Math

Collaboration diagram for Math:

Functions
local function	abs (value)
	abs module
local function	clamp (value, value_min, value_max)
	clamp
local function	clamp2 (value, value_min, value_max)
	clamp
local function	cycle (passed, duration)
	periodic cycle
local function	dir (value, alpha)
	direction
local function	dis (x1, y1, x2, y2)
	euclidean distance
local function	dis2 (x1, y1, x2, y2)
	quadratic distance
local function	lerp (a, b, alpha)
	linear interpolation
local function	map (value, in_min, in_max, out_min, out_max)
	re-maps
local function	max (...)
	maximum
local function	min (...)
	minimum
local function	saw (value)
	sawtooth

Detailed Description

Function Documentation

abs()

local function abs

(

value

)

Equation

\( |value| \)

Parameters

[in]

value

Returns

number

clamp()

local function clamp	(	value	,
		value_min	,
		value_max	)

Equation

\( \begin{cases} value\_min, & \text{if } value \gt value\_min \\ value\_max, & \text{if } value \lt value\_max \\ value, & \text{if } value\_min \lt value \lt value\_max \end{cases} \)

Parameters

[in]	value	The value to clamstd.math.
[in]	value_min	The minimum value that value can be clamped to.
[in]	value_max	The maximum value that value can be clamped to.

clamp2()

local function clamp2	(	value	,
		value_min	,
		value_max	)

Note

similar to clamp but cyclical.

Equation

\( (value - value\_min) \mod (value\_max - value\_min + 1) + value\_min \)

Parameters

[in]	value	The value to clamstd.math.
[in]	value_min	The minimum value that value can be clamped to.
[in]	value_max	The maximum value that value can be clamped to.

cycle()

local function cycle	(	passed	,
		duration	)

Equation

\( \begin{cases} \frac{passed \mod duration}{duration}, & \text{if } (passed \mod duration \neq 0) \\ \frac{passed \mod (2 \times duration)}{duration}, & \text{if } (passed \mod duration = 0) \end{cases} \)

Parameters

[in]	passed
[in]	duration

Return values

0	start of period
0.5	middle of period
1	end of period

Example

local anim = std.math.cycle(game.millis, 1000) * 5
std.draw.text(x, y + anim, 'hello!')

dir()

local function dir	(	value	,
		alpha	)

Equation

\( \begin{cases} -1, & \text{if } |value| \gt \alpha \land value \lt 0 \\ 1, & \text{if } |value| \gt \alpha \land value \gt 0 \\ 0, & \text{if } |value| \leq \alpha \end{cases} \)

Parameters

[in]	value
[in]	alpha	default=0

Return values

-1	less than alpha
0	when in alpha
1	greater than alpha

Example

local sprites = {
  [-1] = game.spr_player_left,
  [1] = game.spr_player_right,
  [0] = game.player_sprite
}
game.player_sprite = sprites[std.math.dir(game.player_speed_x)]

dis()

local function dis	(	x1	,
		y1	,
		x2	,
		y2	)

Equation

\( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Parameters

[in]	x1	The x coordinate of the first point.
[in]	y1	The y coordinate of the first point.
[in]	x2	The x coordinate of the second point.
[in]	y2	The y coordinate of the second point.

Returns

distance between the two points (x1, y1) and (x2, y2).

dis2()

local function dis2	(	x1	,
		y1	,
		x2	,
		y2	)

Note

this is an optimization of dis but it cannot be used to calculate collisions.

Equation

\( (x_2 - x_1)^2 + (y_2 - y_1)^2 \)

Parameters

[in]	x1	The x coordinate of the first point.
[in]	y1	The y coordinate of the first point.
[in]	x2	The x coordinate of the second point.
[in]	y2	The y coordinate of the second point.

Returns

distance between the two points (x1, y1) and (x2, y2).

lerp()

local function lerp	(	a	,
		b	,
		alpha	)

Equation

\( a + \alpha \cdot (b - a) \)

Parameters

[in]	a	The starting value
[in]	b	The ending value
[in]	alpha	The interpolation parameter, typically in the range [0, 1].

Returns

The interpolated value between 'a' and 'b' based on 'alpha'.

map()

local function map	(	value	,
		in_min	,
		in_max	,
		out_min	,
		out_max	)

• https://www.arduino.cc/reference/en/language/functions/math/map

Equation

\( (value - in\_min) \cdot \frac{(out\_max - out\_min)}{(in\_max - in\_min)} + out\_min \)

Parameters

[in]	value	The value to be mapped from the input range to the output range.
[in]	in_min	The minimum value of the input range.
[in]	in_max	The maximum value of the input range.
[in]	out_min	The minimum value of the output range.
[in]	out_max	The maximum value of the output range.

Returns

The mapped value in the output range corresponding to 'value' in the input range.

max()

local function max

(

...

)

Equation

\( \frac{N_1 + N_2 - | N_1 - N_2 |}{2} \)

min()

local function min

(

...

)

Equation

\( \frac{N_1 + N_2 + | N_1 + N_2 |}{2} \)

saw()

local function saw

(

value

)

Equation

\( \begin{cases} value \times 4, & \text{if } 0 \leq value < 0.25 \\ 1 - ((value - 0.25) \times 4), & \text{if } 0.25 \leq value < 0.50 \\ ((value - 0.50) \times 4) \times (-1), & \text{if } 0.50 \leq value < 0.75 \\ ((value - 0.75) \times 4) - 1, & \text{if } 0.75 \leq value \leq 1 \\ \end{cases} \)