为什么我的路径跟踪代码不起作用？

Question

我一直在用纯 Python 编写一个路径跟踪器，只是为了好玩，而且由于我之前的着色东西不太漂亮 (Lambert's cosine law)，我正在尝试实现递归路径跟踪。

我的引擎给出了一个异常的输出：

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

而我的场景（我做了一个自定义的 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>

我很确定我的引擎存在一些根本缺陷，但我就是找不到它......

---

这是我的新追踪功能：

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.

---

我很确定路径跟踪代码可以正常工作，因为我手动投射了一些光线并获得了相当合理的结果。我（现在）遇到的问题是相机没有通过图像平面中的所有像素拍摄光线。我编写了这段代码来查找与像素相交的射线，但它无法正常工作：

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())

Answer 1

我的第一个问题是 if test > result: 应该是 if test < result: 吗？您正在寻找最近的命中，而不是最远的命中。

其次，为什么要在n = Ray(ray.position(result) + direction * 0.00001, direction)这里的命中点上加上direction*0.00001？这会将你的新射线的起点放在球体内。我相信当你递归调用TracePath2时，你乘以的点积将是负数，这将有助于解释问题。

编辑：更新问题

这行让我很困惑：answer += TracePath2(n, scene, bounce_count + 1) * hit.diffuse * dp。首先answer 将只是Color(0.0, 0.0, 0.0)，所以你可以简单地return racePath2(n, scene, bounce_count + 1) * hit.diffuse * dp。但这仍然困扰着我，因为我不明白你为什么将递归调用和hit.diffuse 相乘。这样的事情对我来说更有意义return racePath2(n, scene, bounce_count + 1) * dp + hit.diffuse。还有一件事，你永远不会检查bounce_count。无论如何，你永远不会在这个场景中永远递归，但如果你想渲染更大的场景，你会在开始时需要这样的东西if bounce_count > 15: return black。

编辑 2：

我看到我仍然想知道的一件事是最后的 if-else。首先，我不完全确定那部分代码在做什么。我认为您正在测试射线是否在物体内部。在这种情况下，您的测试将是这样的inside = normal.dot(ray.direction) > 0.0。我只是针对normal 而不是direction 进行测试，因为在半球中使用随机方向可能会给出错误的答案。现在，如果你在物体里面，你想出去，但如果你已经出去了，你想留在外面？就像我说的，我不太确定那部分应该做什么。