Computer graphics-midpoint generation algorithm for parabolic line

Algorithm Description:

　　For parabolic, the most special case is analyzed, that is, the symmetry axis is the y axis, and it passes through the origin point of coordinates. ：

　　

As long as such a parabolic line is generated, the general parabola can be translated and rotated by this special case. Because the parabolic in this special case is symmetrical on both sides of the y-axis, it is only necessary to solve the parabolic formation in the first quadrant to obtain a complete image.
So how to get the parabolic in this special case

By the assumption that a point in the first quadrant of the parabola to move from the origin, and over that point A as a parabola tangent, then according to the slope of the tangent line k=1 can be divided into two parts of the quadrant, part of Point a left, the tangent slope is all less than 1, the other part is point A to the right, the tangent slope is all greater
Based on the idea of the previous midpoint generation algorithm, in the left half, each generation can increment the x coordinate by 1, and determine if the Y coordinate increases according to the decision parameters.

Area 1

In the right half, each build increments the Y coordinate by 1 and determines whether the X coordinate increases based on the decision parameters.

Zone 2

　　The next step is the derivation of the decision parameters:

　　The parabolic equation is, then the curve equation has two forms:

　　

　Zone 1:

　　

At that time: the coordinates of the next point should be selected at this time:

　　

At that time: the coordinates of the next point should be selected at this time:

　　

　　

　　Zone 2:

　　

At that time: the coordinates of the next point should be selected at this time:

　　

At that time: the coordinates of the next point should be selected at this time:

　　

　　Detailed code: Computer Graphics-code_1

Build Result:

　　

Computer graphics-midpoint generation algorithm for parabolic line