Curve Point Distribution by Simpson Rule

C++.  This implementation’s purpose is to equally divide a quadratic equation curve for distributing desired number of points on it. To do that, I applied Simpson rule by  sweeping small increments on x axis instead of using full Integral calculations. Then, I rotated this curve point distribution on x axis by 12 times (including start points) to get a 3D shape. Later on, I will work on some improvements to reduce errors.

Here, I chose the function y = x^2 + 1 as an example by 21 points:

 

References:

[1] Simpson Rule

[2] Arc Length Formula

[3] How to Calculate Integral of the Function y = sqrt(1 + 4x^2)