Select 阵列上未对齐的 2 个坐标之间的像素

Question

It is quite easy to select the pixels in an array that are on the same row or column. But how does one for example select pixels in a semi-straight line between [10,10] and [17,32] in a 40x40 array?

Answer 1

Unfortunately, the case you gave, does not have any integral points on the line segment joining (10,10) and (17,32). Let's say we have to generate a random point on the line segment joining A (10,10) and B (80,130).

This is more of a mathematics problem than programming.

The points on the semi-straight line joining A and B, satisfies this relation:

12x - 7y = 50

This is a Linear Diophantine Equation, its roots satisfy this general expression

x = 10 + 7t
y = 10 + 12t

Now, generate a random integer t, and substitute that value in the above general expression, to get a random point on this straight line.

In order for the random point to be between the given two points, t should be such that (0 <= t <= 10) ( Equality holds for the given two points, ie A and B )