I have drawn the Barth sextic with Haskell OpenGL and there's a problem. I have also drawn it in R (with packages rgl and misc3d) and there's no problem. The two algorithms (in Haskell and R) are very similar. The Barth sextic is an implicit surface, and in Haskell I compute a triangulation of this surface with a marching cubes algorithm that I got by translating the one of misc3d to Haskell and C. I use the vertex normals, each defined by the gradient of the implicit equation.

Here is the problem:

I don't want these black shadows. When I look at the back of the sextic, by a 180° rotation, there's no such shadow:

The full code is available in this Github repo. Here are the parts of the code relevant to the colors:

fuchsia :: Color4 GLfloat

fuchsia = Color4 1.00 0.00 1.00 1

discord :: Color4 GLfloat

discord = Color4 0.21 0.22 0.25 1



  renderPrimitive Triangles $ mapM_ drawTriangle triangles

  swapBuffers

  where

    drawTriangle ((v1,v2,v3), (n1,n2,n3)) = do

      materialDiffuse FrontAndBack $= fuchsia

      normal n1

      vertex v1

      normal n2

      vertex v2

      normal n3

      vertex v3



  clearColor $= discord

  materialAmbient FrontAndBack $= black

  materialDiffuse FrontAndBack $= white

  materialEmission FrontAndBack $= black

  lighting $= Enabled

  lightModelTwoSide $= Enabled

  light (Light 0) $= Enabled

  position (Light 0) $= Vertex4 0 0 (-1000) 1

  ambient (Light 0) $= white

  diffuse (Light 0) $= white

  specular (Light 0) $= white

I have tried to change the colors in this last piece of code, but no way to get rid of these shadows. Am I doing something bad with the colors? I am sure the normals are correct because this works in R. However the shadows appear where the surface is not smooth, so I'm wondering whether the issue is caused by the normals.

The R rendering:

Edit

I have managed to get rid of these shadows:

I don't really know how, I've done so many attempts... But anyway, now the problem is that the back of the sextic is too lighty:

Now the rendering is nice :-)

I don't know what caused the problem because I have done numerous changes... Here are the relevant parts of the code:

resize :: Double -> Size -> IO ()

resize zoom s@(Size w h) = do

  viewport $= (Position 0 0, s)

  matrixMode $= Projection

  loadIdentity

  perspective 45.0 (w'/h') 1.0 100.0

  lookAt (Vertex3 0 0 (-6+zoom)) (Vertex3 0 0 0) (Vector3 0 1 0)

  matrixMode $= Modelview 0

  where

    w' = realToFrac w

    h' = realToFrac h

main :: IO ()

main = do

  _ <- getArgsAndInitialize

  _ <- createWindow "Barth Sextic"

  windowSize $= Size 500 500

  initialDisplayMode $= [RGBMode, DoubleBuffered, WithDepthBuffer]

  clearColor $= discord

  clientState ColorArray $= Disabled -- this is a default option, I think

  materialAmbient Front $= black

  materialDiffuse Front $= white

  materialEmission Front $= Color4 0 0 0 0

  materialSpecular Front $= white

  materialShininess Front $= 50

  lighting $= Enabled

  light (Light 0) $= Enabled

  position (Light 0) $= Vertex4 500 500 (-1000) 1

  diffuse (Light 0) $= white

  specular (Light 0) $= white

  lightModelAmbient $= Color4 0.35 0.35 0.35 1

  depthMask $= Enabled -- this is default option

  depthFunc $= Just Lequal

  shadeModel $= Smooth

  fog $= Disabled -- this is default option, I think

  polygonMode $= (Fill, Fill) -- this is default option

  polygonSmooth $= Enabled

  cullFace $= Just Front

  rescaleNormal $= Enabled

  ......

I have also changed the order of the vertices of each triangle:

drawTriangle ((v1,v2,v3), (n1,n2,n3)) = do

  materialDiffuse Front $= fuchsia

  normal n1

  vertex v1

  normal n3

  vertex v3

  normal n2

  vertex v2

This answer is a bit premature. I will investigate more later, and I'll edit to write my findings.

EDIT

Well, I have done further investigations and sadly, my conclusion is that I have no explanation: I have reverted all my changes, and no way to reproduce the issue !!

Now I use this shorter code:

display :: ...... -> displayCallback

  ......

  renderPrimitive Triangles $

    mapM_ drawTriangle triangles

  swapBuffers

  where

    drawTriangle ((v1,v2,v3), (n1,n2,n3)) = do

      materialDiffuse Front $= fuchsia

      normal n1

      vertex v1

      normal n2

      vertex v2

      normal n3

      vertex v3

resize :: Double -> Size -> IO ()

resize zoom s@(Size w h) = do

  viewport $= (Position 0 0, s)

  matrixMode $= Projection

  loadIdentity

  perspective 45.0 (w'/h') 1.0 100.0

  lookAt (Vertex3 0 0 (-6+zoom)) (Vertex3 0 0 0) (Vector3 0 1 0)

  matrixMode $= Modelview 0

  where

    w' = realToFrac w

    h' = realToFrac h

The two MatrixMode are important.

main :: IO ()

main = do

  _ <- getArgsAndInitialize

  _ <- createWindow "Barth Sextic"

  windowSize $= Size 500 500

  initialDisplayMode $= [RGBMode, DoubleBuffered, WithDepthBuffer]

  clearColor $= discord

  materialAmbient Front $= black

  materialDiffuse Front $= white

  materialEmission Front $= black

  lighting $= Enabled

  light (Light 0) $= Enabled

  position (Light 0) $= Vertex4 500 500 (-1000) 1

  ambient (Light 0) $= white

  diffuse (Light 0) $= white

  specular (Light 0) $= white

  depthFunc $= Just Less

  shadeModel $= Smooth

  cullFace $= Just Back

  ......

polygonSmooth and rescaleNormal were useless. I have also changed the position of the light but this is not the point which caused the issue. The cullFace is not necessary but it is good because there's no visible back face.