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#include <iostream> #include <cmath> using namespace std; // Structure for a 3D vector struct Vec3 { float x, y, z; // Constructor to initialize vector Vec3(float x = 0, float y = 0, float z = 0) : x(x), y(y), z(z) {} // Vector addition Vec3 operator+(const Vec3& v) const { return Vec3(x + v.x, y + v.y, z + v.z); } // Vector subtraction Vec3 operator-(const Vec3& v) const { return Vec3(x - v.x, y - v.y, z - v.z); } // Scalar multiplication Vec3 operator*(float t) const { return Vec3(x * t, y * t, z * t); } // Dot product float dot(const Vec3& v) const { return x * v.x + y * v.y + z * v.z; } // Length of the vector (magnitude) float length() const { return sqrt(x * x + y * y + z * z); } // Normalize the vector Vec3 normalize() const { float len = length(); return Vec3(x / len, y / len, z / len); } }; // Structure for a ray struct Ray { Vec3 origin; Vec3 direction; // Constructor to initialize ray Ray(const Vec3& origin, const Vec3& direction) : origin(origin), direction(direction.normalize()) {} // Get point at distance t along the ray Vec3 pointAtParameter(float t) const { return origin + direction * t; } }; // Structure for a sphere struct Sphere { Vec3 center; float radius; // Constructor to initialize sphere Sphere(const Vec3& center, float radius) : center(center), radius(radius) {} // Check if a ray intersects with the sphere bool intersect(const Ray& ray, float& t) const { Vec3 oc = ray.origin - center; float a = ray.direction.dot(ray.direction); float b = 2.0f * oc.dot(ray.direction); float c = oc.dot(oc) - radius * radius; float discriminant = b * b - 4 * a * c; if (discriminant < 0) { return false; } else { t = (-b - sqrt(discriminant)) / (2.0f * a); return true; } } }; int main() { // Define a sphere at position (0, 0, -5) with radius 1 Sphere sphere(Vec3(0, 0, -5), 1); // Define a ray originating at the camera position (0, 0, 0) and pointing in the z direction Ray ray(Vec3(0, 0, 0), Vec3(0, 0, -1)); float t; if (sphere.intersect(ray, t)) { Vec3 hitPoint = ray.pointAtParameter(t); cout << "Ray intersects the sphere at point (" << hitPoint.x << ", " << hitPoint.y << ", " << hitPoint.z << ")" << endl; } else { cout << "Ray does not intersect the sphere." << endl; } return 0; } |
Explanation
- Vec3 Structure:
Vec3is a structure representing a 3D vector withx,y, andzcomponents. It includes various vector operations such as addition, subtraction, scalar multiplication, dot product, length, and normalization.
- Ray Structure:
- The
Raystructure represents a ray with an origin and a direction. The direction is normalized to ensure it’s a unit vector. ThepointAtParameter()function returns the point along the ray at distancet.
- The
- Sphere Structure:
- The
Spherestructure defines a sphere with a center and a radius. Theintersect()function checks if a given ray intersects with the sphere. It uses the quadratic formula to solve for the intersection points. If the discriminant is positive, there is an intersection, and the function returnstruewith the intersection distancet.
- The
- Main Function:
- In the
main()function, a sphere is defined at position(0, 0, -5)with a radius of1. A ray is defined starting at(0, 0, 0)(camera position) and pointing in the negative z-direction. The program checks if the ray intersects with the sphere and prints the intersection point if it exists.
- In the