我有一个光线追踪器（来自 www.scratchapixel.com），我用它来将图像写入内存，然后使用 Opengl（过剩）立即显示。我使用宽度和高度并划分屏幕以获得每个像素的 Opengl 点。它有点工作。
我的问题是我的宽度必须在 500 到 799 之间。它不能是 <= 499 of >= 800，女巫对我来说没有意义。图像变得倾斜。我已经在 2 台计算机上尝试过，结果相同。
799x480
800x480
这是完整的代码：
#define _USE_MATH_DEFINES
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <fstream>
#include <vector>
#include <iostream>
#include <cassert>
// OpenGl
#include "GL/glut.h"
GLuint width = 799, height = 480;
GLdouble width_step = 2.0f / width, height_step = 2.0f / height;
const int MAX_RAY_DEPTH = 3;
const double INFINITY = HUGE_VAL;
template<typename T>
class Vec3
{
public:
T x, y, z;
// Vector constructors.
Vec3() : x(T(0)), y(T(0)), z(T(0)) {}
Vec3(T xx) : x(xx), y(xx), z(xx) {}
Vec3(T xx, T yy, T zz) : x(xx), y(yy), z(zz) {}
// Vector normalisation.
Vec3& normalize()
{
T nor = x * x + y * y + z * z;
if (nor > 1) {
T invNor = 1 / sqrt(nor);
x *= invNor, y *= invNor, z *= invNor;
}
return *this;
}
// Vector operators.
Vec3<T> operator * (const T &f) const { return Vec3<T>(x * f, y * f, z * f); }
Vec3<T> operator * (const Vec3<T> &v) const { return Vec3<T>(x * v.x, y * v.y, z * v.z); }
T dot(const Vec3<T> &v) const { return x * v.x + y * v.y + z * v.z; }
Vec3<T> operator - (const Vec3<T> &v) const { return Vec3<T>(x - v.x, y - v.y, z - v.z); }
Vec3<T> operator + (const Vec3<T> &v) const { return Vec3<T>(x + v.x, y + v.y, z + v.z); }
Vec3<T>& operator += (const Vec3<T> &v) { x += v.x, y += v.y, z += v.z; return *this; }
Vec3<T>& operator *= (const Vec3<T> &v) { x *= v.x, y *= v.y, z *= v.z; return *this; }
Vec3<T> operator - () const { return Vec3<T>(-x, -y, -z); }
};
template<typename T>
class Sphere
{
public:
// Sphere variables.
Vec3<T> center; /// position of the sphere
T radius, radius2; /// sphere radius and radius^2
Vec3<T> surfaceColor, emissionColor; /// surface color and emission (light)
T transparency, reflection; /// surface transparency and reflectivity
// Sphere constructor.
// position(c), radius(r), surface color(sc), reflectivity(refl), transparency(transp), emission color(ec)
Sphere(const Vec3<T> &c, const T &r, const Vec3<T> &sc,
const T &refl = 0, const T &transp = 0, const Vec3<T> &ec = 0) :
center(c), radius(r), surfaceColor(sc), reflection(refl),
transparency(transp), emissionColor(ec), radius2(r * r)
{}
// compute a ray-sphere intersection using the geometric solution
bool intersect(const Vec3<T> &rayorig, const Vec3<T> &raydir, T *t0 = NULL, T *t1 = NULL) const
{
// we start with a vector (l) from the ray origin (rayorig) to the center of the curent sphere.
Vec3<T> l = center - rayorig;
// tca is a vector length in the direction of the normalise raydir.
// its length is streched using dot until it forms a perfect right angle triangle with the l vector.
T tca = l.dot(raydir);
// if tca is < 0, the raydir is going in the opposite direction. No need to go further. Return false.
if (tca < 0) return false;
// if we keep on into the code, it's because the raydir may still hit the sphere.
// l.dot(l) gives us the l vector length to the power of 2. Then we use Pythagoras' theorem.
// remove the length tca to the power of two (tca * tca) and we get a distance from the center of the sphere to the power of 2 (d2).
T d2 = l.dot(l) - (tca * tca);
// if this distance to the center (d2) is greater than the radius to the power of 2 (radius2), the raydir direction is missing the sphere.
// No need to go further. Return false.
if (d2 > radius2) return false;
// Pythagoras' theorem again: radius2 is the hypotenuse and d2 is one of the side. Substraction gives the third side to the power of 2.
// Using sqrt, we obtain the length thc. thc is how deep tca goes into the sphere.
T thc = sqrt(radius2 - d2);
if (t0 != NULL && t1 != NULL) {
// remove thc to tca and you get the length from the ray origin to the surface hit point of the sphere.
*t0 = tca - thc;
// add thc to tca and you get the length from the ray origin to the surface hit point of the back side of the sphere.
*t1 = tca + thc;
}
// There is a intersection with a sphere, t0 and t1 have surface distances values. Return true.
return true;
}
};
std::vector<Sphere<double> *> spheres;
// function to mix 2 T varables.
template<typename T>
T mix(const T &a, const T &b, const T &mix)
{
return b * mix + a * (T(1) - mix);
}
// This is the main trace function. It takes a ray as argument (defined by its origin
// and direction). We test if this ray intersects any of the geometry in the scene.
// If the ray intersects an object, we compute the intersection point, the normal
// at the intersection point, and shade this point using this information.
// Shading depends on the surface property (is it transparent, reflective, diffuse).
// The function returns a color for the ray. If the ray intersects an object, it
// returns the color of the object at the intersection point, otherwise it returns
// the background color.
template<typename T>
Vec3<T> trace(const Vec3<T> &rayorig, const Vec3<T> &raydir,
const std::vector<Sphere<T> *> &spheres, const int &depth)
{
T tnear = INFINITY;
const Sphere<T> *sphere = NULL;
// Try to find intersection of this raydir with the spheres in the scene
for (unsigned i = 0; i < spheres.size(); ++i) {
T t0 = INFINITY, t1 = INFINITY;
if (spheres[i]->intersect(rayorig, raydir, &t0, &t1)) {
// is the rayorig inside the sphere (t0 < 0)? If so, use the second hit (t0 = t1)
if (t0 < 0) t0 = t1;
// tnear is the last sphere intersection (or infinity). Is t0 in front of tnear?
if (t0 < tnear) {
// if so, update tnear to this closer t0 and update the closest sphere
tnear = t0;
sphere = spheres[i];
}
}
}
// At this moment in the program, we have the closest sphere (sphere) and the closest hit position (tnear)
// For this pixel, if there's no intersection with a sphere, return a Vec3 with the background color.
if (!sphere) return Vec3<T>(.5); // Grey background color.
// if we keep on with the code, it is because we had an intersection with at least one sphere.
Vec3<T> surfaceColor = 0; // initialisation of the color of the ray/surface of the object intersected by the ray.
Vec3<T> phit = rayorig + (raydir * tnear); // point of intersection.
Vec3<T> nhit = phit - sphere->center; // normal at the intersection point.
// if the normal and the view direction are not opposite to each other,
// reverse the normal direction.
if (raydir.dot(nhit) > 0) nhit = -nhit;
nhit.normalize(); // normalize normal direction
// The angle between raydir and the normal at point hit (not used).
//T s_angle = acos(raydir.dot(nhit)) / ( sqrt(raydir.dot(raydir)) * sqrt(nhit.dot(nhit)));
//T s_incidence = sin(s_angle);
T bias = 1e-5; // add some bias to the point from which we will be tracing
// Do we have transparency or reflection?
if ((sphere->transparency > 0 || sphere->reflection > 0) && depth < MAX_RAY_DEPTH) {
T IdotN = raydir.dot(nhit); // raydir.normal
// I and N are not pointing in the same direction, so take the invert.
T facingratio = std::max(T(0), -IdotN);
// change the mix value between reflection and refraction to tweak the effect (fresnel effect)
T fresneleffect = mix<T>(pow(1 - facingratio, 3), 1, 0.1);
// compute reflection direction (not need to normalize because all vectors
// are already normalized)
Vec3<T> refldir = raydir - nhit * 2 * raydir.dot(nhit);
Vec3<T> reflection = trace(phit + (nhit * bias), refldir, spheres, depth + 1);
Vec3<T> refraction = 0;
// if the sphere is also transparent compute refraction ray (transmission)
if (sphere->transparency) {
T ior = 1.2, eta = 1 / ior;
T k = 1 - eta * eta * (1 - IdotN * IdotN);
Vec3<T> refrdir = raydir * eta - nhit * (eta * IdotN + sqrt(k));
refraction = trace(phit - nhit * bias, refrdir, spheres, depth + 1);
}
// the result is a mix of reflection and refraction (if the sphere is transparent)
surfaceColor = (reflection * fresneleffect + refraction * (1 - fresneleffect) * sphere->transparency) * sphere->surfaceColor;
}
else {
// it's a diffuse object, no need to raytrace any further
// Look at all sphere to find lights
double shadow = 1.0;
for (unsigned i = 0; i < spheres.size(); ++i) {
if (spheres[i]->emissionColor.x > 0) {
// this is a light
Vec3<T> transmission = 1.0;
Vec3<T> lightDirection = spheres[i]->center - phit;
lightDirection.normalize();
T light_angle = (acos(raydir.dot(lightDirection)) / ( sqrt(raydir.dot(raydir)) * sqrt(lightDirection.dot(lightDirection))));
T light_incidence = sin(light_angle);
for (unsigned j = 0; j < spheres.size(); ++j) {
if (i != j) {
T t0, t1;
// Does the ray from point hit to the light intersect an object?
// If so, calculate the shadow.
if (spheres[j]->intersect(phit + (nhit * bias), lightDirection, &t0, &t1)) {
shadow = std::max(0.0, shadow - (1.0 - spheres[j]->transparency));
transmission = transmission * spheres[j]->surfaceColor * shadow;
//break;
}
}
}
// For each light found, we add light transmission to the pixel.
surfaceColor += sphere->surfaceColor * transmission *
std::max(T(0), nhit.dot(lightDirection)) * spheres[i]->emissionColor;
}
}
}
return surfaceColor + sphere->emissionColor;
}
// Main rendering function. We compute a camera ray for each pixel of the image,
// trace it and return a color. If the ray hits a sphere, we return the color of the
// sphere at the intersection point, else we return the background color.
Vec3<double> *image = new Vec3<double>[width * height];
static Vec3<double> cam_pos = Vec3<double>(0);
template<typename T>
void render(const std::vector<Sphere<T> *> &spheres)
{
Vec3<T> *pixel = image;
T invWidth = 1 / T(width), invHeight = 1 / T(height);
T fov = 30, aspectratio = T(width) / T(height);
T angle = tan(M_PI * 0.5 * fov / T(180));
// Trace rays
for (GLuint y = 0; y < height; ++y) {
for (GLuint x = 0; x < width; ++x, ++pixel) {
T xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;
T yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;
Vec3<T> raydir(xx, yy, -1);
raydir.normalize();
*pixel = trace(cam_pos, raydir, spheres, 0);
}
}
}
//********************************** OPEN GL ***********************************************
void init(void)
{
/* Select clearing (background) color */
glClearColor(0.0, 0.0, 0.0, 0.0);
glShadeModel(GL_FLAT);
/* Initialize viewing values */
//glMatrixMode(GL_PROJECTION);
gluOrtho2D(0,width,0,height);
}
void advanceDisplay(void)
{
cam_pos.z = cam_pos.z - 2;
glutPostRedisplay();
}
void backDisplay(void)
{
cam_pos.z = cam_pos.z + 2;
glutPostRedisplay();
}
void resetDisplay(void)
{
Vec3<double> new_cam_pos;
new_cam_pos = cam_pos;
cam_pos = new_cam_pos;
glutPostRedisplay();
}
void reshape(int w, int h)
{
glLoadIdentity();
gluOrtho2D(0,width,0,height);
glLoadIdentity();
}
void mouse(int button, int state, int x, int y)
{
switch (button)
{
case GLUT_LEFT_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(advanceDisplay);
}
break;
case GLUT_MIDDLE_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(resetDisplay);
}
break;
case GLUT_RIGHT_BUTTON:
if(state == GLUT_DOWN)
{
glutIdleFunc(backDisplay);
}
break;
}
}
void display(void)
{
int i;
float x, y;
/* clear all pixels */
glClear(GL_COLOR_BUFFER_BIT);
glPushMatrix();
render<double>(spheres); // Creates the image and put it to memory in image[].
i=0;
glBegin(GL_POINTS);
for(y=1.0f;y>-1.0;y=y-height_step)
{
for(x=1.0f;x>-1.0;x=x-width_step)
{
glColor3f((std::min(double(1), image[i].x)),
(std::min(double(1), image[i].y)),
(std::min(double(1), image[i].z)));
glVertex2f(x, y);
if(i < width*height)
{
i = i + 1;
}
}
}
glEnd();
glPopMatrix();
glutSwapBuffers();
}
int main(int argc, char **argv)
{
// position, radius, surface color, reflectivity, transparency, emission color
spheres.push_back(new Sphere<double>(Vec3<double>(0, -10004, -20), 10000, Vec3<double>(0.2), 0.0, 0.0));
spheres.push_back(new Sphere<double>(Vec3<double>(3, 0, -15), 2, Vec3<double>(1.00, 0.1, 0.1), 0.65, 0.95));
spheres.push_back(new Sphere<double>(Vec3<double>(1, -1, -18), 1, Vec3<double>(1.0, 1.0, 1.0), 0.9, 0.9));
spheres.push_back(new Sphere<double>(Vec3<double>(-2, 2, -15), 2, Vec3<double>(0.1, 0.1, 1.0), 0.05, 0.5));
spheres.push_back(new Sphere<double>(Vec3<double>(-4, 3, -18), 1, Vec3<double>(0.1, 1.0, 0.1), 0.3, 0.7));
spheres.push_back(new Sphere<double>(Vec3<double>(-4, 0, -25), 1, Vec3<double>(1.00, 0.1, 0.1), 0.65, 0.95));
spheres.push_back(new Sphere<double>(Vec3<double>(-1, 1, -25), 2, Vec3<double>(1.0, 1.0, 1.0), 0.0, 0.0));
spheres.push_back(new Sphere<double>(Vec3<double>(2, 2, -25), 1, Vec3<double>(0.1, 0.1, 1.0), 0.05, 0.5));
spheres.push_back(new Sphere<double>(Vec3<double>(5, 3, -25), 2, Vec3<double>(0.1, 1.0, 0.1), 0.3, 0.7));
// light
spheres.push_back(new Sphere<double>(Vec3<double>(-10, 20, 0), 3, Vec3<double>(0), 0, 0, Vec3<double>(3)));
spheres.push_back(new Sphere<double>(Vec3<double>(0, 10, 0), 3, Vec3<double>(0), 0, 0, Vec3<double>(1)));
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
glutInitWindowSize(width, height);
glutInitWindowPosition(10,10);
glutCreateWindow(argv[0]);
init();
glutDisplayFunc(display);
glutReshapeFunc(reshape);
glutMouseFunc(mouse);
glutMainLoop();
delete [] image;
while (!spheres.empty()) {
Sphere<double> *sph = spheres.back();
spheres.pop_back();
delete sph;
}
return 0;
}
这是图像写入内存的位置：
Vec3<double> *image = new Vec3<double>[width * height];
static Vec3<double> cam_pos = Vec3<double>(0);
template<typename T>
void render(const std::vector<Sphere<T> *> &spheres)
{
Vec3<T> *pixel = image;
T invWidth = 1 / T(width), invHeight = 1 / T(height);
T fov = 30, aspectratio = T(width) / T(height);
T angle = tan(M_PI * 0.5 * fov / T(180));
// Trace rays
for (GLuint y = 0; y < height; ++y) {
for (GLuint x = 0; x < width; ++x, ++pixel) {
T xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;
T yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;
Vec3<T> raydir(xx, yy, -1);
raydir.normalize();
*pixel = trace(cam_pos, raydir, spheres, 0);
}
}
}
这是我读回它并将其写入 Opengl 的每个点的地方：
void display(void)
{
int i;
float x, y;
/* clear all pixels */
glClear(GL_COLOR_BUFFER_BIT);
glPushMatrix();
render<double>(spheres); // Creates the image and put it to memory in image[].
i=0;
glBegin(GL_POINTS);
for(y=1.0f;y>-1.0;y=y-height_step)
{
for(x=1.0f;x>-1.0;x=x-width_step)
{
glColor3f((std::min(double(1), image[i].x)),
(std::min(double(1), image[i].y)),
(std::min(double(1), image[i].z)));
glVertex2f(x, y);
if(i < width*height)
{
i = i + 1;
}
}
}
glEnd();
glPopMatrix();
glutSwapBuffers();
}
我不知道是什么原因造成的。这是一个糟糕的设计吗？Opengl显示模式？我不知道。