OpenGL 用三角形模擬生成球面

本文轉載自查看原文 2013-10-23 15:52 7136 Opengl/ F#

在看OpenGL紅皮書,看到生成球體這節,講了很多,總感覺不如自己動手寫一些代碼來的實在,用OpenGL中三角形模擬球形生成.主要要點,模型視圖變換,多邊形表面環繞一致性,矩陣堆棧.先貼上代碼.

雖然是用F#寫的,但是處理全是過程式的,很好理解.

  1 #r "F:\3D\1.0\Binaries\OpenTK\Debug\OpenTK.dll"
  2 #r "F:\3D\1.0\Binaries\OpenTK\Debug\OpenTK.GLControl.dll"
  3 
  4 open System
  5 open System.Collections.Generic
  6 open System.Windows.Forms
  7 open System.Threading
  8 open System.Drawing
  9 open System.Drawing.Imaging
 10 open OpenTK
 11 open OpenTK.Graphics
 12 open OpenTK.Graphics.OpenGL
 13 
 14 type loopForm() as form=
 15     inherit Form()
 16     let mutable x = 5.f
 17     let mutable y = 5.f
 18     let mutable z = 5.f
 19     let offest = 1.f
 20     let glControl = new OpenTK.GLControl()
 21     let textX= new TextBox()
 22     let textY= new TextBox()
 23     let textZ= new TextBox()
 24     let textLR = new TextBox()
 25     let textUD= new TextBox()
 26     let textInfo = new TextBox()
 27     let labelX= new Label()
 28     let labelY= new Label()
 29     let labelZ= new Label()
 30     let labelLR = new Label()
 31     let labelUD= new Label()
 32     let mutable first = 0
 33     let mutable buffer = 0
 34     let list = 0
 35     let scale = 3.f
 36     do
 37         form.SuspendLayout()
 38         glControl.Location <- new Point(10,40)
 39         glControl.Size <- new Size(400,300)
 40         glControl.BackColor <- Color.Red
 41         glControl.Resize.Add(form.resize)
 42         glControl.Paint.Add(form.paint)
 43         form.MouseWheel.Add(form.MouseDown)
 44         form.ClientSize <- new Size(600,400)
 45         form.Text <- "opengl"
 46         form.StartPosition <- FormStartPosition.Manual
 47         form.Location <- new Point(1200,600)
 48         form.Controls.Add(glControl)
 49         form.ResumeLayout(false)
 50         labelX.Location <- new Point(420,40)
 51         labelY.Location <- new Point(420,70)
 52         labelZ.Location <- new Point(420,100)
 53         labelLR.Location <- new Point(420,130)
 54         labelUD.Location <- new Point(420,160)
 55         labelX.Text <- "X:"
 56         labelY.Text <- "Y:"
 57         labelZ.Text <- "Z:"
 58         labelLR.Text  <- "水平:"
 59         labelUD.Text <-"上下:"
 60         textX.Location <- new Point(460,40)
 61         textY.Location <- new Point(460,70)
 62         textZ.Location <- new Point(460,100)
 63         textLR.Location <- new Point(460,130)
 64         textUD.Location <- new Point(460,160)
 65         textInfo.Location <- new Point(420,190)
 66         textInfo.Width <- 140
 67         form.Controls.Add(textX)
 68         form.Controls.Add(textY)
 69         form.Controls.Add(textZ)
 70         form.Controls.Add(textLR)
 71         form.Controls.Add(textUD)
 72         form.Controls.Add(labelX)
 73         form.Controls.Add(labelY)
 74         form.Controls.Add(labelZ)
 75         form.Controls.Add(labelLR)
 76         form.Controls.Add(labelUD)
 77         form.Controls.Add(textInfo)
 78         //#endregion 
 79     override v.OnLoad e =
 80         base.OnLoad e
 81         GL.ClearColor Color.MidnightBlue
 82         Application.Idle.Add(v.AIdle)
 83         v.ShowUI        
 84         textX.TextChanged.Add(form.TextChange)
 85         textY.TextChanged.Add(form.TextChange)
 86         textZ.TextChanged.Add(form.TextChange)
 87         textLR.TextChanged.Add(form.TextChange)
 88         textUD.TextChanged.Add(form.TextChange)
 89         //踢除正反面
 90         //GL.Enable EnableCap.CullFace
 91         //GL.CullFace CullFaceMode.Back
 92         //指定正反面
 93         GL.FrontFace FrontFaceDirection.Ccw
 94         //設置材料面填充模式
 95         GL.PolygonMode(MaterialFace.Front,PolygonMode.Fill)
 96         GL.PolygonMode(MaterialFace.Back,PolygonMode.Line)
 97         //啟用數組功能.
 98         GL.EnableClientState(ArrayCap.VertexArray)
 99         //GL.EnableClientState(ArrayCap.ColorArray)
100         GL.EnableClientState(ArrayCap.IndexArray)
101 //#region ""
102     member v.resize (e:EventArgs) =
103         GL.Viewport(0,0,glControl.ClientSize.Width,glControl.ClientSize.Height)
104         let aspect = float32 glControl.ClientSize.Width /float32 glControl.ClientSize.Height
105         let mutable projection = Matrix4.CreatePerspectiveFieldOfView(MathHelper.PiOver4,aspect,0.1f,64.f)
106         GL.MatrixMode MatrixMode.Projection
107         GL.LoadMatrix(&projection)
108     member v.paint (e:PaintEventArgs) =
109         v.Render()
110     member v.AIdle (e:EventArgs) =
111         while (glControl.IsIdle) do
112             v.Render()
113     member v.TextChange (e:EventArgs) =
114         x <- v.UIValue(textX)
115         y <- v.UIValue(textY)
116         z <- v.UIValue(textZ)
117     member v.MouseDown(e:MouseEventArgs) =
118         match v.ActiveControl with
119         | :? TextBox as t1 -> 
120             let mutable t = v.UIValue(t1)
121             t <- t + float32 e.Delta * offest * 0.01f
122             t1.Text <- t.ToString()
123         | _ -> 
124             v.Text <- v.ActiveControl.Text
125             let state =float32 e.Delta * offest * 0.01f
126             x<- x+state
127             y<- y + state
128             z <- z + state
129         v.ShowUI
130     member x.UIValue
131         with get (text:TextBox) = 
132             let mutable value = 0.f
133             if System.Single.TryParse(text.Text,&value) then
134                 value <- value
135             value
136         and set (text:TextBox) (value:float32) = text.Text<- value.ToString()
137     member v.ShowUI =
138         textX.Text <- x.ToString()
139         textY.Text <- y.ToString()
140         textZ.Text <- z.ToString()
141         textLR.Text <- v.UIValue(textLR).ToString()
142         textUD.Text <- v.UIValue(textUD).ToString()
143     member v.Normal (c:Vector3) =
144         c.Normalize() 
145         c * scale
146     member v.Subdivide (v1:Vector3,v2:Vector3,v3:Vector3) =
147         let vs = Array.create 6 Vector3.Zero
148         vs.[0] <- v1
149         vs.[1] <- v.Normal( Vector3.Lerp(v1,v2,0.5f))
150         vs.[2] <- v.Normal( Vector3.Lerp(v3,v1,0.5f))
151         vs.[3] <- v2
152         vs.[4] <- v.Normal( Vector3.Lerp(v2,v3,0.5f))
153         vs.[5] <- v3
154         let is = Array.create 12 0
155         is.[0] <- 0
156         is.[1] <- 1
157         is.[2] <- 2
158         is.[3] <- 2
159         is.[4] <- 1
160         is.[5] <- 4
161         is.[6] <- 4
162         is.[7] <- 1
163         is.[8] <- 3
164         is.[9] <- 2
165         is.[10] <-4
166         is.[11] <- 5
167         (vs,is)
168 //#endregion     
169     member v.CreatePane (angle:float32,x,y,z) =
170         GL.PushMatrix()
171         GL.Color3(Color.Green)
172         GL.Rotate(angle,x,y,z)
173         let mutable vv = [|Vector3.UnitY*scale;Vector3.UnitZ*scale;Vector3.UnitX*scale|]
174         let mutable iv = [|0;1;2|]
175         //let show array = printfn "%A" array
176         let mutable t =int (v.UIValue(textInfo))
177         if t > 6 then
178             t <- 6
179         elif t < 0 then
180             t <- 0                
181         for j in 0 .. t do
182             let mutable av = Array.create 0 Vector3.Zero
183             let mutable ev = Array.create 0 0
184             for i in 0 .. 3 .. iv.Length - 1 do
185                 let (vvv,iiv) = v.Subdivide(vv.[iv.[i]],vv.[iv.[i+1]],vv.[iv.[i+2]])
186                 let length = av.Length
187                 av <- Array.append av vvv
188                 let map = iiv |> Array.map (fun p -> p + length)
189                 ev <- Array.append ev map
190             vv <- av
191             iv <- ev 
192             //show vv
193             //show iv
194         GL.VertexPointer(3,VertexPointerType.Float,0,vv)      
195         GL.DrawElements(BeginMode.Triangles,iv.Length,DrawElementsType.UnsignedInt,iv)
196         GL.PopMatrix()    
197     member v.Render =
198         let mutable lookat = Matrix4.LookAt(new Vector3(x,y,z),Vector3.Zero,Vector3.UnitY)
199         GL.MatrixMode(MatrixMode.Modelview)
200         GL.LoadMatrix(&lookat)        
201         GL.Rotate(v.UIValue(textLR),0.f,1.f,0.f)
202         GL.Rotate(v.UIValue(textUD),1.f,0.f,0.f)
203         GL.Clear(ClearBufferMask.ColorBufferBit ||| ClearBufferMask.DepthBufferBit)
204         GL.Color3(Color.Green)
205         v.CreatePane(0.f,0.f,1.f,0.f)
206         v.CreatePane(90.f,0.f,1.f,0.f)
207         //v.CreatePane(180.f,0.f,1.f,0.f)
208         glControl.SwapBuffers()
209         ignore
210 let t = new loopForm()
211 t.Show()

View Code

首先我們設定逆時針方向為正方向,分別設定正面為畫布填充,反面為線填充,這樣我們就能很容易知道我們生成的三角形倒底是不是正確生成的我們要的面向.

然后分別取用頂點數組和頂點數組索引功能.畢竟后面的點多,一個一個去組裝沒這個腦力,還沒性能.

如何用三角開來模擬生成球面,方法肯定很多種,這里我們可以想象下,在坐標軸的原點就是球的原點,半徑為1,被X,Y,Z軸分成八個部分,我們找到正右上的那邊,與X,Y,Z軸的交點分別為x1(1,0,0),y1(0,1,0),z1(0,0,1).

然后我們把x1,y1,z1連起來畫一個三角形.注意這里就有順序了,想像一下,三個點的位置,要畫正面是用逆時針方向,一算,x1,y1,z1這個方向就是,但是通常為了形象些,我們從y1上開始畫,然后是前z1,然后是右x1.如代碼是這樣

let mutable vv = [|Vector3.UnitY*scale;Vector3.UnitZ*scale;Vector3.UnitX*scale|]
let mutable iv = [|0;1;2|]

然后就是細分這三角形,過程就是這樣,一個三角形分成四個.在for j in 0 .. t 這里,t越多,分的就越多,t是0,分一次成四個,t是1,四個再分別分成四個,就是16個.最后總的三角形就是4的t+1次方.

細分算法,大致如下,已知球面上二點,a1,a2,求在這球二點中間點ax.

已知球心在中間,得知,三個向量有如下關系,向量ax = (向量a2-向量a1)*0.5 + 向量a1.這樣可以算到向量a1,那點ax就是向量a1*半徑.

當一個三角形分成幾個三角形,也就是三個頂點變成六個頂點,那么生成生成三角形的索引也要重新更新.具體過程用圖來說明.

分的越細,球面越光滑,這樣只生成了八分之一的球面,后面的如何畫了,前面講了矩陣堆棧的用法,剛好可以用在這樣能在我方便生成另外幾個面,v.CreatePane(90.f,0.f,1.f,0.f)這個是我們繞Y軸90度后,生成另外的一個面,為了不破壞全局坐標,我們可以在轉之前調用PushMatrix記住當前矩陣,畫完后再用PopMatrix回到當前矩陣.

看一下程序運行后的效果圖.界面上的X,Y,Z指向人眼的位置,左右與上下指旋轉方向.最下面指細分的程度,值越大,細分的越厲害.

大家可以把頂點索引變下順序,然后再來看下效果,也可以把余下的六面全部補起.

免責聲明！

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