Note: Descriptions are shown in the official language in which they were submitted.
CA 02613744 2007-12-07
GAME UTILIZING A NON-SPHERICAL BILLIARD BALL
BACKGROUND OF THE INVENTION
Field of the Invention
[0002] The present invention relates generally to games or other types of
entertainment or amusement, and more specifically to games utilizing balls
used for billiards
or other such games.
Description of the Related Art
[0003] Billiards is a general category of games which are played with balls on
a
table. Billiards includes carom games in which the object is to roll a cue
ball to contact one
or more other balls and a predetermined number of cushions or rails of the
table. Billiards
also include pocket billiard games (e.g., snooker and pool) in which the
object is to roll a cue
ball to hit one or more other balls into pockets of the table. Typically, the
cue ball in billiards
is rolled by striking it with a cue stick.
[0004] The size, weight, and shape of billiard balls are specified in
regulations for
each type of billiard game. For example, for pocket billiards, regulation
balls are spherical
with a diameter of 21/4 inches (57.15 millimeters) and a weight between 51/2
and 6 ounces
(156 to 170 grams). As another example, snooker balls are spherical with a
diameter of 2 /16
inches (52.4 millimeters) and balls for three-cushion billiards are spherical
with a diameter of
2 7/16 inches (61.5 millimeters).
SUMMARY OF THE INVENTION
[0005] In certain embodiments, a method of playing a game comprises placing a
non-spherical billiard ball on a surface. The non-spherical billiard ball has
an ellipsoidal or
ovoidal shape and a generally smooth outer surface lacking a concave portion.
The method
further comprises rolling at least one spherical billiard ball along the
surface generally
towards the non-spherical billiard ball.
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[0006] In certain embodiments, an apparatus for playing a game comprises a non-
spherical billiard ball having an ellipsoidal or ovoidal shape and a generally
smooth outer
surface lacking a concave portion. The apparatus further comprises a first
plurality of
spherical billiard balls.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] These and other features will now be described with reference to the
drawings summarized below. These drawings and the associated description are
provided to
illustrate various embodiments, and not to limit the scope of the invention.
[0008] Figure 1 schematically illustrates an example billiard ball compatible
with
certain embodiments described herein.
[0009] Figures 2A-2E schematically illustrate examples of billiard balls
having an
ellipsoidal-shape body.
[0010] Figures 3A-3D schematically illustrate examples of billiard balls
having an
ovoidal-shaped body.
[0011] Figure 4 schematically illustrates an example billiard ball having a
covering in accordance with certain embodiments described herein.
[0012] Figure 5 is a flowchart of an example method of playing a game in
accordance with certain embodiments described herein.
[0013] Figure 6 schematically illustrates an example non-spherical billiard
ball,
spherical billiard ball, and surface compatible with certain embodiments
described herein.
[0014] Figure 7 schematically illustrates the starting positions of the non-
spherical
billiard ball and the spherical billiard balls at the beginning of the first
game of a set.
[0015] Figure 8 schematically illustrates the starting positions of the non-
spherical
billiard ball for the six games of a set and for a tie-breaking game.
[0016] Figure 9 schematically illustrates a configuration of spherical
billiard balls
and a non-spherical billiard ball for scoring purposes.
[0017] Figure 10 (separated into Figures 10A and lOB) is an example score
sheet
in accordance with certain embodiments described herein.
[0018] Figure 11 schematically illustrates the starting positions of the non-
spherical billiard ball for the bonus round games after each of the sets.
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DETAILED DESCRIPTION OF THE PREFERRED EMBODIlVIENT
Non-Spherical Billiard Ball
[0019] Figure 1 schematically illustrates an example billiard ball 10
compatible
with certain embodiments described herein. The billiard ball 10 comprises a
generally
incompressible body 20 having an ellipsoidal or ovoidal shape. The body 20 has
a generally
smooth outer surface 30 lacking a concave portion.
[0020] The body 20 is generally incompressible such that the body 20 does not
appreciably deform upon application of force due to contact or impact of the
billiard ball 10
with solid materials during normal use. As used herein, the term
"incompressible" has its
broadest ordinary meaning, including resistant to compression. For example, in
certain
embodiments, the body 20 does not comprise either compressible portions (e.g.,
hollow or
air-filled portions) which are configured to allow the body 20 to reduce in
volume upon
compression of the body 20 or deformable portions (e.g., fluid-filled
portions) which are
configured to allow the body 20 to deform upon compression of the body 20. In
certain
embodiments, the body 20 comprises a material which is resilient to forces due
to contact or
impact with solid materials (e.g., other balls, cue sticks, or portions of the
table with which it
is used). The body 20 of certain embodiments can withstand compressive loads
of about
10,000 pounds.
[0021] In certain embodiments, the body 20 is unitary such that the body 10
comprises a single piece of material. In certain such embodiments, the body 20
has a
substantially uniform density throughout the body 20. In certain other
embodiments, the
body 20 comprises two or more solid pieces of material which are generally
irreversibly
coupled together (e.g., chemically bonded together by adhesive or fused
together) to form the
body 20. The body 20 of certain embodiments is generally resistant to
scratches or burn spots
from conditions experienced during normal play. Examples of man-made materials
compatible with certain embodiments described herein include, but are not
limited to, resin
(e.g., phenolic resin, thermoset resin, Kobo resin, Partek resin) and
polyester.
[0022] In certain embodiments, the weight of the body 20 is in a range between
ounces and 8 ounces, in a range between 6 ounces and 8 ounces, in a range
between
5 ounces and 6 ounces, or in a range between 6 ounces and 7 ounces. In certain
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embodiments, the weight of the body 20 is selected to be approximately equal
to the weight
of a spherical ball with which the billiard ball 10 is to be used. Such a
configuration
advantageously provides more predictable collisions between the billiard ball
10 and the
spherical ball since the energy transfer during the collision is similar to
that of collisions
between two spherical balls with the same weight. In certain other
embodiments, the weight
of the billiard ball 10 is selected to be larger than the weight of a
spherical ball with which
the billiard ball 10 is to be used. Such a configuration advantageously
reduces the movement
of the billiard ball 10 after a collision between the billiard ball 10 and the
spherical ball as
compared to collisions in which the weights of the two balls are equivalent.
Other weights
are also compatible with various embodiments described herein.
[0023] As schematically illustrated by Figure 1, the billiard ball 10 of
certain
embodiments has a first diameter along a first direction 22 and a second
diameter along a
second direction 24 substantially perpendicular to the first direction 22,
with the first
diameter larger than the second diameter. In certain embodiments, the first
diameter is in a
range between 2 inches and 3 inches, and the second diameter is in a range
between 1.5
inches and 2.5 inches. In certain other embodiments, the first diameter is in
a range between
2.25 inches and 2.75 inches, and the second diameter is in a range between
1.75 inches and
2.25 inches. In still other embodiments, at least one of the first diameter
and the second
diameter is in a range between 2 inches and 2.5 inches (e.g., equals 2.25
inches) and the
weight is in a range between about 5 ounces and about 8 ounces (e.g., in a
range between 5.5
ounces and 6 ounces).
[0024] In certain embodiments, the body 20 has an ellipsoidal shape, as
schematically illustrated by Figures 2A-2E. For example, the shape of certain
embodiments
is a spheroid (e.g., oblate as shown in Figure 2A or prolate as shown in
Figure 2B). As used
herein, the terms "ellipsoidal" and "spheroid" are used to refer to both their
precise
geometrical definitions as well as to shapes having minor variations from the
precise
geometrical definitions. In certain other embodiments, a first portion 26 of
the body 20 has a
prolate spheroid shape and a second portion 28 of the body 20 has an oblate
spheroid shape,
as schematically illustrated by Figure 2C. In certain such embodiments, the
fust portion 26
and the second portion 28 are joined together at the equator and sharing a
principal axis of
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rotational symmetry 29. The second portion 28 of certain embodiments has a
generally
spherical shape, and is joined to the spheroid-shaped first portion 26 at the
equator and
sharing a principal axis of rotational symmetry 29, as schematically
illustrated by Figure 2D.
Figure 2E schematically illustrates a body 20 having a superellipsoidal shape.
[0025] In certain embodiments, the body 20 has an ovoidal shape. For example,
the shape of certain embodiments is generally egg-shaped, as schematically
illustrated by
Figure 1. In certain embodiments, the ovoidal shape has an axis of rotational
symmetry 29, a
substantially circular cross-section in a plane perpendicular to the axis of
rotational symmetry
29, and an oval cross-section in a plane along the axis of rotational symmetry
29, as
schematically illustrated by Figure 3A. An oval consisting of all the points
for which the sum
of the distance D1 to one focus fl plus twice the distance D2 to a second
focus f2 is a constant,
as schematically illustrated by Figure 3B, is a Cartesian oval. An oval
consisting of all the
points for which the product of their distances to two fixed points is a
constant, as
schematically illustrated by Figure 3C, is a Cassini oval. As used herein, the
terms "Cassini
oval" and "Cartesian oval" are used to refer to both their precise geometrical
defmitions as
well as to shapes having minor variations from the precise geometrical
definitions. Figure
3D schematically illustrates an oval cross-section comprising two semi-circles
joined by
straight sections. Other oval cross-sections can have elliptical or ovoidal
portions joined by
straight sections. Examples of oval cross-sections compatible with certain
embodiments
described herein include, but are not limited to, egg-shaped, Cassini oval,
Cartesian oval, and
shapes having two or more curved sections joined by straight sections (e.g.,
Figure 3D).
[0026] Figure 3B schematically illustrates the oval cross-section of a
billiard ball
for which the oval cross-section is a Cartesian oval. In certain embodiments,
the billiard
ball 10 has the Cartesian oval shape with a length along the axis of
rotational symmetry 29 of
about 2.25 inches. Such a configuration can advantageously optimize the
contact point
between a 2.25-inch-diameter spherical ball and the billiard ball 10. In
certain other
embodiments, the billiard ball 10 has the Cartesian oval shape with a length
along the axis of
rotational symmetry 29 of about 2.5 inches. Such a configuration can
advantageously
optimize the contact point between the billiard ball 10 and a table rail
having a height of
about 1.375 inches. In still other embodiments, the billiard ball 10 has the
Cartesian oval
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shape with a length perpendicular to the axis of rotational symmetry 29 of
about 2.25 inches.
Such a configuration can advantageously allow for the contact point between a
2.25-inch-
diameter spherical ball and the billiard ball 10 to be centered, thereby
allowing for similar
reaction to occur from the contact of a spherical ball and the billiard ball
10 as occurs from
the contact of two spherical balls having the same diameter. The length of the
Cartesian oval
shape along the axis of rotational symmetry 29 or perpendicular to the axis of
rotational
symmetry 29 can be advantageously selected to maximize the desired performance
of the
billiard ball 10 when used with other standard spherical billiard balls.
[0027] In certain embodiments, the billiard ball 10 having the Cartesian oval
shape advantageously has the axis of rotational symmetry 29 for the oval
equidistant from the
table surface at all points when the billiard ball 10 is in a resting
position. Thus, other balls
are able to contact the billiard ball 10 at a point in parallel alignment with
the axis of
rotational symmetry 29 of the billiard ball 10. Because the Cartesian oval
shape allows a
consistent contact point on its axis of rotational symmetry 29, the movement
of the billiard
ball 10 after contact, though chaotic, may be considered predictable and may
be quantified.
For example, the following predictions of the movement of the billiard ball 10
may be made:
Contact in the middle: The billiard ball 10 will roll straight, and the
distance the ball 10 will roll straight before starting to curve toward its
heavier
side is directly proportional to the velocity at which the billiard ball 10
was
hit.
Contact at the larger end: The billiard ball 10 will roll in a radius
direction toward the smaller end. The size of the radius is determined by the
velocity at which the billiard ball 10 was hit.
Contact at the smaller end: The billiard ball 10 will pivot in a radius
direction around the larger end. The rotation of this pivot is directly
proportional to the velocity at which the billiard ball 10 was hit.
In addition to the velocity at which the billiard ball 10 is hit, other
factors of dynamical
systems, such as friction and mass, affect the behavior of the billiard ball
10 when contacted
by other objects.
[0028) In certain embodiments, the outer surface 30 of the body 20 lacks
structures which would at least partially impede smooth rolling of the
billiard ball 10 along a
flat surface. For example, in certain embodiments, the outer surface 30 of the
body lacks a
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depression or a protuberance. In certain embodiments, the outer surface 30 of
the body 20
lacks corners, edges, flats, or ridges.
[0029] In certain embodiments, the outer surface 30 of the body 20 is the
outermost portion of the billiard ball 10. In certain other embodiments, the
outer surface 30
is partially or wholly covered by a covering 40, as schematically illustrated
by Figure 4. In
certain embodiments, the covering 40 comprises one or more layers of a
material that
provides coloring or design to the billiard ball 10. In certain embodiments,
the covering 40
comprises elastomer, rubber, vinyl, plastic, paint, or other material. The
covering 40 of
certain embodiments is compressible such that it provides a cushion between
the body 20 and
any material which contacts or impacts the billiard ball 10 (e.g., other
balls, cue sticks,
portions of the table). In certain such embodiments, the covering 40 has an
outer surface that
is generally parallel to the outer surface 30 of the body 20 such that the
outer surface of the
covering 40 is generally smooth and lacks a concave portion.
Game Utilizing Non-Spherical Billiard Ball
[0030] In a dynamical system,. an object moves according to one or more rules.
For example, for a plurality of moving balls interacting with one another as
they roll on a
table, the rules of motion determine how each ball will move. The ball may
move in a
regular, predictable fashion, or it may move in an irregular, chaotic fashion.
The kinematics
of such dynamical systems include considerations of linear momentum, torque
and angular
acceleration, friction, glancing collisions, moment of inertia, conservation
of energy, and
rotational kinetic energy.
[0031] In certain embodiments, the billiard ball 10 allows a mixture of
regular
and chaotic dynamical behavior to occur when the billiard ball 10 interacts
with the other
elements of the game, including other billiard balls which are spherical and
rails of the table.
Thus, the use of the billiard ball 10 to a game setting introduces an element
of
unpredictability and intrigue. Typically, games are played with spherical
balls and the laws
of physics allow highly skilled players to control the balls to achieve the
desired result to win
the game. The billiard ball 10 of certain embodiments brings to the game an
element of
irregularity which causes the skilled player to consider possible alternative
ball behavior and
gives the unskilled player a certain amount of "luck" when the billiard ball
10 rolls in a
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direction to his favor. Introducing the billiard ball 10 in certain
embodiments provides
structure with both good and bad chaotic results similar to the use of dice in
a game. The roll
of the dice is unpredictable, but the player continues within the structure of
the game based
on the outcome of his last chaotic roll. Players using traditional spherical
balls may plan their
next one, two, or three moves because they depend on the laws of physics to
accurately
achieve the desired results. Onlookers and/or opponents are also great
predictors of future
moves or of moves that the player should have performed. When the billiard
ball 10 of
certain embodiments is introduced into the game, players, onlookers, and
opponents must
now contemplate "Plan B" and "Plan C" ball movements in case "Plan A" fails
due to the
chaotic movement of the billiard ball 10 disrupting the desired ball
placement.
[0032] Figure 5 is a flowchart of an example method 100 of playing a game in
accordance with certain embodiments described herein. Figure 6 schematically
illustrates a
non-spherical billiard ball 210, a spherical billiard ball 220, and a surface
230 compatible
with certain embodiments described herein. The method 100 comprises placing a
non-
spherical billiard ball 210 on a surface 230 in an operational block 110. The
non-spherical
billiard ball 210 has an ellipsoidal or ovoidal shape and a generally smooth
outer surface
lacking a concave portion. The method 100 further comprises rolling at least
one spherical
billiard bal1220 along the surface 230 generally towards the non-spherical
billiard ball 210 in
an operational block 120.
[0033] Examples of non-spherical billiard balls 210 compatible with the method
100 are schematically illustrated by Figures 1, 2A-2E, 3A-3D, and 4 and are
described herein.
In certain embodiments described herein, two or more such non-spherical
billiard balls 210
are used.
[0034] In certain embodiments, the at least one spherical billiard ball 220
comprises one or more regulation billiard balls. For example, a spherical
billiard ball 220
compatible with certain embodiments described herein has a weight between 5.5
ounces and
6 ounces and a diameter of about 2.25 inches with a tolerance of 0.005 inch.
In certain
embodiments, the at least one spherical billiard ball 220 comprises two to
eight spherical
billiard balls.
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[0035] In certain embodiments, the surface 230 is a generally horizontal,
flat, and
smooth surface along which the non-spherical billiard ball 210 and the at
least one spherical
billiard ball 220 are free to roll. For example, the surface 230 of certain
embodiments is the
playing surface of a billiards table. In certain embodiments, the surface 230
is a table surface
having one or more cushioned rails 240 along corresponding edges of the
surface 230, as
schematically illustrated by Figure 6. The rails 240 are configured to allow
the non-spherical
billiard bal1210 and the at least one spherical billiard ball 220 to impact
and bounce from the
rails 240 without damaging either the ball or the rail 240. The rails 240 of
certain
embodiments serve to confine the non-spherical billiard ball 210 and the at
least one
spherical billiard ball 220 on the surface 230. In certain embodiments, the
table comprises
one or more pockets 250 in which the spherical balls 220 can fall. In certain
embodiments,
the non-spherical billiard ball 210 is capable of falling into the pockets 250
as well. The
pockets 250 can be distributed along the edges of the surface 230, at corners
at which two
edges of the surface 230 intersect, at various positions of the surface 230
away from the
edges, or at combinations thereof.
[0036] In certain embodiments, the at least one spherical billiard ball 220
comprises a plurality of spherical billiard balls (e.g., between 2 and 15
spherical billiard balls
220). In certain embodiments, all the spherical billiard balls 220 are
identical to one another,
while in certain other embodiments, each spherical billiard ball 220 has one
or more
identifying indicia (e.g., color, number, letter, image) used to distinguish
the spherical billiard
ball 220 from the others. For example, the spherical billiard balls 220 can
each have different
identifying indicia corresponding to different playing cards.
[0037] The at least one spherical billiard ball 220 of certain embodiments
comprises a first plurality of spherical billiard balls and a second plurality
of spherical billiard
balls. In certain embodiments, the second plurality of spherical billiard
balls comprises the
same number of spherical billiard balls (e.g., 2, 3, 4, 5, 6, 7, or 8
spherical billiard balls) as
does the first plurality of spherical billiard balls. In certain embodiments,
each spherical
billiard ba11220 of the first plurality of spherical billiard balls has one or
more corresponding
indicia with a first element common among the indicia of the first plurality
of spherical
billiard balls. In addition, each spherical billiard ball 220 of the second
plurality of spherical
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billiard balls has one or more corresponding indicia with a second element
common among
the indicia of the second plurality of spherical billiard balls, where the
second element is
different from the first element. The different indicia can be used to
distinguish the first
plurality of spherical billiard balls from the second plurality of spherical
billiard balls, to
distinguish the spherical billiard balls of a common plurality from one
another, or both.
[0038] For example, the first plurality of spherical billiard balls can have a
common first color or range of colors (e.g., red or varying shades of red) and
the second
plurality of spherical billiard balls can have a common second color or range
of colors (e.g.,
blue or varying shades of blue). Thus, each spherical billiard ball of the
first plurality
includes the first color and each spherical billiard ball of the second
plurality includes the
second color which is different from the first color. As another example, the
first plurality of
spherical billiard balls can have varying solid colors (e.g., the solid colors
of the 1-ball
through the 7-ball of a standard set of billiard balls) and the second
plurality of spherical
billiard balls can have stripes of varying colors (e.g., the stripes of
varying colors of the 9-ball
through the 15-ball of a standard set of billiard balls). As still another
example, the first
plurality of spherical billiard balls can have symbols or a type of symbols of
the same or
conunon type (e.g., diamonds) and the second plurality of spherical billiard
balls can have
symbols or a type of symbols of the same or common type but different from
that of the first
plurality of spherical billiard balls (e.g., spades). In certain other
embodiments, these and
other types of indicia may be used individually or together to provide a means
for
distinguishing the spherical billiard balls of the first plurality from the
spherical billiard balls
of the second plurality.
[0039] In certain embodiments, the non-spherical billiard ball 210 has one or
more indicia which are different from the indicia of the first plurality of
spherical billiard
balls and different from the indicia of the second plurality of spherical
billiard balls. For
example, the non-spherical billiard ball 210 can have a different color, a
different pattern, or
a different symbol than do any of the spherical billiard balls of the first
plurality or the second
plurality.
[0040] In certain embodiments, placing the non-spherical billiard ball 210 on
the
surface 230 comprises imparting a force on the non-spherical billiard ball 210
to roll the non-
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spherical billiard ball 210 along the surface 230. The force is imparted on
the non-spherical
billiard ball 210 manually in certain embodiments (e.g., by placing the non-
spherical billiard
ball 210 at a predetermined location on the surface 230 by hand or by rolling
the non-
spherical billiard ball 210 to a location on the surface 230 by rolling the
non-spherical billiard
bal1210 by hand). In certain embodiments, the force is imparted on the non-
spherical billiard
bal1210 by striking the non-spherical billiard ba11210 with a stick (e.g., a
cue stick as used in
a conventional game of billiards). In certain embodiments, the force is
imparted on the non-
spherical billiard ba11210 by striking the non-spherical billiard ba11210 by a
spherical billiard
ball which has been propelled in a direction (e.g., by hand or by striking the
spherical billiard
ball with a cue stick) so as to strike the non-spherical billiard ba11210.
[0041] In certain embodiments, rolling the at least one spherical billiard
ball 220
along the surface 230 comprises imparting a force on the at least one
spherical billiard ball
220 manually (e.g., by rolling the spherical billiard ball 220 by hand), by
striking the at least
one spherical billiard ba11220 with a stick (e.g., a cue stick as used in a
conventional game of
billiards), or by striking the at least one spherical billiard ball 220 with
another spherical.
billiard ball. In certain embodiments in which the surface 230 is a table
surface having one
or more cushioned rails 240 along corresponding edges of the surface 230,
rolling the at least
one spherical billiard bal1220 generally towards the non-spherical billiard
ba11210 comprises
rolling the at least one spherical billiard ball 220 towards the one or more
cushioned rails 240
such that the at least one spherical billiard ball 220 impacts the one or more
cushioned rails
240 and changes trajectory generally towards the non-spherical billiard ball
210. In certain
such embodiments, the at least one spherical billiard ball 220 impacts a first
cushioned rail
240 and changes trajectory towards a second cushioned rail 240, impacts the
second
cushioned rail 240 and changes trajectory generally towards the non-spherical
billiard ball
210.
[0042] In certain embodiments, the method 100 further comprises placing a
second non-spherical billiard ball on the surface. The second non-spherical
billiard ball has
an ellipsoidal or ovoidal shape with a generally smooth outer surface lacking
a concave
portion. In certain embodiments, the second non-spherical billiard ball is
identical to the first
non-spherical billiard bal1210, while in certain other embodiments, the second
non-spherical
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billiard ball has a different shape, color, design, or other indicia than does
the first non-
spherical billiard ball 210 so as to distinguish the two from one another. In
certain
embodiments, the method 100 further comprises rolling the at least one
spherical billiard ball
220 along the surface 230 generally towards the second non-spherical billiard
ball.
[0043] The following description provides various examples of games compatible
with certain embodiments described herein. Persons skilled in the art
recognize that other
games are also compatible with certain embodiments described herein.
Example 1: Hand Billiard Game Using Non-Spherical Billiard Ball
[0044] In the game of Example 1, one non-spherical billiard ball 300, a first
set of
spherical billiard balls 310, a second set of spherical billiard balls 320,
and a billiards table
330 are used. The two sets of spherical billiard balls each have six spherical
billiard balls,
and the two sets have different indicia (e.g., one set is light in color, the
other set is dark in
color). Two to six players are organized in two teams, Team A and Team B, each
having a
team captain. Teams need not have the same number of players. Table 1 provides
possible
combinations of two to six players into Teams A and B:
Table 1:
Number of players Team A Team B
2 1 1
3 2 1
4 2 2
3 2
6 3 3
[0045] Figure 7 schematically illustrates the set-up conditions for the game.
In
the following description, reference is made to various positions on the table
330 by referring
to the markings (e.g., diamonds) that are located on the left side rail 331,
the foot rail 332, the
right side rail 333, and the head rail 334. A notation of Fx-Sx is used herein
where F stands
for foot rail and S stands for side rail. The foot rail 332 has three markings
denoting
positions Fl, F2, and F3. Each of the side rails 331, 333 has six markings
denoting positions
S1, S2, S3, S4, S5, and S6. The position is determined by counting the
markings from left to
right and from bottom to top from the foot rail perspective. The foot string
335 is defined to
be the line at S2, and the long string 336 is defmed to be the line at F2.
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[0046] A standard match consists of four sets and each set consists of six
games,
but other variations are possible. Teams rotate around the table after each
set in order to both
equalize and vary the rolling perspectives of the players. For example,
following the first set,
the teams change sides (left and right); following the second set, the teams
stay on the same
side but change ends (foot and head); and after the third set, the teams
change sides (left and
right). Once the rotation occurs, the new team position is played throughout
all six games of
the set until the next set begins. The rotation of the non-spherical billiard
ball 300 is identical
in all four sets, however, the foot rail 332 and the head rail 334 reverse
during the third and
fourth set so that players may gain experience from both ends of the table.
The rotation
instructions are written on the score sheets.
[0047] At the start of a game, Team A places their six spherical billiard
balls 310
on the table 330 along the left side rail 331 between the foot rail 332 and
the foot string 335,
and Team B places their six spherical billiard balls 320 on the table 330
along the right side
rail 334 between the foot rai1332 and the foot string 333. The spherical
billiard balls placed
along the left side rail 331 and the right side rail 334 are termed "resting
billiard balls"
because they have not yet been rolled into play.
[0048] For the first game in a set, the non-spherical billiard bal1300 is
placed at a
position F1-S5, as shown in Figure 7. For the start of each game of the set,
the non-spherical
billiard ball 300 is placed at a different position. The same rotating
position of the non-
spherical billiard ball is followed in the six games for each of the four
sets. As viewed from
the foot rail, the positioning pattern for the non-spherical billiard ball is
provided in Table 2
and shown schematically in Figure 8.
Table 2:
Game 1 Position F1-S5
Game 2 Position F2-S5
Game 3 Position F3-S5
Game 4 Position F1-S6
Game 5 Position F2-S6
Game 6 Position F3-S6
Tie Breaker Position F2-S4
The placement of the non-spherical billiard ball 300 is approximate to the
intersection of the
positions indicated by Table 2, and the player placing the non-spherical
billiard ball 300 may
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CA 02613744 2007-12-07
position the non-spherical billiard ball 300 at the angle of his choosing.
Exact placement of
the non-spherical billiard ball 300 is not critical to the successful play of
the game. For
example, the non-spherical billiard ball 300 can be placed within two inches
of the
intersection indicated.
[0049] A legal roll is defined as a player standing behind the foot rail and
rolling a
team spherical billiard ball by hand towards the game playing region 340 which
is defined as
the region between the foot string and the head rail. All spherical billiard
balls rolled by
players during game play must be legal rolls. If a player commits a foul, the
appropriate
penalty is employed.
[0050] A legal roll conforms to the following rules. A player who does not
roll a
legal roll has committed a foul. Penalties for fouls vary accordingly to the
type of foul
committed and, in some situations, when the foul occurs during the course of
playing the
game.
[0051] Legal roll rule 1: A player must release his hand from the spherical
billiard
ball by the time the spherical billiard ball reaches the foot string, and a
player's hand may not
extend past the foot string. If a foul of this rule is committed, the game
continues and the
penalty is the notation of a foul being accumulated on the score sheet for the
team
committing the foul and the fmal score will be reduced according to the
scoring rules for each
foul committed.
[0052] Legal roll rule 2: A player may not touch the spherical billiard ball
again
once he has released the spherical billiard ball into a rolling motion. If a
foul of this rule is
committed, the game continues and the penalty is the notation of a foul being
accumulated on
the score sheet for the team committing the foul and the final score will be
reduced according
to the scoring rules for each foul committed.
[0053] Legal roll rule 3: A player must remain to the left or the right of the
long
string depending on which quadrant of the table his team is currently
positioned. A player
may bank a spherical billiard ball against the cushion on the opposing team's
side of the
table, but only from a standing position from his own team's side of the
table. If a foul of
this rule is committed, the game continues and the penalty is the notation of
a foul being
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CA 02613744 2007-12-07
accumulated on the score sheet for the team committing the foul and the final
score will be
reduced according to the scoring rules for each foul committed.
[0054] Legal roll rule 4: A player must roll the spherical billiard ball in
such a
manner that the spherical billiard ball remains in contact with the table
surface at all times.
No player may toss, throw, or bounce any spherical billiard ball at any time
during the game.
If a foul of this rule is committed, the game continues and the penalty is the
notation of a foul
being accumulated on the score sheet for the team committing the foul and the
final score
will be reduced according to the scoring rules for each foul committed.
[0055] Legal roll rule 5: A player must wait for the motion of all spherical
and
non-spherical billiard balls on the table to stop before rolling another
spherical billiard ball
into play or before removing a spherical billiard ball from play. If a foul of
this rule is
committed, the game continues and if the spherical billiard ball contacts
another spherical or
non-spherical billiard ball that is in motion, the penalty is the notation of
a foul being
accumulated on the score sheet for the team committing the foul and the final
score will be
reduced according to the scoring rules for each foul committed.
[0056] Legal roll rule 6: A player must not prematurely stop and remove a
moving
spherical or non-spherical billiard ball that has rolled out of the game
playing region 340 and
into the resting billiard ball area (between the foot rail and the foot
string). If a foul of this
rule is committed, the game continues and the penalty is the notation of a
foul being
accumulated on the score sheet for the team committing the foul and the final
score will be
reduced according to the scoring rules for each foul committed.
[0057] Legal roll rule 7: Unless playing a version of the game in which no
banking of the spherical billiard ball is required, a spherical billiard ball
rolled into motion
must contact a cushion before contacting any other spherical or non-spherical
billiard ball on
the table. If a foul of this rule is committed, the game in play is void and
is replayed, and the
penalty is the notation of a foul being accumulated on the score sheet for the
team
committing the foul and the final score will be reduced according to the
scoring rules for each
foul committed.
[0058] The object of the game is to roll the team spherical billiard balls
310, 320
by hand to a position on the table 330 as close to the non-spherical billiard
ball 300 as
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CA 02613744 2007-12-07
possible. In one variation of the game, the team spherical billiard balls 310,
320 must bank
against a minimum of one cushion on the table before contacting any other
spherical or non-
spherical billiard balls. In another variations, the requirement of using one
bank may be
eliminated (e.g., for beginning players) or the requirement of banking against
two or more
cushions may be added (e.g., for advanced players). In still other variations,
the required
number of banks can be determined on a player-by-player basis, depending on
the skill level
of the individual players.
[0059] Play begins by a chosen player from Team A rolling one of his team's
spherical billiard balls 310 by hand onto the table towards the non-spherical
billiard ball 300,
with the condition that he must bank the spherical billiard ball 310 against a
minimum of one
cushion before contacting any other spherical or non-spherical billiard balls.
Next, the
chosen player from Team B rolls one of his team's spherical billiard balls 320
towards the
non-spherical billiard ball 300, with the same condition of one bank before
contacting any
other spherical or non-spherical billiard balls. These same two players from
Team A and
Team B continue to alternate rolls until all six of the respective team
spherical billiard balls
are rolled. This defines the completion of one game.
[0060] For one-person teams, the same player will play all games in a set and
all
sets in a match. For two-person teams, the team members will alternate playing
the games
through the completion of the set. For three-person teams, the team members
will cycle
playing the games through the completion of the set. Other permutations of the
team
members playing the games of the set may also be used.
[0061] After the first set, the rotation changes so that players are not
continuing to
play against the same opponent for all sets (except for one-person teams). The
rotation for
each of the sets is designated on the score sheet so that referencing the
score sheet will inform
players of their new playing rotation for the set about to be played.
[0062] The non-spherical billiard bal1300 must remain in the game playing
region
340. If the non-spherical billiard ball 300 is hit into a pocket 350, or hit
and stops on the
surface between the foot rail 332 and the foot string 335, or hit off of the
table 330, the game
is void and must be replayed. Strategic playing may cause a team to attempt
voiding a game
by one of the above methods, however, a penalty is imposed if the non-
spherical billiard ball
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CA 02613744 2007-12-07
300 is hit off of the table 330. When the non-spherical billiard ball 300 is
hit off of the table
300, the game is void and is replayed with the team that caused the non-
spherical billiard ball
300 to come off the table 330 receiving a foul recordable on the score sheet.
If the game was
voided by legitimate means (e.g., the non-spherical billiard ball 300 falling
into a pocket
350), then the game is replayed without penalty.
[0063] A player is allowed to bank his spherical billiard ball against any
cushion
during his turn. However, if he chooses to use any cushion between the foot
rail 332 and the
foot string 335, he may not hit any of the resting spherical billiard balls
set up and waiting to
play in that area. If his spherical billiard ball does hit these resting balls
on his initial release
of the roll, it is a foul recordable on the score sheet.
[0064] A player is allowed to bank his spherical billiard ball against any
other
spherical or non-spherical billiard ball in play on the surface. However, as
stated above, the
player must first bank his spherical billiard ball against a cushion prior to
contacting any of
the other spherical or non-spherical billiard balls.
[0065] Any spherical billiard ball which rolls back into and stops between the
foot
rail 332 and the foot string 335 is dead and must be pocketed. No additional
penalty is
imposed. If this same spherical billiard ball hit resting billiard balls not
in play causing these
balls to hit other balls in play, the game is void and must be replayed.
However, if the resting
billiard balls that were hit have not disrupted the game play by hitting balls
within the game
playing region 340 and can be replaced to their set-up positions without
controversy, the
game may continue after doing so.
[0066] A player who hits any team spherical billiard ball off of the table 330
voids the game and the game is replayed. "Off of the table" is defmed as
hitting a ball so that
it does not land on the table surface between the foot rail 332 and the head
rail 334 or into a
pocket 350. When a team spherical billiard ball is hit off of the table 330,
the game is void
and replayed with the team who caused the billiard ball to come off of the
table receiving a
foul recordable on the score sheet. A team spherical billiard ball that is
pocketed is
considered "dead" and no penalty is imposed or foul committed.
[0067] A player may not touch or move by hand any team spherical billiard ball
or
non-spherical billiard ball which is on the game playing region 340 during the
course of a
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CA 02613744 2007-12-07
game. Touching or moving any spherical or non-spherical billiard ball on the
game playing
region 340 by hand voids the game and the game must be replayed. The team
touching or
moving the billiard ball receives a foul recordable on the score sheet.
[0068] A player is not required to call out his play or strategy in advance of
rolling his team spherical billiard ball. However, strategic discussions
between all players
serve to provide the game with fun, controversy, competitiveness, and improved
skills.
Assistance may be requested or offered without solicitation by players within
reason and in a
manner that does not disrupt the flow or atmosphere of the game.
[0069] All players should conduct themselves with manners appropriate to the
game. Socializing and strategy interaction is encouraged. However, actions
which are
intended to distract another player or cause another player to perform under
his capabilities
exhibit poor sportsmanship and should be avoided by all participants and
spectators.
Appropriate language is also encouraged so as not to offend surrounding
players. Team
captains are ultimately responsible for maintaining the integrity of the game,
but all of the
participants share the responsibility to make this happen.
[0070] Scoring is determined after all six spherical billiard balls from both
teams
have been rolled. The locations of the non-spherical billiard ball 300 and the
spherical
billiard balls must remain undisturbed until the score has been tallied and
agreed upon by the
two team captains.
[0071] The team with its spherical billiard ball closest to the non-spherical
billiard
ball 300 receives one point (called Team A for this description). If the
second closest
spherical billiard ball to the non-spherical billiard bal1300 is also from
Team A, then Team A
receives two points. If the third closes spherical billiard ball to the non-
spherical billiard ball
300 is also from Team A, the Team A gets three points and so on up to a
maximum of six
points. Team A can earn the maximum of six points only if all six of their
spherical billiard
balls are closer to the non-spherical billiard ball 300 than are any of the
spherical billiard
balls of the opposing team (called Team B for this description). Team A's
point
accumulation stops when the next closest spherical billiard ball to the non-
spherical billiard
ball 300 is one from Team B. Because Team B's spherical billiard ball was not
closest to the
non-spherical billiard ball 300, Team B receives no points for the game.
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CA 02613744 2007-12-07
[0072] For example, referring to Figure 9, after all the spherical billiard
balls have
been rolled, one of Team A's spherical billiard balls is closest to the non-
spherical billiard
ball 300. The second-closest spherical billiard ball to the non-spherical
billiard bal1300 also
belongs to Team A. The third-closest spherical billiard ball to the non-
spherical billiard ball
300 belongs to Team B. This Team B spherical billiard ball stops the point
accumulation of
Team A, so that Team A receives a fmal score of two points for this game.
Players from both
teams may be involved in the score calculation, but the fmal score must be
agreed upon by
the two team captains and recorded on the score sheet. When the distance
between two
spherical billiard balls and the non-spherical billiard ball is too close to
differentiate which
spherical billiard ball is closer, a measuring device may be used to quantify
the distance.
[0073] In the event of a draw and a decision cannot be determined or agreed
upon,
the following actions by the team captains will finalize the score. In the
situation in which
Team A has accumulated points, but the next possible point is questionable due
to an
equidistant spherical billiard ball belonging to Team B, the team captain of
Team A will flip
a coin and the team captain of Team B will make the call of heads or tails. If
Team A wins
the coin toss, Team A receives the point in question. If Team A loses the coin
toss, Team A
does not receive the point in question. For example, if Team A has two
noncontested points,
but the validity of the third point is questioned because Team A's third
spherical billiard ball
and Team B's first spherical billiard ball are both five inches from the non-
spherical billiard
ball, Team A receives three points if Team A wins the coin flip, and receives
two points if
Team A loses the coin flip. Other means of randomly choosing between Team A
and
Team B can be used instead of the coin flip.
[0074] In the situation in which both Team A and Team B both have their first
spherical billiard balls equidistant from the non-spherical billiard ball so
that the first point is
questionable, both teams will receive one point toward their accumulated game
points when a
point scoring system is used and one-half point toward their accumulated game
wins when a
win scoring system is used. In one example of this situation, Team A has a
spherical billiard
ball which is touching the non-spherical billiard ball and Team B also has a
spherical billiard
ball which is touching the non-spherical billiard ball.
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CA 02613744 2007-12-07
[0075] Before a measuring device is used, a preliminary score must be agreed
upon by the two team captains. The location of the non-spherical billiard ball
and the
spherical billiard balls must continue to remain undisturbed until this
preliminary score has
been agreed upon. This preliminary score will be the basis for the final score
in the event that
a controversy or movement of the spherical billiard balls or non-spherical
billiard ball occurs
during the measurement process. Either or both of team captains may use the
measuring
device, but if both captains are hesitant to measure, the team captain of Team
A will bear the
responsibility to attempt a decision-making measurement. In the event that the
measurement
is inconclusive, controversial, or negated due to ball movement occurring
during the
measurement process, the agreed upon preliminary score will be finalized based
on the
appropriate action of the team captains applying the rules from the situations
outlined above.
[0076] As in any game or competition, fairness and good sportsmanship should
prevail. All players should strive to agreeably and accurately calculate
points and wins so
that controversy and questions may be minimized. When team captains are
required to make
final score decisions, the members of both teams should support the final
outcome.
[0077] By using a score sheet (e.g., as illustrated by Figure 10), teams may
determine the winner by calculating their scores either on a point basis, a
win basis or both
(many league settings use a combination of both). Prior to the beginning of
play, both teams
or both captains should agree on the calculation method of determining the
winner and also
on how many games will be played if it will be different from the standard
play of four sets.
Fouls are scored and deducted as directed on the score sheet. The winner is
the team that has
the most points or wins as of the last game played after deducting for foul
penalties.
[0078] In the event of a tie and a tie breaker game is desired, one final game
may
be played by a team player of the team captain's choice. The non-spherical
billiard ball 300
can be placed in Position F2-S4 for this tie-breaking game.
[0079] Players may utilize various strategies (e.g., offensive andlor
defensive
strategies) during any roll executed. A player may chose to offensively roll
his spherical
billiard ball close to the non-spherical billiard ball 300 or defensively
knock an opponent's
spherical billiard ball away from the non-spherical billiard ball 300. Any
strategy is
acceptable as long as the rules are followed.
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CA 02613744 2007-12-07
[0080] Many variations are possible for the game in terms of banking
requirements, scoring requirements, and rotation requirements. One variation
would be to
play the game with a cue stick rather than rolling the billiard balls by hand.
Because a cue
stick brings more velocity and precision to the game, certain games require
that only the
spherical billiard ball which a player just shot may contact a cushion. After
possible contact
with other billiard balls, no other billiard ball (either his own or his
opponents), except for the
non-spherical billiard ball 300 may contact a cushion. If any other billiard
ball, (other than
the one just shot or the non-spherical billiard bal1300) touches a cushion, a
foul is committed
and the final score will be reduced according to the rules on the score sheet
and the game
continues.
Example 2: Individual Bonus Round
[0081] A separate bonus round game may be incorporated between sets in order
to
allow players an opportunity to practice and exhibit their individual skills.
During this bonus
round game, individuals may accumulate points based on their own performance.
[0082] In this bonus round game, one non-spherical billiard ball and six
spherical
billiard balls are used. The non-spherical billiard ball 300 is set in the
positions listed in
Table 3, and schematically illustrated by Figure 11, based on the set which is
being played.
Table 3:
After first set Position F1-S5
After second set Position F2-S6
After third set Position F3-S5
[0083] The six spherical billiard balls are lined up on either the right or
left side
rail between the foot rail and the foot string. A player may stand in any
position behind the
foot rail. A player is not required to stand on either the left or the right
of the long string for
this bonus round game.
[0084] The object of this bonus round game is to roll each of the six
spherical
billiard balls by hand toward the non-spherical billiard ball with the purpose
of the spherical
billiard ball contacting the non-spherical billiard ball. The spherical
billiard ball rolled must
bank against a minimum of one cushion on the table before contacting the non-
spherical
billiard ball. In one game variation, the requirement of using one bank may be
eliminated for
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CA 02613744 2007-12-07
beginning players and the requirement of banking against two or more cushions
may be
added for advanced players.
[0085] The player rolls one spherical billiard ball at a time toward the non-
spherical billiard ball with the goal of contacting the non-spherical billiard
ball. The rolled
spherical billiard ball must contact at least one cushion before contacting
the non-spherical
billiard ball. After contact with the cushion, the rolled spherical billiard
ball may contact
additional cushions or previously rolled spherical billiard balls without
penalty. The rolled
spherical billiard ball itself must contact the non-spherical billiard ball.
If the rolled spherical
billiard ball contacts another spherical billiard ball which in turn contacts
the non-spherical
billiard ball, but the rolled spherical billiard ball itself does not contact
the non-spherical
billiard ball, the roll does not result in a score.
[0086] If a rolled spherical billiard ball falls into a pocket, it is
considered dead.
If the rolled spherical billiard ball contacted the non-spherical billiard
ball prior to falling into
the pocket, the contact still results in a score. If the rolled spherical
billiard ball did not
contact the non-spherical billiard ball prior to falling into the pocket, the
roll does not result
in a score.
[0087] If the non-spherical billiard ball falls into a pocket, it is spotted
to its
original position. If the non-spherical billiard ball falls into a pocket upon
being contacted by
the rolled spherical billiard ball, the contact still results in a score. If
the non-spherical
billiard ball falls into a pocket due to contact by other spherical billiard
balls, but was not
contacted by the rolled spherical billiard ball, the roll does not result in a
score.
[0088] The player receives one point for each spherical billiard ball that
directly
contacts the non-spherical ball up to a maximum of six points. The individual
with the
highest score is the winner.
Example 3: Pocket Billiard Game of Eight-Ball Using a Non-Spherical Billiard
Ball
[0089] In an example variation of Eight-Ball using a non-spherical billiard
ball,
the eight-ball is replaced with the non-spherical billiard ball within the
rack of fifteen billiard
balls. For this example, the cue ball and the other 14 numbered billiard balls
are spherical.
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CA 02613744 2007-12-07
[0090] All official rules of standard Eight-Ball apply when players are
shooting at
the spherical numbered billiard balls. When players are attempting to "tag"
the non-spherical
billiard ball, the following variation from the official rules apply.
[0091] A player must "tag" the non-spherical billiard ball with the cue ball
prior
to shooting at a numbered spherical billiard ball on the table. In certain
variations, novice
players may choose to allow the cue ball to tag the non-spherical billiard
ball with a direct
shot while skilled players may require the cue ball to contact a cushion prior
to tagging the
non-spherical billiard ball. After legally contacting a cushion, if required,
a tag is considered
legitimate as long as the cue ball contacts the non-spherical billiard ball. A
player may
contact either his own or his opponent's numbered spherical billiard balls in
the attempt to
tag the non-spherical billiard ball. However, if contacting a cushion first is
required, the
cushion must be contacted first before contacting any other numbered spherical
billiard balls.
A player does not have to call his shot, method, or indicate details such as
number of
cushions, banks, kisses, or caroms when attempting to tag the non-spherical
billiard ball.
[0092] If a player pockets the non-spherical billiard ball during the tagging
attempt, the non-spherical billiard ball is spotted on the foot spot. If the
cue ball legally
tagged the non-spherical billiard ball prior to the non-spherical billiard
ball being pocketed,
the non-spherical billiard ball is spotted and the player may continue his
turn. If the cue ball
did not legally tag the non-spherical billiard ball prior to the non-spherical
billiard ball being
pocketed, the non-spherical billiard ball is spotted, the player loses his
turn, and the incoming
player has an opportunity to tag the non-spherical billiard ball with the cue
ball.
[0093] If a player fails to tag the non-spherical billiard ball during the
tagging
attempt, the player loses his turn and the incoming player has an opportunity
to tag the non-
spherical billiard ball with the cue ball. Any opponent's billiard ball
pocketed during the
attempt to tag the non-spherical billiard ball remains pocketed. Any billiard
ball pocketed of
one's own team during the attempt to tag the non-spherical billiard ball is
spotted on the foot
spot. Failing to tag the non-spherical billiard ball always results in loss of
turn. If a player
pockets the cue ball in his attempt to "tag" the non-spherical billiard ball,
the player loses his
turn and the incoming player has ball in hand with the cue ball.
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CA 02613744 2007-12-07
[0094] Once a player has successfully "tagged" the non-spherical billiard
ball, the
player may shoot at a numbered spherical billiard ball within his designated
group. All
official rules of Eight-Ball apply during the player's shot attempt at this
point. If the player
does not successfully pocket his numbered spherical billiard ball, he loses
his turn and the
incoming player begins his turn by attempting to successfully "tag" the non-
spherical billiard
ball with the cue ball. If the player does successfully pocket his numbered
spherical billiard
ball, his play continues, but he must successfully "tag" the non-spherical
billiard ball again
with the cue ball before attempting to pocket the next numbered spherical ball
in his group.
If he once again successfully "tags" the non-spherical billiard ball, his turn
continues. If he
fails to successfully "tag" the non-spherical billiard ball, he loses his turn
and the incoming
player begins his turn by attempting to successfully "tag" the non-spherical
billiard ball with
the cue ball. In summary, the non-spherical billiard ball must always by
"tagged" by the cue
ball prior to a player shooting at a numbered spherical billiard ball of his
grouping.
[0095] When a player has pocketed all of the numbered spherical billiard balls
of
his group, he must contact the non-spherical billiard ball with the cue ball
by hitting a
minimum of two cushions first. Novice players may require contacting only one
cushion and
skilled players may require contacting up to three or four cushions. If he
fails to contact the
non-spherical billiard ball with the cue ball, he loses his turn and the
incoming player begins
his turn by attempting to successfully "tag" the non-spherical billiard ball
with the cue ball.
If the incoming player also has pocketed all the numbered spherical billiard
balls in his group,
he must "tag" the non-spherical billiard ball with the minimum number of
cushion contacts
required. The player pocketing either group of numbered spherical billiard
balls first and
then legally "tagging" the non-spherical billiard ball wins the game.
[0096] After a player pockets his group of numbered spherical billiard balls
and is
attempting to win the game with a legal tag, various scenarios may occur. If
the non-
spherical billiard ball is pocketed, but a legal contact by the cue ball was
made, the player
wins the game. If the non-spherical billiard ball is pocketed, but a legal
contact by the cue
ball was not made, the player loses his turn, the non-spherical billiard ball
is spotted on the
foot spot, and the incoming player begins his turn by attempting to
successfully "tag" the
non-spherical billiard ball. If the cue ball is pocketed after a legal contact
to the non-
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CA 02613744 2007-12-07
spherical billiard ball was made, the player loses his turn and the incoming
player receives
ball in hand with the cue ball. If the cue ball is pocketed, but a legal
contact by the cue ball to
the non-spherical billiard ball was not made, the player loses his turn and
the incoming player
receives ball in hand with the cue ball.
[0097] Other standard billiard games may also be modified to be played by
using
the variation of "tagging" the non-spherical billiard ball as described above.
Examples
include, but are not limited to, Nine-Ball in which the nine-ball is replaced
by the non-
spherical billiard ball, Poker Pool in which the eight-ball is replaced by the
non-spherical
billiard ball, Seven-Ball in which the seven-ball is replaced by the non-
spherical billiard ball,
and Ten-Ball in which the ten-ball is replaced by the non-spherical billiard
ball.
[0098] Various embodiments have been described above. Although this invention
has been described with reference to these specific embodiments, the
descriptions are intended
to be illustrative of the invention and are not intended to be limiting.
Various modifications and
applications may occur to those skilled in the art without departing from the
true spirit and
scope of the invention as defined in the appended claims.
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