[RESOLVED] how to calculate x & y in a sine wave?

[aseminov]

Hello,

I have the following initial code:

double objectAngle = -90.0f;
double objectSpeed = 3.0f; // meters per second
double objectDistance = 300.0f;
double objectTime = 0.0f;
double objectHeading = 90.0f;
double elapsedTimePerCycle = 1.0f;

My coordinate system looks like this:

	                        90 y
                                 |
                                 | 
                                 |
                   +-180 -------------------- 0 x
                                 |
                                 |
                                 |
                                -90

I want to calculate a new x,y such that it follows a sine wave like pattern until it gets to point (0,0). I want the width of the arc to go out to about -45 degrees, and the same on the other side to about -135 degrees.

How can I compute these new x,y coordinates in C++?

Thanks!
Alex

[monarch_dodra]

I want to calculate a new x,y such that it follows a sine wave like pattern until it gets to point (0,0). I want the width of the arc to go out to about -45 degrees, and the same on the other side to about -135 degrees.

I don't understand.

You want the formula that gives you the function you describe? The function you describe is y = -sin(x), so just do that.

sin can be found in <math.h> or <cmath>. Just remember that all C trig functions operate on radians.

[aseminov]

Yes, but doesn't distance and play a key in the equation? Do I decrement the distance each calculation? How can I extend the x coordinate so it's around + or - 45 degrees from the y axis?

Can you provide some simple example C++ code so I can learn how this works?

Thanks,
Alex

[monarch_dodra]

You posted code, but what you are trying to do is not very clear.

If I understood correctly, you are trying to find the equation of a plot?
This plot describes the motion of an object?
And you want this object to cross the (0,0) coordinate at a given angle?

Please try to give a bit more background to what you are trying to do, and we'll have an easier time with the how.

[aseminov]

Hello Monarch_Dodra,

I am trying to calculate the x and y position of the object ever second. Sorry if I was not clear on that. I would also like to calculate the new distance based on the speed. I want the object to move toward point (0,0) in a sine wave pattern.

Thanks,
Alex

[PredicateNormative]

Hello,

I have the following initial code:

double objectAngle = -90.0f;
double objectSpeed = 3.0f; // meters per second
double objectDistance = 300.0f;
double objectTime = 0.0f;
double objectHeading = 90.0f;
double elapsedTimePerCycle = 1.0f;

My coordinate system looks like this:

                            90 y
                                 |
                                 | 
                                 |
                   +-180 -------------------- 0 x
                                 |
                                 |
                                 |
                                -90

I want to calculate a new x,y such that it follows a sine wave like pattern until it gets to point (0,0). I want the width of the arc to go out to about -45 degrees, and the same on the other side to about -135 degrees.

How can I compute these new x,y coordinates in C++?

Thanks!
Alex

Alex, what you are asking does not match the data you are supplying.

For example, the following data

double objectAngle = -90.0f;
double objectSpeed = 3.0f; // meters per second
double objectDistance = 300.0f;
double objectTime = 0.0f;
double objectHeading = 90.0f;
double elapsedTimePerCycle = 1.0f;

suggests that at t=0, the object is lying on the y axis at x=0, y=-300, and that the object is travelling on the y axis in a positive direction at a constant speed of 3m/s.

Therefore the data suggests that the points that you should plot are going to be

x = 0, y = -300
x = 0, y = -297
x = 0, y = -294
...
x = 0, y = 0
x = 0, y = 3
x = 0, y = 6
...

Newtons first law of motion states that an object will continue at a constant velocity, unless acted on by an external force.

There are no accelerations mentioned, or anything else in the data that would suggest that the object should oscillate around a point or have wave like behaviour. This information is missing from your description and is required in order to help you come up with a solution to your, as yet, unbound problem. Please can you explain why you think that the object should be moving in a sine wave pattern?

[aseminov]

Hello PredicateNormative,

I just want to be able to generate the x/y pairs in a sin wave pattern.

[PredicateNormative]

Does that mean that your data can be modified? e.g:

double objectAngle = -90.0f;
double objectSpeed = 30.0f; // meters per second
double objectDistance = 0.0f;
double objectTime = 0.0f;
double objectHeading = 90.0f;
double elapsedTimePerCycle = 1.0f;
double accelerationDueToGravity = 3.0; //meters per second squared
double centreOfGravityX= 0.0;
double centerOfGravityY = 0.0;

The above modifications would cause the object to oscillate around point (0,0) in a sine wave pattern.

[TheGreatCthulhu]

Yes, but, you must understand that "I just want to be able to generate the x/y pairs in a sin wave pattern" doesn't clearly describe what you want to do.

The best guess I can deduce from what you've posted thus far is that you want to construct a parametric curve that will increase or decrease it's distance from a fixed circle based on the angle between the radius and the x-axis, ranging in (-180, +180)?
This would produce a flower-like pattern.
Am I right?

P.S. Please don't double post.
P.P.S. As I said there - a simple sketch of the end result would help us understand; you can attach it here, or link to some online image repository.

[aseminov]

ok attached is the drawing of what I want to do.

Thanks!

[TheGreatCthulhu]

Ok.

Take a look at the sine function graph:


It has a period of 2Pi, (0-360 deg), so this just repeats left and right.

In your case, the easiest thing to do is to think of your curve being on a transformed coordinate system, and calculating x=f(y), instead of y=f(x).
By this, I don't mean an inverse function, because the curve you described is not a function (by definition, for each x, f(x) must have no more than one value in order to qualify as a function - that's why arcsin has a limited codomain.)
I'm saying to think of y as input, and x as output.

I rotated your sketch:


Note that the x-axis is oriented downwards. This means this is basically a sligtly modified x= -sin(y) function.

If you count, there are 2.5 periods from y1 to y2.
So you need to map [-2.5Pi, 0] range to the [y1, y2] range.
EDIT: by using the two point form for a linear map:

t = y*(y2-y1)/(2.5Pi) + y2 // ERROR - confused the axes and corresponding points...

EDIT1: Sry, made a mistake:

t = y * 2.5Pi/(-y1)
EDIT2: Sry, made a mistake, again - I said 2.5 periods, and the period is 2Pi, so:
t = y * (2.5 * 2 * Pi) / (-y1)

Then you find x = -sin(t).

The sine function values range from -1 to 1, so to get the "peaks" at x2 and "valleys" at x1, you symply need to multiply the result to x2 (remember, it's upside-down).

[aseminov]

ok I will take a look at this.. do you have any example code for each second? like:

new_x = ?
new_y = ?

Thanks!
Alex

[TheGreatCthulhu]

After re-reading your posts, it occurred to me that this better corresponds to what you're looking for, right?


If so, the principle is the same, you only need to scale the [-1,1] range returned by the sine function to the [-45, 45] range (just multiply by 45), and move the graph along the x-axis by subtracting -90 from the result.

Remember, the way I set it up, is that you're calculating x based on y.
So, x = f(y).

If you want to update per time step, then you can make your be a function of time t (note: this t (italic&blue) is not the same as the t (regular) in my previous post).

So, you now have:

• x = f(y), which decides how far to the side the object will go, and
• y = g(t), which tells where along the y-axis the object is;

Assuming that the y-speed is constant, you would calculate y like this:

y = y1 + v*t,
where v is y-speed, y1 is the starting position, and t is the time elapsed since the last step

Then you would calculate x, scaling the result by 45, and moving it along the x-axis by -90:

x = -sin( y * 2.5 * 2*Pi / -y1 ) * 45 - 90,
where y1 is your "start" (a negative value, see graph).

Note that this approach requires you to calculate y first.

P.S. With this setup, the object traveling at v of 1 unit per second will reach y = 0 when t reaches -y1.
You can modify this behavior by modifying the equation for y, or the value of v.

[aseminov]

Yes that is exactly what I want!

What is the 2.5 part in the calculation of x?

Thanks so much for your help!

Alex

[TheGreatCthulhu]

In my older post (the one where I rotated the image) I said that if you count the number of periods for the sine function you sketched, you get 2.5.

Sin(x) is a periodic function - the same values repeat for every 360 degs (or 2*Pi radians).
This is one period:


In your case, that image repeats itself 2.5 times - so that's what's 2.5 for.