I am trying to build a micromouse. My question is when i turn a corner, i have two option, to follow an arc, or, to turn 45 degree then move 1/2 diagonal unit and then turn 45 degree again. Which of these options will be logically faster?
Of course a straight line is always the shortest. Imagine pulling a string tight between the start & stop points.
But if you drive a car or ride a bicycle you know that you can't instantly change directions and if you were on a race track it you might be able to make a straight line once you've changed directions but you would have to turn-and turn-out of the connected straights. It depends on your speed and the cornering forces that you can get without skidding.
Do you drive a car? Test yourself on a 45 degree corner. You can maintain the straight line speed as you enter the corner if you drive in a curve, but cannot maintain the speed if you make TWO corners out of the one corner.