理解 OpenGL 中的光照

Question

我正在尝试使用 Haskell / GLUT 从一堆三角形中创建一个 3D 球体。它工作得很好：绿色的是“我的”球体，红色的是用 GLUT 的 renderObject Sphere 完成的。当我四处移动相机时，我可以看到“我的”球体实际上是 3D 的，这很好。

那么为什么 GLUT 有很好的照明，而我的没有？ （我是一个新手，真的不知道我在 initGL 下面在做什么，从 Hackage 的 cuboid 包中复制了这些东西......）

代码如下：

module Main where

import Graphics.UI.GLUT 

main :: IO ()
main = do
  initGL
  displayCallback $= render
  mainLoop

initGL :: IO ()
initGL = do
    getArgsAndInitialize
    initialDisplayMode $= [DoubleBuffered]
    createWindow "Chip!"
    initialDisplayMode $= [ WithDepthBuffer ]
    depthFunc          $= Just Less
    clearColor         $= Color4 0 0 0 0
    light (Light 0)    $= Enabled
    lighting           $= Enabled 
    lightModelAmbient  $= Color4 0.5 0.5 0.5 1 
    diffuse (Light 0)  $= Color4 1 1 1 1
    blend              $= Enabled
    blendFunc          $= (SrcAlpha, OneMinusSrcAlpha) 
    colorMaterial      $= Just (FrontAndBack, AmbientAndDiffuse)
    reshapeCallback    $= Just resizeScene
    return () 

render :: DisplayCallback
render = do
    clear [ ColorBuffer, DepthBuffer ]

    loadIdentity

    color $ Color3 (1 :: GLdouble) 1 1
    position (Light 0) $= Vertex4 0 50 (50) 1  

    preservingMatrix $ do 
        translate $ Vector3 ((-0.5) :: GLfloat) (-0.5) (-5)
        color green
        ball 12 8 0.03

    preservingMatrix $ do 
        translate $ Vector3 (0.5 :: GLfloat) 0.5 (-5)
        color red
        renderObject Solid (Sphere' 0.25 20 20)

    flush
    swapBuffers
    where green  = Color4 0.8 1.0 0.7 0.9 :: Color4 GLdouble
          red    = Color4 1.0 0.7 0.8 1.0 :: Color4 GLdouble

vertex3f :: (GLfloat, GLfloat, GLfloat) -> IO ()
vertex3f (x, y, z) = vertex $ Vertex3 x y z

upperInnerCircle :: Int -> [(GLfloat, GLfloat)]
upperInnerCircle numSegs =
    concat [[(0,0)
            ,(cos a, sqrt(1-(cos a)*(cos a)))
            ,(cos b, sqrt(1-(cos b)*(cos b)))] 
                 | (a,b)<-as ]
    where 
        seg'=pi/(fromIntegral numSegs)
        as = [(fromIntegral n * seg', fromIntegral (n+1) * seg') | n<-[0..numSegs-1]]

lowerInnerCircle :: Int -> [(GLfloat, GLfloat)]
lowerInnerCircle numSegs =
    map (\(x,y) -> (x,-y)) $ upperInnerCircle numSegs

innerCircle :: Int -> [(GLfloat, GLfloat)]
innerCircle numSegs = upperInnerCircle numSegs ++ (lowerInnerCircle numSegs)

upperOutSegment :: Int -> Int -> Int -> [(GLfloat, GLfloat)]
upperOutSegment numSegs ring seg =
   [x,y,u, u,v,y]
    where 
        seg'=pi/(fromIntegral numSegs)
        (a, b)  = (fromIntegral seg * seg', fromIntegral (seg+1) * seg')
        x =  (fromIntegral ring * cos a, fromIntegral ring * sqrt(1-(cos a)*(cos a)))
        y = (fromIntegral ring * cos b, fromIntegral ring * sqrt(1-(cos b)*(cos b)))
        u =  (fromIntegral (ring+1) * cos a, fromIntegral (ring+1) * sqrt(1-(cos a)*(cos a)))
        v = (fromIntegral (ring+1) * cos b, fromIntegral (ring+1) * sqrt(1-(cos b)*(cos b)))

lowerOutSegment :: Int -> Int -> Int -> [(GLfloat, GLfloat)]
lowerOutSegment numSegs ring seg =
    map (\(x,y) -> (x,-y)) $ upperOutSegment numSegs ring seg 

outSegment :: Int -> Int -> Int -> [(GLfloat, GLfloat)]
outSegment numSegs ring seg = upperOutSegment numSegs ring seg ++ (lowerOutSegment numSegs ring seg)

outerRing :: Int -> Int -> [(GLfloat, GLfloat)]
outerRing numSegs ring =
    concat [outSegment numSegs ring n | n<-[0..numSegs-1]] 

ball numSegs numRings factor =
  let ips = innerCircle numSegs
      ops = concat [outerRing numSegs i | i<-[1..numRings]]
      height dir ps = 
           map (\(x,y) -> 
                  let dist = sqrt(x*x+y*y)/(fromIntegral (numRings+1))
                      height' = sqrt(1.001-dist*dist)*factor*(fromIntegral (numRings+1))
                  in (x*factor,y*factor,dir*height')) $ ps
      ups = height 1 $ ips ++ ops
      lps = height (-1) $ ips ++ ops
  in  renderPrimitive Triangles $ mapM_ vertex3f (ups++lps)


resizeScene :: Size -> IO ()
resizeScene (Size w 0) = resizeScene (Size w 1) -- prevent divide by zero
resizeScene s@(Size width height) = do
  viewport   $= (Position 0 0, s)
  matrixMode $= Projection
  loadIdentity
  perspective 45 (w2/h2) 1 1000
  matrixMode $= Modelview 0
  flush
 where
   w2 = half width
   h2 = half height
   half z = realToFrac z / 2

编辑：现在可以使用，感谢 Spektre！

图片如下：

这是代码：

module Main where

import Graphics.UI.GLUT 

main :: IO ()
main = do
  initGL
  displayCallback $= render
  mainLoop

initGL :: IO ()
initGL = do
    getArgsAndInitialize
    initialDisplayMode $= [DoubleBuffered]
    createWindow "Chip!"
    initialDisplayMode $= [ WithDepthBuffer ]
    depthFunc          $= Just Less
    clearColor         $= Color4 0 0 0 0
    light (Light 0)    $= Enabled
    lighting           $= Enabled 
    lightModelAmbient  $= Color4 0.5 0.5 0.5 1 
    diffuse (Light 0)  $= Color4 1 1 1 1
    blend              $= Enabled
    blendFunc          $= (SrcAlpha, OneMinusSrcAlpha) 
    colorMaterial      $= Just (FrontAndBack, AmbientAndDiffuse)
    reshapeCallback    $= Just resizeScene
    return () 

render :: DisplayCallback
render = do
    clear [ ColorBuffer, DepthBuffer ]

    loadIdentity

    color $ Color3 (1 :: GLdouble) 1 1
    position (Light 0) $= Vertex4 0 50 (50) 1  

    preservingMatrix $ do 
        translate $ Vector3 ((-0.5) :: GLfloat) (-0.5) (-5)
        color green
        ball 12 8 0.03

    preservingMatrix $ do 
        translate $ Vector3 (0.5 :: GLfloat) 0.5 (-5)
        color red
        renderObject Solid (Sphere' 0.25 20 20)

    flush
    swapBuffers
    where green  = Color4 0.8 1.0 0.7 0.9 :: Color4 GLdouble
          red    = Color4 1.0 0.7 0.8 1.0 :: Color4 GLdouble

pushTriangle :: ((GLfloat, GLfloat, GLfloat) 
                ,(GLfloat, GLfloat, GLfloat) 
                ,(GLfloat, GLfloat, GLfloat)) -> 
                IO ()
pushTriangle (p0, p1, p2) = do
    let (_,d0,_)=p0
    let (_,d1,_)=p1
    let (_,d2,_)=p2

    --if it points upwards, reverse normal
    let d=if d0+d1+d2>0 then (-1) else 1
    let n = cross (minus p1 p0) (minus p2 p1)
    let nL = 1/lenVec n
    let (n1, n2, n3) = scaleVec n (nL*d)
    normal $ Normal3 n1 n2 n3

    vertex3f p0
    vertex3f p1
    vertex3f p2

vertex3f :: (GLfloat, GLfloat, GLfloat) -> IO ()
vertex3f (x, y, z) = 
   vertex $ Vertex3 x y z

lenVec (a1,a2,a3) = sqrt $ a1*a1 + a2*a2 + a3*a3

scaleVec (a1,a2,a3) x = (a1*x,a2*x,a3*x)

cross (a1,a2,a3) (b1,b2,b3) =
   (a2*b3-a3*b2
   ,a3*b1-a1*b3
   ,a1*b2-a2*b1)

minus (a1,a2,a3) (b1,b2,b3) =
  (a1-b1, a2-b2, a3-b3)

upperInnerCircle :: Int -> [(GLfloat, GLfloat)]
upperInnerCircle numSegs =
    concat [[(cos a, sqrt(1-(cos a)*(cos a)))
            ,(0,0)
            ,(cos b, sqrt(1-(cos b)*(cos b)))] 
                 | (a,b)<-as ]
    where 
        seg'=pi/(fromIntegral numSegs)
        as = [(fromIntegral n * seg', fromIntegral (n+1) * seg') | n<-[0..numSegs-1]]

lowerInnerCircle :: Int -> [(GLfloat, GLfloat)]
lowerInnerCircle numSegs =
    map (\(x,y) -> (x,-y)) $ upperInnerCircle numSegs

innerCircle :: Int -> [(GLfloat, GLfloat)]
innerCircle numSegs = upperInnerCircle numSegs ++ (lowerInnerCircle numSegs)

upperOutSegment :: Int -> Int -> Int -> [(GLfloat, GLfloat)]
upperOutSegment numSegs ring seg =
   [x,y,u, v,u,y]
    where 
        seg'=pi/(fromIntegral numSegs)
        (a, b)  = (fromIntegral seg * seg', fromIntegral (seg+1) * seg')
        x =  (fromIntegral ring * cos a, fromIntegral ring * sqrt(1-(cos a)*(cos a)))
        y = (fromIntegral ring * cos b, fromIntegral ring * sqrt(1-(cos b)*(cos b)))
        u =  (fromIntegral (ring+1) * cos a, fromIntegral (ring+1) * sqrt(1-(cos a)*(cos a)))
        v = (fromIntegral (ring+1) * cos b, fromIntegral (ring+1) * sqrt(1-(cos b)*(cos b)))

lowerOutSegment :: Int -> Int -> Int -> [(GLfloat, GLfloat)]
lowerOutSegment numSegs ring seg =
    map (\(x,y) -> (x,-y)) $ upperOutSegment numSegs ring seg 

outSegment :: Int -> Int -> Int -> [(GLfloat, GLfloat)]
outSegment numSegs ring seg = upperOutSegment numSegs ring seg ++ (lowerOutSegment numSegs ring seg)

outerRing :: Int -> Int -> [(GLfloat, GLfloat)]
outerRing numSegs ring =
    concat [outSegment numSegs ring n | n<-[0..numSegs-1]] 

ball numSegs numRings factor =
  let ips = innerCircle numSegs
      ops = concat [outerRing numSegs i | i<-[1..numRings]]
      height dir ps = 
           map (\(x,y) -> 
                  let dist = sqrt(x*x+y*y)/(fromIntegral (numRings+1))
                      height' = sqrt(1.001-dist*dist)*factor*(fromIntegral (numRings+1))
                  in (x*factor,y*factor,dir*height')) $ ps
      ups = height 1 $ ips ++ ops
      lps = height (-1) $ ips ++ ops
  in  renderPrimitive Triangles $ mapM_ pushTriangle (toTriples (ups++lps))

toTriples :: [a] -> [(a,a,a)]
toTriples [] = []
toTriples (a:b:c:rest) = (a,b,c):toTriples rest 

resizeScene :: Size -> IO ()
resizeScene (Size w 0) = resizeScene (Size w 1) -- prevent divide by zero
resizeScene s@(Size width height) = do
  viewport   $= (Position 0 0, s)
  matrixMode $= Projection
  loadIdentity
  perspective 45 (w2/h2) 1 1000
  matrixMode $= Modelview 0
  flush
 where
   w2 = half width
   h2 = half height
   half z = realToFrac z / 2

Answer 1

1. 表面法线对于光照方程至关重要

   表面法线是垂直于表面的向量。因为三角形是通过其任意 2 个顶点向量的叉积计算的，所以如果三角形点是 p0,p1,p2，那么法线是 n=cross(p1-p0,p2-p1) 或任何其他组合。

   法线告诉像素/面/多边形转向的方式通常具有光方向的点积由渲染引擎计算，并给出cos(angle_between light and surface normal)。这个数字是照射到表面的光量的比例乘以光源强度，你得到光的颜色...... 结合表面颜色渲染得到像素颜色有很多光照模型，这个很简单（普通着色）。

   为了使点积正常工作，法线应该是单位向量，所以除以它的长度n=n/|n|

   这里是法线的小例子

   对于球体来说，法线很容易正常n对于任何点p是n=(p-center)/radius

2. 如果法线与表面不对应

   然后您可以制作灯光效果，例如视觉上平滑网格的锐利边缘。例如如何看这里：

   • smoothing normals

   也可以实现完全相反的效果（平滑的网格但锐利的边缘渲染）

3. OpenGL 接口

   旧式 gl 使用类似 glNormal3f(nx,ny,nz); 的东西 VBO/VAO/arrays 也知道法线。在新样式中，glNormal 与大多数参数一样已弃用，因此您需要自行将其绑定到自定义布局

4. 法线方向

   任何表面都有两个可能的垂直于它的方向。通常使用从网格向外指向的那个。有时 3D 曲线使用双面材料，这意味着点积被处理为abs 值，因此法线指向的方向并不重要。没有这个，表面的另一面将永远是黑暗的

   因此，如果您有法线并且看不到光照，请尝试否定法线