct(rayOriginPosition - mBottomCenter) / rayDirectionDotAxis;
if (root > 0.0)
{
Vector topToPoint = ray.getPointAt(root) - mBottomCenter;
if (topToPoint.dotProduct(topToPoint) < mRadius * mRadius)
{
intersectionDistances.push_back(root);
if (closestRoot < 0.0) {
closestRoot = root;
rayExit = root;
} else if (root < closestRoot) {
rayExit = closestRoot;
closestRoot = root;
} else {
rayExit = root;
}
}
}
if (closestRoot > 0.0) {
if (rayExit < 0.0) {
intersectionDistances.insert(intersectionDistances.begin(), 0.f);
}
ConePointer pointer = ConePointer(new Cone(*this));
return RayIntersection(true, pointer, closestRoot, getNormal(ray, closestRoot), intersectionDistances);
}
return RayIntersection();
}