used for most diagrams to give border padding

When a specific Backend B is in scope, padBorder:: Diagram B -> Diagram B

chunks n l - split a list l into chunks of length n (n>0)

arrangeRowsGap s n diags - arranges diags into n per row, centering each row horizontally, with a seperation gap (horizontally and vertically) of s. The result is a single diagram.

When a specific Backend B is in scope, arrangeRowsGap :: Double -> Int -> [Diagram B] -> Diagram B

arrangeRows n diags - arranges diags into n per row, centering each row horizontally. The result is a single diagram (seperation is 1 unit vertically and horizontally).

When a specific Backend B is in scope, arrangeRows :: Int -> [Diagram B] -> Diagram B

add a given label at a given point offset from the centre of the given diagram.

When a specific Backend B is in scope, labelAt :: Point V2 Double -> String -> Diagram B -> Diagram B

Tgraph for a sun (sun vertex type)

Tgraph for vertex type jack.

Tgraph for vertex type king.

Tgraph for vertex type queen.

Tgraph for vertex type ace (same as fool).

Tgraph for vertextype deuce.

Tgraph for vertex type star.

Tgraph for kite

Tgraph for a dart

fool: fool's kite - also called an ace.

a once decomposed fool (= foolDs!!1)

foolDminus: 3 faces removed from foolD - still a valid Tgraph

an infinite list of decompositions of fool

an infinite list of decompositions of sunGraph

an infinite list of decompositions of a kite

an infinite list of decompositions of a dart

Tgraph of 4 times decomposed dartGraph (used in several examples)

A sun with 3 darts on the boundary NOT all adjacent (Used in superForceRocketsFig).

diagram of just fool.

When a specific Backend B is in scope, foolFig :: Diagram B

diagram of fool with foolD.

When a specific Backend B is in scope, foolAndFoolD :: Diagram B

Figure for a 3 times decomposed sun with a 2 times decomposed sun.

When a specific Backend B is in scope, figSunD3D2 :: Diagram B

vertexTypesFig is 7 vertex types in a single diagram as a row.

When a specific Backend B is in scope, vertexTypesFig :: Diagram B

forceVFigures is a list of 7 diagrams - force of 7 vertex types.

When a specific Backend B is in scope, forceVFigures :: [Diagram B]

diagram showing partial composition of a forced 3 times decomposed dart (with remainder faces in pale green).

When a specific Backend B is in scope, pCompFig1 :: Diagram B

diagram showing partial composition of a forced 3 times decomposed kite (with remainder faces in pale green).

When a specific Backend B is in scope, pCompFig2 :: Diagram B

diagram showing two partial compositions (with remainder faces in pale green).

When a specific Backend B is in scope, pCompFig :: Diagram B

diagram of foolDminus and the result of forcing.

When a specific Backend B is in scope, forceFoolDminus :: Diagram B

diagram of forced 5 times decomposed dart.

When a specific Backend B is in scope, forceDartD5Fig :: Diagram B

diagram of forced 5 times decomposed kite.

When a specific Backend B is in scope, forceKiteD5Fig :: Diagram B

diagram of forced 5 times decomposed sun.

When a specific Backend B is in scope, forceSunD5Fig :: Diagram B

diagram of forced 5 times decomposed dart (left) and kite (right).

When a specific Backend B is in scope, forceFig :: Diagram B

brokenDart is a 4 times decomposed dart (dartD4) with 5 halftile faces removed. Forcing will repair to produce the same Tgraph as force dartD4. This graph can also be repeatedly composed (without forcing) to get a maximal Tgraph.

badlyBrokenDart has more faces removed from brokenDart. This will also get repaired by forcing (to produce the same as force dartD4). However it will fail to produce a valid Tgraph if composed twice without forcing.

brokenDartFig shows the faces removed from dartD4 to make brokenDart and badlyBrokenDart.

When a specific Backend B is in scope, brokenDartFig :: Diagram B

badlyBrokenDartFig shows badlyBrokenDart, followed by its composition, followed by the faces that would result from an unchecked second composition which are not tile-connected. (Simply applying compose twice to badlyBrokenDart will raise an error).

When a specific Backend B is in scope, badlyBrokenDartFig :: Diagram B

figure showing the result of removing incomplete tiles (those that do not have their matching halftile) to a 3 times decomposed sun.

When a specific Backend B is in scope, removeIncompletesFig :: Diagram B

mistake is a legal but incorrect Tgraph - a kite with 2 darts on its long edges

mistake1 is a kite bordered by 2 half darts (subgraph of mistake and still incorrect)

Diagram showing superForce with initial Tgraph g (red), force g (red and black), and superForce g (red and black and blue).

When a specific Backend B is in scope, superForceFig :: Diagram B

Diagram showing 4 rockets formed by applying superForce to successive decompositions of sun3Dart. The decompositions are in red with normal force additions in black and superforce additions in blue.

When a specific Backend B is in scope, superForceRocketsFig :: Diagram B

graph of the boundary faces only of a forced graph (dartDs!!4)

graph of the boundary faces only of a forced graph (dartDs!!5)

figure of the boundary faces only of a forced graph (dartDs!!4).

When a specific Backend B is in scope, boundaryFDart4Fig :: Diagram B

figure of the boundary faces only of a forced graph (dartDs!!5).

When a specific Backend B is in scope, boundaryFDart5Fig :: Diagram B

graph of the boundary faces only of a forced graph - with extra faces removed to make a gap

graph of the boundary faces only of a forced graph - with extra faces removed to make a gap

figure for the boundary gap graph boundaryGapFDart4.

When a specific Backend B is in scope, boundaryGap4Fig :: Diagram B

figure for the boundary gap graph boundaryGapFDart5.

When a specific Backend B is in scope, boundaryGap5Fig :: Diagram B

boundaryVCoveringFigs bd - produces a list of diagrams for the boundaryVCovering of bd (with the Tgraph represented by bd shown in red in each case).

When a specific Backend B is in scope, boundaryVCoveringFigs :: BoundaryState -> [Diagram B]

boundaryECoveringFigs bd - produces a list of diagrams for the boundaryECovering of bd (with the Tgraph represented by bd shown in red in each case).

When a specific Backend B is in scope, boundaryECoveringFigs :: BoundaryState -> [Diagram B]

diagram showing the boundaryECovering of a forced kingGraph.

When a specific Backend B is in scope, kingECoveringFig :: Diagram B

diagram showing the boundaryVCovering of a forced kingGraph.

When a specific Backend B is in scope, kingVCoveringFig :: Diagram B

figure showing King's empires (1 and 2).

When a specific Backend B is in scope, kingEmpiresFig :: Diagram B

figure showing King's empires 1.

When a specific Backend B is in scope, kingEmpire1Fig :: Diagram B

figure showing King's empire 2.

When a specific Backend B is in scope, kingEmpire2Fig :: Diagram B