编辑：这是一个库错误。我将它报告给了 HOpenGL 邮件列表。
我使用 9 点矩形方法将圆/椭圆表示为 NURBS。
点是p1, p2, ..., p9, p9 = p1。它们如图所示：
y2 | p2 p3 p4
y1 | p1 p5
y0 | p8 p7 p6
-------------
| x0 x1 x2
x1 = (x0 + x2) / 2
y1 = (y0 + y2) / 2
即p1 = (x0, y1), p2 = (x0, y2)等等。
权重是：
1对于中点 (p1,p3,p5,p7)sqrt(0.5)对于角点 (p2,p4,p6,p8)
我使用两种方法将权重应用为齐次坐标：
- 对 -
(x,y)随着重量w变成Vertex4 (w*x) (w*y) 0 w - 错了——它变成了
Vertex4 x y 0 w
结果（首先正确，其次错误，如果它们太大，请见谅）：
你看，两者都不是正确的圆圈（虽然第二个看起来不错），我不明白为什么。
以下是基于Lines.hsGLUT 示例的代码：
import System.Exit ( exitWith, ExitCode(ExitSuccess) )
import Graphics.UI.GLUT
import Foreign.Marshal.Array
import Graphics.Rendering.OpenGL.GLU.NURBS
myInit :: IO ()
myInit = do
clearColor $= Color4 0 0 0 0
display :: DisplayCallback
display = do
clear [ ColorBuffer, DepthBuffer ]
color (Color3 1.0 1.0 1.0 :: Color3 GLfloat)
withNURBSObj () $ \nurbsObj -> do
nurbsBeginEndCurve nurbsObj $
withArrayLen knots $ \nKnots knots ->
withArray controls $ \controls -> do
nurbsCurve nurbsObj (fromIntegral nKnots) knots stride controls order
flush
where
order = 3
stride = 4 -- number of floats in Vertex
controls = zipWith mkControl points weights
mkControl (x, y) w = Vertex4 (x*w) (y*w) 0 w
-- mkControl (x, y) w = Vertex4 x y 0 w
knots = [0, 0, 0, 0.25, 0.25, 0.5, 0.5, 0.75, 0.75, 1, 1, 1]
weights = let a = sqrt 0.5 in [1, a, 1, a, 1, a, 1, a, 1]
points = [
(x0, y1), (x0, y2), (x1, y2),
(x2, y2), (x2, y1), (x2, y0),
(x1, y0), (x0, y0), (x0, y1)
]
y1 = (y0 + y2) / 2
x1 = (x0 + x2) / 2
(x0, x2) = (50, 450)
(y0, y2) = (x0, x2)
reshape :: ReshapeCallback
reshape size@(Size w h) = do
viewport $= (Position 0 0, size)
matrixMode $= Projection
loadIdentity
ortho2D 0 (fromIntegral w) 0 (fromIntegral h)
-- the following line is not in the original example, but it's good style...
matrixMode $= Modelview 0
keyboard :: KeyboardMouseCallback
keyboard (Char '\27') Down _ _ = exitWith ExitSuccess
keyboard _ _ _ _ = return ()
-- Request double buffer display mode.
-- Register mouse input callback functions
main :: IO ()
main = do
(progName, _args) <- getArgsAndInitialize
initialDisplayMode $= [ SingleBuffered, RGBMode ]
initialWindowSize $= Size 500 500
initialWindowPosition $= Position 100 100
createWindow "Test"
myInit
displayCallback $= display
reshapeCallback $= Just reshape
keyboardMouseCallback $= Just keyboard
mainLoop
编辑：我多次重新检查系数，在矩形表示之前我使用了 7 点三角形方法，并且有非常相似的失真。所以具体表现应该不成问题。
