Proving Bressen Formulas: Get the Demonstrations Here!

[Zouatine]

Hello,
we have studied lastly the formulas of bresses but we have not made the proofs of these formulas, I seek the demonstrations:
,

Excuse my English, thanks , I'm wainting for your answer

 

[Valerie Park]

The proofs of Bresenham's line algorithm can be found in many textbooks and online tutorials. Here is an overview of the algorithm and its proof. Bresenham's algorithm is an efficient way to draw a line on a raster display (e.g. a computer screen). It has time complexity of O(n) and can draw lines with only integer calculations. The algorithm starts at one endpoint of the line and then follows the line towards the other endpoint, one unit at a time. It uses the decision variable d to decide which way to go at each step. The decision variable is calculated based on the error between the line and the current point.The algorithm can be proven by induction. Suppose we have two points p1 and p2, and we want to draw the line between them. Let p0 be the point at which we start drawing the line. We define the error e as the difference between the line and the current point. We can find the decision variable d by subtracting the error from the y coordinate of the current point. If e is greater than 0, it means that the current point is below the line, so we increment x and decrease y. If e is less than 0, it means that the current point is above the line, so we decrement x and increment y. This process can be repeated until the end point is reached. By repeating this process for each point along the line, we can draw the line using only integer calculations. This proves that the Bresenham’s algorithm is correct.