线描算法

线描算法 (Line drawing algorithms)

The equation for a straight line is y=mx+b
直线方程为y = mx + b
In this m represent a slope of a line which can be calculated by the m=y2-y1/x2-x1 where (x1, y1) are the starting position of the points and (x2, y2) are the end positions of the points.
在此m表示可以通过m = y2-y1 / x2-x1计算的直线的斜率，其中(x1，y1)是点的起始位置， (x2，y2)是点的终止位置。
There are generally three cases arises, which are:
通常会出现三种情况，分别是：
1. If an angle is greater than 45 degree then it means the slope is greater than 1 which also mean that dy/dx>1.
2. 如果角度大于45度，则意味着斜率大于1，这也意味着dy / dx> 1 。
3. If an angle is less than 45 degree then it means the slope is less than 1 which also mean that dy/dx<1.
4. 如果角度小于45度，则意味着斜率小于1，这也意味着dy / dx <1 。
5. If an angle is equal to 45 degrees then it means the slope is 1 which also means that dy/dx=1.
6. 如果角度等于45度，则意味着斜率为1，这也意味着dy / dx = 1 。
The increment in x can be calculated by the x2-x1 divided by a total number of steps. Similarly increment of y can be calculated by the y2-y1 divided by the total number of steps.
x的增量可以通过x2-x1除以总步数来计算。类似地，可以通过y2-y1除以总步数来计算y的增量。

DDA算法 (DDA Algorithm)

This is a line drawing algorithm which is named as Digital Differential Analyzer (DDA). Basically, it uses the floor function which takes the extra time for generating a line. The DDA algorithm is a faster method for calculating a pixel position for a direct use of it. In some cases, the line drawn by the DDA algorithm is not smooth.

这是一种画线算法，称为数字差分分析器(DDA)。基本上，它使用发言权功能，这会花费额外的时间来生成一条线。 DDA算法是一种用于直接使用像素位置来计算像素位置的更快方法。在某些情况下，DDA算法绘制的线不平滑。

    Algorithm DDA (x1, y1, x2, y2)
{
dx=x2-x1;
dy=y2-y1;
if (abs(dx)>abs(dy))
step=abs(dx)
else
step=abs(dy)
x increment= dx/step
y increment= dy/step
for(i=1;i<=step;i++)
{
putpixel (x1,y1);
x1=x1+increment;
y1=y1+increment;
}
}

Conclusion:

结论：

In this algorithm for finding a position of a point, there can be an increment in both x coordinate or can be in a y coordinate. On the basis of it, there are three cases generated which are as given below:

在用于查找点位置的该算法中， x坐标或y坐标都可以增加。在此基础上，生成了以下三种情况：

If the value of m is less than 1, then x=x+1 and y=y+m.
如果m的值小于1，则x = x + 1和y = y + m 。
If the value of m is greater than 1, then x=x+m and y=y+1.
如果m的值大于1，则x = x + m和y = y + 1 。
If the value of m is equal to 1, then x=x and y=y.
如果m的值等于1，则x = x和y = y 。

布雷森纳姆算法 (Bresenham’s Algorithm)

This is an algorithm which is used for drawing a line accurately and efficiently which was developed by Bresenham’s. Here generally, decision parameter is used for finding the next value from the initial one. According to this algorithm value of x will always be incremented but the value of y will be incremented or not it depends upon the decision parameter. This is a faster algorithm and less expensive to implement. There are no criteria of a round of the value in this algorithm which makes this algorithm faster and accurate.

这是由布雷森汉姆(Bresenham's)开发的一种算法，用于精确有效地绘制线。通常，这里使用决策参数从初始值中查找下一个值。根据该算法，x的值将始终增加，但是y的值将增加或不增加，这取决于决策参数。这是一种更快的算法，实现起来成本较低。此算法中没有轮取值的标准，这会使该算法更快，更准确。

Steps for implementing Bresenham’s algorithm:

实施布雷森汉姆算法的步骤：

    1.	Read the end points (x1, y1) and (x2, y2).
2.	dx=x2-x1 
dy=y2-y1
3.	x=x1, y=y1
4.	e=2dy-dx where, e is a decision parameter.
5.	While(e>=0)
{
y=y+1
e=e-2dx
}
X=x+1
e=e+2dy
6.	i<=dx , here i is only dependent upon the value of x.