使用C语言实现二维,三维绘图算法(2)-解析曲面的显示

使用C语言实现二维,三维绘图算法(2)-解析曲面的显示

---- 引言----

每次使用OpenGL或DirectX写三维程序的时候, 都有一种隔靴搔痒的感觉, 对于内部的三维算法的实现不甚了解. 其实想想, Win32中既然存在画线画点函数, 利用计算机图形学的知识, 我们用可以用纯C调用Win32实现三维绘图, 完全不用借助OpenGL和DirectX, 这有重复造*的嫌疑, 但是自己动手实现一遍, 毕竟也是有意义的.

[效果演示]

原始效果(100条浮动曲线)

加密以后的效果(200条浮动曲线)

[浮动水平线法绘图过程]

固定一个y值按步长变换给定一个x值, 从而可计算出平面截线一个点的z坐标值. 将改点投影到xoy平面上, 然后再变换到屏幕上. 如果是曲线端点要填充边界值. 接着检验此点的可见性,并用1表示上方可见, 0表示不可见, -1表示下方可见. 可见性检测就是用当前点的y值与上下浮动水平线数组中相应的元素值进行比较,y值大于上水平线数组中元素值或小于下水平线数组中元素值, 则当前点可见, 否则不可见. 往下再计算同一平面截线的另一点, 和上面点一样, 先投影到坐标平面上, 再变换到屏幕上. 先前的点叫紧前点, 当前的点为当前点. 紧前点和当前点的可见性主要有下面一些可能情形:

[编程实现要点]

曲面函数的定义

float SurfaceFun(float X, float Y)
{
    float w1, w2, w3, FV;
    w1=*(X-)*(X-) + (Y-)*(Y-) - ;
    w2=(X-)*(X-)/ + *(Y-)*(Y-) - ;
    w3=(X-)*(X-)/ + *(Y-)*(Y-) - ;

    if(w1>) w1=;
    if(w2>) w2=;
    if(w3>) w3=;    

    FV=w1*w1*exp(-w1) + w2*w2*exp(-w2) + w3*w3*exp(-w3);

    return(FV);

}

绘制曲面函数

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=; 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=; 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]==) || (HMin[XCur]==LimY) ) VisCur = VisPre;

            if(VisCur == VisPre)
            {
                if( (VisCur==) || (VisCur==-) )
                {
                    if(<=XCur)
                        PlotLine(XPre, LimY--YPre, Xi, LimY--YCur);
                    else if(<=YCur)
                        PlotLine(XPre, LimY--YPre, XPre, LimY--YCur);
                    else
                        PlotLine(Xi, LimY--YPre, XPre, LimY--YPre);

                    HorizonInc(XPre, YPre, XCur, YCur);
                }
            }
            else    // VisCur!=VisPre
            {
                if(VisCur==)
                {
                    if(VisPre == )
                    {
                        pi = Inter(XPre, YPre, XCur, YCur, HMax);
                        Xi = *pi;
                        Yi = *(pi+);
                    }
                    else
                    {
                        pi = Inter(XPre, YPre, XCur, YCur, HMin);
                        Xi = *pi;
                        Yi = *(pi+);
                    }

                    if(<=Xi)
                        PlotLine(XPre, LimY--YPre, Xi, LimY--Yi);
                    else if(<=Yi)
                        PlotLine(XPre, LimY--Yi, XPre, LimY--Yi);
                    else
                        PlotLine(XPre, LimY--YPre, XPre, LimY--YPre);

                    HorizonInc(XPre, YPre, Xi, Yi);
                }
                else
                {
                    if(VisCur == )
                    {
                        if(VisPre == )
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMax);
                            Xi = *pi;
                            Yi = *(pi+);  

                            if(<=Xi)
                                PlotLine(Xi, LimY--Yi, XCur, LimY--YCur);
                            else if(<=Yi)
                                PlotLine(XCur, LimY--YCur, XCur, LimY--YCur);
                            else
                                PlotLine(XCur, LimY--YCur, XCur, LimY--YCur);

                            HorizonInc(Xi, Yi, XCur, YCur);
                        }
                        else
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMin);
                            Xi = *pi;
                            Yi = *(pi+);  

                            if(<=Xi)
                                PlotLine(XPre, LimY--YPre, Xi, LimY--Yi);
                            else if(<=Yi)
                                PlotLine(XPre, LimY--YPre, XPre, LimY--Yi);
                            else
                                PlotLine(XPre, LimY--YPre, XPre, LimY--YPre);

                            HorizonInc(XPre, YPre, Xi, Yi);    

                            pi = Inter(XPre, YPre, XCur, YCur, HMax);
                            Xi = *pi;
                            Yi = *(pi+);  

                            if(<=Xi)
                                PlotLine(Xi, LimY--YCur, XCur, LimY--YCur);
                            else if(<=Yi)
                                PlotLine(XCur, LimY--Yi, XCur, LimY--YCur);
                            else
                                PlotLine(XCur, LimY--YCur, XCur, LimY--YCur);

                            HorizonInc(Xi, Yi, XCur, YCur);
                        }
                    }
                    else    // VisCur!=0, VisCur!=1
                    {
                        if(VisPre == )
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMin);
                            Xi = *pi;
                            Yi = *(pi+);  

                            if(<=Xi)
                                PlotLine(Xi, LimY--YCur, XCur, LimY--YCur);
                            else if(<=Yi)
                                PlotLine(XCur, LimY--Yi, XCur, LimY--YCur);
                            else
                                PlotLine(XCur, LimY--YCur, XCur, LimY--YCur);

                            HorizonInc(Xi, Yi, XCur, YCur);
                        }
                        else    // VisCur!=0, VisCur!=1, VisPre!=0
                        {
                            pi = Inter(XPre, YPre, XCur, YCur, HMax);
                            Xi = *pi;
                            Yi = *(pi+);  

                            if(<=Xi)
                                PlotLine(XPre, LimY--YPre, Xi, LimY--Yi);
                            else if(<=Yi)
                                PlotLine(XPre, LimY--YPre, XPre, LimY--Yi);
                            else
                                PlotLine(XPre, LimY--YPre, XPre, LimY--YPre);

                            HorizonInc(XPre, YPre, Xi, Yi);    

                            pi = Inter(XPre, YPre, XCur, YCur, HMin);
                            Xi = *pi;
                            Yi = *(pi+);  

                            if(<=Xi)
                                PlotLine(Xi, LimY--Yi, XCur, LimY--YCur);
                            else
                                PlotLine(XCur, LimY--YCur, XCur, LimY--YCur);

                            HorizonInc(Xi, Yi, XCur, YCur);
                        }
                    }
                }
            }

            VisPre = VisCur;
            XPre   = XCur;
            YPre   = YCur;
        }

        FillEdge(XCur, YCur, Xg, Yg);
    }
}