上的球的边缘绘制的点 [英] Plotting a point on the edge of a sphere

问题描述

因此​​，从闪光背景的我有一些简单的2D触发的正常理解。在2D与圈口，我知道数学上放置使用特定的角度和半径边缘的一个项目。

So coming from a flash background I have an OK understanding of some simple 2D trig. In 2d with I circle, I know the math to place an item on the edge given an angle and a radius using.

x = cos(a) * r;
y = sin(a) * r;

现在如果我有在三维空间中的一个点，我知道我的球体的半径，我知道我要它绕Z轴定位角度和角度，我想周围放置它，比方说，y轴。什么是数学发现的X，在我的3D空间Y，Z坐标（假设我的出身是0,0,0）？我想我可以从圆触发借用数学，但我似乎无法找到一个解决方案。

Now if i have a point in 3d space, i know the radius of my sphere, i know the angle i want to position it around the z axis and the angle i want to position it around, say, the y axis. What is the math to find the x, y and z coordinates in my 3d space (assume that my origin is 0,0,0)? I would think i could borrow the Math from the circle trig but i can't seem to find a solution.

推荐答案

您的三维位置由两个角度（+半径，而你的情况是常数）给出

Your position in 3d is given by two angles (+ radius, which in your case is constant)

x = r * cos(s) * sin(t)
y = r * sin(s) * sin(t)
z = r * cos(t)

这里，取值是绕Z轴的夹角，和 T 是高的角度，从Z测得的向下轴。

here, s is the angle around the z-axis, and t is the height angle, measured 'down' from the z-axis.

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