CN101316631A - Sphere design exhibiting rotation-induced contrast - Google Patents

Abstract

A method of placing a mark on a ball or sphere is disclosed in which the mark exhibits spin-induced contrast when the ball or sphere is spun at a sufficient speed. The method is based on the design using a plurality of geodesic lines symmetrically arranged around a ball or sphere. Each marking is then applied according to the design so that as the ball or sphere rotates, the markings form a contrast line that is perpendicular to the axis of rotation of the ball or sphere at either axis of rotation. These contrast lines allow the observer to more accurately view the axis of rotation of the ball or sphere and to track the ball or sphere in motion.

Description

Sphere design showing contrast caused by rotation

Cross References to Related Applications

This application claims the benefit of US Provisional Application Serial No. 60/724979, filed October 7, 2005, which is hereby incorporated by reference in its entirety.

Background technique

The present invention relates to the field of balls. In particular, the invention relates to patterns on balls that exhibit spins that produce contrast.

Vision science research shows that the human visual system distinguishes objects from their surroundings by seeing differences in brightness, color, texture, motion, and depth.

Moving and spinning balls are a central part of many sports and other recreational activities. In most situations, it is important for the players and/or spectators to watch the ball as it moves. This may be especially important when the sporting event is televised and the ball is small and/or moving at high speed. Likewise, it is helpful for the player to determine exactly what spin is on the ball, and thus to accurately foresee the ball's trajectory and interaction with other objects.

Also, some people, especially professional athletes, are very good at looking at the ball and getting down to their "zone" of contact with the ball. In fact, they can keep their eyes on the ball exceptionally well. Effectively looking at the ball provides a considerable technical advantage to the athlete in successfully hitting or catching the ball.

One way to improve an individual's ability to fixate on a moving object, such as a ball, is to make the moving object visually contrast with its surrounding objects. For example, tennis balls are a colored, highly pronounced yellow that contrasts with the court and surrounding objects that are usually visible around the court. As another example, the ball may include multiple contrasting colors. That way, the contrast created on the ball helps the individual to gaze at the ball more easily.

Parts of adding contrast to a ball are known. For example, a traditional soccer ball was originally formed to have a black pentagon surrounded by a white hexagon to improve the visibility of the ball to black and white television viewers. As another example, soccer balls used in American colleges and high schools include white tape partially surrounding each end of the soccer ball. In both examples, the markings add contrasting colors that enhance the visual trajectory of the ball for participants and spectators. However, there are other benefits that can be achieved with ball markings that these limited examples do not provide. For example, balls can be marked to improve visual recognition of ball spin. Also, existing markers are not necessarily optimized for specific conditions such as ambient light and/or distance between the viewer and the ball.

Research in vision science shows that contrast improves visibility, as shown in experiments with prototypes. Below are several references from Adler's Physiology of the Eve that support contrast for enhanced visibility.

O'Mullane and Knox have shown that the accuracy and speed of eye movements that smoothly track trajectories increase with increasing object contrast. O'Mullane G and Knox PC: Modification of smooth pursuit initiation by target contrast, Vision Res 39:3459, 1999. Collewijn and Erkelens have shown that smooth gaze tracking improves with increasing depth stimuli. Collewijn H and ErkelensCJ: Binocular eye movements and the perception of depth. In Kowler E(ed): Eye movements and their role in visual and cognitive processes), New York, 1990, Elsevier.

Legge and Gu have shown that depth perception improves with increased object contrast. Legge GE and Gu Y: Stereopsis and contrast, Vision Res 29: 989, 1989. This can be explained by increased visual intensity which increases and/or restores more More signals from deeply (non-uniformly) selected neurons. Harwerth RS and Schor CM: Binocular Vision. In Kauffman PL and Aim A (ed): Adler's physiology of the eye, 2003, Mosby.

The "Bruche brightness enhancement effect" confirms that flickering light appears brighter than non-flickering light. Brucke E.: Uber die Nutzeffect intermitterender Netzhautreizungen. Sitzungsberichte der Mathematisch Naturwissenschaftlichen, Classe der Kaiserlichen Akademieder Wissenschaften 49:128, 1848.

Regan has shown that the human visual system distinguishes objects from their surroundings by perceiving differences in brightness, color, stripes, motion, and depth. Regan D's: A brief review of some of the stimiliand analysis methods used in spatiotemporal vision research. In ReganD.(ed): Spatial vision ), London, 1991, MacMillan.

Hogervorst, Bradshaw, and Eagle have proposed that the human visual system includes filters that are sensitive to the contrast of formed motion patterns. Hogervorst MA, Bradshaw MF, and EagleRA: Spatial frequency tuning for 3D correlations from motion parallax, Vision Res 40: 2149, 2000.

Kwan and Regan have proposed that the human visual system includes orientation-sensitive filters that are defined by stripes. Kwan L and Reagan D: Orientation-tuned spatial filters for texture-defined form, Vision Res 38:3849, 1998.

Stark, Vossius, and Young have found that eye-tracking reaction times are significantly shorter for predictable target changes compared to unpredictable changes. Stark L, Vossius G, and Young LR: Predictive control of eyetracking movements, ZRE Trans Hum Factors Electron 3:52, 1962.

Contents of the invention

One form of the invention is a sphere marked to exhibit contrasting lines caused by the rotation when the sphere is rotated. Another form of the invention is a game ball that exhibits contrasting lines caused by spin as the ball spins. Other forms include the unique method of marking a sphere or ball with markings that, when rotated, exhibit contrasting lines caused by the rotation.

In one aspect of the invention, a ball is disclosed having indicia exhibiting spin-induced contrast, comprising: a design pattern, corresponding to the diameter of the ball, made of a plurality of symmetrically arranged geodesics, wherein the geodesics The number of lines is greater than 3, and the design pattern has a plurality of vertices and a plurality of triangular cells; the color of the ball; and a plurality of marks positioned on the ball according to the design pattern, wherein the plurality of marks are painted with a color that contrasts with the color of the ball , and when the ball rotates about either axis of rotation, the multiple markers exhibit contrasting lines caused by the rotation.

In another aspect of the invention, a method of marking a ball having markings exhibiting contrast lines caused by spin is disclosed, comprising the steps of: a) selecting a Coxeter Complex pattern from among A3, B3 and H3, which Including multiple geodesics and multiple geodesic vertices; b) drawing a selected Coxeter Complex pattern on the surface of the ball; c) selecting marks that exhibit contrast caused by rotation; and d) applying the selected marks to The surface of a ball where the markings are positioned in relation to the selected Coxeter Complex pattern and the markings are in contrast to the ball.

In yet another aspect of the invention, a method of detecting the axis of rotation of a ball is disclosed, comprising the steps of: providing a ball with a plurality of markers exhibiting rotation-induced Contrast lines where the multiple marks are positioned on the ball according to the Coxeter Complex pattern from A3, B3 and H3; rotate the ball about the axis of rotation; observe the contrast visible on the surface of the rotating ball produced by the marks on the surface of the ball line, wherein the contrast line is approximately perpendicular to the axis of rotation; and the axis of rotation of the ball is determined by translating the visible contrast line by about 90 degrees.

Other structures, embodiments, objects, advantages, benefits, features and aspects of the present invention will become apparent from the detailed description and drawings contained herein.

Description of drawings

Figure 1 is a schematic diagram of a single Coxeter Complex area shown in Figures 2-4.

Figure 2 is a schematic illustration of a sphere or sphere incorporating an A3 embodiment of a Coxeter Complex pattern of the method of the present invention.

Figure 3 is a schematic illustration of a ball or sphere comprising a Type B3 embodiment of a Coxeter Complex pattern of the method of the present invention.

Figure 4 is a schematic illustration of a sphere or sphere incorporating a Type H3 embodiment of a Coxeter Complex pattern of the method of the present invention.

FIG. 5 is a schematic illustration of a ball or sphere comprising one embodiment of the Type A3 of FIG. 2 .

FIG. 6 is a schematic illustration of a ball or sphere comprising one embodiment of the Type A3 of FIG. 2 .

FIG. 7 is a schematic illustration of a ball or sphere comprising one embodiment of the Type B3 of FIG. 3 .

FIG. 8 is a schematic illustration of a ball or sphere comprising one embodiment of the Type B3 of FIG. 3 .

FIG. 9 is a schematic illustration of a ball or sphere comprising one embodiment of the Type B3 of FIG. 3 .

FIG. 10 is a schematic illustration of a ball or sphere comprising one embodiment of the Type B3 of FIG. 3 .

FIG. 11 is a schematic illustration of a ball or sphere comprising one embodiment of the H3 type of FIG. 4 .

FIG. 12 is a schematic illustration of a ball or sphere comprising one embodiment of the H3 type of FIG. 4 .

FIG. 13 is a schematic illustration of a ball or sphere comprising one embodiment of the H3 type of FIG. 4 .

FIG. 14 is a schematic illustration of a ball or sphere comprising one embodiment of the H3 type of FIG. 4 .

Figure 15a is a picture of a table tennis ball comprising one embodiment of the type A3 of Figure 2 .

Fig. 15b is a picture of the table tennis ball of Fig. 15a rotating around a rotation axis.

Fig. 15c is a picture of the table tennis ball of Fig. 15a rotating around another axis of rotation.

Figure 16a is a picture of a table tennis ball comprising one embodiment of the H3 type of Figure 4 .

Fig. 16b is a picture of the table tennis ball of Fig. 16a rotating about a rotation axis.

Figure 17a is a picture of a table tennis ball comprising one embodiment of the H3 type of Figure 12 .

Fig. 17b is a picture of the table tennis ball of Fig. 17a rotating about a rotation axis.

Figure 18a is a picture of a table tennis ball comprising one embodiment of the H3 type of Figure 14 .

Fig. 18b is a picture of the table tennis ball of Fig. 18a rotating about a rotation axis.

FIG. 19 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 20 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 21 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 22 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 23 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 24 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 25 is a schematic view of another embodiment of a ball or sphere comprising type A3 according to FIG. 2 .

FIG. 26 is a schematic illustration of another embodiment of a ball or sphere comprising the type H3 according to FIG. 4 .

FIG. 27 is a schematic illustration of another embodiment of a ball or sphere comprising the type H3 according to FIG. 4 .

Detailed ways

To facilitate an understanding of the subject matter of the invention, reference will now be made to some embodiments thereof, and specific language will be used to describe these embodiments. It is to be understood, however, that no limitation of the scope of the claims is thereby intended, and that alterations, further modifications and further applications of the principles of the invention described herein will generally occur to one skilled in the art to which the invention pertains.

A method of forming a regular pattern applied to a ball is provided. The regular pattern can be applied to the surface of the ball by known printing or marking means, or alternatively or alternatively, the regular pattern can be incorporated into a tiled pattern for the construction of the ball.

Once the regular pattern is applied or incorporated on the ball, the regular pattern increases the visual contrast of the ball, thereby making the ball easier to see and track for the human eye. In several embodiments, the regular pattern includes a pattern disposed on the surface of the ball in such a way that when the ball is spun, the lines of contrast appear perpendicular to the axis of spin. Such contrasting lines desirably increase the visual contrast of the spinning ball, thereby making the ball easier to see and track, as well as providing the viewer with a sense of the ball's axis of spin. Further, the contrast line can also represent the amount of rotation. Knowing the axis of rotation and the amount of rotation of the ball can make it easier for the viewer to foresee how the ball will fly through the air and/or how the ball will interact with other objects.

By positioning the design according to several geodesic patterns derived from the Coxeter Complex, a contrasting line effect induced by rotation is created. The Coxeter Complex consists of the intersection lines of a sphere with the planes of symmetry of the Platonic polyhedra (tetrahedron, cube, octahedron, icosahedron, and dodecahedron) whose corners lie on the sphere. In this example, each geodesic corresponds to each plane of symmetry. Applying the pattern of the Coxeter Complex provides a symmetrical arrangement of geodesics on a spherical surface. Three geodesic patterns are applied. The first line pattern, designated A3, has tetrahedral symmetry and includes 6 geodesics arranged symmetrically around a sphere. The second line pattern, labeled B3, has cubic and octahedral symmetries and includes 9 geodesics arranged symmetrically around a sphere. The third line pattern, designated H3, has icosahedral and dodecahedral symmetries and includes 15 geodesics arranged symmetrically around a sphere.

The following paragraphs describe how to lay out the geodesic patterns corresponding to A3, B3 and H3 using the following common notation. As described below, "#" represents a discrete number such as 1, 2, 3, etc., and is used to distinguish a fiducial point in a pattern from other similar fiducial points. "G#" indicates a particular geodesic within a single pattern. In this paper, a geodesic refers to a great arc on a sphere. "P#" indicates the position of the pole on the surface of the sphere. In this context, "pole" is understood to mean the position on the surface of a sphere where two geodesics meet at a perpendicular angle or an angle of 90 degrees. "DM#" indicates the position of the distance marker corresponding to the point where the surface of the ball intersects two or more geodesics.

The following description describing the arrangement of the geodesic pattern is based on a 40 mm spherical table tennis ball. Therefore, the dimensions provided are for a 40mm sphere only. To apply these instructions to spheres other than 40mm, use the following formula:

In Formula 1, "40 mm size" means the size described below and the size shown in FIG. 1 as described below. "New size" means a size used in place of the special size for calculation described below. "New sphere diameter" indicates the diameter of a non-40mm sphere to which these instructions apply.

The placement method described below involves actually measuring and marking the surface of the ball. It should be understood that these guidelines only provide one how to arrange the geodesic patterns corresponding to A3, B3 and H3. A3, B3 and H3 are known geometric spherical patterns that can be drawn in several ways known to those skilled in the art. For example, these patterns can be arranged using a computer with suitable software. As another example, roughly the same pattern can be computed for later combination to form specific area elements for a ball. Thus, it is not necessary to actually mark the balls to base the design on the disclosed design patterns described below.

In several embodiments, the geodesic is actually marked on the ball by a combination of a masking device that precisely matches the diameter of the ball and a marking device such as a pencil or marker. This enables smooth geodesic patterns and distance marker (DM) arrangements to be placed on the geodesics. In these embodiments, a protractor may also be used to ensure accurate angles.

In a first embodiment, the pattern of the tetrahedral symmetric pattern (A3) passes through first a marked geodesic (G1) drawn and then an angle of 90 degrees (π/2) to the first geodesic (G1) Another geodesic (G2) forms. Then, the two intersections of G1 and G2 are labeled as poles P1 and P2. Multiple DMs were then formed by placing the tip of the compass (non-marked end) to P1 and marking G1 and G2 at two points respectively with a geometric radius of 18.388 mm. The four points are DM1, DM2, DM3 and DM4. This process was then repeated at P2 to form DM5, DM6, DM7 and DM8. The DMs of P1 are then labeled 1, 2, 3, and 4 by having DM1 selected over G1 and continuing to select DM2, DM3, and DM4 along the small arc clockwise. Now DM1 and DM3 are marked on G1, and DM2 and DM4 are marked on G2. Then leave pole P1 by moving from DM1 along G1 to the next DM. Then marked as DM5. Looking down at P2, 12 o'clock with DM5, continue clockwise along the small arc and then mark DM6, DM7 and DM8 sequentially. G3 is formed by placing a ball on a masking device so that DM1, DM2, DM7 and DM6 are all located on the geodesic to be marked, then marking the periphery of the ball with the masking device and marking G3 with the marking device. Similarly, G4 is formed by arranging DM3, DM4, DM5 and DM8 in a masking device, and marking G4 with a marking device. G5 is formed by arranging DM2, DM3, DM5 and DM6 in a masking device and marking G5 with a marking device. Finally, G6 is formed by arranging DM1, DM4, DM7 and DM8 in a masking device and marking G6 with a marking device.

In a second example, cubic and octahedral (B3) symmetric patterns were formed by first marking the A3 pattern as described above, and then forming more than three geodesics in the following manner. Pole points P3, P4, P5 and P6 are labeled as follows. The intersection of G3 and G4 closest to DM1, DM4, DM6 and DM5 is marked as P3. The intersection of G3 and G4 closest to DM2, DM3, DM7 and DM8 is marked as P4. The intersection of G5 and G6 closest to DM1, DM2, DM8 and DM5 is marked as P5. The intersection of G5 and G6 closest to DM3, DM4, DM6 and DM7 is marked as P6. G7 is formed by arranging P4, P5, P3 and P6 in a masking arrangement and marking G7 with a marking arrangement. G8 is formed by arranging P1, P5, P2 and P6 in a masking arrangement and marking G8 with a marking arrangement. G9 is formed by arranging P2, P3, P1 and P4 in a masking arrangement and marking G9 with a marking arrangement.

In a third embodiment, formed by first drawing and marking a geodesic (G1), followed by another geodesic (G2) at an angle of 90 degrees (π/2) to the first geodesic (G1) Twelve/twenty-sided (H3) symmetrical pattern. Then label the intersection of G1 and G2 as P1 and P2. Next draw G3 as a great arc between P1 and P2 and form four more 90 degree (π/2) angles. With ball P1 at the top and P2 at the bottom, the intersection of G2 and G3 is facing forward, and the intersection of G2 and G3 facing forward is labeled P3. Continuing to the right on G#, the next intersection (G1 and G3) is labeled P4. Continuing in the same direction on G3, the next point of intersection (G2 and G3) is labeled P5. Continuing in the same direction on G3, the next intersection (G1 and G3) is labeled P6. At the level of G1 and P6 is on the left of P1, use a compass to mark DM1 on G1 at 7.257 mm from the left of P1, and mark DM2 on G1 at 7.257 mm from the right of P1. At the level of G2 and P5 is on the left of P1, use a compass to mark DM3 on G2 at 10.931 mm to the left of P1, and mark DM4 on G2 at 10.931 mm to the right of P1.

Continue to discuss the third embodiment, at the level of G1 and P6 is on the left at P2, use a compass to mark DM5 at the left 7.257 mm from P2 on G1, and mark DM6 at 7.257 mm from the right of P2 on G1. At the level of G2 and P5 is on the left of P2, use a compass to mark DM7 on G2 at 10.931 mm to the left of P2, and mark DM8 on G2 at 10.931 mm to the right of P2. At the G2 level and P1 is on the left of P3, use a compass to mark DM9 on G2 at 7.257 mm from the left of P3, and mark DM10 on G2 at 7.257 mm from the right of P3. At the level of G2 and P5 is on the left of P1, use a compass to mark DM3 on G2 at 10.931 mm to the left of P1, and mark DM4 on G2 at 10.931 mm to the right of P1. At the level of G3 and P4 is on the left of P3, use a compass to mark DM11 on G3 at 10.931 mm to the left of P3, and mark DM12 on G3 at 10.931 mm to the right of P3. At the level of G3 and P3 is on the left of P4, use a compass to mark DM13 on G3 at 7.257 mm to the left of P4, and mark DM14 on G3 at 7.257 mm to the right of P4. At the level of G1 and P2 is on the left at P4, use a compass to mark DM15 on G1 at 10.931 mm to the left of P4, and mark DM16 on G1 at 10.931 mm to the right of P4. At the G2 level and P1 is on the left of P5, use a compass to mark DM17 on G2 at 7.257mm left from P5, and mark DM18 on G2 at 7.257mm from P5 to the right. At the level of G3 and P4 is on the left of P5, use a compass to mark DM19 on G3 at 10.931 mm to the left of P5, and mark DM20 on G3 at 10.931 mm to the right of P5. At the level of G3 and P5 is on the left of P6, use a compass to mark DM21 on G3 at 7.257mm from the left of P6, and mark DM22 on G3 at 7.257mm from the right of P6. At the level of G1 and P2 is on the left of P6, use a compass to mark DM23 on G1 at 10.931 mm from the left of P6, and mark DM24 on G1 at 10.931 mm from the right of P6.

Continuing with the third embodiment, G4 is formed by placing balls in a masking device to align all DM1, DM3, DM19, DM6, DM8 and DM12, and marking G4 with a marking device. G5 is formed by placing balls in a masking device to align DM1 , DM20 , DM7 , DM6 , DM11 and DM4 and marking G5 with a marking device. G6 is formed by placing balls in a masking device to align DM2, DM4, DM12, DM5, DM7 and DM19, and marking G6 with a marking device. G7 is formed by placing balls in a masking device to align DM20, DM3, DM2, DM11, DM8, and DM5, and marking G7 with a marking device. G8 is formed by placing balls in a masking device to align DM14, DM15, DM8, DM22, DM24, and DM3, and marking G8 with a marking device. G9 is formed by placing balls in a masking device to align DM16, DM14, DM7, DM23, DM22 and DM4, and marking G9 with a marking device. G10 is formed by placing balls in a masking device to align DM15, DM13, DM4, DM24, DM21 and DM7, and marking G10 with a marking device. G11 is formed by placing balls in a masking device to align DM13, DM16, DM3, DM21, DM23, and DM8, and marking G11 with a marking device. G12 is formed by placing balls in a masking device to align DM11, DM10, DM23, DM20, DM17, and DM16, and marking G12 with a marking device. G13 is formed by placing balls in a masking device to align DM10, DM12, DM24, DM17, DM19, and DM15, and marking G13 with a marking device. G14 is formed by placing balls in a masking device to align DM12, DM9, DM16, DM19, DM18 and DM23, and marking G14 with a marking device. G15 is formed by placing balls in a masking device to align DM9, DM11, DM15, DM18, DM20 and DM24, and marking G15 with a marking device.

In any of the first, second or third embodiments described above, the specific orientation of G1 and G2 should not be significant relative to other pre-existing features of the ball. However, in some embodiments it may be desirable to align G1 and/or G2 with pre-existing markings to provide a more pleasing final appearance. For example, if marking a tennis ball, it is best to line up G1 and G2 tangent to a pre-existing seam.

In any of the first, second or third embodiments described above, further modification of the A3, B3 or H3 pattern of the markings may be made. For example, in some embodiments, the geodesic pattern may be marked with a non-permanent marking device such as a pencil. This allows portions of each geodesic to be removed as necessary to form a specific pattern. In other embodiments, the geodesic pattern may be marked with a permanent marking device such as permanent ink. In still other embodiments, the triangular portion formed by the geodesics may be colored or filled to add further contrast to the ball. Specific examples of these other embodiments are discussed below with reference to FIGS. 5-14.

Also for the design patterns A3, B3 and H3, these patterns exhibit several features that differ from other known patterns of the usual design ball patterns. First, the triangles formed by the geodesics in these patterns are all right triangles of the same shape and size. However, the vertices formed by these identical geodesics are not all identical or identical. Also, these design patterns exhibit symmetry along respective geodesics.

Referring now to FIG. 1 , a triangular unit 5 is shown. Triangular cell 5 is a two-dimensional triangular illustration of the spherical triangle formed by the intersection of the respective geodesics in the A3, B3 and H3 patterns shown. Figure 1 includes interior angles A, B, and C, legs X and Y, hypotenuse Z, and vertices 1, 2, and 3. It should be noted that the triangular unit 5 is a non-planar triangle, and the sum of the interior angles A, B and C is greater than 180 degrees, which is different from the result obtained by a two-dimensional aspheric triangle.

Still referring to FIG. 1 , in the following paragraphs, specific dimensions for interior angles A, B and C, legs X, Y and hypotenuse Z are provided. Note that there are two dimensions specified for each pattern for each leg and hypotenuse. The first specific dimension is the Euclidean distance, which is the straight-line distance between two points passing through the spherical surface of a sphere. This distance does not take into account the spherical curvature of each of these "straight" lines placed on the sphere. Therefore, this dimension correlates with the dimension of drawing each pattern using a compass, for example. Instead, the second specific dimension is the spherical distance. This spherical distance takes into account the spherical curvature of each of the "straight" lines placed on the sphere. Thus, this spherical distance can be used to form face area portions for forming faceted spherical balls. In each of the foregoing cases, the specific dimensions are for a 40 mm sphere. These dimensions can be scaled up or down using Equation 1 detailed above to determine the proper size for any diameter ball.

Referring particularly to the Figures 1 and A3 patterns, angle A is equal to π/3, angle B is also equal to π/3, and angle C is a right angle equal to π/2. The Euclidean distance of the right-angled side X is 18.388mm, and the spherical distance is 19.106mm, and the Euclidean distance of the right-angled side Y is 18.388mm, and the spherical distance is 19.106mm. The Euclidean distance of hypotenuse Z is 23.094mm, and the spherical distance is 24.619mm. As for the vertices, it is worth noting that there are four vertices on the entire ball corresponding to vertex 1 on the A3 pattern. Similarly, there are four vertices corresponding to vertex 2 and six vertices corresponding to vertex 3 on the A3 spherical pattern. In the end, there are 24 triangular units 5 in total on the A3 faceted sphere.

Referring specifically to the patterns in Figures 1 and B3, angle A is equal to π/3, angle B is also equal to π/3, and angle C is a right angle equal to π/2. The Euclidean distance of the right-angled side X is 15.307mm, and the spherical distance is 15.708mm, and the Euclidean distance of the right-angled side Y is 12.116mm, and the spherical distance is 12.309mm. The Euclidean distance of hypotenuse Z is 18.388mm, and the spherical distance is 19.106mm. As for the vertices, it is worth noting that there are six vertices on the entire ball corresponding to vertex 1 on the B3 pattern. Similarly, there are eight vertices corresponding to vertex 2 and twelve vertices corresponding to vertex 3 on the A3 spherical pattern. In the end, there are a total of 48 triangular units 5 on the B3 faceted sphere.

Referring particularly to Figures 1 and C3, angle A is equal to π/5, angle B is also equal to π/3, and angle C is a right angle equal to π/2. The Euclidean distance of the right-angled side X is 10.931mm, and the spherical distance is 11.072mm, and the Euclidean distance of the right-angled side Y is 7.257mm, and the spherical distance is 7.297mm. The Euclidean distance of hypotenuse Z is 12.817mm, and the spherical distance is 13.047mm. As for the vertices, it is worth noting that there are twelve vertices on the entire ball corresponding to vertex 1 on the B3 pattern. There are twenty vertices corresponding to vertex 2 and thirty vertices corresponding to vertex 3 on the A3 spherical pattern. Finally, there are a total of 120 triangular units 5 on the H3 faceted sphere.

For reference purposes, the respective dimensions of the legs x and y and hypotenuse z of A3, B3 and H3 in relation to triangular element 5 are summarized in Table 1 below.

Table 1

Turning now to Figures 2-4, representations of the A3, B3 and H3 patterns are shown. Specifically, FIG. 2 shows an A3 pattern 100 , FIG. 3 shows a B3 pattern 200 , and FIG. 4 shows an H3 pattern 300 . Each of the graphs in FIGS. 2-4 includes a plurality of geodesics 10 and a plurality of vertices 20 , which are locations where two or more geodesics 10 intersect. The geodesics 10 form a plurality of triangles 15 covering the surface of the sphere. Note that for each pattern or embodiment discussed in the figures below, a typical number of structures has been labeled with a reference number. To maintain clarity, however, not all repeating structures are labeled with reference numerals. Each of Figures 2-4 is shaded to show the three-dimensional circle of the ball. Figures 2-4 only show a single hemisphere for all typical patterns. However, since it is a symmetrical pattern, the other hemisphere, which cannot be seen, is the exact mirror image of the visible hemisphere. Moreover, a comparison of FIG. 2 and FIG. 3 shows that the A3 pattern is completely included in the B3 pattern.

While FIGS. 2-4 illustrate basic examples of the A3, B3, and H3 patterns disclosed herein, this disclosure is not limiting. For example, other and/or different contrasting patterns may be formed by shading individual geodesics and/or individual pattern elements such as triangles formed from A3, B3 or H3 patterns with various contrasting colors. Similarly, shapes of various shapes and sizes may be positioned along geodesics or at some vertices. Alternatively, portions of each geodesic may be removed or omitted. In still other embodiments, the width and/or color of the geodesics may vary. In any of these embodiments, one purpose of selecting specific patterns and/or colors is to create the best contrasting pattern for a particular application. Variables such as lighting conditions, recording technique, size of the ball, the sport being played, the expected spin speed of the marked ball, the desired predetermined distance at which the spin formed by the contrast markings can be observed, and the player's level of ability to utilize each contrast pattern all affect the Preferred patterns and/or colors included.

5-14 are non-limiting examples of different contrasting patterns based on A3, B3 or H3 patterns. Advantages and disadvantages specific to each of these various embodiments are discussed below. In each of Figures 5-14, the respective geodesics are shown in black to provide a contrasting color from the white base color of the ball. In these particular examples, the geodesics have been included to show the relationship of the patterns to the bottom A3, B3 and H3 patterns. However, it should be understood that alternative embodiments are envisioned in which the geodesics are not painted a contrasting color.

FIG. 5 shows a comparative pattern embodiment based on the A3 pattern 100 . This pattern provides larger contrasting triangles 15' that fully incorporate four of the six geodesics used to form the A3 pattern. One-third of the pattern's surface area is covered by contrasting triangles. This combination provides a generally good overall contrast due to the larger shape of the contrasting parts. However, the pattern is not particularly symmetrical, so when a ball with the pattern is rotated, the resultant contrasting lines appear to some observers as wobbly.

FIG. 6 is also an example of a comparative pattern shown based on the A3 pattern 100 . This pattern provides larger contrasting triangles 15' that fully incorporate each of the six geodesics used to form the A3 pattern. Half the surface area of the pattern is covered by contrasting triangles. This combination provides good contrast at low rotational speeds due to the larger shape of the contrasting parts and the larger ratio of the contrasting parts. But at high spin speeds, these patterns may appear too dark or gray to some observers or lighting conditions.

FIG. 7 is a comparative pattern example shown based on the B3 pattern 200 . This pattern provides contrasting triangles 15' of medium size. The main feature of this pattern is that each contrasting triangle 15' is connected at two vertices 20 to other contrasting triangles 15'. The entire pattern tries to mimic the seam pattern of a standard baseball/ping pong ball. Only 17% of the surface area of the pattern is covered by contrasting triangles 15'. The pattern offers a good combination of enhanced visibility at low spin speeds and sufficient contrast at high spin speeds, but still presents a predominantly white tint or base color of the ball.

FIG. 8 is also a comparative pattern example shown based on the B3 pattern 200 . This pattern provides contrasting triangles 15' of medium size. The main features of this pattern are that each contrasting triangle 15' is connected at two vertices 20 to at least two other contrasting triangles 15', and at least half of each geodesic merges into the contrasting triangle 15'. This feature provides good contrast at high spin speeds, as well as good contrast at low spin speeds. The pattern covers 25% of the ball's surface area with contrasting triangles.

FIG. 9 is also an embodiment of a comparative pattern shown based on the B3 pattern 200 . This pattern provides contrasting triangles 15' of medium size. The main feature of the pattern is that the contrasting triangles 15' fully incorporate three of the nine geodesics 10 in the pattern and that all contrasting triangles 15' are interconnected. The pattern covers one third of the surface area of the ball with contrasting triangles 15'. Another feature is that all of the "white" or non-contrasting portions forming the adjoining triangles 15 in this embodiment are identical in shape, combining four adjoining (sharing a common geodesic) triangles 15 of the pattern so that this embodiment Cases are especially suitable for use with faceted balls.

FIG. 10 is also an embodiment of a comparative pattern shown based on the B3 pattern 200 . This pattern provides contrasting triangles 15' of medium size. The main feature of the pattern is that the contrasting triangles 15' fully incorporate all nine geodesics 10 in the pattern, and that all contrasting triangles 15' alternate with non-contrasting "white" triangles 15. This pattern covers half of the surface area of the ball by contrasting triangles 15'. The pattern also provides good contrast at low spin speeds. But similar to the embodiment shown in Figure 6, at high spin speeds, the pattern appears too dark or gray to some observers or lighting conditions.

FIG. 11 is a comparative pattern example shown based on the H3 pattern 300 . This pattern provides contrasting triangles 15' of small size. The main feature of the pattern is that the contrasting triangles 15' fully incorporate three of the 15 geodesics 10 in the pattern and that all contrasting triangles 15' are interconnected. The pattern covers one-fifth of the surface area of the sphere with contrasting triangles 15' and has good symmetry. The pattern provides good contrast at low spin speeds as well as at high spin speeds, but still looks mostly white or the base color of the ball.

FIG. 12 is also an embodiment of a comparative pattern shown based on the H3 pattern 300 . This pattern provides contrasting triangles 15' of small size. The main feature of the pattern is that the contrasting triangles 15' incorporate substantially all 15 geodesics 10 in the pattern and that all contrasting triangles 15' are interconnected. The pattern covers one-fifth of the surface area of the sphere with contrasting triangles 15' and has good symmetry. This embodiment provides a good contrast at low spin speeds as well as at high spin speeds, without "greying out" at high spin speeds. See Figure 17b and the accompanying description for a specific example below.

FIG. 13 is also an embodiment of a comparative pattern shown based on the H3 pattern 300 . This pattern provides small-sized contrasting triangles 15', which are always in pairs (sharing a common geodesic 10), thereby forming medium-sized contrasting sections. The main feature of the pattern is that the contrasting triangles 15' incorporate a substantial proportion of each of the 15 geodesics 10 in the pattern, and that said contrasting triangles 15' are interconnected. The pattern covers two-fifths of the ball's surface area with contrasting triangles and has excellent symmetry. This embodiment provides the same contrast as the embodiment shown in Figure 10, but it also has better high spin speed contrast in most applications and generally does not appear gray.

FIG. 14 is also an example of a comparative pattern shown based on the H3 pattern 300 . This pattern provides contrasting triangles 15' of small size. The main feature of the pattern is that the contrasting triangles 15' fully incorporate all 15 geodesics 10 in the pattern, and that all contrasting triangles 15' alternate with non-contrasting "white" triangles 15 (sharing a common geodesic 10). This pattern covers half of the surface area of the ball by contrasting triangles 15'. Due to the larger number of contrasting triangles 15' and the larger ratio of contrasting parts, this pattern provides a good contrasting effect at low rotation speeds. But similar to the embodiments shown in Figures 6 and 10, at high spin speeds, the pattern appears too dark or too gray for some observers or lighting conditions. See the discussion of Figure 18b below for a specific example.

With regard to the width of the geodesics shown in Figures 2-14, in each example the width shown is approximately 0.15% of the full diameter of the sphere shown. The choice of line width should not be considered as an example, as the width is a simple by-product of the drawing technique that formed Figures 2-14. In many applications, the line width can be too thin to be seen. However, in other applications, the line width is preferred or particularly wide. It is envisioned that the line width may vary from 0.25% of the full diameter of the ball to 15% of the full diameter of the ball. For example, for a 40mm diameter ping pong ball with an H3 line pattern, a line width of 1 mm or 2.5% of full diameter produces sufficient spin-induced contrast for most players under typical indoor lighting conditions.

Turning now to FIGS. 15-18 , specific non-limiting examples are provided showing how several different embodiments may look when rotated. With particular reference to Figures 15a, 15b and 15c, an embodiment of an A3 pattern 100 is shown. FIG. 15a is a picture of a table tennis ball 40 that has been marked with a geodesic 10 corresponding to the A3 pattern 100 . In this embodiment, the geodesic width is approximately 4% of the full diameter of the table tennis ball. Figures 15b and 15c show a table tennis ball 40 rotating at high speed about two different axes of rotation. In FIG. 15 b, the contrast lines 50 appear to wobble a bit, while gray areas 55 are evident between the contrast lines 50 . In Fig. 15c, the contrast line 50 appears as a generally straight line, whereas the gray area 55 is more uniform. The reason for the dramatic difference in the appearance of the contrast line 50 caused by rotation between Figures 15b and 15c is the difference in the arrangement of the axis of rotation on the table tennis ball relative to the geodesic. In Fig. 15c it is evident that the axis of rotation is approximately perpendicular to a geodesic 10 because a geodesic 50 appears in the middle of the ball 40, whereas in Fig. The gray area 55 is less uniform and darker, so it is evident that the axis of rotation of the ball 40 is not exactly perpendicular to any single geodesic 10 . However, even though none of the geodesics 10 is exactly perpendicular to the axis of rotation of the ball 40, several lines of contrast can be observed.

An example of an H3 pattern 300 is shown in Figures 16a and 16b. FIG. 16a is a picture of a ping pong ball 42 that has been marked with the geodesic 10 corresponding to the H3 pattern 300 . In this embodiment, the geodesic line width is about 2.5% of the full diameter of the table tennis ball. Figure 16b shows a table tennis ball 42 spinning at high speed. In Fig. 16b, the contrast line 50 appears as a substantially straight line, and the gray area 55 is relatively consistent. Comparing Figures 15c and 16b, it is evident that the embodiment corresponding to the H3 pattern shown in Figure 16b forms a greater number of contrasting lines when rotated than the embodiment corresponding to the A3 pattern shown in Figure 15c. As a result, the oscillating contrast line shown in Figure 15b is less pronounced than when the axis of rotation is varied in the embodiment shown in Figures 16a and 16b. This improvement is related to an increase in the number of geodesics on the ball. Using 15 geodesics instead of 6 reduces the degree to which the axis of rotation may not be perpendicular to one geodesic.

Figures 17a and 17b show an embodiment similar to that shown in Figure 12 . 17a is a picture of a table tennis ball 44 with a pattern applied to contrasting triangles 15' based on the H3 pattern 300. FIG. But the geodesic 10 has been omitted from the ball 44 . This can be done by removing the geodesics after marking the contrasting triangle 15', or, for example, by computer-aided drawing and marking. Regardless, Figure 17b is a picture of a ping pong ball 44 spinning at high speed. The contrast line 50 appears as a roughly straight line, and the gray area 55 is relatively uniform.

Figures 18a and 18b show an embodiment similar to that shown in Figure 13 . Also, the geodesic 10 has been omitted from the ball 46 in this embodiment. Figure 18a is a picture of a table tennis ball 46 with a pattern applied to a contrasting triangle 15' based on the H3 pattern. Figure 18b is a picture of a table tennis ball 46 spinning at high speed. Contrast line 50 appears non-uniform. Similarly, gray area 55 is non-uniform and appears to change shade proportionally to distance from contrast line 50 .

As another non-limiting example of the application of contrasting markings, FIG. 19 shows several dots 35 based on the A3 pattern 100 . The geodesic corresponding to the A3 pattern is shown for reference purposes only, the inclusion of the geodesic 10 is optional. The center of the dot 35 lies on the vertices 20 of several symmetrically arranged geodesics 10 . In this particular embodiment, each apex 20 comprises a circular point 35 . However, other embodiments are envisioned that do not include a dot 35 at each vertex 20 . It is also envisioned that other geodesic patterns may include dots 35 . In this embodiment, the dot 35 has a diameter approximately equal to 16% of the diameter of the ball. While dots 35 are shown in this embodiment, other embodiments incorporating other contrasting indicia are also envisioned.

FIG. 20 shows another embodiment similar to the embodiment shown in FIG. 19 . FIG. 20 shows several annular wires 30 having a diameter and a line width 32, wherein the center of each annular wire 30 is arranged at the apex of the geodesic. In the illustrated embodiment, the geodesic is based on the A3 pattern 100 and the vertex 20' as the center of the annular line 30 corresponds to the center of the radial projection of the solid surface of the sphere.

Still referring to the embodiment shown in FIG. 20 , the diameters of the plurality of annular wires 30 have been selected so that each annular wire 30 does not touch other annular wires 30 and there is a minimum distance between different annular wires 30 . The gap between points is approximately equal to the line width of 32. In this embodiment, the geodesic 10 is shown primarily for reference, including contrast geodesic 10 being an optional part of the marker. For reference only, the looped wire shown in FIG. 20 has a wire width 32 of approximately 9% of the diameter of the ball.

FIG. 21 shows another embodiment similar to the embodiment shown in FIG. 20 . Fig. 21 shows several looped wires 30 having a diameter and a line width 32, wherein the center of each looped wire 30 is arranged at the apex of the geodesic. In the illustrated embodiment, the geodesic is based on the A3 pattern 100, and the vertex 20' as the center of the annular line 30 corresponds to the center of the radial projection plane of the cube on the sphere, while the vertex 20' as the center of the annular line 30 Vertex 20' corresponds to the center of the radially projected face of the tetrahedron on the sphere.

Still referring to the embodiment shown in FIG. 21 , the diameters of the plurality of loop wires 30 have been selected such that each loop wire 30 substantially overlaps the other loop wires 30 . In particular, the diameter of each annular wire 30 has been selected so that each annular wire 30 is substantially tangent to each adjacent geodesic 10, each adjacent geodesic surrounding the vertices 20' and 20". In the present embodiment In the example, the annular line corresponding to the center of the radial projection plane of the cube on the sphere has a different diameter than the annular line corresponding to the center of the radial projection plane of the tetrahedron on the sphere. The shown geodesic 10 Primarily for reference, the contrast geodesic 10 is included as an optional part of the contrast markers. For reference only, the line width 32 of the annular line shown in Figure 21 is approximately 5% of the diameter of the ball.

FIG. 22 shows another embodiment similar to the embodiment shown in FIG. 20 . FIG. 22 shows several looped wires 30 having a diameter and a line width 32, wherein the center of each looped wire 30 is arranged at the apex of the geodesic. In the illustrated embodiment, the geodesic is based on the A3 pattern 100 and the vertex 20' as the center of the annular line 30 corresponds to the center of the radial projection plane of the cube on the sphere.

Still referring to the embodiment shown in FIG. 22 , the diameter of each loop wire 30 has been selected so that each loop wire 30 touches but does not overlap other loop wires 30 . In this way, several points on the circular line 30 are tangent to the plurality of geodesics 10 . In this embodiment, the geodesic 10 is shown primarily for reference and the inclusion of the contrast geodesic 10 is an optional part of the label. For reference only, the looped wire shown in Figure 22 has a wire width 32 of approximately 10% of the diameter of the ball.

While Figures 19-22 illustrate several different embodiments of contrast markings in the form of dots 35 or looped lines 30, the illustrated embodiments do not disclose the various possible uses of these features. For example, it is envisioned that it may be advantageous to have loop wires with larger or smaller diameters than the examples provided. Furthermore, it is envisioned to use other patterns of geodesics, such as the B3 pattern 200 or the H3 pattern 300, as the basis for the centering of these features. Similarly, the centers of other radially projected planes on a sphere in other ideal solids, such as octahedrons, icosahedrons, dodecahedrons, or combinations of other patterns can be used to form attractive, usable contrasting patterns. It is also envisioned that these different patterns can be mixed or matched to suit a particular application or desired appearance.

As another non-limiting example of the application of markings that represent rotation for contrast, Figures 23-26 illustrate different triangular patterns that are all attractive and when rotated produce nice contrasting lines. Specifically, Figures 23-26 illustrate different variations of triangular contrast marks as follows.

The comparative pattern embodiment shown in FIG. 23 is based on the A3 pattern 100 and relates to the embodiment shown in FIG. 6 . FIG. 23 shows a plurality of triangular patterns 50 positioned based on the A3 pattern 100 . The triangular pattern 50 comprises hollow triangles whose edges are formed by three different geodesics 10 . This same effect can be achieved by using the pattern shown in Figure 6 and adding a white or base colored triangle inside the contrasting triangle 15'. The result is a hollow triangle with a lineweight. In the illustrated embodiment, the line width is approximately 3% of the ball diameter.

The comparative pattern embodiment shown in FIG. 24 is also based on the A3 pattern 100 and also relates to the embodiment shown in FIG. 6 . FIG. 24 shows a plurality of triangular patterns 52 positioned based on the A3 pattern 100 . Also shown is the geodesic 10 corresponding to the A3 pattern 100 . In this embodiment, the triangular pattern 52 is smaller than the corresponding triangle 15 formed by the geodesic 10 so that there is a gap between the triangular pattern 52 and the geodesic 10 . In this embodiment, triangle 52 is approximately centered within triangle 15 so that the respective gaps between triangle pattern 52 and geodesic 10 are approximately equal. The embodiment shown in Fig. 24 relates to the embodiment shown in Fig. 23, so in fact the triangular patterns 50, 52 are mutually black/white inverted images. Also, while the triangular pattern 54 has been shown as being located at the center of the triangle 15, it should be understood that the triangular pattern may be positioned at any desired location including off-center or touching one or more geodesics.

The comparative pattern embodiment shown in FIG. 25 is also based on the A3 pattern 100 and also relates to the embodiments shown in FIGS. 6 and 24 . FIG. 25 shows a plurality of triangular patterns 54 positioned based on the A3 pattern 100 . Also shown is the geodesic 10 corresponding to the A3 pattern 100 . In this embodiment, the triangular pattern 54 is smaller than the corresponding triangle 15 formed by the geodesic 10 so that there is a gap between the triangular pattern 54 and the geodesic 10 . Also, the triangular pattern 54 has a hollow interior similar to the triangular pattern 50 shown in FIG. 23 . In the embodiment shown in FIG. 25 , triangle 54 is approximately centered within triangle 15 such that the respective gaps between triangle pattern 54 and geodesic 10 are approximately equal. Another feature of this embodiment is that the gap between the triangular pattern 54 and the geodesic 10 is approximately equal to the line width of the triangular pattern 54 . Also, while the triangular pattern 54 has been shown centered on the triangle 15, it should be understood that the triangular pattern may be positioned at any desired location including off-center or touching one or more geodesics.

The comparative pattern shown in FIG. 26 is based on the H3 pattern 300 . The pattern provides small-sized contrasting triangles 15' and larger-sized contrasting areas formed by a plurality of contrasting triangles 15'. The main feature of this pattern is the combination of smaller contrasting features with larger ones. In this embodiment, each contrasting triangle 15' is interconnected with at least two other contrasting triangles 15'. Also, including the geodesic 10 as a contrast line is optional. The geodesics are shown in Figure 26 primarily for reference. The pattern covers thirty percent of the surface area of the ball with contrasting triangles 15'. This pattern provides good low spin speed contrast due to the dramatic change in pattern appearance. Another advantage of this embodiment is good contrast perception at near and far distances and for individuals with different visual sensitivities.

FIG. 27 shows another embodiment of a contrast pattern based on the H3 pattern 300 . In this example, three different colors are used. In this particular example, a white triangle 60, a yellow triangle 62, and a black triangle 64 are shown. The use of other contrasting colors can enhance the overall visibility of the ball or sphere as follows.

Light sources of different colors (or light reflected by objects) transmit light of different wavelengths. The human visual system processes different color stimuli at different speeds. For monochromatic stimuli, light at 555 nm (yellow-green/optical yellow) produces a faster response from the human visual system due to the overlapping responses of the cone sensitivities within the human eye. White light at 555 nanometers, which includes light emission at all visible wavelengths, produces a faster response than any monochromatic light. An exceptional combination has been found to be optical yellow with as much contained white as possible. This may be due to the usual environmental background of the sports venue. In particular, white is a color commonly encountered in many environments, while optical yellow is not. Thus, while white light may produce a faster response, optical yellow provides a color that is easier to track than white in a possible environment. In this example, combining an optical yellow panel with a white panel yields another contrast in human visual system tracking, which also corresponds to a faster response of the human visual system. Also, combining yellow with white allows for a more vibrant yellow to be used in contrasting parts than is used for monochrome balls. When the ball with the optical yellow color plate and the white plate is rotated, the colors blur together to create the appearance of a brighter shade of yellow that is also easy to see. In this way, the combination of optical yellow plate and white plate can form a pattern with better overall visibility than white or yellow balls. Including plates painted black provides additional contrast (white/black and yellow/black) and also creates contrasting lines when the ball or sphere is spun.

Still referring to the embodiment shown in Figure 27, it is worth noting that there are many different variations on this subject that can be envisioned. And, the most important considerations are the lighting and playing conditions used by a particular ball or sphere. It is also very important that the ball or sphere looks attractive. Other combinations of patterns and colors exhibiting the contrast and enhanced visibility caused by rotation will be apparent to those skilled in the art on the basis of the present invention.

With regard to the choice of color to use as a contrasting pattern, the primary factor is choosing a color that contrasts sufficiently with the base color of a particular ball to be visible under likely lighting and playing conditions. In this regard, different colors can be used for different elements of the contrasting pattern. In general, however, it has been found that using multiple colors can result in blurring of contrasting lines caused by rotation compared to using a single contrasting color. Alternatively, in some specific applications, the use of multiple colors will provide the observer with more specific information about the specific axis of rotation observed, especially when there is a known reference point, such as when the ball When positioned at a known starting location such as the pitcher's hold before pitching. In such applications, specific geodesics and/or patterns corresponding to different specific axes of rotation are colored to provide a specific representation of a specific spin created by a specific pitching motion and/or a ball handle (not shown). feedback.

With regard to the configuration of the ball to which the pattern is applied, the ball can be constructed in any known manner. For example, a ball may have a bladder covered by areas whose edges correspond to respective geodesics. Alternatively, the sphere can consist of areas whose edges do not correspond to the respective geodesics. Here, these face areas may be formed from leather, synthetic material or any material known to a person skilled in the art for the facing of balls. In other embodiments, the ball may have a solid interior or an interior formed of entangled matter. In still other embodiments, the ball may be molded to have a hollow interior with a molded surface. Regardless, any known type of ball or method of manufacture is envisioned within the scope of this invention.

Referring specifically to the application of the invention to constructing balls using the tiling method, it is envisioned that the geodesic patterns A3, B3 and H3 could all be used as the basis for the tiling pattern. In that method, the natural seams that form when the ball is faceted will also serve as contrasting marks. Similarly, in the above embodiment, where some of the "triangles" formed by these geodesic patterns are colored differently, the same effect can be achieved by creating differently colored face regions for assembly into spheres. In this regard, it is not necessary that each area have the same geodesic or that each area correspond to a single "triangle". In several of the above embodiments, multiple "triangles" are grouped together, with the same color, without any distinguishing geodesic separation lines. Thus, it is envisioned that each facet member used to face a ball may consist of a plurality of individual "triangular" cells as formed in the A3, B3 and H3 geodesic patterns.

Along these lines, it is envisioned that the ball may be faced with a single face area comprising multiple contrasting colors corresponding to these geodesic patterns. In one embodiment, it may comprise a single area composed of a plurality of individual "triangular" cells formed as A3, B3 and H3 geodesic patterns, where one or more "triangles" have the same Some contrasting colors. Similarly, in another embodiment, a single facet composed of multiple individual "triangular" cells formed by geodesic patterns such as A3, B3, and H3 may incorporate contrasting markings, such as a specific pattern or included in a single A segment of a single geodesic within an area cell.

It should be noted that not all balls used in sports are preferably spherical, or even necessarily approximately spherical. From a mathematical point of view, the geodesics described here are all based on the ideal symmetry of an ideal sphere. However, it is impossible to achieve perfect symmetry in an irregular, approximately spherical sphere. The present invention is not so limited. The method described here applies to any approximately spherical ball. The only significant limitation foreseen is that if the ball is so irregular that it cannot form a stable spin, it may be difficult to create visible spin-induced contrast lines. When marking irregular balls, it can be seen that while the technique described here does not result in a perfect pattern, the resulting pattern does produce visible contrasting lines caused by rotation, as long as it is as close as possible to the given Irregular spheres accurately apply patterns. As a specific example, the ping pong ball 42 shown in Figure 16a does not have a perfectly applied geodesic. For example, apex 20 appears wider than a single geodesic 10, indicating that the geodesics 10 are not perfectly aligned. However, it is believed that this particular embodiment still exhibits satisfactory rotation-induced contrast, as shown in Figure 16b. Thus, terms such as geodesic or symmetry as applied to a sphere may generally be limited to a perfect sphere, but here these terms may be applied to any object with an approximately spherical shape.

Applying a contrasting section based on a symmetrical set of multiple geodesics derived from the Coxeter Complex to a sportsball provides a great possibility that one or more of the geodesics will be perpendicular or approximately perpendicular to a particular axis of rotation of the ball. As a result, one or more lines perpendicular to the axis of rotation are apparent to an observer of the spinning ball. In cases where no single geodesic is perpendicular to the axis of rotation, segments of several individual geodesics combine to form the appearance of one or more lines perpendicular to the axis of rotation. A viewer of the ball, or particularly a player, can use the appearance of the vertical lines to predict the axis of spin and the amount of ball spin, based on the specific appearance of the spinning ball. In particular, to predict the axis of rotation, the observer need only translate the apparent contrast line by approximately 90 degrees. Note in particular that, often, this shifting of the axis usually occurs subconsciously, rather than a process that requires a deliberate decision.

This effect depends in part on the ability or lack thereof of the human visual system to track fast moving objects such as the intermittent pattern on a spinning ball. In the spinning ball example, when the object/pattern moves (rotates) faster than the visual system's ability to accurately execute its movement, the visual system actually sends the fast moving object/pattern to the human brain in combination with its surroundings to form an overall pattern , creating a blurred effect. Where the object/pattern on the ball has a contrasting base color, the color of the object/pattern and the ball are integrated by the vision system to form an integrated color approximately midway between the color of the object/pattern and the ball. When the objects/patterns are effectively aligned perpendicular to the axis of rotation, this combining/integrating effect forms the lines of contrast described herein. This is also the case when multiple parts of different objects/patterns are arranged along areas perpendicular to the axis of rotation. The shading/contrast of the resulting integrated image is proportional to the percentage of objects/patterns aligned along a particular face area opposite the base portion of the ball. When the main part of the arrangement along a particular plane comes from the object/pattern, then contrasting lines are seen. For example, in Figures 16-18, it is evident that the lines of contrast are formed by contributions from a collection of parts of different objects/patterns on a single ball.

Such a ball is useful as a training device for athletes of all abilities, by helping the athlete understand the spin of the ball to improve prediction of the future position of the spinning ball, and by providing enhanced contrast of the ball to help the athlete in general accurately Visually track the spinning ball. It is believed that this training has the transformative effect of increasing the ability of the athlete to track any ball more precisely and training the athlete to predict the range of any spinning ball. Thus, it is believed that by playing or practicing with a ball that exhibits contrasting lines caused by spin, a player can improve his subsequent performance with a monochromatic ball.

As is well known in the art, balls in various sports reflect spin in different ways. For example, a spinning ball can create aerodynamic forces that can cause the ball to follow a trajectory other than a strictly ballistic one. Similarly, a spinning ball may bounce in unexpected directions when it interacts with other objects such as a playing surface, racket, or bat. This spinning effect is considerable in many of the aforementioned sports.

As a non-limiting example, baseball is a sport in which the ball spins a lot. Successfully throwing the ball to the batter involves throwing the ball faster than the batter is able to react to the throw, and deceiving the batter about where the pitched ball will end up when it "over the plate." Therefore, it is useful for a batter to be able to accurately predict the final position of a thrown ball so that the batter can contact the ball with the bat. Thus, providing the batter with additional information about the likely trajectory of a thrown ball can improve the batter's ability to hit the ball.

In this regard, although unheard of, it is unlikely that the entities governing various sports leagues, especially professional leagues, would authorize the use in games of balls with contrasting parts exhibiting contrasts caused by spin, since this would make sports Unfair or make the exercise too easy. An example is baseball, where such a change might favor a hitter over a pitcher. On the other hand, however, it is believed that a ball having a contrasting portion would be useful even if such a ball would not be used in a game. For example, batters train extensively to improve their ability to hit thrown balls. One factor that makes hitting a thrown ball difficult is the varying spin applied to a single throw. For example, curveballs and slide curveballs are spinning throws that are thrown with the intention of causing the ball to move substantially sideways in order to confuse the batter as to the position of the ball when it reaches the batter. It is believed that a hitter can improve his batting performance by utilizing ball training with contrasting portions exhibiting spin-induced contrast. It is believed that due to the presence of the spinning part, the batter can generally improve his ability to track pitches thrown, even non-spinning ones. Furthermore, it is believed that by training with a ball having a contrasting portion, the hitter will learn to recognize signals in addition to those provided by the additional contrasting portion. Additionally, a pitcher may benefit from using ball practice that exhibits the contrast caused by spin, providing the pitcher with feedback on the amount of spin and axis of spin for a particular pitch. This will help the bowler train himself with repeatable accuracy of throwing.

Further by way of non-limiting example, it is believed that similar improvements in athlete performance can be achieved in other sports, such as tennis, squash, handball, table tennis, volleyball, basketball, soccer, or any other sport that requires a player to interact with a spinning ball . Providing the player with additional information about the spin of the ball allows the player to better predict the trajectory of the ball and the interaction of the ball with other objects such as walls, the floor or rackets. Using the above-described ball drills with contrasting sections is believed to improve the athlete's ability to track the ball and help train the athlete to better understand other signs of ball spin.

In one aspect of the invention, a ball is disclosed having indicia exhibiting spin-induced contrast, comprising: a design pattern, corresponding to the diameter of the ball, made of a plurality of symmetrically arranged geodesics, wherein the geodesics The number of lines is selected from 6, 9 and 15, and the design pattern has a plurality of vertices and a plurality of triangular units; the color of the ball; and a plurality of marks positioned on the ball according to the design pattern, wherein the plurality of marks are painted with The color of the ball forms a contrasting marking color, and when the ball is rotated about either axis of rotation, the multiple markings exhibit contrasting lines caused by the rotation.

In another aspect of the invention, a method of marking a ball having markings exhibiting contrast lines caused by spin is disclosed, comprising the steps of: a) selecting a Coxeter Complex pattern from among A3, B3 and H3, which Including multiple geodesics and multiple geodesic vertices; b) drawing a selected Coxeter Complex pattern on the surface of the ball; c) selecting marks that exhibit contrast caused by rotation; and d) applying the selected marks to The surface of a ball where the markings are positioned in relation to the selected Coxeter Complex pattern and the markings are in contrast to the ball.

In yet another aspect of the invention, a method of detecting the axis of rotation of a ball is disclosed, comprising the steps of: providing a ball with a plurality of markers exhibiting rotation-induced Contrast lines where the multiple marks are positioned on the ball according to the Coxeter Complex pattern from A3, B3 and H3; rotate the ball about the axis of rotation; observe the contrast visible on the surface of the rotating ball produced by the marks on the surface of the ball line, wherein the contrast line is approximately perpendicular to the axis of rotation; and the axis of rotation of the ball is determined by translating the visible contrast line by about 90 degrees.

While the invention has been described in detail in the drawings and foregoing description, it is also to be considered illustrative and non-limiting in nature, it being understood that only a limited number of embodiments have been shown and described, and in the scope of the invention All changes and modifications between principles are intended to be protected.

Claims (22)

1, a kind of ball with mark, described mark represents the contrast that is caused by rotation, comprising:

Layout, corresponding with the diameter of ball, this layout is made by a plurality of symmetrically arranged geodesic lines, and wherein, geodesic quantity is greater than 3, and this layout has a plurality of summits and a plurality of triangular element;

The color of ball; And

A plurality of marks are positioned on the ball according to layout, and wherein said a plurality of marks scribble the marker color that forms contrast with the color of ball, and when ball rotated around arbitrary rotating shaft, these a plurality of marks represented the reference line that is caused by rotation.

2, the ball of claim 1, wherein, described a plurality of summits are incomplete same, and the similar right angled triangle of described a plurality of triangular element.

3, the ball of claim 1, wherein, described geodesic quantity is selected from 6,9 and 15.

4, the ball of claim 3, wherein, described a plurality of marks cover the 5%-20% on ball surface.

5, the ball of claim 1, wherein, described a plurality of marks comprise many lines with live width.

6, the ball of claim 5, wherein, described live width is less than 10% of the diameter of described ball.

7, the ball of claim 5, wherein, described live width the diameter of ball 1/3 to 3 percent between.

8, the ball of claim 1, wherein, described a plurality of marks comprise a plurality of triangular markers, described a plurality of triangular markers are positioned to corresponding to some described a plurality of triangular elements.

9, the ball of claim 1, wherein, described a plurality of marks comprise a plurality of circular indexing units.

10, the ball of claim 9, wherein, each unit in described a plurality of circular indexing units contacts other circular indexing unit.

11, the ball of claim 9, wherein, each unit and other circular indexing unit in described a plurality of circular indexing units are overlapping substantially.

12, the ball of claim 1, wherein, the surface of described ball comprises the face district of a plurality of combinations, and the edge in each face district is corresponding with at least two geodesic lines of layout.

13, the ball of claim 1 also comprises significant color, and wherein said significant color is different from the color of described ball and the color of described mark.

14, a kind of method of mark ball makes described ball that the mark that represents the reference line that is caused by rotation be arranged, and comprises step:

A) select Coxeter Complex pattern from A3, B3 and H3, it comprises many geodesic lines and a plurality of geodesic lines summit;

B) with selected Coxeter Complex Patten drawing on the surface of ball;

C) selection represents the mark of the contrast that is caused by rotation; And

D) selected mark is put on the surface of ball, wherein the position of mark is relevant with the Coxeter Complex pattern of selecting, and mark and sphere in pairs than.

15, the method for claim 14 also comprises step:

E) select and the described selected relevant assembly face pattern of Coxeter Complex pattern so that each face district comprise can be relevant with the geodesic line of separating two edges; With

F) utilize the face district to piece together the face ball from selected assembly face pattern.

16, the method for claim 14, wherein said mark cover the ball surface area less than 50%.

17, the method for claim 14, wherein said mark covers the 5%-20% of ball surface area.

18, the method for claim 14, wherein said selected being labeled as has a plurality of lines of live width.

19, the method for claim 18, wherein said selected live width is less than 10% of bulb diameter.

20, the method for claim 14, wherein said selected a plurality of triangular markers that are labeled as, these a plurality of triangular markers are positioned to have and are parallel to described geodesic limit.

21, the method for claim 14, wherein said selected a plurality of circular marks that are labeled as, the center of described circular mark is centrally located on the spheroid on the polyhedral radially projecting of the Plato face substantially.

22, a kind of method that detects the rotating shaft of ball comprises step:

Ball with a plurality of marks is provided, and when ball rotated around any rotating shaft, described a plurality of marks represented the reference line that is caused by rotation, and wherein these a plurality of marks are positioned on the ball according to the Coxeter Complex pattern from A3, B3 and H3;

Make ball center on the rotating shaft rotation;

The visible reference line on the surface of screw that observation is produced by the lip-deep mark of ball, wherein this reference line is approximately perpendicular to rotating shaft; And

By about 90 degree of visible reference line translation being determined the rotating shaft of ball.

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