Dynamic Visual Scoring Calculator

To calculate a single categoryScore, the main principle is the difference between the categoryTarget and the actual categoryValue. Things to note for the user adjustable properties are as follows:

• The categoryValue can not be dynamically adjusted by the front end user, because it is a measured value in open world.

• The categoryTarget is adjustable, with the min or max value automatically being set to the categoryValue. Should the categoryValue>= categoryTarget, then the categoryDirection should be set to 1.
  (E.g. the category goal is it to optimize the measured process for as little time as possible). If set correctly the categoryTarget cannot be set bigger than the categoryValue. The Result is the adjustable categoryTarget will automatically stop at max = categoryValue.
  Now The other way around: Should the categoryValue <= categoryTarget, then the categoryDirection should be set to -1 . (E.g. the category goal is it to optimize the measured process for the hightest efficiency possible). If set correctly the categoryTarget cannot be set smaller than the categoryValue. The Result is the adjustable categoryTarget will automatically stop at min = categoryValue.
  
  The min and max values for the range sliders are estimated with the following assumption:

  1. if the categoryUnit is "%":

     Depending on the categoryDirection the min is set to "0" or max is set to "100"

  2. if the categoryUnit is not "%":

     Lets say our value should always be larger than our categoryTarget, so therefore the categoryDirection is "1". This also already defines the max value to categoryValue. The min value is then "guessed" by calculating $${\displaystyle \begin{array}{c}\text{min}=\text{categoryValue}-5\cdot \text{categoryGrain}\end{array}}$$ This assumes that the measured categoryValue is already as low as possible, so a factor larger than 5 makes no sense. Reducing things to some amount, generally speaking, tend to have an absolute limit, which can be reached.
     This changes when the categoryValue is lower than the categoryTarget, so therefore the categoryDirection is "-1". Since we already know the min value, which is the categoryValue, only the max value needs to be calculated. $${\displaystyle \begin{array}{c}\text{max}=\text{categoryValue}+14\cdot \text{categoryGrain}\end{array}}$$ Here is it the other way around. Trying to increase a value can be almost limitless with no definable limit, so therefore a factor of 14 was used.

• The categoryBias is adjustable, with the categoryBias accepting any Integer between -5 and 5. If the categoryBias is grater than 0, the category will experience a favored rating method and therefore giving it a better score.
  If the categoryBias is smaller than 0, the category will experience a unfavored rating method and therefore giving it a lower score.
  Once the categoryBias reaches the upper or lower limit the score tries to be the as close to the hightest or lowest score possible, this beeing ¹⁰⁰⁰/₁₀₀₀ or ⁰/₁₀₀₀

• The categoryWeight can be adjusted, which affects the overall score, but not the individual categoryScore! When adjusting one categoryWeight all the other Weights will adjust accordingly, so all percentages added up together will always be 100%.

  $${\displaystyle \begin{array}{c}\sum _{\text{categoryNumber}=0}^{\text{categoryCount}}\frac{{\text{categoryScore}}_{\text{categoryNumber}}}{1000}=1=100\mathrm{\%}\end{array}}$$

  For ease of use the lowest individual categoryWeight is 0.01 %. This ensures, that no single categoryWeight will be stuck at 0%.
  Due to the nature of using linear Algebra (more specific Matrix calculations) for calculation the weights. Depending on the number of categories, if one category reaches 0% it will stay at 0% and the other weight will compensate, which is an unwanted effect
  To avoid errors don't leave the categoryWeight value empty, and instead set a preset.

Things to note for the static properties are as follows:

• categoryNumber:
  This is important to keep Track of the different categories. Remember to stat with 0 when numbering the categories.
  
  
• categoryNames:
  These will be displayed in the category column as the category name.
  
  
• categoryUnits:
  These are the units which should be displayed
  
  
• categoryTargets:
  Remember this a dynamically adjustable value. But you must give a preset for initialization. Also make sure the values are in line with the categoryDirection and the categoryValues
  
  
• categorySteps:
  This will set the step of the all target value range sliders. Basically by how much fine control of the slide is wanted.
  
  
• categoryDirections:
  This defines, whether the categoryValue is trying to reach a value greater than it self, in which case the categoryDirection should be set to "-1", or if the categoryValue is trying to reach a categoryTarget which is smaller than itself, in which case the categoryDirection should be set to "1".
  Any other values other than "-1" or "1" are strictly forbidden.
  NOTE: If the category value is larger than its target (more ---> positive ---> +) the direction should be set to "1"
  If the category value is lower than its target (less --> negative ---> -) the direction should be set to "-1"
  
  
• categoryGrains:
  With the categoryGrain the dimensions of the numbers can be tuned to the category need. The categoryGrain should be set to the minimal relevant increment or decrement the categoryValue has relevancy to. Another thing, which might help is this equation, which states, that the categoryScore is always "500", when the categoryValue is equals to the categoryGrain times the categoryDirection plus the times the categoryTarget times the squared categoryDirection. Note that the category Bias is Zero $${\displaystyle \begin{array}{c}\text{categoryScoreFunction}(\text{categoryValue})=\text{categoryScore}\\ d=\text{categoryGrain}\cdot \text{categoryDirection}+\text{cateogryTarget}\cdot {\text{categoryDirection}}^2\\ \text{categoryScoreFunction}(d)=500\end{array}}$$
  
  
• categoryEvaluations:
  There are a few Evaluation methods. each one with different characteristics.

  

  These are functions, which act as the base for all the evaluation methods.

  $${\displaystyle \begin{array}{c}b=\frac{\text{caregoryBias}-5.01}{\text{categoryBias}+5.01}\\ j(x)=\text{categoryDirection}\cdot (x-\text{categoryTarget})\\ f(x)=\frac{1}{\pi }\cdot \arctan \left(x\right)+\frac{1}{2}\end{array}}$$

  1. Default Evaluation:

     valid values are "def" or "default" $${\displaystyle \begin{array}{c}{g}_d=\frac{1}{2^1\cdot \text{categoryGrain}}\\ h_d(x)=2\cdot f(2\cdot x)-1\\ S_d(x)=1000\cdot f(1000\cdot j(x))\cdot h_d(g_l\cdot b\cdot j(x))\end{array}}$$

  2. Linear Evaluation:

     valid values are "lin" or "linear" $${\displaystyle \begin{array}{c}{g}_l(x)=\frac{1}{2^1\cdot \text{categoryGrain}}\\ \\ S_l(x)=1000\cdot (f(-1000\cdot j(x))-\frac{1}{2})+1000\cdot (f(1000\cdot j(x))-\frac{1}{2})\cdot (b\cdot g_l\cdot j(x)+1)\\ +1000\cdot (f(1000\cdot j(x+\frac{1}{\text{categoryDirection}\cdot b\cdot g_l}))-\frac{1}{2})\cdot (-b\cdot g_l\ast j(x)-1)+500\end{array}}$$

  3. Quadratic Evaluation:

     valid values are "quad" or "quadratic" $${\displaystyle \begin{array}{c}{g}_q=\frac{1}{2^{\frac{1}{2}}\cdot \text{categoryGrain}}\\ \\ h_q(x)=2\cdot f(-2\cdot x^2)-1\\ \\ S_q(x)=1000\cdot f(1000\cdot j(x))\cdot h_q(g_q\cdot b\cdot j(x))+1000\end{array}}$$

  4. Cubic Evaluation:

     valid values are "cube" or "cubic" $${\displaystyle \begin{array}{c}{g}_c=\frac{1}{2^{\frac{1}{3}}\cdot \text{categoryGrain}}\\ \\ h_c(x)=2\cdot f(2\cdot x^3)-1\\ \\ S_c(x)=1000\cdot f(1000\cdot j(x))\cdot h_c(g_c\cdot b\cdot j(x))+1000\end{array}}$$
  
  
  
• categoryColors:
  Sets the circle Colors.