我的Javascript游戏的坐标 - 基于角度，我什么时候使用Sin Cos和Tan？ [英] Coordinates for my Javascript game - based on an angle, when do I use Sin Cos and Tan?

问题描述

JavaScript协调Sin，Cos或Tan？
我试图在web浏览器中学习一些基本的三角学游戏开发。我知道soh cah toa规则等。我知道我们也在-1和1之间工作。

我很困惑，但我需要计算出x和y坐标

这里是我必须在x和y中确定我的角度的方向，这是工作（感谢Loktar）。

p>

  velY = -Math.cos（angle * Math.PI / 180） 
 velX = Math.sin（angle * Math.PI / 180）* thrust; 
  

我的理解是，我发现x和y的cos基于一个小公式将我的角度变量转换为弧度。

但是，为什么cos需要用于x和sin为y？ tan在哪里进来？这是与一个圆的四个象限有关吗？

我怎么知道什么时候使用sin cos或tan，当我只给一个角度，我需要工作

任何简单的图表或解释都会非常有帮助！

感谢

解决方案

基本定义（来自您的三角书）：

  cosΘ= x / h，sinΘ= y / h 
  

$ b b

用于描述x，y和H的无关ASCII艺术：

  _ 
 / \假设我们'这样去
 / 
 / | 
 / | 
 h / | 
 / | Y 
 / | 
 /Θ| 
 + ------- 
 X 
  

分成两个向量的和。 （在图中，你可以认为这是H东北向X米，北向Y米）

H在这种情况下对应到你当前的推力。你想找到推力的X和Y分量。

由于cosΘ= X / H（余弦的基本定义），我们可以说（通过简单代数）

  X = H * cosΘ
  

假定为弧度测量。如果您使用度数，则必须乘以Math.PI / 180以获取正确的值。因此，您有

 Θ= angle * Math.PI / 180 
  pre> 
 
 
我们非常接近！现在我们经典的余弦公式定义如下：
  cos（angle * Math.PI / 180）= X / H 
  
 H是我们的推力向量，X只是我们推力的水平部分
 
 
 
现在，等一下，你说。 为什么我使用余弦来计算垂直速度？你的轴似乎翻转了我。是啊。这是标准几何定向 - 角度被测量为从 --------> 直接向右旋转的逆时针旋转。您的轴被翻转，因为您将角度存储为时钟角，即0度处于12:00。为了使用标准几何方程，我们必须镜像我们的整个宇宙，使得X和Y轴被翻转。幸运的是，这样做的数学方法只是在方程中切换所有的X和Y。
 坐标系
 _ 
 / \ 
 / 
 / | 
 / |角度逆时针增加
 h / | 
 / | Y 
 / | 
 /Θ| 
 + -----------（零度从这里开始）
（0,0）X 
 
 
您的坐标系
 
（零度从这里开始）
 ^ 
 |角度顺时针增加
 | / 
 | / 
 |Θ/ 
 | / 
 + 
  
为什么在余弦有一个负？因为这里是笛卡尔系统，我们在这里做我们的数学
  ^ y轴
 | 
 | 
 + ----> x轴
  
这里是你要绘制的笛卡尔坐标系> 
 
 
  + ------> x轴
 | 
 | 
v y轴
  
因为y轴朝向另一个方向，所以y值取负数1以获得正确的方向
 
JavaScript coordinates Sin, Cos or Tan?
I am trying to learn some basic trigonometry for game development in the web browser. I know the soh cah toa rule etc. I know we are also working between -1 and 1.

I am confused though, I need to work out x and y coordinates separately depending on an angle.

Here is what I have to work out the direction of my angle in x and y, which does work (Thanks to Loktar).
velY = -Math.cos(angle * Math.PI / 180) * thrust;
velX = Math.sin(angle * Math.PI / 180) * thrust;
What I understand from this is I am finding the cos of x and y based on a small formula to convert my angle variable to radians.

But, why does cos need to be used for x and sin for y? Where does tan come into this? Is this to do with the 4 quadrants of a circle?

How do I know when to use sin cos or tan when I am only given an angle and I need to work out where on a circle that angle places using x,y?

Any simple diagrams or explanations would be extremely helpful!

Thanks
解决方案
Basic Definitions (from your trigonometry book):  
cos ϴ = x/h, sin ϴ = y/h
Gratuitous ASCII art to describe x,y,and H : 
         _
         /\  assume we're going this way 
        /
       /|
      / |
  h  /  |
    /   |  Y
   /    |
  /ϴ    |
 +-------
    X
A vector can be split into a sum of two vectors. (you can think of this in the diagram as going northeast for H meters is the same as going east for X meters and north for Y meters)

H in this case corresponds to your current thrust. You want to find the X and Y components of that thrust. 

since   cos ϴ = X / H  (basic definition of cosine),  we can say (via simple algebra) 
X = H * cos ϴ
however, ϴ is assumed to be a radian measure. if you're using degrees, you have to multiply by Math.PI / 180 to get the correct value. hence, you have 
ϴ = angle * Math.PI / 180
We're very close! Now our classic definition-of-cosine formula (when translated to our terms) looks like
cos (angle * Math.PI / 180) = X / H
H being our Thrust vector, X being only the horizontal part of our thrust vector.

"Now, wait a minute," you say. "why am I using cosine to calculate the vertical velocity then? Your axes seem flipped to me." Ah, yes. This is standard geometric orientation -- angles are measured as a counter-clockwise rotation from --------> directly to the right. Your axes are flipped because you are storing your angle as a "clock-angle", i.e. 0 degrees is at 12:00. In order to use the standard geometric equation, we have to mirror our entire universe so that the X and Y axes are flipped. Luckily, the mathematical way to do this is simply to switch all your X's and Y's around in the equations.
standard 'math' coordinate system
            _
             /\  
            /
           /|
          / |       angles increase counterclockwise
      h  /  |
        /   |  Y
       /    |
      /ϴ    |
     +----------- (zero degrees starts here)
  (0,0)  X       


your coordinate system

  (zero degrees starts here)
       ^
       |   angles increase clockwise
       |   /
       |  /
       |ϴ/
       |/
       +
Finally, why is there a negative in the cosine? Because here is the cartesian system where we do our math in
 ^ y-axis
 |
 |
 +----> x-axis
here is the cartesian system that you are drawing to (probably a canvas)
+------> x-axis
|
|
v y-axis
since the y-axis is facing the other direction, you multiply all y-values by a negative 1 to get the correct orientation

                        
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