Where Vp is the volume and Ap is the area of the object. For example, the sphericity factor for an sphere is 1 and for a cube 0.806.

• Resultados Examen De Admision

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Sphericity is a comparison ratio between the area of an ideal sphere calculated with the volume of the object (numerator) and the real area (denominator). In order to applied this equation you need the surface and volume measurements.Consider now an spheroid with three semi axes a, b and c. When a=b=c, an spherical shape with a 1 factor is obtained.

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Resultados Examen De Admision

When a=b and c≠a, an oblate spheroid is obtained; the same shape of the earth. The area and volume can be calculate with the following equations for a 3D ellipsoid having 3 different semi-axis a, b and c, as follows. WhereA is the area and P the perimeter of an ellipse (with semi axis a andsemi axis b). For a perfect circle ɸ=1.

Circularity is a comparison ratio between the real area of the object (numerator) with an ideal area of a circlecalculated with the perimeter of the object (denominator). In equation 6, you need the area and perimeter measurements of a plane cut in a sphere. You can get them with a photo pic of the sphere and image processing software.Using the Ramujan approximationfor the ellipse's perimeter in equation 6, one can obtain:In equation 7, you needthe area and the semi-axis measurements of a plane cut in a sphere. You canget them with a photo pic of the sphere and image processing software. For example with Photoshop you can calculate area, vertical and horizontal distance.

4-Mesuring the aspect ratio (roundness) The roundness is defined as follows for a 2D ellipse. Where and and b are the semi-axis of the ellipse with the condition a ≥ b. A circle have the property that ℛ=1. 5-Comparing the sensibility of sphericity, circularity and roundness with regard the shape of a circle. In figure 10, it was calculated the 3 parameters (sphericity, circularity and roundness) for different cut's plane of an spheroid. The yellow figure is the circle (a plane's cut of an sphere). Orange and red figures are the cut's plane of an oblate spheroid.

It was noted, that the roundness factor is the most sensitive to changes in the size between the three parameters. For a reduction in the b semi axis of 21%, the roundness factor changes 28% (Red ellipsis, the semi axis (a) was not changed). For the same reduction in the semi axis b, a changes of only 1.2% was observed in the sphericity parameter and a 2.5% change in circularity one is obtained. This two shape parameters are rigid with regard changes in the rounded shape.Figure 10. Impact of shape in sphericity, circularity and roundness parameters.

1-Take two shots of the sphere where you can see all the contour as it is showed in Figure 13. The shots are 90º separated, same distance from the sphere and situated in its center. You can take the shot at two different distances if you have an object of known size (a reference one). In this way you can get the absolute value of diameter. Or to take the shot to the same distance from the stone having only relative measures (with pixels units in Photoshop).Figure 13: Method of two shots to measures sphericity.Estimate parameters a, b, c for an ellipsoidal shape (orthogonal semi-axis). B- One shot method to estimate sphericity and circularity.In the case where only one shot is available, anapproximation of the sphericity can be obtained with a ≠b and c=b.

Inthis way sphericity can be obtained with equation 5, supposing an oblate spheroid. Also you cancalculate circularity applying equation 7. The contour of an sphere obtained in one shot is equivalent to a plane cut of an sphere that results in a circle.1- Take a shot with an angle where you can see the full circle contour of the sphere. Note that, sphere have a hidden section in the part that have contact with soil. See Figure 14. C-Applying the one shot graphic method1- Testing the method with the UCR ball (Agri-food faculty)Four pics were taken to the ball located at the Costa Rica University (UCR), in front of the Agri-food Faculty. The same that the Lanmme³⁻⁴ test with a laser scanner.

First picture was taken pointing out to the north, second picture to the S45°E, third one to the E and the fourth one to the N45°E. The angle of the camera was about 30° from the equator plane to avoid the support section. 15 to 18 you can see the resulting pics and also the results of area, vertical axis and horizontal axis. These results were tabulated in Table 1. Applying equations 5, 7 and 8 with these data you can compute the values of sphericity, circularity and roundness that were also tabulated in Table 1.Figure 15. View S45°EFigure 16. North viewFigure 17.

East view.Figure 18. N45°ETable 1. Results of sphericity, circularity and roundness for the ball of Agri-food Faculty in UCR.Remember that the parameters of ψ, ɸ and ℛ are dimensionless.

The results agrees with the Lanamme ³⁻⁴ results as they are close to 1. Most sensitive parameter to the shape is roundness. The maximum error in roundness for the ball is 2% in the east view.

2-Testing the method with the stone ball at the Costa Rica Museum in the central yard.The ball, located in the central yard of Costa Rica museum, was selected in the second test for the graphic method. This ball is about 1.8 m, have observable errors in symmetry and different level in the polishing quality. It is possible that this ball was unfinished.

The less symmetry side of the ball is shown in Figure 19. This picture was rotated to take 3 measurement of the area and axis. These results are tabulated in Table 2. Finally the sphericity, circularity and roundness were calculated and presented in Table 2.Figure 19. Ball at the Costa Rica Museum. Central yard.Table 2.

Results of sphericity, circularity and roundness for the ball of the Costa Rica Museum, central yard.You can see that roundness is the most sensitive parameter. In this case about a 6% of error was obtained.

Some changes are observed in sphericity in the fourth decimal, a some in the second decimal for sphericity.3-Museum BallsSome of the most beautiful (symmetrical) spheres can be find in some museums in Costa Rica and United States. In this study, it were selected six symmetrical spheres (to the naked eye) from different parts of the world to calculated its sphericity, circularity and roundness applying the one shot method. Inthe next table you can see the results of the sphericity, circularity and roundness applying the graphic method of one shot. Area and diameter wasobtained processing the pics. Next, sphericity, circularity androundness shape parameters were calculated with equation 6, 7 and 8respectively.Table 3.

Results for six museum spheres of sphericity, circularity androundness. For sphericity and circularity, the results were truncated to 1decimals, but in all the cases the numbers have three nines. The (Boston) have the opinion that is better to call the stones as balls, quoting the museum:Some people refer to these objects as 'spheres,' but since all are notperfectly round and 'sphere' generally refers to a hollow form, Ibelieve that 'ball' is a better term as it does not pretend to aprecision that is not always present.The measured shericity, circularity and roundness shape parameters shows that the adjective sphericalfor these stones can be apply as a recognition to the skilled Canquerrique craftsmen. There are many types of stones, some are made inlimestone but majority are gabbroid.

The size varies from somecentimeters until the 2.66 meters of the Silencio Stone. About 300stones was estimated to exist.

Many of them are not so perfect as theSan Pedro. But it is amazing how some of the Canquerrique sculptors havereached a such perfection in his art with rudimentary stones tools.