Patent Application
20100282234
The present invention relates to a cut design of ornamental diamond and, more particularly, to a novel cut design allowing a viewer of a diamond to sense more beauty.
Diamond is cut for use in ornamentation to obtain a brilliant diamond and accessory and there are the round brilliant cut ornamental diamond and accessory of a 58-faceted body.
Mathematician Tolkowsky proposed a cut believed to be ideal, as a design to enhance brilliance of the round brilliant cut ornamental diamond, which has the pavilion angle of 40.75°, the crown angle of 34.50°, and the table diameter of 53% of the girdle diameter. A design developed from it is one called the GIA (Gemological Institute of America) system.
The inventors conducted study on cuts to enhance brilliance of ornamental diamonds and proposed in Patent Document 1, the cut design wherein the pavilion angle p was between 45° and 37.5° both inclusive and the crown angle (c) fell within the range of −3.5×p+163.6≧c≧−3.8333×p+174.232, as one permitting a viewer who views a round brilliant cut diamond from above the table facet thereof, to simultaneously view light emerging from the crown facets after incidence into the crown facets, light emerging from the crown facets after incidence into the table facet, and light emerging from the table facet after incidence into the crown facets. In the cut design, the center value of the pavilion angle p is 38.5° and that of the crown angle (c) is 27.92°. Since the round brilliant cut diamonds are designed with emphasis on the brilliance of the crown facets as well as the brilliance of the table facet, the diameter of the table facet is from 40 to 60% of that of the girdle, and it is from 33 to 60% in the diamond proposed before by the inventors.
The brilliance of an ornamental diamond is sensed by a viewer in such a manner that light is incident from the outside into the diamond and the incident light is reflected inside the diamond to reach the viewer. The degree of brilliance of a diamond is determined by a quantity of the reflected light from the diamond. The quantity of reflected light is usually evaluated by a physical quantity of reflected light.
The human perception, however, is not determined by the physical quantity of reflected light only. For letting a viewer sense beauty of a diamond, the diamond needs to provide a large quantity of light to be sensed by the viewer, i.e., a large quantity of physiologically or psychologically visually-perceived reflected light. There are the Fechner's law and Stevens' law as to the quantity of light perceived by humans (cf. Non-patent Document 1). The Fechner's law states that the quantity of visually-perceived light is the logarithm of the physical quantity of light. When the Stevens' law is applied on the assumption that a light source is a point light source, the quantity of visually-perceived light is the square root of the physical quantity of light. Based on either of the Fechner's and Stevens' laws, many conclusions are considered to be substantially identical without significant error though they are quantitatively different. Then the inventors adopted the Stevens' law to evaluate the quantity of reflected light from the diamond and thereby to determine the quantity of visually-perceived light, and evaluated the brilliance of diamond, based on the quantity of visually-perceived reflected light in the case of the visually-perceived light being the reflected light. We proposed in Patent Document 2 that the quantity of reflected light from the diamond, though it must be different depending upon illumination conditions, was to be evaluated in such a practical condition that incident light to be blocked by the viewer and incident light coming from sufficiently far distances were excluded from incident light from a planar light source with uniform luminance and the quantity of effective visually-perceived reflected light was evaluated using reflection of the remaining incident light, and also proposed a design of brilliant cut diamond capable of increasing the quantity of effective visually-perceived reflected light.
Non-patent Document 1: “Shichikaku” 2000, pp 10-12, authored by Takao Matsuda and published by BAIFUKAN CO., LTD
We studied how to further increase the quantity of effective visually-perceived reflected light by modifying the round brilliant cut design of diamond and accomplished the present invention. It is thus an object of the present invention to provide an ornamental diamond having a two-stage pavilion with numerous reflection patterns, which allows a viewer to sense extreme brightness when the diamond is viewed from above the table facet and crown facets thereof.
An ornamental diamond having a two-stage pavilion according to the present invention comprises: a girdle of a round or polygonal shape having an upper horizontal section surrounded by an upper periphery and, a lower horizontal section surrounded by a lower periphery and being parallel to the upper horizontal section; a crown of a substantially polygonal frustum formed above the upper horizontal section of the girdle and upward from the girdle, the crown having a table facet of a regular octagon which forms a top surface of the polygonal frustum; and a pavilion of a substantially polygonal pyramid formed below the lower horizontal section of the girdle and downward from the girdle and having a bottom apex. The pavilion comprises a first pavilion and a second pavilion separated by a horizontal division plane parallel to the lower horizontal section of the girdle. It should be noted herein that there is no face like a facet between the first pavilion and the second pavilion and that a horizontal plane to separate the first pavilion and the second pavilion is called the “horizontal division plane,” for convenience' sake of description in the present invention.
The crown has eight bezel facets, eight star facets, and sixteen upper girdle facets, as well as the table facet. The first pavilion has eight first pavilion main facets and sixteen first lower girdle facets. The second pavilion has eight second pavilion main facets.
In the diamond of the present invention, a Z-axis is defined along a straight line extending from the bottom apex of the polygonal pyramid pavilion through a center of the table facet; first planes are defined as planes including the Z-axis and passing eight respective vertexes of the table facet; an X-axis is defined along a straight line passing a point where a first plane intersects with the girdle lower periphery, and being perpendicular to the Z-axis; a Y-axis is defined along a straight line passing a point where a first plane perpendicular to the Z-axis and the X-axis intersects with the girdle lower periphery, and being perpendicular to the Z-axis and the X-axis; and second planes are defined as planes each of which includes the Z-axis and bisects an angle between two adjacent first planes.
In the crown, each bezel facet is a quadrilateral plane whose opposite vertexes are a vertex of the table facet and a point where a first plane passing the mentioned vertex intersects with the girdle upper periphery, and the quadrilateral plane has the other two opposite vertexes on respective adjacent second planes and shares a vertex out of the other two opposite vertexes with an adjacent bezel facet. Each star facet is an isosceles triangle composed of the base of a side of the table facet and the vertex shared by two adjacent bezel facets whose vertexes are at the two ends of the base. Each upper girdle facet is a triangle composed of one side intersecting at one end with the girdle upper periphery, out of the sides of each bezel facet, and a point where a second plane passing the other end of the side intersects with the girdle upper periphery.
The second pavilion is an octagonal pyramid located between the bottom apex and the horizontal division plane and having ridge lines passing the bottom apex, on the respective first planes, and the side faces of the octagonal pyramid form the second pavilion main facets. The first pavilion is a hexadecagonal frustum located between the girdle lower periphery and the horizontal division plane and having ridge lines on the respective first planes and on the respective second planes, and the side faces of the hexadecagonal frustum form the first lower girdle facets. Each first pavilion main facet is a quadrilateral plane having a vertex at a point where a first plane intersects with the girdle lower periphery, being perpendicular to the first plane, and having a predetermined angle with respect to the lower horizontal section of the girdle (which corresponds to “first pavilion angle” described below), the quadrilateral plane has another vertex on a ridge line between two adjacent second pavilion main facets extending in the second pavilion, and the other two vertexes on the horizontal division plane, and these two vertexes are equidistant from the first plane. The first pavilion main facet extends into the second pavilion so as to cut off a part of each side face of the octagonal pyramid of the second pavilion whereby the second pavilion main facets are formed from the respective side faces of the octagonal pyramid of the second pavilion, and it cuts off a part of each side face of the hexadecagonal frustum of the first pavilion whereby the first lower girdle facets are formed from the respective side faces of the hexadecagonal frustum of the first pavilion. Since each second pavilion main facet extends into the first pavilion and has one vertex on a ridge line between two adjacent first girdle facets, the side faces of the hexadecagonal frustum of the first pavilion are further cut off by the second pavilion main facets to form the first lower girdle facets.
In the first pavilion, each first pavilion main facet is a quadrilateral plane having a vertex at a point where a first plane intersects with the girdle lower periphery, opposite vertexes at two points on the horizontal division plane equidistant from the first plane, and the other vertex on the first plane, and being perpendicular to the first plane. Each first lower girdle facet can be said to be a quadrilateral plane located between the lower horizontal section of the girdle and the horizontal division plane, sharing a side connecting the vertex on the girdle lower periphery and the vertex on the horizontal division plane of the first pavilion main facet, with the first pavilion main facet, and located between the mentioned side and a second plane.
In the second pavilion, each second pavilion main facet can be said to be a hexagonal plane located between two adjacent first planes and surrounded by two sides connecting the bottom apex and the other vertexes on the first planes of two respective adjacent first pavilion main facets intersecting with the two respective first planes, two sides connecting the other vertexes and the vertexes on the horizontal division plane shared with the two respective adjacent first pavilion main facets, and two sides connecting the vertexes on the horizontal division plane of two respective first lower girdle facets located between the two first pavilion main facets, and a vertex on a second plane shared by the two first lower girdle facets.
In the ornamental diamond having the two-stage pavilion according to the present invention, a first pavilion angle (p1) between the first pavilion main facet and the lower horizontal section of the girdle is from 40° to 46°; in a graph with the first pavilion angle (p1) on the horizontal axis and a crown angle (c) between the bezel facet and the lower horizontal section of the girdle on the vertical axis, the crown angle (c) falls within a region between two straight lines, one connecting two points where (p1, c) is (40, 29.6) and (43, 14.4) and the other connecting two points where (p1, c) is (43, 14.4) and (46, 14.4), and two straight lines, one connecting two points where (p1, c) is (40, 36.3) and (43, 23.3) and the other connecting two points where (p1, c) is (43, 23.3) and (46, 17.8); in a graph with the first pavilion angle (p1) on the horizontal axis and a second pavilion angle (p2) between the second pavilion main facet and the lower horizontal section of the girdle on the vertical axis, the second pavilion angle (p2) falls within a region between two straight lines, one connecting two points where (p1, p2) is (40, 35.7) and (44, 37.55) and the other connecting two points where (p1, p2) is (44, 37.55) and (46, 37.3), and a straight line connecting two points where (p1, p2) is (40, 39.35) and (46, 39.35).
When an X-axis coordinate of a point where the girdle lower periphery intersects with the X-axis is 2.0, an X-axis coordinate (del) of a vertex of the regular octagon of the table facet present on the X-axis is from 0.9 to 1.2.
A reflection rating index of the ornamental diamond with the two-stage pavilion of the present invention is far greater than that of the excellent-grade round brilliant cut diamond, 400.
The number of reflection patterns of the ornamental diamond with the two-stage pavilion of the present invention is nearly double that of the excellent-grade round brilliant cut diamond, 67, and larger than that of the round brilliant cut diamond proposed before by the inventors, 85.
As described above, the ornamental diamond with the two-stage pavilion of the present invention shows the greater brilliance of reflection and the larger number of reflection patterns than the conventional ones and is thus excellent for ornamental use.
Let us define a Z-axis along a straight line extending from the bottom apex G of the octagonal pyramid pavilion 130 through the center of the table facet, first planes 102 as planes including the Z-axis and passing the respective vertexes of the octagon of the table facet, and second planes 104 as planes each passing the Z-axis and bisecting an angle between two adjacent first planes 102.
For convenience' sake of description, as shown in
The first planes are the ZX plane, the YZ plane, and planes obtained by rotating those planes by 45° around the Z-axis, and are denoted by 102 in
With reference to
With reference to
In the second pavilion 142, each second pavilion main facet 146 is a hexagonal plane GHKLK″H′ having a vertex at the pavilion bottom apex G and surrounded by two sides GH and GH′ on two adjacent first planes 102, side HK and side H′K″ of two adjacent first pavilion main facets 136, and side KL and side K″L connecting vertexes K and K″ of two respective first lower girdle facets 138 on the horizontal division plane 134 between two adjacent first pavilion main facets 136, and a vertex L on the second plane shared by the two first lower girdle facets 138. The second pavilion 142 is a portion of the pavilion 130 between the horizontal division plane 134 and the pavilion bottom apex G, but each second pavilion main facet 146 projects through the horizontal division plane 134 toward the girdle 120. The second pavilion 142 has the peripheral surface composed of eight second pavilion main facets 146. When the projecting portions of the first pavilion main facets 136 through the horizontal division plane 134 toward the bottom apex G and the projecting portions of the second pavilion main facets 146 through the horizontal division plane 134 toward the girdle 120 are excluded, the second pavilion 142 can be regarded as an octagonal pyramid having an apex at the bottom apex G and a bottom surface on the horizontal division plane 134, each side face of the octagonal pyramid corresponds to a second pavilion main facet 146, and the second pavilion main facets 146 are made by removing parts of the respective side faces by the first pavilion main facets 136.
Each of the bezel facets 114 and each of the first pavilion main facets 136 are located between two adjacent second planes 104. Each first pavilion main facet 136 is located between two adjacent second planes 104 and is perpendicular to a first plane 102. The common side CE of two adjacent upper girdle facets 118, and the common side LJ of two adjacent first lower girdle facets 138 are on a second plane 104. Each star facet 116, two upper girdle facets 118 sharing the side CE, and two first lower girdle facets 138 sharing the side LJ are located between two adjacent first planes 102. These two upper girdle facets 118 and these two first lower girdle facets 138 are located at positions approximately opposite to each other with the girdle 120 in between.
Each of the first planes 102 divides the center of each bezel facet 114 and the center of each first pavilion main facet 136. For this reason, each bezel facet 114 is approximately opposed to each first pavilion main facet 136 with the girdle 120 in between.
In the description hereinafter, the size of each part of the diamond will be expressed based on the radius of the girdle as a reference. Namely, each part is expressed by its X-axis coordinate based on the definition that the X-axis coordinate of a point where the girdle lower periphery 126 intersects with the X-axis is defined as 2.0. The girdle height (h) is a length in the Z-axis direction of the girdle 120 and is expressed by a value based on the girdle radius of 2.0.
In the sectional view in the ZX plane shown in
The girdle height (h), table radius (del), distance to the tip of the star facet (fx), distance to the lower vertex of the first pavilion main facet extending into the second pavilion (Gd), and position of the horizontal division plane of the pavilion (ax) are indicated by their respective X-axis coordinates, as shown in
For defining the dimensions (size) of the diamond, the crown height, pavilion depth, and total depth are sometimes used in addition to the table radius, pavilion angle, and crown angle, but these are not adopted in the present specification because they are uniquely determined once the table radius, first pavilion angle (p1), second pavilion angle (p2), and crown angle (c) are given.
Introduction of Reflection Rating Index
In the study below, the diamond is set so that the Z-axis of the diamond becomes vertical, and the diamond is observed from above the Z-axis while being illuminated with light from light sources uniformly distributed over a horizontal ceiling. Light incident at angles of less than 20° relative to the Z-axis into the table facet and crown facets of the diamond is highly likely to be blocked by a viewer. Light incident at angles of more than 45° relative to the Z-axis has low illuminance because of attenuation by distance and is highly likely to be blocked by obstacles; therefore, it has little contribution to reflection. Therefore, the light quantity of reflection patterns shall be determined with consideration to contribution rates according to angles of incidence of incident light relative to the Z-axis.
The visual perception of human is to sense the intensity of a small light spot as an amount of stimulus. Therefore, the quantity of light of reflection patterns physically obtained also needs to be converted into an amount of visual perception sensed as a stimulus. According to the Stevens' law, the amount of visual perception as the intensity of stimulus sensed by a man in the case of a small light spot is proportional to the square root of the physical quantity of light.
By applying this law, a reflection rating index is introduced as an index obtained by using an aesthetically-perceivable minimum physical reflection quantity as a unit, calculating a square root of a quantity of light per reflection pattern represented as a multiple of the unit, and taking the sum thereof. For determining the physical reflection quantity, the radius of the diamond is cut into 200 equal meshes, a quantity of reflected light taking account of the contribution rates is determined for each mesh, and the sum of quantities for an identical pattern is defined as a physical quantity of reflected light in that pattern. Since a diamond has the radius of about several mm, each mesh has several hundred μm2. The amount of visual perception was calculated for only patterns having the area of not less than 100 meshes with consideration to the level of human discrimination, and the sum thereof was defined as the reflection rating index.
Namely, the reflection rating index=E{(physical quantity of reflected light with consideration to contribution rates per pattern of not less than 100 meshes)/unit of quantity of perceivable minimum physical reflection}1/2. In this equation Σ is the summation for reflection patterns.
Reflection Rating Index
The ornamental diamonds having the two-stage pavilion according to the present invention were prepared with the girdle radius: 2.0 and the table radius (radius to a vertex of the octagon) (del): 1.0, with the first pavilion angle (p1) of 40°, 41°, 42°, 43°, 44°, 45° or 46°, and with the crown angle (c) varying from 14° to 37°, and the reflection rating index was determined for each of the diamonds;
Next, the ornamental diamonds having the two-stage pavilion according to the present invention were prepared with the girdle radius: 2.0 and the table radius (del): 1.0, with the first pavilion angle (p1) of 40°, 41°, 42°, 43°, 44°, 45° or 46°, and with the second pavilion angle (p2) varying from 35° to 40°, and the reflection rating index was determined for each of them;
When the conventional excellent-grade round brilliant cut diamond has the pavilion angle: 41.4°, the crown angle: 32.8°, the girdle radius: 2.0, the table radius (del): 1.14, the star facet tip distance (fx): 1.454, the lower girdle facet lower tip distance (Gd): 0.4, and the girdle height (h): 0.12, the reflection rating index thereof obtained is 370 and no excellent-grade round brilliant cut diamond has the maximum index over 400. As shown in
Number of Reflection Patterns
The ornamental diamond having the two-stage pavilion according to the present invention has the number of reflection patterns approximately twice that in the case of the conventional excellent-grade round brilliant cut diamond and 1.2 times that of the brilliant cut proposed before by the inventors. For this reason, the ornamental diamond having the two-stage pavilion according to the present invention is applicable to ornamental use.
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/JP2008/050144 | 1/9/2008 | WO | 00 | 7/2/2010 |
