C语言在光线追踪代码基础上使用Eigenvalue库生成一段小球从天而降的动画的具体代码

以下是一个使用C语言和Eigenvalue库生成小球从天而降的动画的示例代码：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "Eigen/Dense"
using namespace Eigen;

struct Ray {
  Vector3f origin;
  Vector3f direction;
};

struct Sphere {
  Vector3f center;
  float radius;
  Vector3f color;
};

struct Hit {
  Sphere* sphere;
  float t;
  Vector3f hitPoint;
  Vector3f normal;
};

Sphere* intersectScene(Ray ray, Sphere* spheres, int numSpheres, Hit& hit) {
  float tmin = INFINITY;
  for (int i = 0; i < numSpheres; i++) {
    Sphere sphere = spheres[i];
    Vector3f oc = ray.origin - sphere.center;
    float a = ray.direction.dot(ray.direction);
    float b = 2.0f * oc.dot(ray.direction);
    float c = oc.dot(oc) - sphere.radius * sphere.radius;
    float discriminant = b * b - 4 * a * c;
    if (discriminant >= 0) {
      float t = (-b - sqrt(discriminant)) / (2.0f * a);
      if (t > 0 && t < tmin) {
        hit.t = t;
        hit.sphere = &sphere;
        hit.hitPoint = ray.origin + t * ray.direction;
        hit.normal = (hit.hitPoint - sphere.center).normalized();
        tmin = t;
      }
    }
  }
  return hit.sphere;
}

int main() {
  const int width = 640;
  const int height = 480;
  const int numSpheres = 2;
  const float ballRadius = 50.0f;
  const float ballSpeed = 100.0f;
  const float gravity = 9.8f;
  const float deltaTime = 0.016f;

  Sphere spheres[numSpheres] = {
    {Vector3f(0, -1000, 0), 1000, Vector3f(0.5, 0.5, 0.5)},
    {Vector3f(0, ballRadius + 1, 0), ballRadius, Vector3f(1, 0, 0)}
  };

  Vector3f ballPos(0, ballRadius + 1, 0);
  Vector3f ballVel(0, 0, 0);

  FILE* file = fopen("output.ppm", "wb");
  fprintf(file, "P3\n%d %d\n255\n", width, height);

  for (int y = 0; y < height; y++) {
    for (int x = 0; x < width; x++) {
      Ray ray;
      ray.origin = Vector3f(x - width / 2.0f, height / 2.0f - y, -1000);
      ray.direction = Vector3f(0, 0, 1);

      Hit hit = {};
      intersectScene(ray, spheres, numSpheres, hit);

      if (hit.sphere) {
        Vector3f color = hit.sphere->color;
        fprintf(file, "%d %d %d ", (int)(255 * color[0]), (int)(255 * color[1]), (int)(255 * color[2]));
      } else {
        fprintf(file, "%d %d %d ", 0, 0, 0);
      }
    }
  }

  for (int i = 0; i < 240; i++) {
    ballVel[1] -= gravity * deltaTime;
    ballPos += ballVel * deltaTime;

    spheres[numSpheres - 1].center = ballPos;

    for (int y = 0; y < height; y++) {
      for (int x = 0; x < width; x++) {
        Ray ray;
        ray.origin = Vector3f(x - width / 2.0f, height / 2.0f - y, -1000);
        ray.direction = Vector3f(0, 0, 1);

        Hit hit = {};
        intersectScene(ray, spheres, numSpheres, hit);

        if (hit.sphere) {
          Vector3f color = hit.sphere->color;
          if (hit.sphere == &spheres[numSpheres - 1]) {
            color = Vector3f(1, 0, 0);
          }
          fprintf(file, "%d %d %d ", (int)(255 * color[0]), (int)(255 * color[1]), (int)(255 * color[2]));
        } else {
          fprintf(file, "%d %d %d ", 0, 0, 0);
        }
      }
    }
  }

  fclose(file);
  return 0;
}

该代码使用了Eigenvalue库来进行向量和矩阵计算，并定义了光线和球体的结构体。在主循环中，首先定义了场景中的球体，包括地面和小球。然后，在每个时间步骤中更新小球的位置，并更新场景中球体的位置。在渲染每个像素时，使用 `intersectScene()` 函数来检测光线是否与球体相交，并计算相交点的颜色。最后，将渲染结果写入PPM图像文件中。在这个示例中，我们使用红色表示小球。

请注意，这个代码示例并不完整，因为它没有实现光线追踪算法的全部功能，例如阴影和反射等。但是，这个代码示例可以作为一个起点，帮助你了解如何使用Eigenvalue库来生成小球从天而降的动画。