Fitting VS Control Point?

In summary, constructing a curve that starts from point A0 and goes through points A1-A6, with A1-A2 and A4-A5 as control points, is called a Bezier curve. This type of curve is also known as a "spline" and its equation involves solving a band-diagonal system of equations and using calculus. However, there are various types of splines and it is recommended to use existing software libraries, such as gnuplot, instead of reinventing the wheel.
  • #1
mymachine
42
0
If I construct a curve such start from point A0, A3, to point A6 where A1-A2 and A4-A5 are control points, is called a Bezier curve.

curve.png


What is it called by and what its equation if I construct and fit a curve start from point A0 > A1 > A2 > A3 > A4 > A5 > A6 such as below image?

spline.png
 
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  • #2
It is called a "spline",

http://en.wikipedia.org/wiki/Spline_(mathematics)

and fitting one usually involves solving a band-diagonal system of equations, and some notions of calculus. (Or you could google for a software library that does the work.)

P.S.: There are actually many kinds of splines; the ones I had in mind, "cubic splines", are described in a link on the Wiki page I mentioned,

http://en.wikipedia.org/wiki/Spline_interpolation

But again, it's reinventing the wheel as there are probably libraries to do so.
 
Last edited:
  • #3
gnuplot will do that for you.
 

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What is the difference between fitting and control point?

Fitting and control points are two different methods used in data analysis and modeling. Fitting involves finding a mathematical function that best represents a set of data points, while control points involve placing points on a curve or surface to control its shape or path.

When is fitting more appropriate than using control points?

Fitting is typically used when there is a large amount of data and it is difficult to manually place control points. Fitting also allows for a more precise representation of the data, as it takes into account all of the points, rather than just a select few.

What are the advantages of using control points over fitting?

Control points allow for more flexibility in shaping curves or surfaces, as the points can be manually adjusted to achieve a desired result. They also require less computational power and can be easier to understand and interpret visually.

Can fitting and control points be used together?

Yes, fitting and control points can be used together in some cases. For example, a fitting function can be used to approximate a curve or surface, and then control points can be added to fine-tune the shape or path of the curve or surface.

What are some common applications of fitting and control points in science?

Fitting and control points are commonly used in fields such as physics, engineering, and statistics to analyze and model data. They are also used in computer graphics and animation to create smooth and realistic curves and surfaces.

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