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Sine wave with half circle waves?

abuabed84abuabed84 Posts: 510Member, PRO

I need a function where the Sine wave is thickened to the point where when the positive and negative waves are half circles.

Comments

  • tintrantintran Posts: 453Member

    you didn't specify what diameter of the circle is..
    but this should help you.
    It has diameter of 4.

    I first started with a graph of sqrt(4 - (x-2)^2)
    then i played around with floor and coefficients to get the other 2 graphs and then i modded the values to get repeating pattern, then added into my original equation.

  • abuabed84abuabed84 Posts: 510Member, PRO
    edited July 2015

    @tintran said:
    you didn't specify what diameter of the circle is..
    but this should help you.
    It has diameter of 4.

    I first started with a graph of sqrt(4 - (x-2)^2)
    then i played around with floor and coefficients to get the other 2 graphs and then i modded the values to get repeating pattern, then added into my original equation.

    thanks tintran,
    What I did was simply square root the Sine function.
    I haven't experimented enough with it, but it seems the smaller the exponent the flatter the wave appears.
    I haven't reached the precise exponents where it's 100% circular, I'm assuming it has something to do with pi, probably

    y=(sin(x))^(1/pi)

  • SLOCM3ZSLOCM3Z Posts: 797Member

    @abuabed84 said:
    y=(sin(x))^(1/pi)

    woah

  • abuabed84abuabed84 Posts: 510Member, PRO

    The circular Sine wave during implementation was a bit too narrow for me.

    I ended up using

    y=(Sin(x))^0.6

  • tintrantintran Posts: 453Member
    edited July 2015

    i don't expect any exponent that will get you perfect circle because by using sin(x) you're specifying x as an angle and not x coordinate of a circle (but i could be wrong :D)
    I arrived at mine by using y^2+x^2 = r where r is just a radius using pythegorean theorem.
    here's a graph to show the negative of my curve as well, as you can see it's perfect circle.
    If you want you can just play with the coefficients to get the circle of the proper radius size.

    and one with actual circle formula to compare

  • abuabed84abuabed84 Posts: 510Member, PRO
    edited July 2015

    Excellent man, thanks a lot

  • abuabed84abuabed84 Posts: 510Member, PRO

    @tintran said:
    i don't expect any exponent that will get you perfect circle because by using sin(x) you're specifying x as an angle and not x coordinate of a circle (but i could be wrong :D)

    I'm pretty sure you can draw half a circle with a sine wave, I've seen it before in college, I just can't remember the function.

  • abuabed84abuabed84 Posts: 510Member, PRO

    @tintran said:
    i don't expect any exponent that will get you perfect circle because by using sin(x) you're specifying x as an angle and not x coordinate of a circle (but i could be wrong :D)

    As long as it's a variable, the possibilities are limitless.

  • tintrantintran Posts: 453Member

    As i said, i could be wrong but until i see the proof, i don't think it's possible.

  • tintrantintran Posts: 453Member
    edited July 2015

    I got curious and tried to prove myself wrong but so far, i can't
    I got pretty close though

    it's close enough, I'd rather use your equation because it's simpler.

  • SocksSocks London, UK.Posts: 12,822Member

    You could also simply rotate a moving actor in opposite directions every 180° . . . hold on let me try it out . . .

  • SocksSocks London, UK.Posts: 12,822Member
    edited July 2015

    Here you go, I didn't use any clever maths, so I made up for it with an undulating rainbow coloured line :tongue:

  • tintrantintran Posts: 453Member

    @Socks said:
    Here you go, I didn't use any clever maths, so I made up for it with an undulating rainbow coloured line :tongue:

    cool.

  • SocksSocks London, UK.Posts: 12,822Member
    edited July 2015

    @tintran said:
    cool.

    Cheers.

    P.S. You're right that sin(x) specifies x as an angle, so it's not clear how this could produce a circle.

    This circle fill question had similar demands:

    http://forums.gamesalad.com/discussion/67889/mathematical-expression-question-for-circle-fill

  • RThurmanRThurman Posts: 2,822Member, Sous Chef, PRO

    The formula goes something like this:

    150+((-1)^floor(( self.Position.X /(2* self.r ))-.5))(sqrt(( self.r ^2)-(( self.Position.X -((2 self.r )floor((( self.Position.X /(2 self.r ))+.5))))^2)))

    "150" is the horizontal middle
    "self.r" is the radius

    "((-1)^floor(( self.Position.X /(2* self.r ))-.5))" is used to flip from 1 to -1 so that you get the upper part and the lower part. Without it, you just get a semicircle.

    The rest is an equation for a semicircle.

    Here is a demo.

  • SocksSocks London, UK.Posts: 12,822Member
    edited July 2015

    @RThurman

    Sure that's clever, and it actually works and is mathematically sound and all that, but my example had a rainbow coloured line.

    :tongue:

  • LovejoyLovejoy Posts: 2,078Member

    Battle of the geniuses. I bet that 1% of the GS population understands this black magic.

    Fortuna Infortuna Forti Una

  • RThurmanRThurman Posts: 2,822Member, Sous Chef, PRO
    edited July 2015

    rainbows?
    Rainbows!
    RAINBOWS!!

    I forgot the stinking rainbows!

  • RThurmanRThurman Posts: 2,822Member, Sous Chef, PRO
    edited July 2015

    @Lovejoy said:
    Battle of the geniuses. I bet that 1% of the GS population understands this black magic.

    Sorry -- no geniuses here! I just Googled something like "circle wave form" and found an image that looked promising. Then shoved the formula I found here into GameSalad:
    http://math.stackexchange.com/questions/44329/function-for-concatenated-semicircles

    And it worked!

  • SocksSocks London, UK.Posts: 12,822Member

    @RThurman said:

    rainbows?
    Rainbows!
    RAINBOWS!!

    I forgot the stinking rainbows!

    You're not going to get very far in life without razzmatazz and showmanship, sure a doctor can carry out a heart bypass, but what a patent wants to wake up with is a bypass scar in the shape of dolphin.

  • RThurmanRThurman Posts: 2,822Member, Sous Chef, PRO
    edited July 2015

    @Socks said:
    You're not going to get very far in life without razzmatazz and showmanship, sure a doctor can carry out a heart bypass, but what a patent wants to wake up with is a bypass scar in the shape of dolphin.

    Yes, a dolphin shaped heart-bypass scar is just what I need to impress the ladies!

    Hmmm..... I wonder what the function is for creating a dolphin shaped plot?

  • SocksSocks London, UK.Posts: 12,822Member
    edited July 2015

    @RThurman said:
    Hmmm..... I wonder what the function is for creating a dolphin shaped plot?

    AAA *sin(game.time *BBB)+CCC

    You just need to play around with the numbers.

  • RThurmanRThurman Posts: 2,822Member, Sous Chef, PRO

    @Socks said:
    AAA *sin(game.time *BBB)+CCC
    You just need to play around with the numbers.

    yup... should have seen that one coming around the bend
    :)

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