如何获取椭圆内像素的坐标? (截屏) [英] How to get the coordinates of the pixels inside an ellipse? (screenshot)

问题描述

我需要获取椭圆的特定区域内所有像素的坐标.

I need to get the coordinates of all the pixels inside this particular region of an ellipse.

我知道网格的大小，椭圆的中心，vertical_radix和horizo​​ntal_radix.

I know the size of the grid, the center of the elipse and the vertical_radix and horizontal_radix.

我在数学论坛上进行了搜索，但找不到有用的东西.

I searched on the math forums but couldn't find anything useful.

因此，在下一个示例中，网格为26 x 26. 椭圆的中心为(13，7)，vertical_radix为7，horizo​​ntal_radix = 13.

So for the next example the grid is 26 by 26. Center of the ellipse is at (13, 7) and vertical_radix is 7 and horizontal_radix = 13.

知道这一点后，我需要所有灰色像素的坐标(x和y对).

Knowing this I need the coordinates (pair of x and y) of all the grey pixels.

我只需要一个知道这6个参数(grid_width，grid_height，x_center，y_center，vertical_radix，horizo​​ntal_radix)的函数即可获取我的坐标. (任何标记的语言)

I just need like a function that knowing this 6 params (grid_width, grid_height, x_center, y_center, vertical_radix, horizontal_radix) could get my coordinates. (any of the tagged languages)

谢谢.

推荐答案

将点距中心的x和y偏移量缩放为一个单位圆，然后检查距中心的距离.

Scale the x and y offsets of the dots from the center into a unit circle, then check the distance from the center.

假设(x，y)的中心，(x ₁ ，y ₁ )的点以及轴为(a，b)的椭圆:

Assuming a center of (x, y), a point at (x₁, y₁), and an ellipse with axes of (a, b):

定标点为(2(x ₁ -x)/a，2(y ₁ -y)/b).从(0，0)看这是大于还是小于1，即将每个分量平方并与1进行比较.

The scaled point is (2(x₁-x)/a, 2(y₁-y)/b). See if this is more or less than 1 from (0, 0), i.e. square each component and compare the sum with 1.

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