An hGraph is a simple representation of a patients health and allows one to quickly identify areas which needs improvements. It works by mapping or converting measurements or observations to a number between -1 and 1. This number specifies how far from the center the point should be drawn. The location of the points then gives a quick visual impression of a patients health.

This page describes the mathematics behind drawing the hGraph. This hGraph is not based on risk but on generally accepted (personalized) thresholds for observations. The mathematics for converting an observation into a hGraph number is not part of this page but is described on the pages describing the procedures.

The hGraph is based on the work from http://hgraph.org/ The main difference is in the way the locations on the hGraph are calculated.

In the following image an example hGraph is shown. The numbers above are the hGraph scores. In this hGraph the scores are between -1 and 1 with a score of 0 being the optimal score. Any score between -0.5 and 0.5 is considered acceptable. Any score below -0.5 is too low and scores above 0.5 are considered to be too high.

These score values and radii (see below) are chosen because it looks good and can be mapped onto the hGraph easily.

$$r_{min} = \frac{1}{4} r_{max}$$

$$r_{low} = \frac{7}{16} r_{max}$$

$$r_{0} = \frac{5}{8} r_{max}$$

$$r_{high} = \frac{13}{16} r_{max}$$

To calculate the radius of a point in the hGraph use the following:

$$r_{p} = \frac{5r_{max} + 3r_{max} \cdot score}{8}\text{ with }score = [-1,1]$$

To draw points on the screen use basic trigonometry:

$$x_{p} = x_{center} + r_{p} \sin \alpha $$

$$y_{p} = y_{center} + r_{p} \cos \alpha $$