Teach you how to do interpolation algorithm on a single chip microcomputer

Step 1: Learn what you need to learn, even if you don’t understand it. Here comes the most boring math formula

In numerical analysis, Lagrange interpolation is a polynomial interpolation method named after the French mathematician Joseph Lagrange in the 18th century. In many practical problems, functions are used to represent some internal connections or laws, and many functions can only be understood through experiments and observations.

For example, if we observe a physical quantity in practice and obtain corresponding observation values ​​at several different places, the Lagrange interpolation method can find a polynomial that takes the observed value at each observation point. Such a polynomial is called a Lagrange (interpolation) polynomial.

Mathematically speaking, the Lagrange interpolation method can give a polynomial function that passes through a number of known points on a two-dimensional plane. The Lagrange interpolation method was first discovered by the British mathematician Edward Waring in 1779, and was rediscovered by Leonhard Euler shortly afterwards (1783). In 1795, Lagrange published this interpolation method in his book "A Course in Elementary Mathematics for Normal Schools", and his name has been associated with this method ever since.



Step 2: Construct the Lagrange interpolation algorithm function and implement it in C/C++

//Predefine the number of interpolation nodes to 1000, and determine the number of interpolation nodes according to the number num input by the console const int N=1000; // Lagrange interpolation algorithm float lglr(float x[], float y[],int n,float t){float yResult=0.0; //LValue[N] stores the general term of the interpolation basis function solved each time float LValue[N]; //Loop variables k, mint k, m; //Up and down multiplications in the interpolation basis function temp1, temp2 float temp1, temp2; for(k=0;k

Step 3: Test the linear interpolation effect
1. Input 3 points of the oblique line to the written algorithm to predict other points in this interval. It is found that the predicted linear value is very good and the linearity is full.


2. Also input 3 points of the sine curve to the written algorithm to predict other points in this interval. It is found that the predicted sine curve is not ideal and the correlation is very poor.



3. Increase the number of points of the sine curve input to the written algorithm to 10 points to predict other points in this interval. It is found that the predicted sine curve has met the requirements and the correlation is very good.


4. The following is an image drawn using matlab, which is an image of the comparison of 3 linear points, sine 3, 5, 10 and the original value.


Step 4: Transplant to the microcontroller and use the serial port output to test the interpolation effect. The effect is OK!


Step 4: Advanced perfection, a little unwilling, using Qt to build an interface and do some visualization.
You can say the effect is good. The Qt interface code is on gitee. If you are interested, please come and improve it together. https://gitee.com/lumengcode/my-qt/tree/master/MathTool/MathTool


Interpolation off-topic:
Regarding the interpolation algorithm: Newton interpolation, cubic spline interpolation, etc. can be further improved. They are all very interesting!
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