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                ## 點到直線的最短距離 &emsp;&emsp;根據直線的表示方式![](https://box.kancloud.cn/77e0744dfa83debd66bb54c3aaf8ad9f_200x48.png =100x25),可以設一個點![](https://box.kancloud.cn/ff70c6ccae3a687142d7088a55a484bb_220x48.png =110x25),任意一點![](https://box.kancloud.cn/ab1a51a029a0b62e67f0f70bea050e23_218x50.png =110x25)到點P的距離可以根據兩點間距離公式求出。 :-: ![](https://box.kancloud.cn/cbcb061eb5944fe10bc0feff4c51d35b_1300x118.png) &emsp;&emsp;然后根據對表達式求二階導數,可以證明該函數存在最小值。 &emsp;&emsp;令一階導數等于零可以求得取最小值時,t的取值。將t帶入可以計算出最短距離的平方。最后算得 :-: ![](https://box.kancloud.cn/5d23114e7927f4ffa554e9e452b2a943_500x120.png) ## 點到線段的最短距離 &emsp;&emsp;根據點到直線的距離的計算方式,把線段看成是直線,最后計算出t,然后根據t的值將t縮小到[0,1]之間。 ``` if t < 0 than t = 0 if t > 1 than t = 1 ``` &emsp;&emsp;這樣就可以計算點到線段的最短距離了。
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