WO2002089934A1

WO2002089934A1 - Game and tile set

Info

Publication number: WO2002089934A1
Application number: PCT/AU2002/000560
Authority: WO
Inventors: Donald James Bone
Original assignee: Advanced Image Research Pty Ltd
Priority date: 2001-05-07
Filing date: 2002-05-07
Publication date: 2002-11-14
Also published as: AU745257B3

Abstract

A tiling set for a game having a plurality of individually unique tiles having shapes derived from at least one basic tiling polygonal tile shape, for each basic polygonal shape there being a plurality of derived shapes said tiles having vertices corresponding to the vertices of the basic polygonal shape. The shape of the sides of the basic shapes is modified such that the first and second subgroups of sides have non straight line forms which are assymetric, each tile having a surface design.

Description

"GAME AND TILE SET"

Technical field

This invention relates to a game or the like and to a tile set therefore. As used herein the expression "game or the like" is to be given a broad meaning. The expression includes, inter alia, board games (with or without a board per se), puzzles and the like, toys, and assemblies and arrangements which include a set of tiles for recreational, educational, learning, assessment, teaching, therapeutic, psychological and other such purposes. As used herein the expression "tile" is also to be given a broad meaning and is not limited to conventional tiles in the sense of being substantially flat or slab like and having two substantially flat sides. Whilst this configuration is preferred, the expression is to be construed as extending to include any pieces suitable to cover a surface when appropriately juxtaposed. The invention has particular but not exclusive application to a tile set for a jigsaw-like game or puzzle.

The invention also relates to a method of generating a tile set for a game or the like.

As used herein the expression "generating a tile set" is to be construed as including producing the design of the tile set as well as well as production of the tile set per se, and production of computer programs for controlling the cutting or other manufacturing technique to manufacture the tile set etc.

Background of Invention Jigsaw-like games and puzzles and other board games using tile sets are known. US Patents 4219194, 5062637, 5067714 and 5893560 illustrate some known arrangements. The so-called "penrose" tiles are also known and are described in US patent 4133152.

Summary of Invention

The present invention aims to provide an alternative to known games and the like and tile sets therefor. This invention in one aspect resides broadly in a tiling set for .a game or the like, the tile set including:- a plurality of individually unique tiles having shapes derived from at least one basic tiling polygonal tile shape, for each basic polygonal tile shape there being a plurality of derived tile shapes; wherein said tiles have vertices corresponding to the vertices of said basic polygonal tile shapes; wherein the shape of the sides of said basic polygonal tile shapes is modified such that first and second subgroups of the sides of the tiles have respective non-straight line forms which are asymmetric with respect to a rotation of 180 degrees about an axis perpendicular to the plane containing said vertices, the shape of the sides of the first and second subgroups being oppositely configured and adapted to closely abut along said sides, the shape of the side of a tile constituting an edge shape, and wherein said tiles each include one of a plurality of surface designs extending to at least some of the sides of the tiles to constitute an edge pattern, for each derived shape there being a plurality of tiles each having a different surface design; the surface design and the shape of each tile being such that no tiles in the tile set share the same combination of shape and edge pattern; the arrangement being such that when tiles which each have at least one side matching in edge shape and edge pattern closely abut along the respective matching sides, the surface designs of adjoining tiles cooperate to form a surface design pattern. As used herein the expression "tiling set" refers to a set of tiles wherein the tiles are tilings in that they abut to cover a plane without leaving a space therebetween.

As used herein the expression "vertex" or "vertices" refers to the point(s) of intersection of the straight line boundary elements of the basic polygons from which the tile shapes are derived.

It is preferred that any side of any tile in the set matches in edge shape and edge pattern at least one side of at least one other tile in the set. It is further preferred that any side of any tile in the set matches in edge shape and edge pattern at least one side of a plurality of other tiles in the set.

It is preferred that the non-straight line form includes a jigsaw-like lobe such that two adjoining tiles can lockingly abut along sides with the same non-straight line form.

It is also preferred that the basic polygonal tile shape has included angles of 60°, 120°, 60° and 120°. Alternatively the basic polygonal tile shapes may include two quadrilaterals having included angles of 36^Q, 72^Q, 36^s and 216⁵, and 72°, 72^s, 72° and 144^s respectively. It is also preferred that the non-straight line form is one of a set of non- straight line forms.

In one embodiment the non-straight line form is a single arcuate curve. It is preferred that the partial surface design is part of a two dimensional design. In one embodiment this may be a geometric pattern. In this embodiment it is preferred that the partial surface design is a circular arc or segment such that when a plurality of tiles adjoin the surface design pattern is a circle.

Alternatively the two dimensional design need not be a geometric pattern.

In this embodiment the partial surface design is such that when a plurality of tiles adjoin the surface design pattern constitutes a map or plan of an area. Preferably the map or plan has a plurality of themes including vegetation, green spaces, buildings, cities, islands, oceans, land and water.

Alternatively, the partial surface design can be part of a three dimensional design. Thus the partial surface design could be a three-dimensional shape such that when a plurality of tiles adjoin the surface design pattern is a three dimensional icon or the like such as a crown or a cube. Alternatively, when a plurality of tiles adjoin, the surface design pattern thus formed could be buildings, trees, mountains etc corresponding with respective themes.

In another aspect this invention resides broadly in a method of generating a tiling set for a game or the like, the method including:- modifying the shape of a plurality of individually unique tiles having shapes derived from at least one basic tiling polygonal tile shape, for each basic polygonal tile shape there being a plurality of derived tile shapes such that first and second subgroups of the sides of the tiles have respective non-straight line forms which are asymmetric with respect to a rotation of 180 degrees about an axis perpendicular to the plane containing said vertices, the shape of the sides of the first and second subgroups being oppositely configured and adapted to closely abut along said sides, the shape of the side of a tile constituting an edge shape, whereby a plurality of unique tile shapes can be generated, each tile shape having vertices corresponding to the vertices of said basic polygonal tile shapes, and marking the tiles thus formed with one of a plurality of surface designs extending to at least some of the sides of the tiles to constitute an edge pattern, for each derived shape there being a plurality of tiles each having a different surface design; the surface design and the shape of each tile being such that no tiles in the tile set share the same combination of shape and edge pattern; the arrangement being such that when tiles which each have at least one side matching in edge shape and edge pattern closely abut along the respective matching sides, the surface designs of adjoining tiles cooperate to form a surface design pattern.

Description of Drawings

In order that this invention may be more easily understood and put into practical effect, reference will now be made to the accompanying drawings which illustrate a preferred embodiment of the invention, wherein:-

FIG 1 shows a first basic polygonal tiling shape in the form of a rhombus, and an arcuate modification to the shape of the sides of the basic shape;

FIG 2 shows the basic polygonal tiling shape of FIG 1 and a jigsaw-like modification to the shape of the sides of the basic shape;

FIG 3 shows a set of ten tiles of unique shape derived from the basic polygonal tiling shape of FIG 1 ; FIG 4 shows a set of ten tiles having the shape of the first tile of the tile set of FIG 3, each tile having a unique partial surface design; FIG 5 shows a set of sixteen tiles having the shape of the second tile of the tile set of FIG 3, each tile having a unique partial surface design;

FIG 6 shows a second pair of basic polygonal tiling shapes in the form of kite and dart Penrose tilings, and with four asymmetric jigsaw-like modifications to the shape of the sides of the basic shapes;

FIG 7 shows a set of sixteen tiles of unique shape derived from the basic kite tile shape of FIG 6;

FIG 8 shows a set of sixteen tiles of unique shape derived from the basic dart tile shape of FIG 6; FIG 9 is a set of 128 unique tiles having four sub-sets of thirty two tiles having each of the shapes of tiles illustrated in FIGS 7 and 8, with each of the shapes from FIGS 7 and 8 having four unique partial surface designs;

FIG 10 shows some of the tiles of the set illustrated in FIG 9 joined to generate two different surface design patterns based on the same polygonal tiling; FIG 11 illustrates another embodiment of the invention wherein the set of tiles is based on a hexagon and with partial surface designs constituted by straight lines forming edge patterns adjacent the vertices of the tiles:

FIG 12 illustrates how the partial surface designs of a hexagonally based tile can result in the same edge patterns, and FIG 13 illustrates a hexagonally based tile having the surface design themes of houses and vegetation.

Description of Preferred Embodiment of Invention

As is best seen in FIGS 2 and 3 a tile set for a game or the like includes a plurality of tiles as for example numbered 0-3, 5-7, 10, 1 1 and 15 in FIG 3. Each tile has a shape which is derived from a basic tiling polygonal shape. As seen in FIG 2, the basic shape of the tiles in FIG 3 is a rhombus having included angles of 60°, 120°, 60° and 120^s. The tiles seen in FIG 3 have vertices A, B, C and D corresponding to the vertices A, B, C and D of the basic rhombus shape seen in FIG 2.

The shape of tiles numbered 0-3, 5-7, 10, 11 and 15 in FIG 3 has been modified from the basic polygonal shape such that all sides of the tiles have the non-straight line shape in either an inward or outward configuration. As seen in FIG 2 in its outward configuration 21 , the shape XX' includes a jigsaw-like lobe protruding from the tile while in the complimentary inward configuration 22 the curve XX' includes a jigsaw-like recess such that sides of the tiles in these complementary configurations are adapted to closely abut along the sides. The jigsaw-like lobe and recess arrangement 21 ,22 allow two adjoining tiles to lockingly abut along a side.

Alternatively as best seen in FIGS 6, 7 and 8 a tile set for a game or the like includes a plurality of tile shapes as for example numbered 0-15 in FIG 7 and 0-15 in FIG 8. The tile shapes in the sets seen in FIGS 7 and 8 are derived respectively from the two quadrilaterals seen in FIG 6. These quadrilaterals comprise the kite and dart pair of the Penrose tilings having included angles of 36°, 72°, 36° and 216°, and 72°, 72^s, 72^s and 144^s respectively. The tiles seen in FIG 7 have vertices E, F, G and H corresponding to the vertices E, F, G and H of the kite shaped quadrilateral seen in FIG 6 and the tiles seen in FIG 8 have vertices J, K, L and M corresponding to the vertices J, K, L and M of the dart shaped quadrilateral seen in FIG 6.

The shape of tiles seen in FIGS 7 and 8 has been modified from the basic kite and dart shapes of FIG 6 such that all sides of the tiles have one of four possible non-straight line shapes in either an inward or an outward configuration. Two of these shapes are used for the shorter sides and two are used for the longer sides. As seen in FIG 6 a first non-straight line shape PP' includes a jigsaw-like lobe which can be configured in either an outward 31 or an inward 32 configuration such that sides of tiles modified with these complementary configurations are adapted to closely abut along their sides. The jigsaw-like lobe and recess arrangement 31 ,32 allow two adjoining tiles to lockingly abut along a side. The other shapes QQ', RR' and SS' in FIG 6 are also similarly adapted and include lobe and recess arrangements 33,34 and 41 ,42 and 43,44 respectively. Note that not all possible configurations of the 4 shapes can be used on all sides. Each side can have only two possible shapes. The two shorter non-straight line shapes can only be used on the shorter sides and the two longer non-straight line shapes can only be used on the longer sides. Also, even on sides of the same length and configuration (inward or outward lobe), the number of possible shapes are restricted so that any side of a tile based on a one of the quadrilaterals cannot join to the equivalent side of another tile based on the same quadrilateral, and can join to only one of the sides of the same length on a shape derived from the other quadrilateral.

As is best seen in FIGS 4, 5 and 9, the tiles include a partial surface design associated with the sides such that when tiles closely abut along those sides, the partial surface designs of adjoining tiles cooperate to form a surface design pattern. This is best seen in FIG 10. It will be thus seen that the design of the pieces is based on a small set of polygonal shapes chosen so that the length of the sides of the polygons take one of a small number of possible values, and the angles at the vertices of the polygonal shapes take one of a small number of possible values. The polygons are further constrained so that they must be capable of being combined in a number of different ways to form a tiling pattern which completely covers a planar region.

To construct the game pieces the straight line boundary elements of the same length are replaced by a curved boundary element that joins the same end points as the straight line boundary element. This curved boundary element will have either an 'inward' or an 'outward' configuration such that an inward configured boundary element on one piece matches and joins to an outward configured boundary element on another piece. This allows the production from the small set of polygons of a multitude of unique shapes by selecting for each line element one of the two possible configurations of the curved boundary element. The resulting pieces can still be fitted together in a large number of ways to cover a region, but are constrained in doing so by the configuration of the matching boundary elements. This curved boundary element may be as simple as a circular arc or, if an interlocking design is required, it could for example take the form of a more complex curve containing a jigsaw like lobe. The surface design on each piece contain components which when put together with components on other pieces would form completed design components in the final picture. For example each piece might contain parts of a circle such that a complete circle could be assembled by joining several pieces. These surface design elements are designed in such a way that wherever they intersect a curved boundary element they do so in such a way as to form one of a small number of possible patterns along the boundary of the piece.

In this preferred embodiment, fitting two pieces together then requires that both the shape and the boundary pattern match along the abutted boundaries of the pieces. Within the boundary, the surface design can take any form. This allows the surface design to be more natural in appearance. Only the key surface design elements formed by the intersection of the surface design with the boundaries of the pieces would constrain the assembly of the pieces and the surface design may contain other elements which do not intersect the boundary of the piece.

The combination of the shape and the surface design elements in this way allows a large number of unique pieces to be constructed in a manner not contemplated by the prior art while still permitting the pieces to be assembled in a large number of ways. The unique configuration of each piece offers a challenging visual matching task in fitting a piece onto the edge of an assembly of pieces. The multiplicity of possible assemblies allows individual players to direct the construction by a suitable choice of piece to add.

As a first example of the design of a set of pieces we choose as the basis of the pieces the simple polygon in FIGS 1 and 2. Each side of this rhombus is of the same length and the angles at each vertex are either 60° or 120°. This rhombus may be tiled in a large number of possible ways to cover a plane.

The symmetric curved boundary element shown in FIG 2 is used to generate the shapes. Because the underlying polygon is rotationally symmetric and the two configurations of the boundary element are symmetric under rotation, some of the shapes generated by substituting the curved boundary element for the straight boundary elements are the same under some rotation, so there are in this case only 10 unique shapes. These shapes are shown in FIG 3, where the numbers labelling the pieces arise by interpreting the set of configurations of the curved boundary elements as the bits- in a binary representation of a number.

A suitable surface design comprises copies of a simple circular disc centred on the vertices of the base polygon. For the rotationally symmetric shapes, there will be 10 possible configurations of the surface patterns for each shape. For the rotationally asymmetric shapes there are 16 possible unique configurations of the key surface design elements for each unique shape. The surface designs for two of the shapes are shown in FIGS 4 and 5.

Another design example is based on the 'Kite and Dart' version of the Penrose Tiling pattern. This tiling uses the two polygons illustrated in FIG 6.

These are constructed with two straight line elements whose lengths are in the

ratio 1 : . To construct the shapes, two curved boundary elements .are

generated, one for the long side and one for the short side. These curved elements are designed with a lobe so that the pieces will interlock. In order to partially encode the rules which ensure the Penrose tiling can be continued, the curved boundary elements are made asymmetric with the lobe off-centre. The inward and outward configurations for each side are then chosen such that the complementary configuration of a given curve cannot be used on a side of any other piece which is equivalent in the base polygon to the side occupied by the curve itself. The allowed configuration of the curves on the two pieces are also constrained so that the tiles cannot be assembled with points L and E together or the points J and G together on abutted tiles..

The substitution of the curved boundary elements in all combinations of the allowed configurations for each of the straight line boundary elements in the polygons results in the set of 32 possible shapes shown in FIGS 7 and 8.

FIG 9 illustrates four sub-sets 51 ,52,53,54 each of thirty two tiles corresponding to each of the shapes of tiles illustrated in FIGS 7 and 8. Each individual tile shape in each sub-set, for example the first shape in each of the FIGS 7 and 8 ie tiles 55a, 55b, 55c, 55d and 56a, 56b, 56c, 56d respectively, has four unique partial surface designs. The four unique partial surface designs are common to each of the FIG 7 and FIG 8 tile shapes in each of the four sub-sets 51 ,52,53,54. The full set of shapes thus results in 128 tiles each having a unique combination of shape and surface design. This design satisfies the requirement that the intersection of the surface design with the boundary element forms a small number of possible patterns for each curved boundary element (in this case two possible configurations) such that each piece will match with boundaries of a large subset of the other pieces.

FIG 10 illustrates two distinct matched tilings of this small subset of pieces each based on the same underlying polygon tiling.

FIG 11 illustrates another embodiment of the invention wherein the set of tiles is based on a hexagon. If all possible shapes were used with substitution of the sides by two configurations of the interlocking tongue and groove, the number of tiles would be extremely large. Accordingly in the embodiment shown the set of shapes has been limited to those shapes which have a rotational symmetry under rotations of 60^s, 120^s or 180^s. This limits the set of shapes to the five shapes seen in the top row of FIG 1 1.

The surface designs seen in FIG 11 simulate roads or road-like patterns and result in all possible configuration of edge patterns with a road intersection at or adjacent one or more of the vertices of the basic hexagon shape. The resulting set of tiles seen in FIG 1 1 are each unique with a unique combination of basic shape and edge pattern.

It will be appreciated that although the same internal surface design is shown in the tiles of FIG 1 1 , this is not necessary and can be varied. Thus FIG 12 illustrates how the variation of the partial surface designs of a hexagonally based tile can result in the same edge patterns. As has been previously indicated the surface design pattern can constitute a map or plan of an area and can incorporate complimentary themes such as vegetation and buildings, green spaces and cities, islands and oceans, land and water etc. It is further envisaged that games having such themes can be combined with other games having other themes to constitute a macro- or super game.

Thus FIG 13 illustrates a hexagonally based tile having the surface design themes of houses and vegetation. It will be appreciated that the "surface" design may be three-dimensional in the sense that the shape of the surface of the tiles may be etched or raised to form a design as well as the case of a two dimensional colouring of the surface. Furthermore, there can also be non-key design elements which may or may not partially overlap the edges of the tiles. Thus for example, the tiles may carry land and sea elements which can form the key design elements, but there may also be birds animals and trees which are not key but which are likely to overlap the boundaries in some places by a small amount due perhaps to inaccuracies during in manufacture, or due to design constraints. It will be appreciated that games can be played using the tile set of the present invention in a number of ways. For example a number of players can compete using a single set of tiles with each player randomly taking tiles turned face up in a central location and joining tiles to create their own individual tiling pattern, with the winner being the player who has made the most number of completed patterns (such as complete circles). Alternatively, players can take turns to take tiles from individually coloured sets of tiles, one set to each player, and compose a single tiling pattern with the winner being the player having most of his/her coloured tiles forming part of completed patterns. Many alternatives exist to play games solo, as individuals or in teams. It will be appreciated that in one of the preferred embodiments, the present invention involves a method for the design of game or puzzle pieces such that all pieces are unique but so that the pieces may be joined to construct a large number of possible designs, each possible design constrained so that any two joined pieces forming part of the design match in shape and surface design across the junction between the two joined pieces.

In this embodiment a large set of pieces, each with a unique combination of shape and surface design, is constructed in such a way that for any given piece there are a large subset of the other pieces in the set which can be joined to the piece along a boundary such that the boundary shape and the surface design match along this boundary. By basing the shapes of the pieces on a set of polygonal shapes which can be fitted together to tile a surface, the pieces can be combined in a large number of possible ways while still providing sufficient constraints on the fitting to allow scope for tactical and strategic play in a game and for challenging puzzles to be constructed.

It will of course be realised that whilst the above has been given by way of an illustrative example of this invention, all such and other modifications and variations hereto, as would be apparent to persons skilled in the art, are deemed to fall within the broad scope and ambit of this invention as is herein set forth.

Claims

1 . A tiling set for a game or the like, the tile set including: a plurality of individually unique tiles having shapes derived from at least one basic tiling polygonal tile shape, for each basic polygonal tile shape there being a plurality of derived tile shapes; wherein said tiles have vertices corresponding to the vertices of said basic polygonal tile shapes; wherein the shape of the sides of said basic polygonal tile shapes is modified such that first and second subgroups of the sides of the tiles have respective non-straight line forms which are asymmetric with respect to a rotation of 180 degrees about an axis perpendicular to the plane containing said vertices, the shape of the sides of the first and second subgroups being oppositely configured and adapted to closely abut along said sides, the shape of the side of a tile constituting an edge shape, and wherein said tiles each include one of a plurality of surface designs extending to at least some of the sides of the tiles to constitute an edge pattern, for each derived shape there being a plurality of tiles each having a different surface design; the surface design and the shape of each tile being such that no tiles in the tile set share the same combination of shape and edge pattern; the arrangement being such that when tiles which each have at least one side matching in edge shape and edge pattern closely abut along the respective matching sides, the surface designs of adjoining tiles cooperate to form a surface design pattern.

2. A tiling set as claimed in claim 1 , wherein any side of any tile in the set matches in edge shape and edge pattern at least one side of at least one other tile in the set.

3. A tiling set as claimed in claim 2, wherein any side of any .tile in the set matches in edge shape and edge pattern at least one side of a plurality of other tiles in the set.

4. A tiling set as claimed in claim 1 , wherein said basic polygonal tile shape has included angles of 60^s, 120^s, 60^s and 120^s.

5. A tiling set as claimed in claim 1 , wherein said non-straight line form includes a jigsaw-like lobe such that two adjoining tiles can lockingly abut along sides with the same non-straight line form.

6. A tiling set as claimed in claim 1 , wherein said basic polygonal tile shape has included angles of 60^s, 120°, 60^s and 120°.

7. A tiling set as claimed in claim 1 , wherein said basic polygonal tile shapes includes two quadrilaterals having included angles of 36^s, 72^s, 36^s and 216^s, and 72^s, 72^s, 72^s and 144^s respectively.

8. A tile set as claimed in claim 1 , wherein said non-rectilinear curve is one of a set of non-rectilinear curves.

9. A tile set as claimed in claim 1 , wherein said non-rectilinear curve is a single arcuate curve.

10. A tile set as claimed in claim 1 , wherein said partial surface design is part of a two dimensional design.

1 1. A tile set as claimed in claim 10, wherein said partial surface design is part of a two dimensional geometric pattern.

12. A tile set as claimed in claim 11 , wherein said partial surface design is a circular arc or segment such that when a plurality of tiles adjoin the surface design pattern is a circle.

13. A tile set as claimed in claim 10, wherein said partial surface design is such that when a plurality of tiles adjoin the surface design pattern constitutes a map or plan of an area.

14. A tile set as claimed in claim 13, wherein said map or plan has a plurality of themes including vegetation, green spaces, buildings, cities, islands, oceans, land and water.

15. A tile set as claimed in claim 1 , wherein said partial surface design is part of a three dimensional design.

16. A method of generating a tiling set for a game or the like, the method including:- modifying the shape of a plurality of individually unique tiles having shapes derived from at least one basic tiling polygonal tile shape, for each basic polygonal tile shape there being a plurality of derived tile shapes such that first and second subgroups of the sides of the tiles have respective non-straight line forms which are asymmetric with respect to a rotation of 180 degrees about an axis perpendicular to the plane containing said vertices, the shape of the sides of the first and second subgroups being oppositely configured and adapted to closely abut along said sides, the shape of the side of a tile constituting an edge shape, whereby a plurality of unique tile shapes can be generated, each tile shape having vertices corresponding to the vertices of said basic polygonal tile shapes, and marking the tiles thus formed with one of a plurality of surface designs extending to at least some of the sides of the tiles to constitute an edge pattern, for each derived shape there being a plurality of tiles each having a different surface design; the surface design and the shape of each tile being such that no tiles in the tile set share the same combination of shape and edge pattern; the arrangement being such that when tiles which each have at least one side matching in edge shape and edge pattern closely abut along the respective matching sides, the surface designs of adjoining tiles cooperate to form a surface design pattern.