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chore: remove trailing whitespace outside of app-proto/src as well

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Glen Whitney 2025-10-14 12:42:51 -07:00
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notes/theory.md
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@ -22,9 +22,10 @@ Jürgen also emphasized the need for an intuitive user interface. Notes on that
His final mathematical advice was reasonably encouraging, however:
"But still I would consider it all more or less doable. One should very precisely think about a doable scope.
I think three things are essential for the math no matter what you exactly plan.
I think three things are essential for the math no matter what you exactly
plan.
1. Think projectively,
1. Think projectively.
Use Projective Geometry, Homogeneous Coordinates (or to a certain extent Quaternions, and Clifford Algebras, which are more or less an elegant way to merge Complex numbers with projective concepts.)
2. Consider ambient complex spaces.
The true nature of the objects can only be understood if embedded into a complex ambient space.
@ -37,10 +38,8 @@ I think three things are essential for the math no matter what you exactly plan.
It would be nice to see how Jürgen handled some of these issues in a 2D system that he designed. Unfortunately, Cinderella was and remains closed-source; it was distributed for profit for some stretch of time. However, (a part of?) it was reimplemented in JavaScript as CindyJS, which is open source. I took a relatively quick look at that source code at one point, and these were my observations:
CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically. There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.)
CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically. There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.)
Lines are given by explicit coordinates as well (not sure of the internal details/exact coordinatization, or of how a "LineThrough" is represented).
Was unclear to me how the complex parametrization for preserving continuity was handled in the code, even though Jürgen harps on complex ambient spaces; where are the complex numbers? Perhaps that part of Cinderella was never re-implemented?