The library documents itself · Diagramming & graphs

stzMathDiagram

83 own methods · 10 forms written with extensions, listed under their method

the source: base/graph/stzMathDiagram.ring(opens in a new tab) · All classes · The area reference: Diagramming & graphs

Under each method, its extensions (Q CS XT Z ZZ IB W U): bold and ticked, it exists; struck, it does not. The extensions and what they mean

Examples: 0 come from the library's tests; 25 were composed from each method's signature and run for this page, on a fresh object, for example o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle()). 58 methods have none yet. Examples run on 2026-10-03 20:34 inside the library at commit 0e72e2e2c.

Method

Explanation, as the source carries it

init

(no comment in the source: the name reads as a sentence) initno extension

SetFont

knobsQCSXTZZZIBWU

SetVariation

Penrose's "variation": the same string, the same picture. Any text folds to a seed; a number is used as it is. SeedRandom refuses a seed at or above 1,999,999,999, so the fold stays under it.QCSXTZZZIBWU

SolveProfile

the live figure (DN8g) -------------------------------------------------- A RE-SOLVE FROM WHERE THE FIGURE STANDS. Nothing is recompiled and no start is drawn: the current values are the start, and the solver settles the picture nearby. LayoutMs() then reports this solve. where the last solve spent its time, in ms: building the energy text, compiling it, minimising, reading the violations, and folding derived names to numbers (counted inside :text) -- plus the roundsno extension

Relayout

(no comment in the source: the name reads as a sentence) relayoutin the section Same as Layout: the answerQCSXTZZZIBWU

DragTo

THE DRAG. The shape's centre is put where the author released it, held there while the rest of the figure re-solves around it, and let go again unless it was pinned before. A shape whose centre no rule left free -- a placed name, a square derived from its triangle -- is refused: there is nothing there to drag.QCSXTZZZIBWU

A PIN holds every free property of a shape at its current value through any re-solve, cold or warm -- the plastic editor's pin, for a figure whose coordinates are solved rather than laid out.QCSXTZZZIBWU

Unpin

(no comment in the source: the name reads as a sentence) unpinQCSXTZZZIBWU

UnpinAll

(no comment in the source: the name reads as a sentence) unpin allno extension

IsPinned

(no comment in the source: the name reads as a sentence) is pinned

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.IsPinned("a")
#--> 0

composed from the signature, run for this page

no extension

Pins

the shapes pinned, by pathno extension

Draggable

the shapes a gesture can take hold of: a free centre, and a bodyno extension

PickAt

WHAT IS UNDER THE POINTER: the nearest draggable shape whose body -- or a ten-pixel reach around its centre -- holds the point; "" when the pointer is on the paper.no extension

OnPress

THE GESTURE, in the plastic editor's three verbs. A press takes hold of what is under the pointer; a move previews and re-solves NOTHING -- the window paints the dragged shape where DragPreview() says -- and the release is the one drag, from where the author let go.no extension

OnMove

(no comment in the source: the name reads as a sentence) on moveno extension

DragPreview

(no comment in the source: the name reads as a sentence) drag previewno extension

OnRelease

(no comment in the source: the name reads as a sentence) on releaseno extension

UiState

(no comment in the source: the name reads as a sentence) ui state

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.UiState()
#--> idle

composed from the signature, run for this page

no extension

Layout

the answerQCSXTZZZIBWU

IsFeasible

(no comment in the source: the name reads as a sentence) is feasiblein the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.IsFeasible()
#--> 1

composed from the signature, run for this page

no extension

Violation

The largest constraint violation, in pixels. Zero is a lawful picture.

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.Violation()
#--> 0

composed from the signature, run for this page

no extension

Violations

Every constraint with its violation, in the house rule shape so a CI gate can ingest it: a contradictory substance is a FINDING, not a crash -- Penrose's Fig. 2, a logically inconsistent program that "fails gracefully, providing visual intuition for why".no extension

Energy

(no comment in the source: the name reads as a sentence) energyin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.Energy()
#--> 0

composed from the signature, run for this page

no extension

Rounds

(no comment in the source: the name reads as a sentence) roundsin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.Rounds()
#--> 0

composed from the signature, run for this page

no extension

Evaluations

(no comment in the source: the name reads as a sentence) evaluationsin the section Same as Layout: the answerno extension

LayoutMs

(no comment in the source: the name reads as a sentence) layout msin the section Same as Layout: the answerno extension

NumberOfUnknowns

(no comment in the source: the name reads as a sentence) number of unknownsin the section Same as Layout: the answerno extension

NumberOfConstraints

(no comment in the source: the name reads as a sentence) number of constraintsin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.NumberOfConstraints()
#--> 0

composed from the signature, run for this page

no extension

Why

(no comment in the source: the name reads as a sentence) whyin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.Why()
#--> nothing to lay out -- no rule minted an unknown

composed from the signature, run for this page

no extension

CanvasWidth

the paper, and what a shape is beyond its geometry -- for the rules that judge a picture rather than solve it (DN8c)

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.CanvasWidth()
#--> 720

composed from the signature, run for this page

no extension

CanvasHeight

(no comment in the source: the name reads as a sentence) canvas height

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.CanvasHeight()
#--> 640

composed from the signature, run for this page

no extension

ShapeOwnerOf

(no comment in the source: the name reads as a sentence) shape owner ofin the section Same as Layout: the answerno extension

IsHidden

(no comment in the source: the name reads as a sentence) is hiddenin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.IsHidden("a")
#--> 1

composed from the signature, run for this page

no extension

PropOf

(no comment in the source: the name reads as a sentence) prop ofin the section Same as Layout: the answerno extension

ShapeOf

The solved geometry of one shape: [ :kind, :cx, :cy, :r ] for a circle, [ :kind, :cx, :cy, :w, :h ] for a rect or text, [ :kind, :x1, :y1, :x2, :y2 ] for a line.no extension

ValueOf

The solved value of any name: an unknown, a constant, a field, a derived property -- "u.arrow.x2", "U.ox".

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.ValueOf("a")
#--> 0

composed from the signature, run for this page

no extension

Shapes

(no comment in the source: the name reads as a sentence) shapesin the section Same as Layout: the answerno extension

NumberOfShapes

(no comment in the source: the name reads as a sentence) number of shapesin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.NumberOfShapes()
#--> 0

composed from the signature, run for this page

no extension

DrawIndexOf

Where a shape falls in the drawing order: 1 is painted first and so sits at the back. A shape that must not be buried has to come out with a HIGHER index than everything that could cover it, and that is a fact about the picture worth asserting rather than eyeballing -- layering is a partial order, and the depths it relaxes to are not obvious from reading the rules.no extension

PolygonOf

A polygon's vertices, or a spline's control points, in order: [ x1, y1, x2, y2, ... ].no extension

SplinePointsOf

The polyline a spline is drawn as, in px -- the control points are in PolygonOf. CATMULL-ROM, CENTRIPETAL: for each span P1-P2 the four points P0..P3 are blended with knots spaced by the square root of the chord, which is the parametrisation that never cusps or loops between two points however they are spaced (Yuksel, Schaefer, Keyser 2011). An open spline doubles its end points so the curve reaches them; a closed one wraps. Twelve samples per span.no extension

CurvePointsOf

The polyline a geodesic is drawn as: [ x1, y1, x2, y2, ... ] in px.no extension

MarkStrokesOf

The strokes a mark is drawn as: a list of polylines, each flat in px.no extension

ToCanvas

drawingno extension

ToSVG

(no comment in the source: the name reads as a sentence) to svg

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.ToSVG()
#--> <svg xmlns="http://www.w3.org/2000/svg" width="720" height="640" viewBox="0 0 720 640">
#--> <rect x="0" y="0" width="720" height="640" fill="rgb(255,255,255)"/>
#--> </svg>

composed from the signature, run for this page

no extension

Rendition

A VALUE THAT SAYS WHAT IT IS (DN9g) --------------------------------- A picture's natural rendition is its drawn geometry, which travels as text and needs no file. The raster and the substance's graph are the same picture seen the other two ways a consumer asked for.no extension

RenditionKinds

(no comment in the source: the name reads as a sentence) rendition kinds

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? @@( o1.RenditionKinds() )
#--> [ "vector", "image", "graph", "text" ]

composed from the signature, run for this page

no extension

RenditionAs

(no comment in the source: the name reads as a sentence) rendition asQCSXTZZZIBWU

RenditionAtQ

Same as RenditionAsXT: An empty path means the name this class would have chosen, so every caller written before today means exactly what it meant. A path given for a CARRIED kind is refused by name rather than ignored: a caller who asks for an SVG at a path is not asking for nothing, they are holding a wrong belief about the contract, and being told is the cheaper outcome.no extension

Substance

(no comment in the source: the name reads as a sentence) substanceno extension

ToPNG

(no comment in the source: the name reads as a sentence) to pngno extension

Fact

THE GENERAL KIND IS :expr, and the others are its named shortcuts. A picture already has a language for talking about itself -- the one a Style writes its rules in -- so a fact asks a question in that language and the answer comes off the same tape the solver used. That is what makes a caption's number the picture's number rather than a second calculation that could drift from it.no extension

ConstraintText

the energy text of a rule, so a narration can show what the engine was handed and how big it becameno extension

SetPictureTheme

WHAT A FRAME MAY CHANGE BETWEEN TWO PICTURES (DN9f). Haro copies an object on assignment, so a caller holding the substance or the style is holding a different one from the picture's; these are the doors through which a narration's action reaches the picture it is about.no extension

SetSubstanceData

A DATUM IS CONTENT, so changing one means the picture is compiled again -- unlike a theme, which changes only what a role resolves to.no extension

SetWindow

WHAT DOES NOT SCALE IS THE TYPE. A zoom here is for reading, not a photographic enlargement: the names keep their size and only their positions move, so a close view is more legible rather than merely bigger. Stroke widths do scale, because a hairline blown up eight times and still one pixel wide reads as a different picture.QCSXTZZZIBWU

WindowOn

centred on what a frame is about, with a reach around it -- the form an author actually writesQCSXTZZZIBWU

ClearWindow

(no comment in the source: the name reads as a sentence) clear windowno extension

HasWindow

(no comment in the source: the name reads as a sentence) has window

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.HasWindow()
#--> 0

composed from the signature, run for this page

no extension

Window

(no comment in the source: the name reads as a sentence) windowno extension

WindowScale

how much bigger the view is than the figure; 1 with no window

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.WindowScale()
#--> 1

composed from the signature, run for this page

no extension

IsInWindow

IS THIS THING IN VIEW? What a frame shows decides whether a mark is any use, and a mark pointing at something outside the window is a narration defect the one gate reports.

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.IsInWindow("a")
#--> 1

composed from the signature, run for this page

no extension

VisibleShapes

the shapes a reader can actually see, in draw orderno extension

Emphasis

EVERY MARK IS DERIVED, NEVER PLACED. Its geometry comes from the picture's solved values or from a rule actually in force -- which is the whole point of the plane, because a mark a person positions is a mark nobody checks. Marks are minted AFTER the solve and hold every existing unknown pinned while they place themselves, so adding one cannot move the figure it describes: frame two's figure is frame one's figure, to the last pixel. A HARO, A FOCUS OR A DIM. Emphasis changes how a shape already in the picture reads, so it mints nothing for :focus and :dim -- it rewrites the shape's own stroke -- and mints one circle for :ring.no extension

Measure

A DIMENSION BETWEEN TWO THINGS, WITH ITS NUMBER. The line runs centre to centre, the number is the distance FACT -- so the figure and the caption cannot disagree -- and the number's own label is solved off the ink like any other name.no extension

Callout

A SENTENCE ATTACHED TO A THING. The sentence may carry a hole, and a hole is filled from a FACT rather than typed -- which is the rule the whole plane exists to enforce. The label is solved: off the ink, off other names, on the paper, exactly as a vertex's name is, which is why a callout needed no new solver.no extension

Show

A RULE'S OWN BOUNDARY, AS A SHAPE. The leash a name must stay inside is a circle nobody ever drew, because it exists only as a term in the energy; showing it is reading that term's own arguments and turning them into geometry. Only the forms whose boundary IS a shape are shown, and the rest are refused by name rather than approximated.no extension

Region

AN AREA, TINTED. Where Show draws a boundary, Region fills what the boundary encloses -- the strip an edge forbids, the disc a clearance reserves. A strip is the segment's own rectangle, four corners derived from the segment's direction, so it bends with the picture.no extension

Marks

what this picture carries, as [ path, kind ] -- so a frame can say what it added and a later frame can take it away againno extension

NumberOfMarks

(no comment in the source: the name reads as a sentence) number of marks

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.NumberOfMarks()
#--> 0

composed from the signature, run for this page

no extension

ClearMarks

(no comment in the source: the name reads as a sentence) clear marksno extension

FillOf

The colour a shape is drawn with, after its rule is resolved: what the guard reads, and what a consumer of the SVG gets.no extension

StrokeOf

(no comment in the source: the name reads as a sentence) stroke ofin the section Same as Layout: the answerno extension

Background

the paper's colour: the theme's background

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.Background()
#--> #FFFFFF

composed from the signature, run for this page

no extension

MatchCandidates

how many candidate bindings the last compile enumerated

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.MatchCandidates()
#--> 0

composed from the signature, run for this page

no extension

StartsTried

Uniform over the canvas, as Penrose samples; radii and sizes from a band that gives the solver room. Three draws, the one with the least initial energy kept -- Penrose 4.2.1. How many starts the last layout needed, and which one it kept. A start the graph could not give -- a planar one on a tree, a layout on a substance with no graph -- falls back to random and says so.

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.StartsTried()
#--> 0

composed from the signature, run for this page

no extension

AdvisoryUnmet

Crossing rules left unmet when the start was not planar and the rule was therefore advice: zero for a planar start, and for any picture that has no crossing rule.

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.AdvisoryUnmet()
#--> 0

composed from the signature, run for this page

no extension

StartUsed

(no comment in the source: the name reads as a sentence) start usedin the section Same as Layout: the answer

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.StartUsed()
#--> random

composed from the signature, run for this page

no extension

StartedPlanar

Did the last layout begin from a planar embedding? False when the style asked for none, and false when it asked and the graph could not give one -- a tree, a path, anything Tutte collapses.

composed example

o1 = new stzMathDiagram(StzGraphDomain(), new stzMathSubstance(StzGraphDomain()), StzCurvedGraphStyle())
? o1.StartedPlanar()
#--> 0

composed from the signature, run for this page

no extension

OuterFace

The face the planar start was built on, as object names in cycle order; empty when there was no planar start.no extension

Touch

(no comment in the source: the name reads as a sentence) touchno extension

Ink

Every drawn stroke as a segment, [ x1, y1, x2, y2, cOwner, cPath ] -- what a rule that judges the picture reads, once per solveno extension

Texts

EVERY DRAWN NAME -- the text shapes that are visible and say something -- once per solve, like the ink. Every name rule's scope listed them by resolving every shape of the picture, and the governance asks a scope thousands of times: on the five-thousand-dot picture that was five thousand resolutions per ask.no extension