List of coordinates between irregular points in python

Question

Imagine we have two randomly selected points between 0 and 100 for both x and y.

For example:

(95,7), (35,6)

Now using the simple pygame.draw.line() function we could easily draw a line between these points without any gaps.

My question is, how could we find a list of all the coordinates in a single pixel thick line between the two points without any gaps in the line?

Secondly, is this even possible?

I am using this list of pixel for the crack maze algorithm that needs to "shoot" another pixel while regarding any blocking walls that may interfere with its path.

http://www.astrolog.org/labyrnth/algrithm.htm

By irregular, I refer to points which would not generate simple straight lines.

For example, it would be easy to find all the points between:

(0,5) and (5,5)

This has already been covered in this question:

List coordinates between a set of coordinates

Answer 1

Use Bresenham's line algorithm. You can find a simple python implementation here. Here’s a modified version of that implementation, which, given a starting and ending point, can return a list of intermediate points:

def line(x0, y0, x1, y1):
        "Bresenham's line algorithm"
        points_in_line = []
        dx = abs(x1 - x0)
        dy = abs(y1 - y0)
        x, y = x0, y0
        sx = -1 if x0 > x1 else 1
        sy = -1 if y0 > y1 else 1
        if dx > dy:
            err = dx / 2.0
            while x != x1:
                points_in_line.append((x, y))
                err -= dy
                if err < 0:
                    y += sy
                    err += dx
                x += sx
        else:
            err = dy / 2.0
            while y != y1:
                points_in_line.append((x, y))
                err -= dx
                if err < 0:
                    x += sx
                    err += dy
                y += sy
        points_in_line.append((x, y))
        return points_in_line

Answer 2

Perhaps it's an overkill but I'd just find the line equation and use a generator expression. To find the equation you can use this example algorithm which will return something like

lambda x: 2*x +1

With that we can do:

f = find_line_equation(A, B) #A B are tuples
points = [(x, f(x)) for x in range(min(A[0], B[0]), max(A[0], B[0]))]

This is assuming you want only integer points. You can also use this loop:

points = []
x = min(A[0], B[0])
increment = 0.1
while x <= max(A[0], B[0]):
    points.append((x, f(x))
    x += increment