Imagine a rectangular plane with dimensions X and Y. On that plane is a car. The car is about Z meters wide (the front bumper width, or up-down width in the image below). The car travels at a velocity v and moves across the entire surface as shown below:
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The car in the image above can move left-right or up-down or diagonal or whatever. The car takes T seconds to make a 90 degree turn. The car will need to move across every square inch of the area in the fastest possible time.
I'm trying to come up with an algorithm (perhaps a regression model) to prove the fastest possible time for this car to transverse the entire surface area. I thought that going left-right will be fastest, since the car will take t*2 seconds to make the 180 degree rotation once per row. Going up-down just adds more turns, and I'm not even sure about diagonal movements or moving around the perimeter etc. How would I tackle this problem (ignoring friction, internal resistance, etc, but I'll need to come back to that later)?
(This is not a homework question, I'm working on a project where I need to move an object across the area in the fastest possible time.)
The car in the image above can move left-right or up-down or diagonal or whatever. The car takes T seconds to make a 90 degree turn. The car will need to move across every square inch of the area in the fastest possible time.
I'm trying to come up with an algorithm (perhaps a regression model) to prove the fastest possible time for this car to transverse the entire surface area. I thought that going left-right will be fastest, since the car will take t*2 seconds to make the 180 degree rotation once per row. Going up-down just adds more turns, and I'm not even sure about diagonal movements or moving around the perimeter etc. How would I tackle this problem (ignoring friction, internal resistance, etc, but I'll need to come back to that later)?
(This is not a homework question, I'm working on a project where I need to move an object across the area in the fastest possible time.)