線描算法 (Line drawing algorithms)

• The equation for a straight line is y=mx+b

  直線方程為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表示可以通過m = y2-y1 / x2-x1計算的直線的斜率，其中(x1，y1)是點的起始位置， (x2，y2)是點的終止位置。

• There are generally three cases arises, which are:

  通常會出現三種情況，分別是：

  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，則意味著斜率大于1，這也意味著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，則意味著斜率小于1，這也意味著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，則意味著斜率為1，這也意味著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的增量可以通過x2-x1除以總步數來計算。 類似地，可以通過y2-y1除以總步數來計算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.

這是一種畫線算法，稱為數字差分分析器(DDA)。 基本上，它使用發言權功能，這會花費額外的時間來生成一條線。 DDA算法是一種用于直接使用像素位置來計算像素位置的更快方法。 在某些情況下，DDA算法繪制的線不平滑。

    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:

結論：

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:

在用于查找點位置的該算法中， x坐標或y坐標都可以增加。 在此基礎上，生成了以下三種情況：

1. 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，則x = x + 1和y = y + m 。

2. 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，則x = x + m和y = y + 1 。

3. If the value of m is equal to 1, then x=x and y=y.

   如果m的值等于1，則x = x和y = y 。

布雷森納姆算法 (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.

這是由布雷森漢姆(Bresenham's)開發的一種算法，用于精確有效地繪制線。 通常，這里使用決策參數從初始值中查找下一個值。 根據該算法，x的值將始終增加，但是y的值將增加或不增加，這取決于決策參數。 這是一種更快的算法，實現起來成本較低。 此算法中沒有輪取值的標準，這會使該算法更快，更準確。

Steps for implementing Bresenham’s algorithm:

實施布雷森漢姆算法的步驟：

    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. 

翻譯自: https://www.includehelp.com/algorithms/line-drawing.aspx