在 JavaScript 中获取填充椭圆的点
我想知道是否有人可以指出我如何生成填充椭圆或圆形的点的正确方向。
我知道绘制轮廓的算法，但也不知道绘制内容。
我所需要的只是一系列点。但我不知道从哪里开始，而且似乎无法在谷歌上找到我的答案。
非常感谢任何帮助。
谢谢。
I was wondering if anyone could point me in the right direction as to how I would generate the points of a filled ellipse or circle.
I know of algorithms to draw the outline, but not the contents as well.
All I require are an array of points. But I have no idea where to start and can't seem to find my answer on Google.
Any help is much appreciated.
Thanks.
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您知道轮廓的点，因此您可以按行（即按 y 坐标）对它们进行排序。当两个y坐标相等时，按x坐标排序。
现在，对于具有相同 y 坐标的两个点，您知道它们之间的所有点都必须位于椭圆内。
You know the points of the outline, so you could just sort them by line (i.e. by the y-coordinate). When the two y-coordinates are equal, sort them by x-coordinate.
Now, for two points with the same y-coordinate you know that all points between them must be in the ellipse.
您可以通过扫描线生成点。椭圆的方程是
因此迭代y 并求解 x。您将得到一个具有两个解的 x 二次方程，为您提供扫描线左端和右端的点。其间的所有点都在椭圆内部。
如果您想快速生成端点的坐标，请参阅 John Kennedy 的论文，一种快速 Bresenham 型算法用于绘制椭圆。
You can generate the points by scanline. The equation of an ellipse is
So iterate over the values of y and solve for x. You'll get a quadratic equation in x with two solutions, giving you the points at the left and right end of the scanline. All the point in between are inside the ellipse.
If you want fast generation of the coordinates for the endpoints, see John Kennedy's paper, A fast Bresenham-type algorithm for drawing ellipses.
您可能想看看像 jsDraw2d 这样的图形库。
虽然更有效的方法可能是使用 Javascript 生成 SVG 图像，但不幸的是 Internet Explorer 最高版本 8 不支持 SVG。
You may want to have a look at some graphics library like jsDraw2d
A more efficient method though is probably to use Javascript to generate SVG images but unfortunately Internet Explorer up to version 8 does not support SVG.