Irregular sine curve

[HazyGeoGeek]

Hi
I'm a beginner and I would like to obtain an equation to generate an irregular sin curve.
Please find the image attached.

Also, can someone suggest me some good books to start with? I would be interested to draw a curve with equations.

 

[pka]

It appears to me that your diagram is itself is incorrect. Clearly the intervals \(\displaystyle [0,\pi]=[\pi,2\pi]\) which implies \(\displaystyle \bf{a=b}\).
That is not what is not what is shown in the diagram?

 

[Dr.Peterson]

I would like to obtain an equation to generate an irregular sin curve.
Please find the image attached.

Also, can someone suggest me some good books to start with? I would be interested to draw a curve with equations.

There is no such thing literally as an "irregular sine curve". Can you define exactly what you want this curve to be? What is your goal?

For example, do you expect each part you marked out to be exactly a sine curve, but scaled differently in each part? Or are they just curves that look sort of like sines, but not curved in exactly the same way, maybe fatter or thinner, or sharper or blunter, for example?

The same is true of your broader question about a book. There are many kinds of equations for various kinds of curves, so you need to narrow down your goal, or we'll just be recommending algebra books.

 

[HazyGeoGeek]

It appears to me that your diagram is itself is incorrect. Clearly the intervals \(\displaystyle [0,\pi]=[\pi,2\pi]\) which implies \(\displaystyle \bf{a=b}\).
That is not what is not what is shown in the diagram?

Thank you for the response.
Mentioning 0,\pi, and 2\pi was a mistake. I need control over the variables a,b,c,d. What kind of equation and function is used to generate this curve.

 

[HazyGeoGeek]

There is no such thing literally as an "irregular sine curve". Can you define exactly what you want this curve to be? What is your goal?

For example, do you expect each part you marked out to be exactly a sine curve, but scaled differently in each part? Or are they just curves that look sort of like sines, but not curved in exactly the same way, maybe fatter or thinner, or sharper or blunter, for example?

The same is true of your broader question about a book. There are many kinds of equations for various kinds of curves, so you need to narrow down your goal, or we'll just be recommending algebra books.

Thank you for your response.
I used the term "irregular sine curve" because I don't know how to describe them.

I'm trying to generate architectural design using mathematical functions. In the above example, I would like to have control over the variables a,b,c,d.
When I had a regular pattern, I used sin and cos functions to achieve them. But now I'm starting with the irregular pattern so I have trouble in generating them using equations.

I need to generate a curve with the number of variables available. For example, I have attached a picture below.
I need a book to know about this kind of curves.

Also, can we generate an equation for a curve in 3D i.e., having variables in x,y,z coordinates?

I'm also interested to learn about the geometrical patterns and relations. i.e., various geometrical shapes and their properties and to how to obtain them through mathematical equations.

Can you suggest a good book to start with and where can I find resources to learn them.

Thank you

 

[Dr.Peterson]

The trouble is that you are describing only the overall dimensions of parts of the curve, and not the curve itself! There are infinitely many possible curves between any two points, so you need some idea of what kind of curve to make. That's why I asked about the ultimate goal.

I wonder if you are thinking of some broad class of curves that can be easily adjusted, such as splines. That would be a term to search for in looking for a book to get you started; a book on math for computer graphics, for example, might be a place to look.