Math

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Math defines several useful functions for mathematical purpose. The following list gives a short overview:

• sgn(value): Returns the sign of the given value.
  • Example: sgn(10) = 1, sgn(-3) = -1

• min(value1, value2): Returns the smaller of two values.
  • Example: min(3, 10) = 3, min(2, -2) = -2
  • This is useful, if you don't want a value to be greater than a threshold. Use min(value, threshold).
• max(value1, value2): Returns the greater of two values.
  • Example: max(3, 10) = 10, max(2, -2) = 2
  • This is useful, if you don't want a value to be smaller than a threshold. Use max(value, threshold).
• clamp(value, min, max): Keeps a value between a lower and an upper limit.
  • Example: clamp(5, 0, 10) = 5, clamp(100, 0, 10) = 10, clamp(-1, 0, 10) = 0
  • This is like a combination of max and min, used for thresholds

• square(value): Returns the square value (x²).
  • Example: square(3) = 9
• cube(value): Returns the cube value (x³).
  • Example: cube(3) = 27

• floor(value): Rounds the value down.
  • Example: floor(0.2) = 0, floor(0.7) = 0
• ceil(value): Rounds the value up.
  • Example: floor(0.2) = 1, floor(0.7) = 1
• round(value): Rounds the value.
  • Example: floor(0.2) = 0, floor(0.7) = 1

• mod(value, max): The modulo operation, enhanced to work properly with negative values.
  • Example: mod(8, 10) = 8, mod(14, 10) = 4, mod(-8, 10) = 2, mod(-14, 10) = 6

• rnd(): Returns a random number between 0 and almost 1: 0 ⇐ rnd < 1.
• rnd(max): Returns a random number between 0 and almost max: 0 ⇐ rnd < max.
• rnd(min, max): Returns a random number between min and almost max: min ⇐ rnd < max.

• interpolate(time, start, end): Interpolates between two values for a time between 0 and 1.
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• interpolateSmooth(time, start, end): Interpolates smoothly between two values for a time between 0 and 1. The function starts slowly, increases faster and stops slowly again.
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