Clarifications on Movement
( ⇪ House Rules )
(See also, the improvements to the 5-foot step)
I use Euclidean distances for movement specifically, while I use a ruler for ranges (center to center, rounding down to the closer 5-foot increment like shown on the grid below), and a protractor for standard D&D 53.13° cones (circular sectors with height = chord) and 90° quarter-circle arcs. Just like it says in the SRD, you can’t move diagonally past (through) a corner (half of a wall is in the way). You can move diagonally past a creature, even an opponent. You can also move diagonally past other impassable obstacles, such as pits.
To turn a corner, you have to first move such that your space is touching the corner in only one corner of your grid space (not touching any of the sides of that corner with your space). Then you basically “have spent” that much of your movement speed in the middle of your movement action, and “count up from 0” more of your movement from there.
For example , in the grid imagine you’re at the green underlined “” box in the diagram above and the corner you want to move around is located at the upper right corner of the blue underlined “” box, where you wanted to turn that corner and go directly North 20 ft past that (ending at the blue “30” box above the blue underlined “” box). If you have 30 ft of movement speed, you spend 10 ft of it getting to the blue underlined “” box, and then count up the remaining 20 ft of your movement speed North from there.