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Drawing geometric objects as shapes, and moving them

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Valutazione

Difficoltà
5/5
Tempo stimato
Più di una settimana
Idoneità per principianti
35/100
Tipo di issue
Funzionalità
Chiarezza
Specificata chiaramente
Stato di attività
Attiva
Stack tecnologico
csharp, plotly
Ambito
data-visualization

Direzione di ricerca

Start by reading the referenced issues #2149, #2151, #2150, #330, and #2148, then inspect the existing plotting support in AngouriMath.Interactive and its use of Plotly.NET. The proposed work spans geometry objects, construction dependencies, loci, branch tracking, and interactive or static rendering, so first establish which parts the parent issue provides. Done means the design is implemented across those areas, with shapes rendered and dependent constructions updating as free points move.

Scritto dal modello di indicizzazione a partire dal testo della issue.

Descrizione

Asked for on #2131: "we'd also want a design for plotting and interacting with geometry as shapes instead of equations too".

What exists. AngouriMath.Interactive plots functions with Plotly.NET: curves, polar plots and surfaces, with a slider over one parameter (Chart.withSlider). A circle can be drawn only as the curve of its equation. Nothing knows that it is a circle with a centre and a radius, or that a point was constructed from two others.

What dynamic geometry does. Interactive geometry software, as GeoGebra, Cinderella, Cabri and GCLC implement it:

  • Constructions are "abstract, formal procedures and not figures", and a figure is generated from one.
  • After a construction is made, "one can move the points one started with and see how the construction changes".
  • Deterministic programs re-solve every step from the free points. Continuous ones, such as Cinderella and GeoGebra, follow each intersection along the path of the drag, so a branch does not jump.

A design, in four parts:

  1. Objects carry their geometry. A point is a pair (#2149), and circle(O, r), line(A, B) and segment(A, B) (#2151) know their centre, radius and ends. A renderer draws a circle as a circle (a Plotly shape, an SVG <circle>, TikZ \draw (O) circle (r)), exactly and at any zoom, without sampling an equation.
  2. A construction is an expression. circumcentre(A, B, C) is a node in the free points, as everything here already is. Dragging A substitutes its new coordinates and evaluates the dependents. The dependency graph is the expression tree, so no second model is needed.
  3. A locus is the image of a parameter. The set a dependent point traces as a free one moves along a curve is an image set (#2150, #330). The existing slider shows the motion, and the set is the answer when one is asked for.
  4. Branches follow the motion. Where a construction takes a root, as an intersection of two circles does, the choice has to carry over from one position to the next, or a dragged figure jumps. That is the shared-branch question the reading of the book also found, and it belongs with the 3.0 assumption work (#2148).

Output: interactive in AngouriMath.Interactive (Plotly, dragging and sliders), and static as SVG, or as TikZ to go with Latexize.

On 3.2 with its parent #2151, since parts 1 and 2 need the pair and the object nodes first.

Lingua principale
C#
Stelle
831
Fork
79
Merge medio
1h 16m
PR unite (30g)
521

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