SOFTIST 编程方法筆記 →目録

递归曲线C-曲线(算法)

C Curve Recursive Algorithm

本文是关于递归曲线C-曲線算法的笔记。C-曲線的生成算法如下图所示。

n级中的一根线段可以分解为２根(n-1)级的线段。如果n级的线段的长度是1.0，那么(n-1)级的线段的长度就是0.7010(=1/√2)。它们与n级的线段成４５°夹角。上面右侧的图，是10级C-曲線。下面是本人编写的VC++程序片断。

typedef struct tagFPOINT
{
    double x;
    double y;
} FPOINT;

void CRecursiveCurvesView::DrawLine(FPOINT p1,FPOINT p2, CDC* pDC)
{
    pDC->MoveTo((int)(p1.x+0.5), (int)(p1.y+0.5));
    pDC->LineTo((int)(p2.x+0.5), (int)(p2.y+0.5));
}

FPOINT CRecursiveCurvesView::RotateLine(FPOINT p1, FPOINT p2, double alpha)
{
    double x0 = p1.x;
    double y0 = p1.y;
    double x1 = p2.x - x0;
    double y1 = p2.y - y0;

    FPOINT pntRet;
    pntRet.x = x1 * cos(alpha) - y1 * sin(alpha) + x0;
    pntRet.y = x1 * sin(alpha) + y1 * cos(alpha) + y0;

    return pntRet;
}

FPOINT CRecursiveCurvesView::ShortenLine(FPOINT p1,FPOINT p2, double Ratio)
{
    FPOINT pntRet;

    if (p1.x == p2.x && p1.y == p2.y)
    {
        pntRet = p1;
    }
    if (p1.x == p2.x)
    {
        pntRet.x = p1.x;
        pntRet.y = p1.y + (p2.y - p1.y) * Ratio;
    }
    else if (p1.y == p2.y)
    {
        pntRet.y = p1.y;
        pntRet.x = p1.x + (p2.x - p1.x) * Ratio;
    }
    else
    {
        pntRet.x = p1.x + (p2.x - p1.x) * Ratio;
        pntRet.y = p1.y + (p2.y - p1.y) * Ratio;
    }
    return pntRet;
}

void CRecursiveCurvesView::C_Curve(int n, FPOINT p1, FPOINT p2, CDC* pDC)
{
    if (n == 1)
    {
        DrawLine(p1, p2, pDC);
    }
    else
    {
        FPOINT pc = ShortenLine(p1, p2, 1.0 / sqrt(2.0));
        pc = RotateLine(p1, pc, -atan(1.0));
        C_Curve(n - 1, p1, pc, pDC);
        C_Curve(n - 1, pc, p2, pDC);
    }
}

void CRecursiveCurvesView::OnCCirve() 
{
    CClientDC dc(this);
    FPOINT p1 = {400, 328};
    FPOINT p2 = {400, 200};
    C_Curve(10, p1, p2, &dc);
}