How can I make Sine and Cosine waves move smoothly into different waves?
So when using sine and cosine, and switching between how powerful they are, there can be some jagged movement. The reason I am asking is because I am making a game where player input can change the power of the sine and cosine. I made a sample script to show what I mean and people can test (if you want to know what I mean):
01 | local Part = script.Parent |
02 | local RS = game:GetService("RunService") |
03 |
04 |
05 | local sine |
06 | do |
07 | local frequency |
08 | local phase = 0 |
09 | sine = function(amplitude, newFrequency) |
10 | local t = tick() |
11 | if not frequency then |
12 | frequency = newFrequency |
13 | elseif math.abs(newFrequency - frequency) < 0.01 then |
14 | local oldArgument = t*frequency + phase |
15 | frequency = newFrequency |
However when the sine and cosine powers change, there can be some jagged movement, If anyone knows how to make the changes more smooth, it would be greatly appreciated! :)
0
1 answer
Problem here, is that the argument of sine/cosine function changes dramatically once you change the frequency. What you actually want here, is to keep the current argument the same, yet it would change faster on the next iterations.
Fortunately, you can fix this by figuring out by how much the argument has changed for and correct it by adding that difference as sine/cosine function's phase.
That would look something like this:
1 | -- At beginning phase would be 0 |
2 | local oldArgument = frequency*t + phase |
3 | frequency = newFrequency |
4 | phase = oldArgument - frequency*t -- Phase is simply the difference between old and new sine function's argument |
In order to use this in the way you're currently using it, you'd have to define few local variables, that would remember the phase and frequency of the last function call:
01 | local sine |
02 | do -- Using do block, in order to hide "phase" and "frequency" variables from global scope |
03 | local frequency |
04 | local phase = 0 |
05 |
06 | function sine(amplitude, newFrequency) |
07 | local t = tick() |
08 |
09 | if not frequency then |
10 | frequency = newFrequency |
11 | elseif math.abs(newFrequency - frequency) < 0.01 then |
12 | -- Frequency has changed, calculate phase |
13 | local oldArgument = t*frequency + phase |
14 | frequency = newFrequency |
15 | phase = oldArgument - t*frequency |
Don't have any options to test this, but it should do the job.