mystery wave: what to call it?
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I recently stumbled on a useful periodic waveform, but I don't know what to call it. It's drawn in blue in the enclosed image, with a sine wave drawn in red for reference. Do you know what to properly call this wave?
The most efficient way I've found to generate the wave is by offsetting each quadrant of a sine wave, as in the following C code. The even quadrants are displaced, while the odd quadrants are inverted and displaced.
double MysteryWave(double fPhase)
{
double r = fmod(fPhase + 0.25, 1);
double s = sin(r * PI * 2);
if (r < 0.25)
return s - 1;
else if (r < 0.5)
return 1 - s;
else if (r < 0.75)
return s + 1;
else
return -1 - s;
}
A wave that is very similar but NOT identical to my mystery wave can be generated via the arcsine of the cubed sine, rescaled to $[-1..1]$ by dividing by $pi / 2$. In other words the following function is close but not quite the same:
2 * asin(pow(sin(fPhase * PI * 2), 3)) / PI
trigonometry periodic-functions
edited Oct 17 '17 at 14:35
iadvd
5,357102656
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
$endgroup$
add a comment |
$begingroup$
I recently stumbled on a useful periodic waveform, but I don't know what to call it. It's drawn in blue in the enclosed image, with a sine wave drawn in red for reference. Do you know what to properly call this wave?
The most efficient way I've found to generate the wave is by offsetting each quadrant of a sine wave, as in the following C code. The even quadrants are displaced, while the odd quadrants are inverted and displaced.
double MysteryWave(double fPhase)
{
double r = fmod(fPhase + 0.25, 1);
double s = sin(r * PI * 2);
if (r < 0.25)
return s - 1;
else if (r < 0.5)
return 1 - s;
else if (r < 0.75)
return s + 1;
else
return -1 - s;
}
A wave that is very similar but NOT identical to my mystery wave can be generated via the arcsine of the cubed sine, rescaled to $[-1..1]$ by dividing by $pi / 2$. In other words the following function is close but not quite the same:
2 * asin(pow(sin(fPhase * PI * 2), 3)) / PI
trigonometry periodic-functions
edited Oct 17 '17 at 14:35
iadvd
5,357102656
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
$endgroup$
$begingroup$
So if I understand correctly, each quarter period of your waveform is an actual sine wave, displaced and possibly reflected?
$endgroup$
– Arthur
Oct 17 '17 at 6:32
3
$begingroup$
Come up with a name that you like and use it. I don't think there is one already.
$endgroup$
– Ivan Neretin
Oct 17 '17 at 8:29
$begingroup$
In what way is it useful?
$endgroup$
– md2perpe
Oct 17 '17 at 16:13
$begingroup$
What's the context where such a "useful" function appears ?
$endgroup$
– Yves Daoust
Oct 17 '17 at 22:07
$begingroup$
@victimofleisure just a funny curiosity: In this other question, the very last graph shows a waveform similar to yours getting smoother cycle by cycle. math.stackexchange.com/questions/1431415/…
$endgroup$
– iadvd
Oct 18 '17 at 4:41
add a comment |
$begingroup$
I recently stumbled on a useful periodic waveform, but I don't know what to call it. It's drawn in blue in the enclosed image, with a sine wave drawn in red for reference. Do you know what to properly call this wave?
The most efficient way I've found to generate the wave is by offsetting each quadrant of a sine wave, as in the following C code. The even quadrants are displaced, while the odd quadrants are inverted and displaced.
double MysteryWave(double fPhase)
{
double r = fmod(fPhase + 0.25, 1);
double s = sin(r * PI * 2);
if (r < 0.25)
return s - 1;
else if (r < 0.5)
return 1 - s;
else if (r < 0.75)
return s + 1;
else
return -1 - s;
}
A wave that is very similar but NOT identical to my mystery wave can be generated via the arcsine of the cubed sine, rescaled to $[-1..1]$ by dividing by $pi / 2$. In other words the following function is close but not quite the same:
2 * asin(pow(sin(fPhase * PI * 2), 3)) / PI
trigonometry periodic-functions
edited Oct 17 '17 at 14:35
iadvd
5,357102656
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
$endgroup$
I recently stumbled on a useful periodic waveform, but I don't know what to call it. It's drawn in blue in the enclosed image, with a sine wave drawn in red for reference. Do you know what to properly call this wave?
The most efficient way I've found to generate the wave is by offsetting each quadrant of a sine wave, as in the following C code. The even quadrants are displaced, while the odd quadrants are inverted and displaced.
double MysteryWave(double fPhase)
{
double r = fmod(fPhase + 0.25, 1);
double s = sin(r * PI * 2);
if (r < 0.25)
return s - 1;
else if (r < 0.5)
return 1 - s;
else if (r < 0.75)
return s + 1;
else
return -1 - s;
}
A wave that is very similar but NOT identical to my mystery wave can be generated via the arcsine of the cubed sine, rescaled to $[-1..1]$ by dividing by $pi / 2$. In other words the following function is close but not quite the same:
2 * asin(pow(sin(fPhase * PI * 2), 3)) / PI
trigonometry periodic-functions
trigonometry periodic-functions
edited Oct 17 '17 at 14:35
iadvd
5,357102656
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
edited Oct 17 '17 at 14:35
iadvd
5,357102656
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
edited Oct 17 '17 at 14:35
iadvd
5,357102656
edited Oct 17 '17 at 14:35
iadvd
5,357102656
edited Oct 17 '17 at 14:35
iadvd
5,357102656
5,357102656
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
asked Oct 17 '17 at 5:59
victimofleisurevictimofleisure
162
162
$begingroup$
So if I understand correctly, each quarter period of your waveform is an actual sine wave, displaced and possibly reflected?
$endgroup$
– Arthur
Oct 17 '17 at 6:32
3
$begingroup$
Come up with a name that you like and use it. I don't think there is one already.
$endgroup$
– Ivan Neretin
Oct 17 '17 at 8:29
$begingroup$
In what way is it useful?
$endgroup$
– md2perpe
Oct 17 '17 at 16:13
$begingroup$
What's the context where such a "useful" function appears ?
$endgroup$
– Yves Daoust
Oct 17 '17 at 22:07
$begingroup$
@victimofleisure just a funny curiosity: In this other question, the very last graph shows a waveform similar to yours getting smoother cycle by cycle. math.stackexchange.com/questions/1431415/…
$endgroup$
– iadvd
Oct 18 '17 at 4:41
add a comment |
$begingroup$
So if I understand correctly, each quarter period of your waveform is an actual sine wave, displaced and possibly reflected?
$endgroup$
– Arthur
Oct 17 '17 at 6:32
3
$begingroup$
Come up with a name that you like and use it. I don't think there is one already.
$endgroup$
– Ivan Neretin
Oct 17 '17 at 8:29
$begingroup$
In what way is it useful?
$endgroup$
– md2perpe
Oct 17 '17 at 16:13
$begingroup$
What's the context where such a "useful" function appears ?
$endgroup$
– Yves Daoust
Oct 17 '17 at 22:07
$begingroup$
@victimofleisure just a funny curiosity: In this other question, the very last graph shows a waveform similar to yours getting smoother cycle by cycle. math.stackexchange.com/questions/1431415/…
$endgroup$
– iadvd
Oct 18 '17 at 4:41
$begingroup$
So if I understand correctly, each quarter period of your waveform is an actual sine wave, displaced and possibly reflected?
$endgroup$
– Arthur
Oct 17 '17 at 6:32
$begingroup$
So if I understand correctly, each quarter period of your waveform is an actual sine wave, displaced and possibly reflected?
$endgroup$
– Arthur
Oct 17 '17 at 6:32
3
3
$begingroup$
Come up with a name that you like and use it. I don't think there is one already.
$endgroup$
– Ivan Neretin
Oct 17 '17 at 8:29
$begingroup$
Come up with a name that you like and use it. I don't think there is one already.
$endgroup$
– Ivan Neretin
Oct 17 '17 at 8:29
$begingroup$
In what way is it useful?
$endgroup$
– md2perpe
Oct 17 '17 at 16:13
$begingroup$
In what way is it useful?
$endgroup$
– md2perpe
Oct 17 '17 at 16:13
$begingroup$
What's the context where such a "useful" function appears ?
$endgroup$
– Yves Daoust
Oct 17 '17 at 22:07
$begingroup$
What's the context where such a "useful" function appears ?
$endgroup$
– Yves Daoust
Oct 17 '17 at 22:07
$begingroup$
@victimofleisure just a funny curiosity: In this other question, the very last graph shows a waveform similar to yours getting smoother cycle by cycle. math.stackexchange.com/questions/1431415/…
$endgroup$
– iadvd
Oct 18 '17 at 4:41
$begingroup$
@victimofleisure just a funny curiosity: In this other question, the very last graph shows a waveform similar to yours getting smoother cycle by cycle. math.stackexchange.com/questions/1431415/…
$endgroup$
– iadvd
Oct 18 '17 at 4:41
add a comment |
1 Answer
1
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oldest
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This is a more direct formula: there are two symmetries happening there, so you need to play with the values assigned to each $frac{pi}{2}$ interval in order to retrieve the correct "mapping" (probably it can be simplified more):
$$sin{[x+pi+[frac{pi}{2}cdot(-1)^{lfloorfrac{x}{pi/2}rfloor}]]}+(-1)^{lfloor{x/pi}rfloor}$$
According to Wolfram Alpha if my calculations are correct it matches your waveform:
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
$endgroup$
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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votes
$begingroup$
This is a more direct formula: there are two symmetries happening there, so you need to play with the values assigned to each $frac{pi}{2}$ interval in order to retrieve the correct "mapping" (probably it can be simplified more):
$$sin{[x+pi+[frac{pi}{2}cdot(-1)^{lfloorfrac{x}{pi/2}rfloor}]]}+(-1)^{lfloor{x/pi}rfloor}$$
According to Wolfram Alpha if my calculations are correct it matches your waveform:
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
$endgroup$
add a comment |
$begingroup$
This is a more direct formula: there are two symmetries happening there, so you need to play with the values assigned to each $frac{pi}{2}$ interval in order to retrieve the correct "mapping" (probably it can be simplified more):
$$sin{[x+pi+[frac{pi}{2}cdot(-1)^{lfloorfrac{x}{pi/2}rfloor}]]}+(-1)^{lfloor{x/pi}rfloor}$$
According to Wolfram Alpha if my calculations are correct it matches your waveform:
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
$endgroup$
add a comment |
$begingroup$
This is a more direct formula: there are two symmetries happening there, so you need to play with the values assigned to each $frac{pi}{2}$ interval in order to retrieve the correct "mapping" (probably it can be simplified more):
$$sin{[x+pi+[frac{pi}{2}cdot(-1)^{lfloorfrac{x}{pi/2}rfloor}]]}+(-1)^{lfloor{x/pi}rfloor}$$
According to Wolfram Alpha if my calculations are correct it matches your waveform:
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
$endgroup$
This is a more direct formula: there are two symmetries happening there, so you need to play with the values assigned to each $frac{pi}{2}$ interval in order to retrieve the correct "mapping" (probably it can be simplified more):
$$sin{[x+pi+[frac{pi}{2}cdot(-1)^{lfloorfrac{x}{pi/2}rfloor}]]}+(-1)^{lfloor{x/pi}rfloor}$$
According to Wolfram Alpha if my calculations are correct it matches your waveform:
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
edited Oct 17 '17 at 21:49
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
answered Oct 17 '17 at 8:36
iadvdiadvd
5,357102656
5,357102656
add a comment |
add a comment |
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$begingroup$
So if I understand correctly, each quarter period of your waveform is an actual sine wave, displaced and possibly reflected?
$endgroup$
– Arthur
Oct 17 '17 at 6:32
3
$begingroup$
Come up with a name that you like and use it. I don't think there is one already.
$endgroup$
– Ivan Neretin
Oct 17 '17 at 8:29
$begingroup$
In what way is it useful?
$endgroup$
– md2perpe
Oct 17 '17 at 16:13
$begingroup$
What's the context where such a "useful" function appears ?
$endgroup$
– Yves Daoust
Oct 17 '17 at 22:07
$begingroup$
@victimofleisure just a funny curiosity: In this other question, the very last graph shows a waveform similar to yours getting smoother cycle by cycle. math.stackexchange.com/questions/1431415/…
$endgroup$
– iadvd
Oct 18 '17 at 4:41