Making curves going through given points

In summary, to determine the equation of a curve that goes through a given set of points, you can use the method of interpolation which involves finding a polynomial function that passes through all the points. This process involves plotting the points on a graph and using methods such as Lagrange interpolation, Newton's divided difference interpolation, or spline interpolation. While it is possible to make a curve that goes through any set of points using interpolation, the accuracy of the curve will depend on the number of points and the method used. A straight line can also be used to connect all the points, but a curve is often a better choice as it can better capture the relationship between the points and provide a more accurate representation of the data. However, there are limitations to
  • #1
VishwasG
7
0
Hi!
I am having points set say P = { [x1,y1] , [x2,y2],[x3,y3],...,[xn,yn]}

Now, i want to fit curves going through these points. Is it possible.
I googled and went through something called beziers.. is that helpful here ? Or is there any direct mathematical approach to achieve.

Thanks in advance for answers

:)
 
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  • #2
Assume that x1,x2,.. are all distinct ( if not, we could re-position the axes). We can always find a polynomial curve of degree n passing through the points using Lagrange interpolation.
 

FAQ: Making curves going through given points

1. How do I determine the equation of a curve that goes through a given set of points?

To determine the equation of a curve that goes through a given set of points, you will need to use the method of interpolation. This involves finding a polynomial function that passes through all of the given points. The degree of the polynomial will depend on the number of points you have.

2. What is the process for making a curve that goes through given points?

The process for making a curve that goes through given points involves plotting the points on a graph and then using interpolation to find the equation of the curve. You can use a variety of methods such as Lagrange interpolation, Newton's divided difference interpolation, or spline interpolation to find the equation.

3. Is it possible to make a curve that goes through any set of points?

Yes, it is possible to make a curve that goes through any set of points using interpolation. However, the accuracy of the curve will depend on the number of points and the method used for interpolation. More points and a higher degree polynomial will result in a more accurate curve.

4. Can I use a straight line to connect all the points instead of a curve?

Yes, you can use a straight line to connect all the points, but this may not accurately represent the data. A curve is often a better choice as it can better capture the relationship between the points and provide a more accurate representation of the data.

5. Are there any limitations to making curves through given points?

The main limitation to making curves through given points is that it may not accurately represent the entire data set. This is especially true if there are outliers or if the data is not evenly distributed. In these cases, it may be better to use other methods such as curve fitting to find a more accurate representation of the data.

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