Bot

MCPK-bot is a Discord Bot aiming to replace MathBot for movement calculations. Indeed, it was getting tiresome to redefine functions all the time, and the syntax is not very convenient to use. MathBot is still very useful as a general-purpose calculation tool.

Advantages over using Mathbot:


 * Richer and more descriptive outputs
 * The functions are built-in: no need to redefine them manually.
 * The bot uses float math instead of fractions, so the simulation is more accurate.
 * For simulating movement:
 * X and Z movement are both considered, and momentum threshold is taken into account.
 * Actions are read from left to right, which is way easier to read and write.
 * All actions take direction as an optional argument.

Distance
%distance  [Z]

Returns the real distance of a X by Z jump (distances in blocks, Z is optional)

The formula is simply $$\sqrt{max(0,X-0.6)^2 + max(0,Z-0.6)^2}$$

Examples:

 * 4b jump:    %distance 4
 * 3x3 jump:  %distance 3 3

Duration
%duration  [ceilingHeight]

Returns the duration of a jump with the given height (heights in blocks, ceilingHeight is optional)

Examples:

 * -1.5b jump:     %duration -1.5
 * 3bc +1 jump:  %duration 1 3

Height
%height  [ceilingHeight]

Returns the jump height of the player after n ticks (ceilingHeight is optional)

Examples:

 * 12t jump:      %height 12
 * 2bc 9t jump: %height 9 2

Blip
%blip [initialHeight] [blipHeight] [lastJumpTicks]

Returns the height of the player after chaining consecutive blips (Y=0 is the bottom surface by convention).


 * is the number of chained blips performed
 * [initialHeight] is the player's initial height before the first jump (default: 0.0)
 * [BlipHeight] is the height of the blip's top surface (e.g. 0.0625 for carpet, 0.1875 for trapdoor...)
 * Unless specified with [lastJumpTicks], returns the peak of the jump by default (6 ticks).

Examples:

 * starting from Y=200:            %blip 4
 * 17 chained blips on lilypad: %blip_top 17 0.015625

Simulate
%simulate     (or simply % )

Reads the given actions from left to right, and simulates the resulting movement.

Actions:
Actions take two arguments:
 * Ticks : the duration of the action, in ticks
 * Direction (optional) : the direction (not facing) of the action, in degrees

Add "max_" in front to get the maximum momentum with that action (repeats the action 20 times)

Special Tokens:

 * Momentum, MM, and | sets the previous actions as momentum (resets the position minus the last tick)


 * Blocks and b convert the output landing distance to blocks (± 0.6 to X and Z if nonzero)


 * Meters, and m convert the output landing distance to meters (same values as default)


 * Position, pos, and p convert the output to a relative position (used when you're not calculating jump distance)

Usage:
The parser reads the actions and tokens from left to right. Actions and tokens should be separated by spaces.

The Momentum token can be used anywhere between two actions.

The Blocks, Meters, and Position tokens are to be used at the end of the sequence (mutually exclusive).

Examples:

 * hh timing:   % sprint | sprintjump(12)
 * rex bwmm: % walkjump(12,180) walk(1,180) Lsprintjump(12) | sprintjump(12)
 * 1bm 5-1:     % walkjump(12,170) walk(1,170) Lsprintjump45(1,-10) sprint45_air(11) | sprintjump45(14) b