is this possible to do in less than polynomial time?
这可能在少于多项式时间内完成吗?
2 个解决方案
#1
Hmm... interesting question. I believe the answer is yes. Roughly, find the plane equation of each of the faces; for every pair of conjoined faces, if the angle between them is obtuse, the volume is concave. This should run in O(log(n)) time.
嗯...有趣的问题。我相信答案是肯定的。粗略地,找到每个面的平面方程;对于每对连体面,如果它们之间的角度是钝角,则体积是凹的。这应该在O(log(n))时间内运行。
I'd bet there's some way of working this out using a graph-coloring algorithm, but I'm just not that clever...
我敢打赌,使用图形着色算法可以解决这个问题,但我不是那么聪明......
#2
Use more words.
用更多的话。
We can;t know what exactly you are asking. We can only guess.
我们无法知道你究竟在问什么。我们只能猜测。
I don't think spaces could be convex or concave in general... maybe you mean volume or area? In any case I dont think you are going to beat polynomial time, given the complexity of the surface is going to be polynomial in nature.
我不认为空间通常可以是凸面或凹面...也许你的意思是体积或面积?在任何情况下,我都不认为你会打败多项式时间,因为表面的复杂性本质上是多项式的。
#1
Hmm... interesting question. I believe the answer is yes. Roughly, find the plane equation of each of the faces; for every pair of conjoined faces, if the angle between them is obtuse, the volume is concave. This should run in O(log(n)) time.
嗯...有趣的问题。我相信答案是肯定的。粗略地,找到每个面的平面方程;对于每对连体面,如果它们之间的角度是钝角,则体积是凹的。这应该在O(log(n))时间内运行。
I'd bet there's some way of working this out using a graph-coloring algorithm, but I'm just not that clever...
我敢打赌,使用图形着色算法可以解决这个问题,但我不是那么聪明......
#2
Use more words.
用更多的话。
We can;t know what exactly you are asking. We can only guess.
我们无法知道你究竟在问什么。我们只能猜测。
I don't think spaces could be convex or concave in general... maybe you mean volume or area? In any case I dont think you are going to beat polynomial time, given the complexity of the surface is going to be polynomial in nature.
我不认为空间通常可以是凸面或凹面...也许你的意思是体积或面积?在任何情况下,我都不认为你会打败多项式时间,因为表面的复杂性本质上是多项式的。