PHP 使用atan2 函數時遇到負值角度，應該如何正確處理？

gitbox 2025-09-18

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</span><span><span class="hljs-comment"># PHP 使用 atan2 函數時遇到負值角度，應該如何正確處理？</span></span><span>

在使用 PHP 進行二維圖形計算、坐標變換或遊戲開發時，我們經常需要通過點的坐標來計算角度。PHP 內置的 `atan2` 函數可以方便地根據 **y 坐標** 和 **x 坐標** 返回弧度值。但在實際應用中，很多人會遇到一個常見問題：**返回的角度可能為負值**。

</span><span><span class="hljs-comment">## 1. `atan2` 的返回值範圍</span></span><span>
在 PHP 中，`</span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(y, x)` 的返回值範圍是：
</span></span>

-π 到π （即-180° 到180°）

 <span><span>這意味著，當點位於第四象限時，返回的角度值將會是負數。例如：
```php
</span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-variable">$angle</span></span><span> = </span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(-</span><span><span class="hljs-number">1</span></span><span>, </span><span><span class="hljs-number">1</span></span><span>); 
</span><span><span class="hljs-keyword">echo</span></span><span> </span><span><span class="hljs-variable">$angle</span></span><span>; </span><span><span class="hljs-comment">// 輸出大約 -0.785398163 (即 -45°)</span></span><span>
</span></span>

2. 為什麼會有負角度？

數學上，角度是以x 軸正方向為起點逆時針計算。由於atan2的設計，位於第四象限的點，其角度自然會是負值。這並不是錯誤，而是函數的特性。

3. 如何將角度轉換為0 到2π 之間？

在很多應用場景下（例如圖形旋轉、導航指向），我們希望角度統一在0 到360°（0 到2π 弧度）的範圍內。此時可以簡單地通過判斷進行轉換：

 <span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-function"><span class="hljs-keyword">function</span></span></span><span> </span><span><span class="hljs-title">atan2To360</span></span><span>(</span><span><span class="hljs-params"><span class="hljs-variable">$y</span></span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>) {
    </span><span><span class="hljs-variable">$angle</span></span><span> = </span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(</span><span><span class="hljs-variable">$y</span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>); </span><span><span class="hljs-comment">// 返回 -π 到 π</span></span><span>
    </span><span><span class="hljs-keyword">if</span></span><span> (</span><span><span class="hljs-variable">$angle</span></span><span> &lt; </span><span><span class="hljs-number">0</span></span><span>) {
        </span><span><span class="hljs-variable">$angle</span></span><span> += </span><span><span class="hljs-number">2</span></span><span> * M_PI; </span><span><span class="hljs-comment">// 轉換到 0 到 2π</span></span><span>
    }
    </span><span><span class="hljs-keyword">return</span></span><span> </span><span><span class="hljs-variable">$angle</span></span><span>;
}

</span><span><span class="hljs-keyword">echo</span></span><span> </span><span><span class="hljs-title function_ invoke__">atan2To360</span></span><span>(-</span><span><span class="hljs-number">1</span></span><span>, </span><span><span class="hljs-number">1</span></span><span>); </span><span><span class="hljs-comment">// 輸出約 5.497787143 (即 315°)</span></span><span>
</span></span>

4. 轉換為角度製（0° 到360°）

如果需要以角度製表示，可以結合rad2deg函數：

 <span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-function"><span class="hljs-keyword">function</span></span></span><span> </span><span><span class="hljs-title">atan2ToDegree360</span></span><span>(</span><span><span class="hljs-params"><span class="hljs-variable">$y</span></span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>) {
    </span><span><span class="hljs-variable">$angle</span></span><span> = </span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(</span><span><span class="hljs-variable">$y</span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>);
    </span><span><span class="hljs-keyword">if</span></span><span> (</span><span><span class="hljs-variable">$angle</span></span><span> &lt; </span><span><span class="hljs-number">0</span></span><span>) {
        </span><span><span class="hljs-variable">$angle</span></span><span> += </span><span><span class="hljs-number">2</span></span><span> * M_PI;
    }
    </span><span><span class="hljs-keyword">return</span></span><span> </span><span><span class="hljs-title function_ invoke__">rad2deg</span></span><span>(</span><span><span class="hljs-variable">$angle</span></span><span>); </span><span><span class="hljs-comment">// 轉換為角度</span></span><span>
}

</span><span><span class="hljs-keyword">echo</span></span><span> </span><span><span class="hljs-title function_ invoke__">atan2ToDegree360</span></span><span>(-</span><span><span class="hljs-number">1</span></span><span>, </span><span><span class="hljs-number">1</span></span><span>); </span><span><span class="hljs-comment">// 輸出 315</span></span><span>
</span></span>

5. 總結

atan2在PHP 中返回的範圍是[-π, π] 。
如果出現負角度，不是錯誤，而是函數特性。
需要統一範圍時，可以加2π將結果轉換為[0, 2π] 。
若要角度製，則結合rad2deg ，統一在0°~360° 。

通過這種方式，就能避免負值角度帶來的困惑，並且在坐標計算和角度應用中更好地適配實際需求。