Added more detaled description in readme with example screenshots

README.md

@@ -1,3 +1,89 @@
 # Polynomial Interpolation
 
-ANSI C program which composes polynomial of n - 1 degree that passes through n dots.
+ANSI C program which composes polynomial of n - 1 degree that passes through n dots. It presents it in Newton interpolation polynomial and monic form.
+
+## Interface
+
+Application accepts as standart input decimal below 2147483647 `n` as number of dots, followed by n dots in format: `<x> (space) <y>` on each line, where `x` is an abscisse and `y` is an ordinate of single dot. Dot coordinates must fit [2.22507e-308;1.79769e+308] range by modulo.
+
+Result will be printed to standart output in the following format:
+
+Newton polynomial form:
+
+<img src="http://www.sciweavers.org/tex2img.php?eq=f_0%20-%20f_1%2A%28x-x_0%29%20%2B%20...%20%2B%20f_n%28x-x_0%29%2A%28x-x_1%29%2A...%2A%28x-x_%7Bn-1%7D%29&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="f_0 - f_1*(x-x_0) + ... + f_n(x-x_0)*(x-x_1)*...*(x-x_{n-1})" width="503" height="19" />
+
+Simplified coefficients array (starting from 0 upto n-1 power):
+
+<img src="http://www.sciweavers.org/tex2img.php?eq=a_0%20%5Cquad%20a_1%20%5Cquad%20...%20%5Cquad%20a_%7Bn-1%7D%20%5Cquad%20a_n&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="a_0 a_1 ... a_{n-1} a_n" width="185" height="15" />
+
+Polynomial in monic form:
+
+<img src="http://www.sciweavers.org/tex2img.php?eq=a_0%20-%20a_1%2Ax%20%2B%20...%20%2B%20a_%7Bn-1%7D%2Ax%5Cwedge%28n-2%29%20%2B%20a_n%2Ax%5Cwedge%28n-1%29&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="a_0 - a_1*x + ... + a_{n-1}*x^(n-2) + a_n*x^(n-1)" width="446" height="18" />
+
+Where <img src="http://www.sciweavers.org/tex2img.php?eq=f_i&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="f_i" width="15" height="19" /> is a divided difference of <img src="http://www.sciweavers.org/tex2img.php?eq=y_1%2C%5Cldots%2Cy_i&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="y_1,...,y_i" width="79" height="15" />, <img src="http://www.sciweavers.org/tex2img.php?eq=a_i&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="a_i" width="19" height="15" /> are coefficients of resulting monic polynomial
+
+## Data structure
+
+- `n` is an `unsigned int` variable, that is used to input and store number of dots
+
+- `x` is a pointer to array of `n` `double`s, that is used to store abscisses of dots
+
+- `y` is a pointer to array of `n` `double`s, that is used to store ordinates of dots
+
+- `coefficients` is a pointer to array of `n` `double`s, that is used to store coefficients of monic interpolation polynomial
+
+- `i`, `j` are `int` variables, those are used in loops as iterators
+
+- `tmp_polynomial` is a pointer to array of `n` `double`s, that is used to store coefficients of polynomial, resulting during simplification of interpolation polynomial summands.
+
+## Example
+
+Build and run application:
+
+```bash
+gcc main.c
+./a.out
+```
+
+### Input/output
+
+For input n = 3 and the following dots
+
+```plain
+1 5
+2 3
+4 8
+```
+
+Output is
+
+```plain
+Newton polynomial form:
+5 - 2*(x-1) + 1.5*(x-1)*(x-2)
+Simplified coefficients array (starting from 0 upto n-1 power):
+10 -6.5 1.5
+Polynomial in standart form:
+10 - 6.5*x + 1.5*x^2
+```
+
+### Illustrations
+
+#### Example 1
+
+<img src="./img/console.png" />
+
+<img src="./img/wolfram.png" />
+
+<img src="./img/plot.png" />
+
+#### Example 2
+
+<img src="./img/console2.png" />
+
+or
+
+<img src="./img/console3.png" />
+
+<img src="./img/wolfram2.png" />
+
+<img src="./img/plot2.png" />