定理:
三角形OP2P3的面积,OP2 x OP3,带有符号的面积, 按照右手螺旋定理,为正。同理推测其他三角形。
S总 = ΣSi , S = |S总|;
![](https://www.icode9.com/i/l/?n=22&i=blog/829551/202203/829551-20220328093208053-382024362.png)
推广到表面网格的体积计算, 先看四面体体积计算:
![](https://www.icode9.com/i/l/?n=22&i=blog/829551/202203/829551-20220328100945110-1580940335.png)
![](https://www.icode9.com/i/l/?n=22&i=blog/829551/202203/829551-20220328102330097-263186285.png)
矩阵行列式表达:
![](https://www.icode9.com/i/l/?n=22&i=blog/829551/202203/829551-20220328104130211-1400218566.jpg)
![](https://www.icode9.com/i/l/?n=22&i=blog/829551/202203/829551-20220328104133899-1976826079.jpg)
![](https://www.icode9.com/i/l/?n=22&i=blog/829551/202203/829551-20220328103706929-717206199.png)
V是个带符号的实数,正负号与矩阵的行列式的符号一致,也就是会有正体积和负体积。
参考:https://en.wikipedia.org/wiki/Shoelace_formula
标签:鞋带,Shoelace,定理,矩阵,体积,行列式,三角形
来源: https://www.cnblogs.com/lovebay/p/16066023.html