As usual in D & D 3.5e, I refer to "squares" when I really mean "cubes". Just take "square" as game jargon, which it is in this case.

Anyway, the "5-foot, 10-foot." is an approximation of the cost of diagonals $ 1.5 times $ the distance, which itself approximates the cost $ sqrt {2} times approx.1,414 times $ (Pythagoras' theorem says a right angle $ a $ because the legs have a hypotenuse of $ sqrt {2} times a $).

A "double diagonal" is the hypotenuse of a right angle with legs of $ a $ and $ sqrt {2} times a $, this is how the hypotenuse will be $ sqrt {3} times a $, so we need an approximation of $ sqrt {3} times approx.1,732 times $. If we round it up $ 1.75 times $we need "5 feet, 10 feet, 10 feet, 10 feet". (So moving four squares costs 35 feet of motion – $ 1.75 times $ the 20 ft. it would normally take.

Obviously "5 feet, 10 feet, 10 feet, 10 feet". is a pain, and it is also much more questionable to start with 5 feet on the first square than with the "5 feet, 10 feet". to plan. It's also less clear how to combine it with a "single diagonal" move on the same lap – you probably shouldn't be able to move a double diagonal square 5 feet and then another diagonal for another 5 feet.

The most accurate way to fix this is to imagine the "5 feet, 10 feet". Rule than actually "7.5 feet". every time – it's really "7.5 feet (rounded to 5 feet), 15 feet (rounded to 15 feet, 10 feet above the first)". For the double diagonals, consider 8.75 feet that are still rounded to 5 feet the first time, and then 17.5 feet (rounded to 15 feet total distance), 26.25 feet (25 feet), 35 feet (35 feet) ).

Perhaps easier to see in tabular form. Here, $ d $ is the actual, unrounded distance, $ lfloor d rfloor $ for the rounded distance and $ Delta lfloor d rfloor $ for the cost of the last step. Each step should cost what is listed as $ Delta lfloor d rfloor $.

begin {array} {c | c | c}

{

textbf {even} \

begin {array} {c c c}

d & lfloor d rfloor & Delta lfloor d rfloor \ hline

phantom {0} 5 & phantom {0} 5 & 5 \

10 & 10 & 5 \

15 & 15 & 5 \

20 & 20 & 5 \

end {array}

}}

&

{

textbf {Single Diagonal} \

begin {array} {c c c}

d & lfloor d rfloor & Delta lfloor d rfloor \ hline

phantom {0} 7.5 & phantom {0} 5 & phantom {0} 5 \

15 phantom {.0} & 15 & 10 \

22.5 & 20 & Phantom {0} 5 \

30 phantom {.0} & 30 & 10 \

end {array}

}}

&

{

textbf {double diagonal} \

begin {array} {c c c}

d & lfloor d rfloor & Delta lfloor d rfloor \ hline

phantom {0} 8,75 & phantom {0} 5 & phantom {0} 5 \

17.5 Phantom {0} & 15 & 10 \

26.25 & 25 & 10 \

35 phantom {.00} & 35 & 10 \

end {array}

}}

end {array}

Combining single and double diagonals is then possible using these fractions – 7.5 feet. + 8.75 feet is 16.25 feet, so the second step when moving a single diagonal and a double diagonal is 10 feet, but the 1.25 feet "extra" is less than the 2.5 feet "extra" of two Double diagonal movements. By tracking this extra, you can track how far a character has actually moved.

And if you are actually dealing with this mess, I greet you because it is crazy. Unfortunately, this is the reality of 3D motion in D&D 3.5e. I strongly recommend a gentleman's approval to just keep things on the floor or fly abstract in some way – here's mine.