int Bubble::Collides(R3Mesh* mesh, R3Vector offset) {
R3Box box = mesh -> bbox;
R3Vector SepAxis = pos - (box.Centroid() + offset);
double dist = SepAxis.Length();
SepAxis.Normalize();
double x = SepAxis.X();
double y = SepAxis.Y();
double z = SepAxis.Z();
if (x >= y && x >= z && x != 0)
SepAxis /= x;
else if (y >= x && y >= z != 0)
SepAxis /= y;
else if (z != 0)
SepAxis /= z;
double x_len = box.XLength();
double y_len = box.YLength();
double z_len = box.ZLength();
//effective radius
SepAxis.SetX(x * x_len/2.0);
SepAxis.SetY(y * y_len/2.0);
SepAxis.SetZ(z * z_len/2.0);
if (dist <= (size + SepAxis.Length()))
return 1;
return 0;
}
double R3Distance(const R3Line& line1, const R3Line& line2)
{
// Return distance from line to line (Riddle p. 905)
R3Vector v = line1.Vector();
v.Cross(line2.Vector());
return v.Dot(line1.Point() - line2.Point());
}
// compute the ray reflected from the incoming ray r at intersection i
R3Ray GetReflectedRay(R3Intersection i, R3Ray r)
{
// add offset to point to ensure the same intersection is not found again due to floating point error
R3Point offset = i.position + i.normal * EPSILON;
R3Vector v = -r.Vector();
return R3Ray(offset, 2 * v.Dot(i.normal) * i.normal - v);
}
double R3Distance(const R3Point& point, const R3Line& line)
{
// Return distance from point to line (Riddle p. 904)
R3Vector v = line.Vector();
v.Cross(point - line.Point());
return v.Length();
}
R3Point
operator-(const R3Point& point, const R3Vector& vector)
{
return R3Point(point.X() - vector.X(),
point.Y() - vector.Y(),
point.Z() - vector.Z());
}
RNBoolean R3Contains(const R3Sphere& sphere, const R3Box& box)
{
// Return whether sphere contains box
R3Vector v = box.Centroid() - sphere.Center();
R3Point corner = box.Corner(v.Octant());
return R3Contains(sphere, corner);
}
void R3MeshFace::
UpdatePlane(void)
{
// Check number of vertices
int nvertices = vertices.size();
if (nvertices < 3) {
plane = R3null_plane;
return;
}
// Compute centroid
R3Point centroid = R3zero_point;
for (int i = 0; i < nvertices; i++)
centroid += vertices[i]->position;
centroid /= nvertices;
// Compute best normal for counter-clockwise array of vertices using newell's method
R3Vector normal = R3zero_vector;
const R3Point *p1 = &(vertices[nvertices-1]->position);
for (int i = 0; i < nvertices; i++) {
const R3Point *p2 = &(vertices[i]->position);
normal[0] += (p1->Y() - p2->Y()) * (p1->Z() + p2->Z());
normal[1] += (p1->Z() - p2->Z()) * (p1->X() + p2->X());
normal[2] += (p1->X() - p2->X()) * (p1->Y() + p2->Y());
p1 = p2;
}
// Normalize normal vector
normal.Normalize();
// Update face plane
plane.Reset(centroid, normal);
}
RNRgb R3PointLight::
Reflection(const R3Brdf& brdf, const R3Point& eye,
const R3Point& point, const R3Vector& normal) const
{
// Check if light is active
if (!IsActive()) return RNblack_rgb;
// Get material properties
const RNRgb& Dc = brdf.Diffuse();
const RNRgb& Sc = brdf.Specular();
RNScalar s = brdf.Shininess();
// Get light properties
RNScalar I = IntensityAtPoint(point);
R3Vector L = DirectionFromPoint(point);
const RNRgb& Ic = Color();
// Compute geometric stuff
RNScalar NL = normal.Dot(L);
if (RNIsNegativeOrZero(NL)) return RNblack_rgb;
R3Vector R = (2.0 * NL) * normal - L;
R3Vector V = eye - point;
V.Normalize();
RNScalar VR = V.Dot(R);
// Compute diffuse reflection
RNRgb rgb = (I * NL) * Dc * Ic;
// Compute specular reflection
if (RNIsPositive(VR)) rgb += (I * pow(VR,s)) * Sc * Ic;
// Return total reflection
return rgb;
}
static R3Vector calculate_spring_force(R3Particle* p)
{
R3Vector spring_force = R3Vector(0, 0, 0);
R3Vector vp = p->velocity;
R3Vector D;
double d;
double ks;
double kd;
double s;
R3Particle* q;
R3Vector vq;
for (unsigned int i = 0; i < p->springs.size(); i++)
{
if (p->springs[i]->particles[0] == p)
q = p->springs[i]->particles[1];
else
q = p->springs[i]->particles[0];
vq = q->old_velocity;
s = p->springs[i]->rest_length;
ks = p->springs[i]->ks;
kd = p->springs[i]->kd;
D = q->position - p->position;
d = D.Length();
spring_force += (ks * (d - s) + kd * (vq - vp).Dot(D)) * D;
}
return spring_force;
}
void R3Matrix::
Rotate(const R3Vector& radians)
{
XRotate(radians.X());
YRotate(radians.Y());
ZRotate(radians.Z());
}
void R3Matrix::Scale(const R3Vector& scale)
{
// Scale matrix
XScale(scale.X());
YScale(scale.Y());
ZScale(scale.Z());
}
void R3Matrix::Translate(const R3Vector& offset)
{
// Translate matrix
XTranslate(offset.X());
YTranslate(offset.Y());
ZTranslate(offset.Z());
}
RNRgb R3DirectionalLight::
SpecularReflection(const R3Brdf& brdf, const R3Point& eye,
const R3Point& point, const R3Vector& normal) const
{
// Check if light is active
if (!IsActive()) return RNblack_rgb;
// Get material properties
const RNRgb& Sc = brdf.Specular();
RNScalar s = brdf.Shininess();
// Get light properties
const RNRgb& Ic = Color();
RNScalar I = Intensity();
R3Vector L = -(Direction());
// Compute geometric stuff
RNScalar NL = normal.Dot(L);
if (RNIsNegativeOrZero(NL)) return RNblack_rgb;
R3Vector R = (2.0 * NL) * normal - L;
R3Vector V = eye - point;
V.Normalize();
RNScalar VR = V.Dot(R);
if (RNIsNegativeOrZero(VR)) return RNblack_rgb;
// Return specular component of reflection
return (I * pow(VR,s)) * Sc * Ic;
}
void R3Point::
Rotate(const R3Vector& axis, RNAngle theta)
{
// Rotate point counterclockwise around axis through origin by radians ???
R3Vector v = Vector();
v.Rotate(axis, theta);
*this = v.Point();
}
R3Vector
operator%(const R3Vector& vector1, const R3Vector& vector2)
{
// Return cross product of two vectors
R3Vector v = vector1;
v.Cross(vector2);
return v;
}
R3Vector R3PointLight::
DirectionFromPoint(const R3Point& point) const
{
// Return direction to point
R3Vector L = position - point;
L.Normalize();
return L;
}
void R3Point::
Rotate(const R3Vector& radians)
{
// Rotate first around X, then around Y, and finally around Z
ZRotate(radians.Z());
YRotate(radians.Y());
XRotate(radians.X());
}
void R3Triad::
Rotate(const R3Vector& from, const R3Vector& to)
{
// Rotate each axis
RNAngle angle = R3InteriorAngle(from, to);
R3Vector rotaxis = from % to;
rotaxis.Normalize();
Rotate(rotaxis, angle);
}
R3Point SpawnLocation() {
R3Point playerPos = globals.player->GetPosition();
R3Vector playerDir = globals.player->GetDirection();
R3Vector playerLeft = R3Vector(R3posy_vector);
playerLeft.Cross(playerDir);
return playerPos + Util::SymmetricRandom() * 15.0 * playerLeft +
Util::SymmetricRandom() * 15.0 * R3posy_vector +
(Util::UnitRandom() + 0.3) * 100.0 * playerDir;
}
// compute intersection between a sphere and a ray
R3Intersection ComputeIntersection(R3Sphere *sphere, R3Ray &ray)
{
R3Intersection i;
bool in_front_of_center = false;
bool internal = false;
R3Vector l = sphere->Center() - ray.Start();
double tca = l.Dot(ray.Vector());
if (tca < 0) // case where ray originates within sphere and points away from its center
{
tca = -tca;
in_front_of_center = true;
internal = true;
}
double d2 = l.Dot(l) - tca * tca;
double r2 = sphere->Radius() * sphere->Radius();
if (d2 > r2) // case where ray misses sphere entirely
{
i.hit = false;
return i;
}
double thc = sqrt(r2 - d2);
double t;
if (!in_front_of_center)
{
t = tca - thc;
if (t < 0)
{
t = tca + thc;
internal = true;
}
}
else
{
t = thc - tca;
}
if (t < 0)
{
i.hit = false;
return i;
}
R3Point p = ray.Point(t);
R3Vector n = p - sphere->Center();
n.Normalize();
if (internal)
n = -n;
// populate intersection data
i.hit = true;
i.normal = n;
i.position = p;
i.t = t;
return i;
}
void GLUTMotion(int x, int y)
{
// Invert y coordinate
y = GLUTwindow_height - y;
// Compute mouse movement
int dx = x - GLUTmouse[0];
int dy = y - GLUTmouse[1];
// Process mouse motion event
if ((dx != 0) || (dy != 0)) {
R3Point mesh_center = mesh->Center();
if ((GLUTbutton[0] && (GLUTmodifiers & GLUT_ACTIVE_SHIFT)) || GLUTbutton[1]) {
// Scale world
double factor = (double) dx / (double) GLUTwindow_width;
factor += (double) dy / (double) GLUTwindow_height;
factor = exp(2.0 * factor);
factor = (factor - 1.0) / factor;
R3Vector translation = (mesh_center - camera_eye) * factor;
camera_eye += translation;
glutPostRedisplay();
}
else if (GLUTbutton[0] && (GLUTmodifiers & GLUT_ACTIVE_CTRL)) {
// Translate world
double length = R3Distance(mesh_center, camera_eye) * tan(camera_yfov);
double vx = length * (double) dx / (double) GLUTwindow_width;
double vy = length * (double) dy / (double) GLUTwindow_height;
R3Vector camera_right = camera_up % camera_towards;
R3Vector translation = -((camera_right * vx) + (camera_up * vy));
camera_eye += translation;
glutPostRedisplay();
}
else if (GLUTbutton[0]) {
// Rotate world
double vx = (double) dx / (double) GLUTwindow_width;
double vy = (double) dy / (double) GLUTwindow_height;
double theta = 4.0 * (fabs(vx) + fabs(vy));
R3Vector camera_right = camera_up % camera_towards;
R3Vector vector = (camera_right * vx) + (camera_up * vy);
R3Vector rotation_axis = vector % camera_towards;
rotation_axis.Normalize();
camera_eye.Rotate(R3Line(mesh_center, rotation_axis), theta);
camera_towards.Rotate(rotation_axis, theta);
camera_up.Rotate(rotation_axis, theta);
camera_right = camera_up % camera_towards;
camera_up = camera_towards % camera_right;
camera_towards.Normalize();
camera_up.Normalize();
glutPostRedisplay();
}
}
// Remember mouse position
GLUTmouse[0] = x;
GLUTmouse[1] = y;
}
double R3Distance(const R3Point& point, const R3Ray& ray)
{
// Check if start point is closest
R3Vector v = point - ray.Start();
double dir = v.Dot(ray.Vector());
if (dir < 0) return v.Length();
// Return distance from point to ray line
return R3Distance(point, ray.Line());
}
const R3Point R3Sphere::
ClosestPoint(const R3Point& point) const
{
// Return closest point in sphere
if (radius <= 0) return center;
R3Vector v = point - Center();
RNLength d = v.Length();
if (d < radius) return point;
else return center + radius * v / d;
}
const R3Point R3Sphere::
FurthestPoint(const R3Point& point) const
{
// Return furthest point in sphere
if (radius <= 0) return center;
R3Vector v = point - Center();
RNLength d = v.Length();
if (RNIsZero(d)) return R3Point(center[0] + radius, center[1], center[2]);
else return center - radius * v / d;
}
void R4Matrix::
Rotate(const R3Vector& from, const R3Vector& to)
{
// rotate matrix that takes direction of vector "from" -> "to"
// This is a quickie hack -- there's got to be a better way
RNAngle radians = R3InteriorAngle(from, to);
R3Vector axis = from % to;
axis.Normalize();
Rotate(axis, radians);
}
const RNArea R3Triangle::
Area(void) const
{
// Compute area using Newell's method
R3Vector sum = R3null_vector;
sum += v[0]->Position().Vector() % v[2]->Position().Vector();
sum += v[1]->Position().Vector() % v[0]->Position().Vector();
sum += v[2]->Position().Vector() % v[1]->Position().Vector();
return 0.5 * sum.Length();
}
static R3Vector calculate_sink_force(R3Scene* scene, R3Particle* particle)
{
R3ParticleSink* sink;
R3Vector force = R3Vector(0,0,0);
for (int i = 0; i < scene->NParticleSinks(); i++)
{
sink = scene->ParticleSink(i);
if (sink->shape->type == R3_SPHERE_SHAPE)
{
R3Sphere* sphere = sink->shape->sphere;
R3Point center = sphere->Center();
R3Vector f = -(particle->position - center);
double d = f.Length() - sphere->Radius();
f.Normalize();
double mag = sink->intensity / (sink->constant_attenuation +
sink->linear_attenuation*d +
sink->quadratic_attenuation*d*d);
force += f*mag;
}
else if (sink->shape->type == R3_MESH_SHAPE)
{
R3Mesh* mesh = sink->shape->mesh;
R3Point center = R3Point(0,0,0);
for (unsigned int j = 0; j < mesh->vertices.size(); j++)
{
center += mesh->vertices[i]->position / mesh->vertices.size();
}
R3Vector f = -(particle->position - center);
double d = f.Length();
f.Normalize();
double mag = sink->intensity / (sink->constant_attenuation +
sink->linear_attenuation*d +
sink->quadratic_attenuation*d*d);
force += f*mag;
}
else if (sink->shape->type == R3_BOX_SHAPE)
{
R3Box* box = sink->shape->box;
R3Point center = R3Point((box->XMax() - box->XMin())/2 + box->XMin(),
(box->YMax() - box->YMin())/2 + box->YMin(),
(box->ZMax() - box->ZMin())/2 + box->ZMin());
R3Vector f = -(particle->position - center);
double d = f.Length();
f.Normalize();
double mag = sink->intensity / (sink->constant_attenuation +
sink->linear_attenuation*d +
sink->quadratic_attenuation*d*d);
force += f*mag;
}
}
return force;
}
void R3Point::
Rotate(const R3Line& axis, RNAngle theta)
{
// Translate axis to origin
R3Vector v = *this - axis.Point();
// Rotate point counterclockwise around axis through origin by radians ???
v.Rotate(axis.Vector(), theta);
// Translate axis back from origin
*this = axis.Point() + v;
}
const RNBoolean R3Point::
Collinear(const R3Point& point1, const R3Point& point2) const
{
// Check if two of points are same
if ((*this == point1) || (*this == point2) || (point1 == point2)) return TRUE;
/// Check if three points are collinear
R3Vector v = point1 - *this;
v.Cross(point1 - point2);
if (RNIsZero(v.Length())) return TRUE;
return FALSE;
}
void R3Matrix::Rotate(const R3Vector& from, const R3Vector& to)
{
// rotate matrix that takes direction of vector "from" -> "to"
// This is a quickie hack -- there's got to be a better way
double d1 = from.Length();
if (d1 == 0) return;
double d2 = to.Length();
if (d2 == 0) return;
double cosine = from.Dot(to) / (d1 * d2);
double radians = acos(cosine);
R3Vector axis = from % to;
axis.Normalize();
Rotate(axis, radians);
}