图形学 中点画线法C++实现

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//经过多重优化的中点画线算法，输入为线段两端点的坐标值
//该算法经过数学推导，可以处理斜率不存在，斜率为零，斜率为负数，斜率绝对值大于一等各种情况
void Mid_point(const unsigned& x1, const unsigned& y1, const unsigned& x2, const unsigned& y2)
{
	int dx = x2 - x1, dy = y2 - y1;
	enum Main_ChangeDirection { x, y };
	Main_ChangeDirection MainChange;
	if (abs(dx) >= abs(dy))
		MainChange = x;
	else MainChange = y;

	if ((MainChange == x && x1 > x2) || (MainChange == y && y1 > y2))//如果在主要变化方向上两点不满足升序排列，则递归调用自身，相当于交换两个点
	{
		Mid_point(x2, y2, x1, y1);
		return;
	}

	initgraph(800, 640);
	if (dx == 0)//处理斜率不存在的特殊情况
	{
		for (unsigned y = y1; y <= y2; ++y)
		{
			putpixel(x1, y, RED);
		}
		_getch();
		closegraph();
		return;
	}

	enum trend { Positive, Negative };//用一个枚举变量记录直线的斜率是否大于零，需要对大于零小于零两张情况进行分开考虑
	trend k;
	if (dx * dy >= 0)
		k = Positive;
	else k = Negative;

	int a = -dy, b = dx;
	if (MainChange == x)
	{
		if (k == Positive)
		{
			int d = 2 * a + b;
			int delta1 = 2 * a;
			int delta2 = 2 * (a + b);
			for (unsigned x = x1, y = y1; x <= x2; ++x)
			{
				putpixel(x, y, BLUE);
				if (d > 0)
				{
					d += delta1;
				}
				else
				{
					d += delta2;
					y++;
				}
			}
		}
		else if (k == Negative)
		{
			int d = 2 * a - b;
			int delta1 = 2 * (a - b);
			int delta2 = 2 * a;
			for (unsigned x = x1, y = y1; x <= x2; ++x)
			{
				putpixel(x, y, BLUE);
				if (d > 0)
				{
					d += delta1;
					--y;
				}
				else
				{
					d += delta2;
				}
			}
		}
	}
	else if (MainChange == y)
	{
		if (k == Positive)
		{
			int d = a + 2 * b;
			int delta1 = 2 * (a + b);
			int delta2 = 2 * b;
			for (unsigned y = y1, x = x1; y <= y2; ++y)
			{
				putpixel(x, y, BLUE);
				if (d > 0)
				{
					d += delta1;
					++x;
				}
				else
				{
					d += delta2;
				}
			}
		}
		else if (k == Negative)
		{
			int d = 2 * b - a;
			int delta1 = 2 * b;
			int delta2 = 2 * (b - a);
			for (unsigned y = y1, x = x1; y <= y2; ++y)
			{
				putpixel(x, y, BLUE);
				if (d > 0)
				{
					d += delta1;
				}
				else
				{
					d += delta2;
					x--;
				}
			}
		}
	}
	_getch();
	closegraph();
}

注：使用该函数需要头文件<graphics.h>和<conio.h>，前一个头文件不在系统库中，可以直接百度免费下载。

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