使用C語言實現二維,三維繪圖算法(2)-解析曲面的顯示

使用C語言實現二維,三維繪圖算法(2)-解析曲面的顯示

---- 引言----

每次使用OpenGL或DirectX寫三維程序的時候, 都有一種隔靴搔癢的感受, 對於內部的三維算法的實現不甚瞭解. 其實想一想, Win32中既然存在畫線畫點函數, 利用計算機圖形學的知識, 咱們用能夠用純C調用Win32實現三維繪圖, 徹底不用藉助OpenGL和DirectX, 這有重複造輪子的嫌疑, 可是本身動手實現一遍, 畢竟也是有意義的.

[效果演示]

        原始效果(100條浮動曲線)

       

           加密之後的效果(200條浮動曲線)

           

[浮動水平線法繪圖過程]

      固定一個y值按步長變換給定一個x值, 從而可計算出平面截線一個點的z座標值. 將改點投影到xoy平面上, 而後再變換到屏幕上. 若是是曲線端點要填充邊界值. 接着檢驗此點的可見性,並用1表示上方可見, 0表示不可見, -1表示下方可見. 可見性檢測就是用當前點的y值與上下浮動水平線數組中相應的元素值進行比較,y值大於上水平線數組中元素值或小於下水平線數組中元素值, 則當前點可見, 不然不可見. 往下再計算同一平面截線的另外一點, 和上面點同樣, 先投影到座標平面上, 再變換到屏幕上. 先前的點叫緊前點, 當前的點爲當前點. 緊前點和當前點的可見性主要有下面一些可能情形:

   

 

[編程實現要點]

曲面函數的定義

float SurfaceFun(float X, float Y)
{
    float w1, w2, w3, FV;
    w1=4*(X-2)*(X-2) + (Y-4)*(Y-4) - 1;
    w2=(X-5)*(X-5)/9 + 4*(Y-2)*(Y-2) - 1;
    w3=(X-5)*(X-5)/9 + 4*(Y-6)*(Y-6) - 1;
    
    if(w1>85) w1=85;
    if(w2>85) w2=85;
    if(w3>85) w3=85;    
    
    FV=w1*w1*exp(-w1) + w2*w2*exp(-w2) + w3*w3*exp(-w3);
    
    return(FV);
    
}

 

繪製曲面函數

void DrawSurface()
{
    int Xe, Ye, Ln, Pt, XPre, YPre, XCur, YCur, Xi, Yi;
    int *pi, LimY, VisCur, VisPre;
    float X, Y, Z;
    
    LimY=GetWindowHeight();
    SetLineColor(BLUE); 

    for(Ln=0; Ln<=LNo; ++Ln)
    {
        Y=Y2-Ln*IncY;
        X=X1;
        Z=SurfaceFun(X,Y);
        CalcuProject(X, Y, Z);
        XPre = 0.5 + (XProj-F1)*EchX + C1;
        YPre = 0.5 + (YProj-F3)*EchY + C3;
        
        FillEdge(XPre, YPre, Xd, Yd);
        
        VisPre = VisibilityTest(XPre, YPre);
        
        for(Pt=0; Pt<=PNo; ++Pt)
        {
            X=X1+Pt*IncX;
            Z=SurfaceFun(X,Y);
            CalcuProject(X, Y, Z);
            XCur = 0.5 + (XProj-F1)*EchX + C1;
            YCur = 0.5 + (YProj-F3)*EchY + C3;
            VisCur = VisibilityTest(XCur, YCur);
            
            if( (HMax[XCur]==0) || (HMin[XCur]==LimY) ) VisCur = VisPre;
            
            if(VisCur == VisPre)
            {
                if( (VisCur==1) || (VisCur==-1) )
                {
                    if(0<=XCur)
                        PlotLine(XPre, LimY-60-YPre, Xi, LimY-60-YCur);
                    else if(0<=YCur)
                        PlotLine(XPre, LimY-60-YPre, XPre, LimY-60-YCur);
                    else
                        PlotLine(Xi, LimY-60-YPre, XPre, LimY-60-YPre);
                    
                    HorizonInc(XPre, YPre, XCur, YCur);
                }
            }
            else    // VisCur!=VisPre
            {
                if(VisCur==0)
                {
                    if(VisPre == 1)
                    {
                        pi = Inter(XPre, YPre, XCur, YCur, HMax);
                        Xi = *pi;
                        Yi = *(pi+1);
                    }
                    else
                    {
                        pi = Inter(XPre, YPre, XCur, YCur, HMin);
                        Xi = *pi;
                        Yi = *(pi+1);
                    }
                    
                    if(0<=Xi)
                        PlotLine(XPre, LimY-60-YPre, Xi, LimY-60-Yi);
                    else if(0<=Yi)
                        PlotLine(XPre, LimY-60-Yi, XPre, LimY-60-Yi);
                    else
                        PlotLine(XPre, LimY-60-YPre, XPre, LimY-60-YPre);
                    
                    HorizonInc(XPre, YPre, Xi, Yi);
                }
                else    
                {
                    if(VisCur == 1)
                    {
                        if(VisPre == 0)  
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMax);
                            Xi = *pi;
                            Yi = *(pi+1);  
                            
                            if(0<=Xi)
                                PlotLine(Xi, LimY-60-Yi, XCur, LimY-60-YCur);       
                            else if(0<=Yi)
                                PlotLine(XCur, LimY-60-YCur, XCur, LimY-60-YCur);
                            else
                                PlotLine(XCur, LimY-60-YCur, XCur, LimY-60-YCur);
                            
                            HorizonInc(Xi, Yi, XCur, YCur);   
                        }
                        else   
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMin);
                            Xi = *pi;
                            Yi = *(pi+1);  
                            
                            if(0<=Xi)
                                PlotLine(XPre, LimY-60-YPre, Xi, LimY-60-Yi);       
                            else if(0<=Yi)
                                PlotLine(XPre, LimY-60-YPre, XPre, LimY-60-Yi);
                            else
                                PlotLine(XPre, LimY-60-YPre, XPre, LimY-60-YPre);
                            
                            HorizonInc(XPre, YPre, Xi, Yi);    
                            
                            pi = Inter(XPre, YPre, XCur, YCur, HMax);
                            Xi = *pi;
                            Yi = *(pi+1);  
                            
                            if(0<=Xi)
                                PlotLine(Xi, LimY-60-YCur, XCur, LimY-60-YCur);       
                            else if(0<=Yi)
                                PlotLine(XCur, LimY-60-Yi, XCur, LimY-60-YCur);
                            else
                                PlotLine(XCur, LimY-60-YCur, XCur, LimY-60-YCur);
                            
                            HorizonInc(Xi, Yi, XCur, YCur);
                        }
                    }
                    else    // VisCur!=0, VisCur!=1
                    {
                        if(VisPre == 0)  
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMin);
                            Xi = *pi;
                            Yi = *(pi+1);  
                            
                            if(0<=Xi)
                                PlotLine(Xi, LimY-60-YCur, XCur, LimY-60-YCur); 
                            else if(0<=Yi)
                                PlotLine(XCur, LimY-60-Yi, XCur, LimY-60-YCur);
                            else
                                PlotLine(XCur, LimY-60-YCur, XCur, LimY-60-YCur);
                            
                            HorizonInc(Xi, Yi, XCur, YCur);   
                        }
                        else    // VisCur!=0, VisCur!=1, VisPre!=0
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMax);
                            Xi = *pi;
                            Yi = *(pi+1);  
                            
                            if(0<=Xi)
                                PlotLine(XPre, LimY-60-YPre, Xi, LimY-60-Yi);      
                            else if(0<=Yi)
                                PlotLine(XPre, LimY-60-YPre, XPre, LimY-60-Yi);
                            else
                                PlotLine(XPre, LimY-60-YPre, XPre, LimY-60-YPre);
                            
                            HorizonInc(XPre, YPre, Xi, Yi);    
                            
                            pi = Inter(XPre, YPre, XCur, YCur, HMin);
                            Xi = *pi;
                            Yi = *(pi+1);  
                            
                            if(0<=Xi)
                                PlotLine(Xi, LimY-60-Yi, XCur, LimY-60-YCur);      
                            else
                                PlotLine(XCur, LimY-60-YCur, XCur, LimY-60-YCur);
                            
                            HorizonInc(Xi, Yi, XCur, YCur);
                        }                        
                    }
                }
            }
            
            VisPre = VisCur;
            XPre   = XCur;
            YPre   = YCur;
        }
        
        FillEdge(XCur, YCur, Xg, Yg);
    }
}