How can I determine the position of waterline during the inclining process of a ship（the center of mass and weight are constant） ?

Many ships capsized because of various reasons. I want to know the variation of ship stability in the process of heel angle change.

My thinking is that the waterline must be determined firstly，then the displacement and the centre of buoyancy. The center of mass and weight are constant. So the ship stability can be solved.

I want to calculate the ship stability by MATLAB because of too much data. So I must constantly determining the intersections of ship sections and watersurface.

How to obtain the waterline？
In the book of ship’s hydrostatical theory, the intersections of ship sections and watersurface are given.

My teacher just taught us the calculation method of big-angle tilted ship stability，but he did not tell us the method of determining the position of waterline during the inclining process of a ship.