如何在笛卡尔坐标系中绘制n边的正多边形? [英] How to draw a n sided regular polygon in cartesian coordinates?

问题描述

我一直在试图找出如何编写一个简单的程序来计算x，y点的方法，以创建n边的规则多边形.有人可以给我一些不使用预先绘制多边形的函数的代码示例吗?我想了解这个过程，我假设是这样的:

I have been trying to figure out how to write a simple program to compute the x,y points for creating a regular polygon of n sides. Can someone give me some code examples that don't use preexisting functions that draw polygons? I want to understand the process, which I assume is something like this:

1. 从半径和中心点开始选择角度
2. 以某种方式计算距中心的那个距离的x，y位置(如何?)
3. 将360除以边数，移动该距离，然后从第一个x，y点绘制下一条线
4. 继续直到angle = 360除以那个数字.

假设我的假设是正确的，主要是要了解如何计算x，y点.

Assuming that my assumptions are correct, the main thing is to understand how to compute the x,y points.

建议以视觉基础(甚至是老式的Microsoft/Atari/Commodore BASIC)或易于理解的英语步骤来回答.如果您必须使用数学公式来回答，请使用计算机语言来完成它，以便我可以阅读它，即使使用C或C ++也可以弄清楚，但我不知道如何阅读数学符号.我使用的语言是一种类似于Visual Basic的语言，除了线条画外几乎没有其他图形基元.

Prefer answers in a visual basic (or even old style Microsoft/Atari/Commodore BASIC) or a human readable set of steps in English. If you have to answer with a math formula, do it in a computer language so I can read it, even in C or C++ I can figure it out, but I don't know how to read mathematical notation. The language I'm using is a Visual Basic-like language that has almost no graphics primitives other than line drawing.

推荐答案

让我们假设您要绘制一个半径为 r 的 N 面多边形，其中心为(0 ，0).然后 n 个顶点由下式给出:

Let's assume you want to draw an N-sided polygon of radius r, centred at (0,0). Then the n vertices are given by:

x[n] = r * cos(2*pi*n/N)
y[n] = r * sin(2*pi*n/N)

其中0< = n < N .请注意，这里的cos和sin是弧度的，而不是度数的(在大多数编程语言中，这是很常见的).

where 0 <= n < N. Note that cos and sin here are working in radians, not degrees (this is pretty common in most programming languages).

如果您想要一个不同的中心，只需将中心点的坐标添加到每个坐标( x [n] ， y [n] ).如果要改变方向，只需要增加一个恒定的角度即可.因此，一般形式为:

If you want a different centre, then just add the coordinates of the centre point to each (x[n], y[n]). If you want a different orientation, you just need to add a constant angle. So the general form is:

x[n] = r * cos(2*pi*n/N + theta) + x_centre
y[n] = r * sin(2*pi*n/N + theta) + y_centre

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