Copyright (c) 2014 Brooks Mershon
The MIT License - http://opensource.org/licenses/MIT
Please excuse the awful coding practices that may be found here.
This was more or less my first run at using D3 and JavaScript in an undergraduate math course (where writing code wasn’t even expected, unless it was MATLAB). This was written before modular design, functional programming, and maturity had gripped the author to even a modest extent. This gadget (application seems too strong) was developed as if it were one colossal whiteboard exercise which permitted only small erasures and steady contributions over half of a semester.
The urge to go back and rearrange or modify in any way is strong, but I am choosing to leave this relic of sophomore year as a happy and messy memory of an assignment of which I am quite proud.
I love what I built, but I regret how it was built. I didn’t know better.
A final paper was written about the design process of this and other gadgets created for MATH 412, taught by Paul Bendich during the Fall 2014 semester.
This little gadget allows to you draw a smooth continuous function and generate its zero-dimensional persistence diagram. Zero-dimensional persistence is determined by raising a parameter r from negative infinity to positive infinity, tracking the birth and death of intervals as we go.
Click-and-drag a control point to manipulate the curve. Clicking to the right of the right-most point will create a new control point; the vertical line test must be obeyed.
Click on the button Create Dgm0(F) to generate the zero-dimensional persistence diagram for the user-defined function in the plot to the right. Dots corresponding to birth/death pairs which do not lie on the diagonal are shown with their corresponding height-index (i.e. its unique name). These dots correspond to a local minimum (birth of a component) and local maximum (death of the younger of two components) at their respective function values. Here, the function values are simply the values of r at which these components are formed and destroyed (their heights).
Clicking anywhere in the left-hand plot will bring back control points so that you can adjust the curve and generate another persistence diagram.
Hover-over a red local extremum marker to see its index and coordinates.
Drag the vertical slider to see individual components at each value of r.
The DELETE button will remove the currently selected control point from the spline.