Suppose we are moving in difficult terrain with 2x movement penalty.
Image from Core Rulebook pg. 192 claims moving diagonally in difficult terrain costs 15 feet. Non-diagonal movement takes 10 feet. This kinda makes sense as shown below.
Core Rulebook pg. 194 wrote:
Double Movement Cost: When your movement is hampered in some way, your movement usually costs double. For example, each square of movement through difficult terrain counts as 2 squares, and each diagonal move through such terrain counts as 3 squares (just as two diagonal moves normally do).
Core Rulebook pg. 192 wrote:
Diagonals: When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on.
Core Rulebook pg.170 wrote:
Hampered Movement: Difficult terrain, obstacles, and poor visibility can hamper movement (see Table 7–7 for details). When movement is hampered, each square moved into usually counts as two squares, effectively reducing the distance that a character can cover in a move. If more than one hampering condition applies, multiply all additional costs that apply. This is a specific exception to the normal rule for doubling.
Okay, so when we move diagonally in normal circumstances it counts with this penalty, penalty is time two, so two diagonal moves is 15 ft.
Also there is case with 5-foot-steps:
Core Rulebook pg.189 wrote:
You can only take a 5-foot-step if your movement isn’t hampered by difficult terrain or darkness. Any creature with a speed of 5 feet or less can’t take a 5-foot step, since moving even 5 feet requires a move action for such a slow creature.
Let's introduce snowshoes and cleats with this wonderful little feature:
Ultimate Equipment pg. 91 wrote:
Snowshoes reduce the penalty for walking through heavy snow by 50%; for example, if moving through snow normally costs you 2 squares of movement (1 square plus a 1 square penalty) per square traveled, snowshoes reduce this cost to 1.5 squares per square traveled"
Ultimate Equipment pg. 88 wrote:
Cleats reduce the penalty for walking over slick surfaces by 50%. For example, walking across ice normally costs 2 squares of movement (1 square plus a 1 square penalty) for every square of movement, but with cleats it costs only 1.5 squares for every square.
So...
Option a) It costs 5 feet + (5 feet penalty * 50% ) = 7,5 ft for normal movement. For diagonal movement it costs 11.25 ft as presented here 15 ft, given that diagonal is 7,5 ft. plus (7,5 feet penalty * 50%).
This seems cumbersome, and not really pathfinder like, and weird given fractions in movement, and spell ranges which tend to avoid those, awarding distance only for full levels.
Additionally prevents 5 feet step movement
b) Round down.
It costs 1 square + (1 square penalty * 50%) => 1 square per square. For diagonal movement it costs 1 square, then 3 squares(2 squares + 2 square penalty * 50%).
Seems weird and not really intuitive. Might allow 5 foot steps, as penalty effectively is removed?
c) It costs 1,5 square per square. This means when you move normally it costs you 1 square, 2 sq, 1sq, 2sq. When moving diagonally you...
Well that is problematic. 1,5x1,5per diagonal = ~2,25. Do we go: 2sq,2sq,2sq,3sq,2sq,2sq,2sq,3sq?
Anyway this might, allow 5 foot step? It's similar case to diagonal movement in normal terrain.
Maybe we should interpret this as:
d) It costs 1,5 square per square You take five foot diagonally, and then would take half of next diagonal step. This is 1 sq + (2 sq/2) = 2 sq per step. It's kind of roundabout reasoning but gives nice, simple maths. As in c) anyway this might, allow 5 foot step in straight line? However in this case 5 foot step is allowed only in straight line.
e) Some other idea
f) Is secret hidden by Norgober himself.
Black magic of this movement grows stronger with stronger penalties like: extremely deep snow in Reign of Winter, which is 4x movement penalty.
Core Rulebook pg.194 wrote:
If movement cost is doubled twice, then each square counts as 4 squares (or as 6 squares if moving diagonally). If movement cost is doubled three times, then each square counts as 8 squares (12 if diagonal) and so on. This is an exception to the general rule that two doublings are equivalent to a tripling.
a) 5 feet + (15 feet penalty*50%) = 12,5 ft for normal movement. For diagonals 7,5 feet * (22,5 feet penalty*50%) = 18,75 ft.
b) 1 square + (3 square penalty*50%) => 2 squares per square. For diagonal movement it would be 2 squares then 5 squares (2 squares + 6 square penalty*50%).
c) 2,5 square per square so 2 sq, 3 sq, 2 sq in straight line. In diagonal movement 2,5*1,5per diagonal=3,75. So: 3,4,4,4,3,4,4,4.
d) 2,5 square per square so 2,3,2 in straight line. In diagonal 2 sq + (3 sq/2) = 3,5 sq. So you go like 3,4,3,4,3,4.
Every solution is weird in it's own rights. Which one is right, or am I missing something.