为什么我的路径追踪代码不工作？

Question

我最近在用纯Python编写一个路径追踪器，纯粹是为了好玩。之前的阴影效果做得不太好（参考了朗伯余弦定律），所以我想尝试实现递归路径追踪。

我的引擎输出的结果很糟糕：

这里插入图片描述

我的路径追踪函数是递归定义的，像这样：

def TracePath2(ray, scene, bounce_count):
  result = 100000.0
  hit = False

  answer = Color(0.0, 0.0, 0.0)

  for object in scene.objects:
    test = object.intersection(ray)

    if test and test < result:
      result = test
      hit = object

  if not hit:
    return answer

  if hit.emittance:
    return hit.diffuse * hit.emittance

  if hit.diffuse:
    direction = RandomDirectionInHemisphere(hit.normal(ray.position(result)))

    n = Ray(ray.position(result), direction)
    dp = direction.dot(hit.normal(ray.position(result)))
    answer += TracePath2(n, scene, bounce_count + 1) * hit.diffuse * dp

  return answer

我的场景（我自己做了一个自定义的XML描述格式）是这样的：

<?xml version="1.0" ?>

<scene>
  <camera name="camera">
    <position x="0" y="-5" z="0" />
    <direction x="0" y="1" z="0" />

    <focalplane width="0.5" height="0.5" offset="1.0" pixeldensity="1600" />
  </camera>

  <objects>
    <sphere name="sphere1" radius="1.0">
      <material emittance="0.9" reflectance="0">
        <diffuse r="0.5" g="0.5" b="0.5" />
      </material>

      <position x="1" y="0" z="0" />
    </sphere>

    <sphere name="sphere2" radius="1.0">
      <material emittance="0.0" reflectance="0">
        <diffuse r="0.8" g="0.5" b="0.5" />
      </material>

      <position x="-1" y="0" z="0" />
    </sphere>
  </objects>
</scene>

我很确定我的引擎里有一些根本性的错误，但我就是找不到...

这是我新写的追踪函数：

def Trace(ray, scene, n):
  if n > 10: # Max raydepth of 10. In my scene, the max should be around 4, since there are only a few objects to bounce off, but I agree, there should be a cap.
    return Color(0.0, 0.0, 0.0)

  result = 1000000.0 # It's close to infinity...
  hit = False

  for object in scene.objects:
    test = object.intersection(ray)

    if test and test < result:
      result = test
      hit = object

  if not hit:
    return Color(0.0, 0.0, 0.0)

  point = ray.position(result)

  normal = hit.normal(point)
  direction = RandomNormalInHemisphere(normal) # I won't post that code, but rest assured, it *does* work.

  if direction.dot(ray.direction) > 0.0:
    point = ray.origin + ray.direction * (result + 0.0000001) # We're going inside an object (for use when tracing glass), so move a tad bit inside to prevent floating-point errors.
  else:
    point = ray.origin + ray.direction * (result - 0.0000001) # We're bouncing off. Move away from surface a little bit for same reason.

  newray = Ray(point, direction)

  return Trace(newray, scene, n + 1) * hit.diffuse + Color(hit.emittance, hit.emittance, hit.emittance) # Haven't implemented colored lights, so it's a shade of gray for now.

我很确定路径追踪的代码是有效的，因为我手动发射了一些光线，得到了相当不错的结果。现在我遇到的问题是，相机没有通过图像平面上的所有像素发射光线。我写了这段代码来找到与像素相交的光线，但它没有正常工作：

origin = scene.camera.pos                 # + 0.5 because it      # 
                                          # puts the ray in the   # This calculates the width of one "unit"
                                          # *middle* of the pixel # 
worldX = scene.camera.focalplane.width - (x + 0.5)                * (2 * scene.camera.focalplane.width / scene.camera.focalplane.canvasWidth)
worldY = scene.camera.pos.y - scene.camera.focalplane.offset # Offset of the imaging plane is know, and it's normal to the camera's direction (directly along the Y-axis in this case).
worldZ = scene.camera.focalplane.height - (y + 0.5)               * (2 * scene.camera.focalplane.height / scene.camera.focalplane.canvasHeight)

ray = Ray(origin, (scene.camera.pos + Point(worldX, worldY, worldZ)).norm())

递归算法图像处理计算机图形学渲染引擎路径追踪光线投射朗伯余弦定律自定义场景描述

为什么我的路径追踪代码不工作？

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