计算机图形学

计算机图形学

计算机图形学-直线画法（基于FMC）

• 1.数值微分法算法
• 2.中点画线法算法
• 3.Bresenham 画线算法

1.数值微分法算法

// An highlighted block
void MIDPOINT_Line(CDC *&pDC, CPoint startPoint, CPoint endPoint, COLORREF crColor)
{
	if (endPoint.x != startPoint.x && endPoint.y != startPoint.y) //非特殊直线一般直线
	{
		int kFlag = 0;                    // 0: 斜率 <= 1, 1: 斜率> 1
		int sFlag = 1;                    // 1: 斜率> 0; -1:斜率< 0
		if (startPoint.x > endPoint.x)    // 先判断两个端点， 使起点 x 小于终点 x
		{
			CPoint tem = startPoint;
			startPoint = endPoint;
			endPoint = tem;
		}
		if (abs(endPoint.y - startPoint.y)> abs(endPoint.x - startPoint.x))  //判断斜率是否大于1
		{
			kFlag = 1;
		}
		if (endPoint.y < startPoint.y)  //判断斜率正负
		{
			sFlag = -1;
		}
		int a, b,tA, tAB, d, x, y;
		if (sFlag == -1)
		{
			endPoint.y = startPoint.y + (startPoint.y - endPoint.y);
		}
		a = startPoint.y - endPoint.y;
		b = endPoint.x - startPoint.x;
		tA = 2 * a;
		tAB = 2 * (a + b);
		d = 2 * a + b;
		x = startPoint.x;
		y = startPoint.y;
		pDC->SetPixel(x, y, crColor);

		if (kFlag == 0) {
			for (int i = 0; i < (endPoint.x - startPoint.x); i++)
			{
				if (d>= 0)
				{
					pDC->SetPixel(x + 1, y, crColor);
					x += 1;
					d += tA;
				}
				else
				{
					pDC->SetPixel(x + 1, y + sFlag, crColor);
					x += 1;
					y += sFlag;
					d += tAB;
				}
			}
		}
		else  //斜率 > 1
		{
			if (kFlag == 1)
			{
				tA = 2 * b;
				d = 2*b + a;
			}
			for (int i =0; i< abs(endPoint.y - startPoint.y); i++)
			{
				if (d >= 0) {
					pDC->SetPixel(x + 1, y + sFlag, crColor);
					y += sFlag;
					x += 1;
					d += tAB;
				}
				else { // d < 0
					pDC->SetPixel(x, y + sFlag, crColor);
					y += sFlag;
					d += tAB;
				}
			}

		}

	}
	else if (startPoint.x == endPoint.x)  //画垂直线
	{
		if (startPoint.y < endPoint.y) {
			for (int i = startPoint.y; i < endPoint.y; i++)
			{
				pDC->SetPixel(startPoint.x, i, crColor);
			}
		}
		else {
			for (int i = endPoint.y; i < startPoint.y; i++)
			{
				pDC->SetPixel(startPoint.x, i, crColor);
			}
		}

	}
	else if (startPoint.y == endPoint.y)
	{
		if (startPoint.x < endPoint.x)
		{
			for (int i = startPoint.x; i < endPoint.x; i++)
			{
				pDC->SetPixel(i, startPoint.y, crColor);
			}
		}
		else {
			for (int i = endPoint.x; i < startPoint.x; i++)
			{
				pDC->SetPixel(i, startPoint.y, crColor);
			}
		}
	}

}

2.中点画线法算法

// An highlighted block
void DDA_Line(CDC *&pDC, CPoint &startPoint, CPoint &endPoint, COLORREF crColor)
{
	if (endPoint.x != startPoint.x && endPoint.y != startPoint.y)  //一般直线
	{
		double x, y;
		double k;  //斜率
		k = ((float)(endPoint.y - startPoint.y) - (float)(endPoint.x - startPoint.y));
		x = endPoint.x;
		y = endPoint.y;
		pDC->SetPixel((int)x, (int)y, crColor);
		if (fabs(k) <= 1.0) {
			for (int i =0; i startPoint.x)
				{
					x += 1;
					y += k;
				}
				else
				{
					x -= 1;
					y -= k;
				}
				pDC->SetPixel((int)x, (int)(y + 0.5), crColor);
			}
		}
		else if (fabs(k) > 1)
		{
			for (int i =0; i startPoint.y) {
					y += 1;
					x += 1.0 / k;
				}
				else {
					y -= 1;
					x -= 1.0 / k;
				}
				pDC->SetPixel((int)x + 0.5, (int)y, crColor);
			}

		}

	}
	else if(startPoint.x == endPoint.x)  //画垂直线
	{
		if (startPoint.y < endPoint.y) {
			for (int i =startPoint.y; iSetPixel(startPoint.x, i, crColor);
			}
		}
		else {
			for (int i = endPoint.y; i < startPoint.y; i++)
			{
				pDC->SetPixel(startPoint.x, i, crColor);
			}
		}

	}
	else if (startPoint.y == endPoint.y)
	{
		if (startPoint.x < endPoint.x)
		{
			for (int i = startPoint.x; i < endPoint.x; i++)
			{
				pDC->SetPixel(i, startPoint.y, crColor);
			}
		}
		else {
			for (int i = endPoint.x; i< startPoint.x; i++)
			{
				pDC->SetPixel(i, startPoint.y, crColor);
			}
		}
	}
}

3.Bresenham 画线算法