BrightMath

An Experiment: Math in Color

What if we built a math around colors from another perspective?

What is a Color?

First lets define a Color in the context of BrightMath:

Additive light (projected, LED, CRT, etc) is typically composed of Red, Green, and Blue (RGB).
- When combined with each channel at full intensity, the result will be composed of all colors- white.
- Black is the projection of no light. Any subtractive operation will never go below nothing.
Subtractive light (pigments, toner, etc) is typically composed of Cyan, Magenta, Yellow, and blacK (CMYK).
- They used the last letter of blacK so as not to be confused with Blue from RGB.
- Each pigment blocks all light except the color. Black pigment blocks all other colors. Lighter pigments block less light of the various components.
Additive light can be mitigated by subtractive light, but at the moment BrightMath will not approach this.
- A BrightMath Color is either a CMYK Color, an RGB Color, or an RGBA color. (HSV planned)
- While there are quick conversion functions between them, for now, a Color can only be used directly with another Color of the same type.

Representing colors in computers

Computers usually think in terms of RGB light when thinking about displays, or CMYK pigments when thinking about printing.
Computers keep track of the components using the concept of Channels.
In addition to the Red, Green, Blue or Cyan, Magenta, Yellow, Black channels, we often will add a transparency value, called Alpha.
- The Alpha channel is an additional coefficient used when layering.
  - For instance Royal Blue with an Alpha of 75% will be 25% dimmer.(?)
- BrightMath will include an RGBA type with Alpha (transparency) channel for future use.
- Each BrightMath Color type has either three (RGB), four (CYMK), or five (RGBA) channels.
Brightness for each channel is typically stored as an integer.
- Over the years, depending on the platform and many other factors, computers have used different byte widths and methods to store these values.
- Be careful of the difference between bit per channel and bit per pixel.
  - 1 bit per pixel is monochromatic- Zero intensity or Full intensity.
    - It was likely projected as amber, green or light grey in the earlier years, but is thought of as Black and White.
  - 1 bit per channel when using RGB means there are three channels each with one bit/intensity.
  - 1 bit per channel when using CMYK means there are four channels each with one bit/intensity.
  - 8-bit RGB yields 256256256 = 16,777,216 (approximately 16 Million) Colors.
    - 256 values because it is 0 through and including 255.
    - Referred to as SVGA or 24-bit color because the total bits used for all three channels is 24. (3*8)
- Although the values for each channel appear to be numbers from say 0 to 255, they can also be thought of as fixed point numbers from 0 to 1 as a percentage of full intensity.
- Any number of Colors of the same type can be operated (standard math +, -, *,/ as well as boolean ^, &, |) on.
  - Each channel will combine in standard math operators and cap at the limit.

References

Set Theory

Von Neumann Ordinals

Null is the empty set { } or Φ/∅/Phi
In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 = n ∪ {n} for each n.# BrightMath

This project was generated with Angular CLI version 14.1.3.

Development server

Run ng serve for a dev server. Navigate to http://localhost:4200/. The application will automatically reload if you change any of the source files.

Code scaffolding

Build

Run ng build to build the project. The build artifacts will be stored in the dist/ directory.

Running unit tests

Run ng test to execute the unit tests via Karma.

Running end-to-end tests

Run ng e2e to execute the end-to-end tests via a platform of your choice. To use this command, you need to first add a package that implements end-to-end testing capabilities.

Further help

To get more help on the Angular CLI use ng help or go check out the Angular CLI Overview and Command Reference page.

JessieMercurial/BrightMath