74
edits
Changes
→Ray Tracing
In this function it has a runtime speed of T(n) = O^2.
== Presentation ==
What is Ray Tracing?
Ray tracing is the technique of generating an image by tracing the paths light would travel through pixels in an image plane and simulating the effects it encounters with virtual objects.
[[File:Ray_trace_diagram.svg.png]]
== Code ==
struct Vec3 {
double x, y, z;
Vec3(double x, double y, double z) : x(x), y(y), z(z) {}
Vec3 operator + (const Vec3& v) const { return Vec3(x + v.x, y + v.y, z + v.z); }
Vec3 operator - (const Vec3& v) const { return Vec3(x - v.x, y - v.y, z - v.z); }
Vec3 operator * (double d) const { return Vec3(x*d, y*d, z*d); }
Vec3 operator / (double d) const { return Vec3(x / d, y / d, z / d); }
Vec3 normalize() const {
double mg = sqrt(x*x + y*y + z*z);
return Vec3(x / mg, y / mg, z / mg);
}
};
inline double dot(const Vec3& a, const Vec3& b) {
return (a.x*b.x + a.y*b.y + a.z*b.z);
}
struct Ray {
Vec3 o, d;
Ray(const Vec3& o, const Vec3& d) : o(o), d(d) {}
};
struct Sphere {
Vec3 c;
double r;
Sphere(const Vec3& c, double r) : c(c), r(r) {}
Vec3 getNormal(const Vec3& pi) const { return (pi - c) / r; }
bool intersect(const Ray& ray, double &t) const {
const Vec3 o = ray.o;
const Vec3 d = ray.d;
const Vec3 oc = o - c;
const double b = 2 * dot(oc, d);
const double c = dot(oc, oc) - r*r;
double disc = b*b - 4 * c;
if (disc < 1e-4) return false;
disc = sqrt(disc);
const double t0 = -b - disc;
const double t1 = -b + disc;
t = (t0 < t1) ? t0 : t1;
return true;
}
};
int main() {
steady_clock::time_point ts, te,tm;
ts = steady_clock::now();
const int N = 500;
const Vec3 white(255, 255, 255);
const Vec3 black(0, 0, 0);
const Vec3 red(0, 255, 0);
const Sphere sphere(Vec3(N*0.5, N*0.5, 50), 50);
const Sphere light(Vec3(0, 0, 50), 1);
std::ofstream out("out.ppm");
out << "P3\n" << N << ' ' << N << ' ' << "255\n";
double t;
Vec3 pix_col(black);
int* pixs = new int[N * N * 3];
for (int y = 0; y < N; ++y) {
for (int x = 0; x < N; ++x) {
pix_col = black;
const Ray ray(Vec3(x, y, 0), Vec3(0, 0, 1));
if (sphere.intersect(ray, t)) {
const Vec3 pi = ray.o + ray.d*t;
const Vec3 L = light.c - pi;
const Vec3 N = sphere.getNormal(pi);
const double dt = dot(L.normalize(), N.normalize());
pix_col = (red + white*dt) * 0.5;
clamp255(pix_col);
}
pixs[3 * (y * N + x)] = (int)pix_col.x;
pixs[3 * (y * N + x) + 1] = (int)pix_col.y;
pixs[3 * (y * N + x) + 2] = (int)pix_col.z;
}
}
te = steady_clock::now();
reportTime("matrix-matrix multiplication", te - ts);
for (int y = 0; y < N; ++y) {
for (int x = 0; x < N; ++x) {
out << pixs[3 * (y * N + x)] << ' '
<< pixs[3 * (y * N + x) + 1] << ' '
<< pixs[3 * (y * N + x) + 2] << '\n';
}
}
tm = steady_clock::now();
reportTime("matrix-matrix multiplication", tm - ts);
delete[] pixs;
}
== Points of possible Parallelization ==
for (int y = 0; y < N; ++y) {
for (int x = 0; x < N; ++x) {
pix_col = black;
const Ray ray(Vec3(x, y, 0), Vec3(0, 0, 1));
if (sphere.intersect(ray, t)) {
const Vec3 pi = ray.o + ray.d*t;
const Vec3 L = light.c - pi;
const Vec3 N = sphere.getNormal(pi);
const double dt = dot(L.normalize(), N.normalize());
pix_col = (red + white*dt) * 0.5;
clamp255(pix_col);
}
pixs[3 * (y * N + x)] = (int)pix_col.x;
pixs[3 * (y * N + x) + 1] = (int)pix_col.y;
pixs[3 * (y * N + x) + 2] = (int)pix_col.z;
}
}
for (int y = 0; y < N; ++y) {
for (int x = 0; x < N; ++x) {
out << pixs[3 * (y * N + x)] << ' '
<< pixs[3 * (y * N + x) + 1] << ' '
<< pixs[3 * (y * N + x) + 2] << '\n';
}
}
==Graph==
[[File:GraphDPS915kevin.JPG]]
== Assignment 2 - Parallelization==
2. Calculating in double slowly on Geforce device. <br />
[[File:pyfloat.PNG]]