CN116502371B - Ship-shaped diamond cutting model generation method - Google Patents

Ship-shaped diamond cutting model generation method Download PDF

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CN116502371B
CN116502371B CN202310751242.3A CN202310751242A CN116502371B CN 116502371 B CN116502371 B CN 116502371B CN 202310751242 A CN202310751242 A CN 202310751242A CN 116502371 B CN116502371 B CN 116502371B
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闫丽
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Xiamen Mengyou Internet Software Co ltd
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Abstract

The invention relates to the technical field of three-dimensional model construction, in particular to a ship-shaped diamond cutting model generation method, which comprises the steps of setting ten parameter values such as a girdle length-width ratio, a tangent angle, a girdle thickness ratio, a crown angle, a table width ratio, a table length ratio, a pavilion depth ratio, a exhibition hall ratio, a lunar surface inclination angle and a lunar surface transverse inclination angle by setting the number of vertexes of an upper waist, a lower waist, a crown part, a crescent moon surface, a pavilion part and a bottom tip of a ship-shaped diamond; the coordinate axis is formed, the diamond girdle outline is formed through two ellipses, the coordinates of each vertex of the ship-shaped diamond are obtained through a geometric mathematical formula and mirroring through the set ten parameter values, the 3D model is built through a three-dimensional modeling tool, the modeling speed is high, and the size and the internal different proportion relation of the diamond model can be flexibly adjusted through setting the parameter values according to raw stones or requirements.

Description

Ship-shaped diamond cutting model generation method
Technical Field
The invention relates to the technical field of three-dimensional model construction, in particular to a ship-shaped diamond cutting model generation method.
Background
Ship-shaped diamond is one of the most fashionable precious stone cutting work nowadays, and meanwhile, the ship-shaped diamond can be designed to raise the carat weight to the highest level, so that the diamond looks larger in appearance. In diamond processing, 3D modeling is usually performed by a computer, and then corresponding cutting is performed according to the model.
In the prior art, there are generally two methods for 3D modeling: one is to construct 3D models directly from points, lines, planes by means of a three-dimensional modeling tool; another is to generate a depth photograph of the object by means of some three-dimensional shaping tool, such as a depth camera, and to reconstruct three-dimensionally from the depth photograph. However, the former model has low construction speed, the proportion relation of the ship-shaped internal geometric structures is related with each other, and the proportion adjustment is accurate and difficult; the three-dimensional reconstruction method of depth photos by a depth camera is suitable for restoring the existing 3D model, the ship-shaped diamond is irregular raw stone and is produced through a cutting process, if the existing ship-shaped diamond is used for modeling, the proportion of the raw stone is required to be adjusted according to the proportion of the raw stone due to the difference of the raw stone, the operation is complicated, and the applicability is poor.
Disclosure of Invention
The invention provides a ship-shaped diamond cutting model generation method for solving the problems.
The invention adopts the following technical scheme:
the ship type diamond cutting model generation method is characterized by comprising the following steps of:
(1) Setting the number of vertexes of the boat-shaped diamond, wherein the number comprises a plurality of upper waist vertexes, a plurality of lower waist vertexes, a plurality of crown vertexes, a plurality of crescent surface vertexes, a plurality of pavilion vertexes and one bottom vertex; setting ten parameter values, namely: the girdle aspect ratio lw, tangential angle sigma, girdle thickness ratio girdleThickness, crown angle crownAngle, table width ratio crownTable, table length ratio tableLength, pavilion depth ratio pavilion height, pavilion ratio, lunar tilt angle moonfacet angle, lunar transverse tilt angle moonfataangle.
(2) Constructing a two-dimensional coordinate axis, an ellipse and an inscribed circle of the ellipse, wherein the included angle between the tangent line of the inscribed circle and the tangent line of the ellipse is the tangent angle sigma, the coordinate of the ellipse is (x 0, y 0), the ellipse is copied to form two ellipses, and the two ellipses are intersected to form the girdle profile of the ship-shaped diamond.
(3) Setting a girdle contour center O as an origin, setting a transverse x-axis and a vertical y-axis on the two-dimensional coordinate axis in the step (2), setting A, B, C three-point coordinates, wherein OC=1, OB=girdle length-width ratio lw, and calculating coordinates (x, y) of a lower girdle vertex on the two-dimensional coordinate axis according to the girdle length-width ratio lw and a tangential angle sigma through a triangle mathematical formula and an ellipse parameter equation; based on the two-dimensional coordinate axis, a z-axis is added, a three-dimensional coordinate axis is constructed, and the lower lumbar vertex z-axis coordinate is set to 0, so that the lower lumbar vertex coordinate (x, y, z=0) is obtained.
(4) And (3) on the three-dimensional coordinate axis of the step (3), the x-axis and y-axis coordinates of the upper waist vertex are consistent with those of the lower waist vertex, and the z-axis of the upper waist vertex is the waist thickness ratio girdleThickness, so that the upper waist vertex coordinates (x, y, z=girdlethickness) are obtained.
(5) Setting normal vectors and fixed points on the three-dimensional coordinate axis in the step (4) according to the upper waist vertex coordinates, the parameter waist thickness ratio girdleThickness, the crown angle crownage, the table width ratio crownTable and the table length ratio table length, obtaining a plane where the crown vertex is located by the normal vectors and the fixed points, and obtaining the coordinates of the crown vertex on the three-dimensional coordinate axis according to the intersection point and the mirror image of the plane.
(6) And (3) on the three-dimensional coordinate axis in the step (5), obtaining a lunar plane and a lunar cross-section plane according to the lower waist vertex coordinates, the lunar inclination moonfacetAngle and the lunar transverse inclination moonRotateenge, and obtaining the coordinates of the lunar vertex on the three-dimensional coordinate axis according to the plane intersection point and the mirror image.
(7) Setting a bottom peak point coordinate, a normal vector and a fixed point on the three-dimensional coordinate axis in the step (6) according to the lower waist peak point coordinate, the pavilion depth ratio pavilion height and the pavilion ratio rate, obtaining a plane where the pavilion peak is located according to the normal vector and the fixed point, and obtaining the coordinate of the pavilion peak on the three-dimensional coordinate axis according to the intersection point of the plane and the straight line and the mirror image.
(8) And forming a 3D model by a three-dimensional modeling tool based on the coordinates of the upper lumbar vertex, the lower lumbar vertex, the crown vertex, the crescent plane vertex, the pavilion vertex and the base tip vertex.
Further, 163 vertices of the boat-shaped diamond are set, and the boat-shaped diamond consists of p0 to p162, wherein the vertices comprise 64 upper lumbar vertices, 64 lower lumbar vertices, 16 crown vertices, 10 crescent plane vertices, 8 pavilion vertices and 1 pavilion vertex; wherein, the upper waist vertex is composed of p16 to p79, and takes one upper waist vertex with the largest x-axis coordinate value of the girdle outline as p16, and the p16 to p79 are sequentially arranged on the girdle outline of the boat-shaped diamond according to the x-axis coordinate value from big to small; the lower waist vertex consists of p80 to p143, and an upper waist vertex with the largest x-axis coordinate value of the girdle outline is taken as p80, and the p80 to p143 are sequentially arranged on the girdle outline of the boat-shaped diamond according to the x-axis coordinate value from large to small; crown apex consists of p0 to p 15; the crescent plane vertex is composed of p144 to p 153; pavilion vertex consists of p154 to p161, and base vertex is p162.
Further, the coordinate calculation method of the lower lumbar vertex in the step (3) on the two-dimensional coordinate axis comprises the following steps,
(3.1) obtaining ao×ao+ob×ob=ab×ab by triangle pythagorean theorem, wherein ab=ac=ao+1, and deriving s=ao= (lw×lw-1)/2;
(3.2) setting an F point and an M point on an x axis, and obtaining the angle OAB= angle OBF according to the triangle similarity, wherein fi is the angle OBF, and fi=asin (lw/(s+1));
(3.3) setting t to OM, and obtaining t=lw×tan (fi+σ) according to a trigonometric function;
(3.4) setting a as an elliptic constant half shaft, b as an elliptic vertical half shaft, obtaining a= (t-1)/(t-2) according to the tangential nature of the ellipse,；
(3.5) obtaining x=x0+a×cos (θ) according to an elliptic parameter equation, y=y0+b×sin (θ), wherein θ is a corresponding angle of the waist vertex, and coordinates (x, y) of p80 to p96 in the two-dimensional coordinate axis are obtained, and then coordinates (x, y) of p97 to p143 in the two-dimensional coordinate axis are obtained through mirroring.
Further, the coordinate calculation method of the crown vertices p0 to p15 in the step (5) on the three-dimensional coordinate axis includes the steps of:
(5.1), setting parameters zmax=girdlethickness+0.5x tan (crownAngle), parametersParameter z= (girdetherickness-zMax) ×m+zmax;
(5.2), setting a coordinate top=vector 3 (0, zmax), and a coordinate p6=vector 3 (0, -lwχtablelength/2, 0.5x tan (crownAngle) × (1-crownTable) +girdlethickness); wherein Vector3 is a three-dimensional Vector coordinate;
(5.3) obtaining plane0 where p0 to p7 are located from the normal vector (0, 1) and the fixed point coordinate p 6; plane1 where p8 to p15 are located is obtained by normal vector (0, 1) and fixed point (0, Z), plane pl1 is obtained by normal vector sub (p 69, p 67) and fixed point p68, plane pl2 is obtained by normal vector sub (p 77, p 75) and fixed point p76, plane pl A is obtained by normal vector (vector 3 (1, 0), sub (p 6, p 64)) and fixed point p6, and plane pl C is obtained by normal vector (vector 3 (0, 1, 0), sub (top, p 16)) and fixed point top;
(5.4) obtaining coordinates of a plane intersection point p14= [ plane1, pl1, plA ] three-plane intersection point, and coordinates of a plane intersection point p15= [ plane1, pl2, plA ] three-plane intersection point, and obtaining coordinates of p8 to p13 through mirror images;
(5.5) obtaining a plane plB by coordinates of three points p14, p15 and p 72; the normal vector sub (p 14, p 15) and the middle point thereof are used as fixed points to obtain a plane pl3; setting a YOZ plane of the three-dimensional coordinate axis as a plane pl4;
(5.6) obtaining coordinates of the intersection points of the three planes according to the intersection points of the planes, wherein the coordinates of the intersection points of the three planes are p7= [ plane0, pl3 and plB ], the coordinates of the intersection points of the three planes are p0= [ plane0, pl4 and pl C ], and the coordinates of p1 to p5 are obtained through mirror images.
Further, the method for calculating coordinates of the crescent plane vertices p144 to p153 in the step (6) on the three-dimensional coordinate axis includes the following steps:
(6.1) obtaining a plane M1 from lower lumbar vertex coordinates p132, p136 and a moon inclination moonfacetAngle; obtaining a plane M2 by using lower waist vertex coordinates p136 and p140 and a lunar inclination moonfacetAngle; obtaining a plane M3 by using lower waist vertex coordinates p140 and p80 and a lunar inclination moonfacetAngle; obtaining a plane M4 by using lower waist vertex coordinates p80 and p84 and a lunar inclination moonfacetAngle; obtaining a plane M5 by using lower waist vertex coordinates p84 and p88 and a lunar inclination moonfacetAngle; obtaining a plane M6 by using lower waist vertex coordinates p88 and p92 and a lunar inclination moonfacetAngle;
(6.2) from the lower lumbar apex coordinates p92, p132 and the lunar transverse angle moonRotateangle, a lunar cross-sectional plane plM can be found;
(6.3) obtaining coordinates of a three-plane intersection point according to the plane intersection point, wherein the coordinates are p 152= [ M1, M2, plM ]; p152= [ M1, M2, plM ] coordinates of the three-plane intersection point; p153= [ M2, M3, plM ] coordinates of the three-plane intersection point; p 144= [ M3, M4, plM ] coordinates of the three-plane intersection point; the coordinates of p145 to p151 are then found by mirroring.
Further, the coordinate calculation method of the base peak point p162 and pavilion peak points p154 to p161 in the step (7) on the three-dimensional coordinate axis includes the steps of:
(7.1), bottom spike point coordinates p162=vector 3 (0, 0, -pavilion height);
(7.2) obtaining plane2 in which p154 to p161 are located from normal vector (0, 1) and fixed point (0, -pavilion rate x pavilion height);
(7.3) obtaining a coordinate p160= [ line (p 162, p 128), plane2] according to the intersection point of the line and the plane, wherein the line (p 162, p 128) is a straight line passing through two points of the p162 and the p 128; p159= [ line (p 162, p 151), plane2] straight line intersects with the plane, wherein line (p 162, p 151) is a straight line passing through both points p162 and p 151; p158= [ line (p 162, p 149), plane2] straight line intersects with the plane, wherein line (p 162, p 149) is a straight line passing through two points of p162 and p149, and coordinates of p157, p156, p155, p154 and p161 are obtained by mirroring.
As can be seen from the above description of the structure of the present invention, compared with the prior art, the present invention has the following advantages:
according to the ship-shaped diamond cutting model, two-dimensional coordinate axes and three-dimensional coordinate axes are constructed, two ellipses are intersected to form a ship-shaped diamond girdle outline, parameter values for adjusting the girdle length-width ratio lw and the tangential angle sigma are set, the diamond girdle outline is changed, the ship-shaped diamond cutting model adapts to different diamond raw stones, and through setting the girdle thickness ratio girdlethuckness, crown angle, table width ratio crownTable, table length ratio table length, pavilion depth ratio pavilion height, exhibition hall ratio pavilion rate, lunar inclination angle, lunar rotation angle and other parameter values, the topological structure inside the ship-shaped diamond is adjusted, all vertex coordinates of the ship-shaped diamond can be calculated and output rapidly through a geometric mathematical formula and a coordinate mirroring mode, and finally the 3D model is produced rapidly through a three-dimensional modeling tool, modeling speed is high, and different proportion relations inside the diamond model can be adjusted flexibly according to raw stones or requirements.
Drawings
FIG. 1 is a schematic illustration of the geometry of the present invention for forming a girdle profile of a diamond based on two-dimensional coordinate axes;
FIG. 2 is a top view of a ship-shaped diamond model according to the present invention;
fig. 3 is a bottom view of the diamond model of the ship.
Wherein, the vertices p0 to p162 of the diamond model of fig. 2 and 3 are denoted by numerals 0 to 162.
Detailed Description
The following describes the implementation of the embodiment of the present invention with reference to the drawings.
Referring to fig. 1 to 3, a ship-shaped diamond cutting model generating method includes the steps of:
(1) Setting the number of vertexes of the boat-shaped diamond, wherein the number comprises a plurality of upper waist vertexes, a plurality of lower waist vertexes, a plurality of crown vertexes, a plurality of crescent surface vertexes, a plurality of pavilion vertexes and one bottom vertex; setting ten parameter values, namely: the girdle aspect ratio lw, tangential angle sigma, girdle thickness ratio girdleThickness, crown angle crownAngle, table width ratio crownTable, table length ratio tableLength, pavilion depth ratio pavilion height, pavilion ratio, lunar tilt angle moonfacet angle, lunar transverse tilt angle moonfataangle.
Referring to fig. 2 and 3, the present embodiment specifically includes: setting 163 peaks of the boat-shaped diamond, which consists of p0 to p162, and comprises 64 upper waist peaks, 64 lower waist peaks, 16 crown peaks, 10 crescent surface peaks, 8 pavilion peaks and 1 pavilion peak; wherein, the upper waist vertex is composed of p16 to p79, and takes one upper waist vertex with the largest x-axis coordinate value of the girdle outline as p16, and the p16 to p79 are sequentially arranged on the girdle outline of the boat-shaped diamond according to the x-axis coordinate value from big to small; the lower waist vertex consists of p80 to p143, and an upper waist vertex with the largest x-axis coordinate value of the girdle outline is taken as p80, and the p80 to p143 are sequentially arranged on the girdle outline of the boat-shaped diamond according to the x-axis coordinate value from large to small; crown apex consists of p0 to p 15; the crescent plane vertex is composed of p144 to p 153; pavilion vertex consists of p154 to p161, and base vertex is p162.
(2) Constructing a two-dimensional coordinate axis, an ellipse and an inscribed circle of the ellipse, wherein the included angle between the tangent line of the inscribed circle and the tangent line of the ellipse is the tangent angle sigma, the coordinate of the ellipse is (x 0, y 0), the ellipse is copied to form two ellipses, and the two ellipses are intersected to form the girdle profile of the ship-shaped diamond.
(3) The coordinates of the lower lumbar vertexes p80 to p143 are calculated by setting the center O of the lumbar edge profile as an origin, setting A, B, C three-point coordinates of a transverse x-axis and a vertical y-axis on the two-dimensional coordinate axis in the step (2), and calculating the coordinates (x, y) of the lower lumbar vertexes on the two-dimensional coordinate axis according to the lumbar edge length-width ratio lw and the tangential angle sigma and through a triangle mathematical formula and an ellipse parameter equation; based on the two-dimensional coordinate axis, a z-axis is added, a three-dimensional coordinate axis is constructed, and the lower lumbar vertex z-axis coordinate is set to 0, so that the lower lumbar vertex coordinate (x, y, z=0) is obtained.
Referring to fig. 1, the specific calculation method includes the steps of:
based on parameters of the girdle aspect ratio lw, tangential angle sigma and girdle thickness ratio girdleThickness, the girdle contour center O is set as an origin, the transverse x axis and the vertical y axis are set, A, B, C three-point coordinates are set, and OC=1, OB=the girdle aspect ratio lw.
(3.1) obtaining ao×ao+ob×ob=ab×ab by triangle pythagorean theorem, wherein ab=ac=ao+1, and deriving s=ao= (lw×lw-1)/2;
(3.2) setting an F point and an M point on an x axis, and obtaining the angle OAB= angle OBF according to the triangle similarity, wherein fi is the angle OBF, and fi=asin (lw/(s+1));
(3.3) setting t to OM, and obtaining t=lw×tan (fi+σ) according to a trigonometric function;
(3.4) setting a as an elliptic constant half shaft, b as an elliptic vertical half shaft, obtaining a= (t-1)/(t-2) according to the tangential nature of the ellipse,；
(3.5) obtaining x=x0+a×cos (θ) according to an elliptic parameter equation, y=y0+b×sin (θ), wherein θ is a corresponding angle of the waist vertex, and coordinates (x, y) of p80 to p96 in the two-dimensional coordinate axis are obtained, and then coordinates (x, y) of p97 to p143 in the two-dimensional coordinate axis are obtained through mirroring. Wherein the mirroring process takes the x-axis and the y-axis as symmetry axes, respectively.
(3.6) adding a z-axis based on the two-dimensional coordinate axis, constructing a three-dimensional coordinate axis, setting the z-axis coordinates of all lower lumbar vertexes to 0, and correspondingly obtaining the coordinates (x, y, z=0) of the lower lumbar vertexes p80 to p143 on the three-dimensional coordinate axis.
(4) The coordinates of the upper lumbar vertices p16 to p79 are calculated in such a way that, on the three-dimensional coordinate axis of the step (3), each upper lumbar vertex corresponds to a lower lumbar vertex, the x-axis and y-axis coordinates of the upper lumbar vertex are identical to those of the lower lumbar vertex, and the z-axis of the upper lumbar vertex is the lumbar thickness ratio girdleThickness, so as to obtain the upper lumbar vertex coordinates (x, y, z=girdlethickness).
(5) And (3) calculating coordinates of crown vertexes p0 to p15, namely setting normal vectors and fixed points on the three-dimensional coordinate axis in the step (4) according to the upper waist vertex coordinates, the parameter waist thickness ratio girdleThickness, the crown angle crownAngle, the table width ratio crownTable and the table length ratio table, obtaining a plane where the crown vertexes are located by the normal vectors and the fixed points, and obtaining coordinates of the crown vertexes on the three-dimensional coordinate axis according to the intersection points and the mirror images of the plane.
Referring to fig. 2, the specific calculation method includes the steps of:
based on the parameters crown angle crownable, table width ratio crownTable, table length ratio tableLength, and the upper lumbar vertex p16 to p79 coordinates. And, the analysis of the function expression referred to later is described as follows:
vector3 () represents the coordinates of a three-dimensional Vector; the normal Vector sub (coordinate point a, coordinate point b) is a Vector subtraction of coordinate point a and coordinate point b, denoted as Vector3 (a.x-b.x, a.y-b.y, a.z-b.z), wherein Vector3 of coordinate point a (a.x, a.y, a.z), vector3 of coordinate point b (b.x, b.y, b.z); cross (coordinate point a, coordinate point b) is a Vector cross of coordinate point a and coordinate point b, representing Vector3 (a.x × b.x, a.y × b.y, a.z × b.z); line (coordinate point a, coordinate point b) is a straight line passing through two points, coordinate point a and coordinate point b.
(5.1), setting parameter zmax=girdlethickness+0.5x tan (crownAngle), ginsengNumber of digitsParameter z= (girdetherickness-zMax) ×m+zmax.
(5.2), coordinates top=vector 3 (0, zmax), coordinates p6=vector 3 (0, -lwχtablelength/2, 0.5x tan (crownAngle) × (1-crownTable) +girdlethickness).
(5.3) obtaining plane0 where p0 to p7 are located from the normal vector (0, 1) and the fixed point coordinate p 6; plane1 where p8 to p15 are located is obtained by normal vector (0, 1) and fixed point (0, Z), plane pl1 is obtained by normal vector sub (p 69, p 67) and fixed point p68, plane pl2 is obtained by normal vector sub (p 77, p 75) and fixed point p76, plane pl A is obtained by normal vector (vector 3 (1, 0), sub (p 6, p 64)) and fixed point p6, and plane pl C is obtained by normal vector (vector 3 (0, 1, 0), sub (top, p 16)) and fixed point top.
(5.4) obtaining coordinates of the intersection points of the three planes of the coordinates p14= [ plane1, pl1, plA ] according to the intersection points of the planes, and obtaining coordinates of p8 to p13 through mirror images according to the coordinates of the intersection points of the three planes of the coordinates p15= [ plane1, pl2, plA ]. Wherein the mirroring process takes the x-axis and the y-axis as symmetry axes, respectively.
(5.5) obtaining a plane plB by coordinates of three points p14, p15 and p 72; the normal vector sub (p 14, p 15) and the middle point thereof are used as fixed points to obtain a plane pl3; the YOZ plane of the three-dimensional coordinate axis is set as a plane pl4.
(5.6) obtaining coordinates of the intersection points of the three planes according to the intersection points of the planes, wherein the coordinates of the intersection points of the three planes are p7= [ plane0, pl3 and plB ], the coordinates of the intersection points of the three planes are p0= [ plane0, pl4 and pl C ], and the coordinates of p1 to p5 are obtained through mirror images.
(6) And (3) calculating coordinates of the crescent plane vertexes p144 to p153, namely, on the three-dimensional coordinate axis in the step (5), obtaining a lunar plane and a lunar cross-section plane according to the lower waist vertex coordinates, the lunar inclination moonfacetAngle and the lunar transverse inclination moonRotateenge, and obtaining the coordinates of the crescent plane vertexes on the three-dimensional coordinate axis according to the plane intersection point and the mirror image.
Referring to fig. 3, the specific calculation method includes the steps of:
based on the reference moon tilt moonfacetAngle, moon roll tilt moonfeateAngle, and the coordinates of the lower lumbar vertices p80 to p 143.
(6.1) obtaining a plane M1 from lower lumbar vertex coordinates p132, p136 and a moon inclination moonfacetAngle; obtaining a plane M2 by using lower waist vertex coordinates p136 and p140 and a lunar inclination moonfacetAngle; obtaining a plane M3 by using lower waist vertex coordinates p140 and p80 and a lunar inclination moonfacetAngle; obtaining a plane M4 by using lower waist vertex coordinates p80 and p84 and a lunar inclination moonfacetAngle; obtaining a plane M5 by using lower waist vertex coordinates p84 and p88 and a lunar inclination moonfacetAngle; the plane M6 is obtained from the lower lumbar apex coordinates p88, p92 and the lunar inclination moonfacetAngle.
(6.2) the lunar cross-sectional plane plM can be determined from the lower lumbar apex coordinates p92, p132 and the lunar transverse angle moonRotateangle.
(6.3) obtaining coordinates of a three-plane intersection point according to the plane intersection point, wherein the coordinates are p 152= [ M1, M2, plM ]; p152= [ M1, M2, plM ] coordinates of the three-plane intersection point; p153= [ M2, M3, plM ] coordinates of the three-plane intersection point; p 144= [ M3, M4, plM ] coordinates of the three-plane intersection point; the coordinates of p145 to p151 are then found by mirroring.
(7) The coordinates of the bottom peak point p162 and the pavilion peaks p154 to p161 are calculated as the coordinates of the bottom peak point, the normal vector and the fixed point are set according to the lower waist peak point coordinates, the pavilion depth ratio pavilion height and the pavilion ratio rate on the three-dimensional coordinate axis in the step (6), then the plane where the pavilion peak is located is obtained according to the normal vector and the fixed point, and the coordinates of the pavilion peak on the three-dimensional coordinate axis are obtained according to the intersection point of the plane and the straight line and the mirror image.
Referring to fig. 3, the specific calculation method includes the steps of:
the base parameters pavilion depth versus pavilion height, pavilion ratio (pavilion/pavilion depth), and lower lumbar vertex p80 to p143 coordinates.
(7.1), bottom-cusp vertex coordinates p162=vector 3 (0, 0, -pavilion height).
(7.2) plane2 in which p154 to p161 lie is obtained from the normal vector (0, 1) and the setpoint (0, -pavilion Rate x pavilion height).
(7.3) obtaining coordinates of p160= [ line (p 162, p 128), plane2] straight line and plane intersection point, p159= [ line (p 162, p 151), plane2] straight line and plane intersection point, p158= [ line (p 162, p 149), plane2] straight line and plane intersection point, and obtaining coordinates of p157, p156, p155, p154 and p161 by mirror image.
(8) And forming a coordinate file format which can be opened by an OBJ file format or other 3D model drawing software based on the coordinates of the upper lumbar vertex, the lower lumbar vertex, the crown vertex, the crescent plane vertex, the pavilion vertex and the bottom tip vertex, and forming the 3D model by a three-dimensional modeling tool. The three-dimensional modeling tool is 3D model drawing software such as 3D MAX, MAYA, pro/E and the like.
Ten parameter values are entered as the following values as an example.
Parameter name (symbol) Numerical value
Aspect ratio of girdle lw 1.5
Tangential angle of line σ 5°
Waist-to-thickness ratio girdleThickness 0.04
Crown angle crownAngle 34°
Ratio of table width crownTable 0.551
Length ratio of table tableLength 0.68
Pavilion depth ratio pavilionHeight 0.43
Exhibition hall ratio pavilionRate 0.77
Inclination angle of lunar surface moonFacetAngle 54°
Lunar surface transverse inclination angle moonRotateAngle 17°
Based on the method, the vertex coordinates of the ship-shaped diamond are output.
Crown vertices p0-p15:
[0.27549999999999997， 0， 0.1914271620311248]
[0.1754772845267617， -0.3785956514694411，0.1914271620311248]
[0， -0.51， 0.1914271620311248]
[-0.1754772845267617， -0.3785956514694411，0.1914271620311248]
[-0.27549999999999997， 0， 0.1914271620311248]
[-0.1754772845267617， 0.3785956514694411，0.1914271620311248]
[0， 0.51， 0.1914271620311248]
[0.1754772845267617， 0.3785956514694411， 0.1914271620311248]
[0.33255791821689384， -0.2462189916559264，0.15294111024053123]
[0.10350854125929734， -0.5709973290514678，0.15294111024053123]
[-0.10350854125929734， -0.5709973290514678，0.15294111024053123]
[-0.33255791821689384， -0.2462189916559264， 0.15294111024053123]
[-0.33255791821689384， 0.2462189916559264，0.15294111024053123]
[-0.10350854125929734， 0.5709973290514678，0.15294111024053123]
[0.10350854125929734， 0.5709973290514678，0.15294111024053123]
[0.33255791821689384， 0.2462189916559264， 0.15294111024053123]
upper lumbar apex p16-p79:
[0.5， 0， 0.04]
[0.49696473315926115， -0.0732898144119806， 0.04]
[0.4878858854935463， -0.14592882283077405， 0.04]
[0.47284407623377434， -0.21727199835329142， 0.04]
[0.4519728750948253， -0.28668582093891604， 0.04]
[0.43078245858429187， -0.3413930710151501， 0.04]
[0.40596849418290426， -0.39408691629251325， 0.04]
[0.3776773250922283， -0.4444565887737615， 0.04]
[0.34607580172736885， -0.49220502753733075， 0.04]
[0.3072166026222314， -0.5419497848563444， 0.04]
[0.264767925912775， -0.5877313282323754， 0.04]
[0.21904019369362332， -0.6292148627155797， 0.04]
[0.17036780740006785， -0.6660970241809735， 0.04]
[0.12975790722656527， -0.6919842348405751， 0.04]
[0.08769571817486738， -0.7146646468477592， 0.04]
[0.04437616516432549， -0.7340331544631189， 0.04]
[0， -0.7500000000000001， 0.04]
[-0.04437616516432549， -0.7340331544631189， 0.04]
[-0.08769571817486738， -0.7146646468477592， 0.04]
[-0.12975790722656527， -0.6919842348405751， 0.04]
[-0.17036780740006785， -0.6660970241809735， 0.04]
[-0.21904019369362332， -0.6292148627155797， 0.04]
[-0.264767925912775， -0.5877313282323754， 0.04]
[-0.3072166026222314， -0.5419497848563444， 0.04]
[-0.34607580172736885， -0.49220502753733075， 0.04]
[-0.3776773250922283， -0.4444565887737615， 0.04]
[-0.40596849418290426， -0.39408691629251325， 0.04]
[-0.43078245858429187， -0.3413930710151501， 0.04]
[-0.4519728750948253， -0.28668582093891604， 0.04]
[-0.47284407623377434， -0.21727199835329142， 0.04]
[-0.4878858854935463， -0.14592882283077405， 0.04]
[-0.49696473315926115， -0.0732898144119806， 0.04]
[-0.5， 0， 0.04]
[-0.49696473315926115， 0.0732898144119806， 0.04]
[-0.4878858854935463， 0.14592882283077405， 0.04]
[-0.47284407623377434， 0.21727199835329142， 0.04]
[-0.4519728750948253， 0.28668582093891604， 0.04]
[-0.43078245858429187， 0.3413930710151501， 0.04]
[-0.40596849418290426， 0.39408691629251325， 0.04]
[-0.3776773250922283， 0.4444565887737615， 0.04]
[-0.34607580172736885， 0.49220502753733075， 0.04]
[-0.3072166026222314， 0.5419497848563444， 0.04]
[-0.264767925912775， 0.5877313282323754， 0.04]
[-0.21904019369362332， 0.6292148627155797， 0.04]
[-0.17036780740006785， 0.6660970241809735， 0.04]
[-0.12975790722656527， 0.6919842348405751， 0.04]
[-0.08769571817486738， 0.7146646468477592， 0.04]
[-0.04437616516432549， 0.7340331544631189， 0.04]
[0， 0.7500000000000001， 0.04]
[0.04437616516432549， 0.7340331544631189， 0.04]
[0.08769571817486738， 0.7146646468477592， 0.04]
[0.12975790722656527， 0.6919842348405751， 0.04]
[0.17036780740006785， 0.6660970241809735， 0.04]
[0.21904019369362332， 0.6292148627155797， 0.04]
[0.264767925912775， 0.5877313282323754， 0.04]
[0.3072166026222314， 0.5419497848563444， 0.04]
[0.34607580172736885， 0.49220502753733075， 0.04]
[0.3776773250922283， 0.4444565887737615， 0.04]
[0.40596849418290426， 0.39408691629251325， 0.04]
[0.43078245858429187， 0.3413930710151501， 0.04]
[0.4519728750948253， 0.28668582093891604， 0.04]
[0.47284407623377434， 0.21727199835329142， 0.04]
[0.4878858854935463， 0.14592882283077405， 0.04]
[0.49696473315926115， 0.0732898144119806， 0.04]
lower lumbar apex p80-143:
[0.5， 0， 0]
[0.49696473315926115， -0.0732898144119806， 0]
[0.4878858854935463， -0.14592882283077405， 0]
[0.47284407623377434， -0.21727199835329142， 0]
[0.4519728750948253， -0.28668582093891604， 0]
[0.43078245858429187， -0.3413930710151501， 0]
[0.40596849418290426， -0.39408691629251325， 0]
[0.3776773250922283， -0.4444565887737615， 0]
[0.34607580172736885， -0.49220502753733075，0]
[0.3072166026222314， -0.5419497848563444， 0]
[0.264767925912775， -0.5877313282323754， 0]
[0.21904019369362332， -0.6292148627155797， 0]
[0.17036780740006785， -0.6660970241809735， 0]
[0.12975790722656527， -0.6919842348405751， 0]
[0.08769571817486738， -0.7146646468477592， 0]
[0.04437616516432549， -0.7340331544631189， 0]
[0， -0.7500000000000001， 0]
[-0.04437616516432549， -0.7340331544631189， 0]
[-0.08769571817486738， -0.7146646468477592， 0]
[-0.12975790722656527， -0.6919842348405751， 0]
[-0.17036780740006785， -0.6660970241809735， 0]
[-0.21904019369362332， -0.6292148627155797， 0]
[-0.264767925912775， -0.5877313282323754， 0]
[-0.3072166026222314， -0.5419497848563444， 0]
[-0.34607580172736885， -0.49220502753733075， 0]
[-0.3776773250922283， -0.4444565887737615， 0]
[-0.40596849418290426， -0.39408691629251325， 0]
[-0.43078245858429187， -0.3413930710151501， 0]
[-0.4519728750948253， -0.28668582093891604， 0]
[-0.47284407623377434， -0.21727199835329142， 0]
[-0.4878858854935463， -0.14592882283077405， 0]
[-0.49696473315926115， -0.0732898144119806， 0]
[-0.5， 0， 0]
[-0.49696473315926115， 0.0732898144119806， 0]
[-0.4878858854935463， 0.14592882283077405， 0]
[-0.47284407623377434， 0.21727199835329142， 0]
[-0.4519728750948253， 0.28668582093891604， 0]
[-0.43078245858429187， 0.3413930710151501， 0]
[-0.40596849418290426， 0.39408691629251325， 0]
[-0.3776773250922283， 0.4444565887737615， 0]
[-0.34607580172736885， 0.49220502753733075， 0]
[-0.3072166026222314， 0.5419497848563444， 0]
[-0.264767925912775， 0.5877313282323754， 0]
[-0.21904019369362332， 0.6292148627155797， 0]
[-0.17036780740006785， 0.6660970241809735， 0]
[-0.12975790722656527， 0.6919842348405751， 0]
[-0.08769571817486738， 0.7146646468477592， 0]
[-0.04437616516432549， 0.7340331544631189， 0]
[0， 0.7500000000000001， 0]
[0.04437616516432549， 0.7340331544631189， 0]
[0.08769571817486738， 0.7146646468477592， 0]
[0.12975790722656527， 0.6919842348405751， 0]
[0.17036780740006785， 0.6660970241809735， 0]
[0.21904019369362332， 0.6292148627155797， 0]
[0.264767925912775， 0.5877313282323754， 0]
[0.3072166026222314， 0.5419497848563444， 0]
[0.34607580172736885， 0.49220502753733075， 0]
[0.3776773250922283， 0.4444565887737615， 0]
[0.40596849418290426， 0.39408691629251325， 0]
[0.43078245858429187， 0.3413930710151501， 0]
[0.4519728750948253， 0.28668582093891604， 0]
[0.47284407623377434， 0.21727199835329142， 0]
[0.4878858854935463， 0.14592882283077405， 0]
[0.49696473315926115， 0.0732898144119806， 0]
crescent plane vertex p144-p153:
[0.4394066140639689， 2.220446049250313e-16，-0.08225341770017924]
[0.40245811039371715， -0.27022851305346735， -0.07095712649419542]
[0.319108098298496， -0.4724104445198345，-0.04547447049673579]
[-0.319108098298496， -0.4724104445198345，-0.04547447049673579]
[-0.40245811039371715， -0.27022851305346735，-0.07095712649419542]
[-0.4394066140639689， 2.220446049250313e-16，-0.08225341770017924]
[-0.40245811039371715， 0.27022851305346735，-0.07095712649419542]
[-0.319108098298496， 0.4724104445198345，-0.04547447049673579]
[0.319108098298496， 0.4724104445198345，-0.04547447049673579]
[0.40245811039371715， 0.27022851305346735，-0.07095712649419542]
pavilion vertex p154-p161:
[0.12496834287636052， 6.315004242989771e-17， -0.3311]
[0.08207463094190563， -0.12150400787008088， -0.3311]
[-6.3837823915946496e-18， -0.17250000000000001， -0.3311]
[-0.08207463094190563， -0.12150400787008088， -0.3311]
[-0.12496834287636052， 6.315004242989771e-17， -0.3311]
[-0.08207463094190563， 0.12150400787008088， -0.3311]
[-6.3837823915946496e-18， 0.17250000000000001， -0.3311]
[0.08207463094190563， 0.12150400787008088， -0.3311]
bottom spike point p162:
[0， 0， -0.43]。
the foregoing is merely illustrative of specific embodiments of the present invention, but the design concept of the present invention is not limited thereto, and any insubstantial modification of the present invention by using the design concept shall fall within the scope of the present invention.

Claims (4)

1. The ship type diamond cutting model generation method is characterized by comprising the following steps of:
(1) Setting 163 vertexes of the boat-shaped diamond, wherein the vertexes comprise p0 to p162, and the vertexes comprise 64 upper waist vertexes, 64 lower waist vertexes, 16 crown vertexes, 10 crescent surface vertexes, 8 pavilion vertexes and 1 pavilion vertex; setting ten parameter values, namely: the girdle aspect ratio lw, tangential angle sigma, girdle thickness ratio girdleThickness, crown angle crownAngle, table width ratio crownTable, table length ratio tableLength, pavilion depth ratio pavilion height, pavilion ratio, lunar tilt angle moonfacet angle, lunar transverse tilt angle moonfataangle;
(2) Constructing a two-dimensional coordinate axis, an ellipse and an inscribed circle of the ellipse, wherein the included angle between the tangent line of the inscribed circle and the tangent line of the ellipse is the tangent angle sigma, the coordinate of the ellipse is (x 0, y 0), the ellipse is copied to form two ellipses, and the two ellipses are intersected to form a ship-shaped diamond girdle profile; the upper waist vertex consists of p16 to p79, and takes one upper waist vertex with the largest x-axis coordinate value of the girdle outline as p16, and the p16 to p79 are sequentially arranged on the girdle outline of the boat-shaped diamond according to the x-axis coordinate value from large to small; the lower waist vertex consists of p80 to p143, and an upper waist vertex with the largest x-axis coordinate value of the girdle outline is taken as p80, and the p80 to p143 are sequentially arranged on the girdle outline of the boat-shaped diamond according to the x-axis coordinate value from large to small; crown apex consists of p0 to p 15; the crescent plane vertex is composed of p144 to p 153; pavilion top is composed of p154 to p161, and bottom top is p162;
(3) Setting a girdle contour center O as an origin, setting a transverse x-axis and a vertical y-axis on the two-dimensional coordinate axis in the step (2), setting A, B, C three-point coordinates, wherein OC=1, OB=girdle length-width ratio lw, and calculating coordinates (x, y) of a lower girdle vertex on the two-dimensional coordinate axis according to the girdle length-width ratio lw and a tangential angle sigma through a triangle mathematical formula and an ellipse parameter equation; based on the two-dimensional coordinate axis, adding a z axis, constructing a three-dimensional coordinate axis, setting the z axis coordinate of the lower lumbar vertex to be 0, and obtaining the lower lumbar vertex coordinate (x, y, z=0); wherein, the coordinate calculation method of the lower waist vertex on the two-dimensional coordinate axis comprises the following steps,
(3.1) obtaining ao×ao+ob×ob=ab×ab by triangle pythagorean theorem, wherein ab=ac=ao+1, and deriving s=ao= (lw×lw-1)/2;
(3.2) setting an F point and an M point on an x axis, and obtaining the angle OAB= angle OBF according to the triangle similarity, wherein fi is the angle OBF, and fi=asin (lw/(s+1));
(3.3) setting t to OM, and obtaining t=lw×tan (fi+σ) according to a trigonometric function;
(3.4) setting a as an elliptic transverse half shaft, b as an elliptic vertical half shaft, obtaining a= (t-1)/(t-2) according to the tangential nature of the ellipse,；
(3.5) obtaining x=x0+a×cos (theta) according to an elliptic parameter equation, y=y0+b×sin (theta), wherein theta is a corresponding angle of a waist vertex, so as to obtain coordinates (x, y) of p80 to p96 in a two-dimensional coordinate axis, and then obtaining coordinates (x, y) of p97 to p143 in the two-dimensional coordinate axis through mirror image;
(4) On the three-dimensional coordinate axis in the step (3), the x-axis and y-axis coordinates of the upper waist vertex are consistent with those of the lower waist vertex, the z-axis of the upper waist vertex is the waist thickness ratio girdleThickness, and the upper waist vertex coordinates (x, y, z=girdlethickness) are obtained;
(5) Setting normal vectors and fixed points on the three-dimensional coordinate axis in the step (4) according to the upper waist vertex coordinates, the parameter waist thickness ratio girdleThickness, crown angle crownage, table width ratio crownTable and table length ratio table length, obtaining a plane where the crown vertex is located by the normal vectors and the fixed points, and obtaining the coordinates of the crown vertex on the three-dimensional coordinate axis according to the intersection point and mirror image of the plane;
(6) On the three-dimensional coordinate axis in the step (5), obtaining a lunar plane and a lunar cross-section plane according to the lower waist vertex coordinates, the lunar inclination moonfacetAngle and the lunar transverse inclination moonRotateenge, and obtaining the coordinates of the lunar vertex on the three-dimensional coordinate axis according to the plane intersection point and the mirror image;
(7) Setting a bottom peak point coordinate, a normal vector and a fixed point on the three-dimensional coordinate axis in the step (6) according to the lower waist peak point coordinate, the pavilion depth ratio pavilion height and the pavilion ratio rate, obtaining a plane where the pavilion peak is located according to the normal vector and the fixed point, and obtaining the coordinate of the pavilion peak on the three-dimensional coordinate axis according to the intersection point of the plane and the straight line and the mirror image;
(8) And forming a 3D model by a three-dimensional modeling tool based on the coordinates of the upper lumbar vertex, the lower lumbar vertex, the crown vertex, the crescent plane vertex, the pavilion vertex and the base tip vertex.
2. The method for generating a ship-shaped diamond cutting model according to claim 1, wherein the method comprises the following steps: the coordinate calculation method of the crown vertexes p0 to p15 in the step (5) on the three-dimensional coordinate axis comprises the following steps:
(5.1), setting parameters zmax=girdlethickness+0.5x tan (crownAngle), parametersParameter z= (girdetherickness-zMax) ×m+zmax;
(5.2), setting a coordinate top=vector 3 (0, zmax), and a coordinate p6=vector 3 (0, -lwχtablelength/2, 0.5x tan (crownAngle) × (1-crownTable) +girdlethickness); wherein Vector3 is a three-dimensional Vector coordinate;
(5.3) obtaining plane0 where p0 to p7 are located from the normal vector (0, 1) and the fixed point coordinate p 6; plane1 where p8 to p15 are located is obtained by normal vector (0, 1) and fixed point (0, Z), plane pl1 is obtained by normal vector sub (p 69, p 67) and fixed point p68, plane pl2 is obtained by normal vector sub (p 77, p 75) and fixed point p76, plane pl A is obtained by normal vector (vector 3 (1, 0), sub (p 6, p 64)) and fixed point p6, and plane pl C is obtained by normal vector (vector 3 (0, 1, 0), sub (top, p 16)) and fixed point top;
(5.4) obtaining coordinates of a plane intersection point p14= [ plane1, pl1, plA ] three-plane intersection point, and coordinates of a plane intersection point p15= [ plane1, pl2, plA ] three-plane intersection point, and obtaining coordinates of p8 to p13 through mirror images;
(5.5) obtaining a plane plB by coordinates of three points p14, p15 and p 72; the normal vector sub (p 14, p 15) and the middle point thereof are used as fixed points to obtain a plane pl3; setting a YOZ plane of the three-dimensional coordinate axis as a plane pl4;
(5.6) obtaining coordinates of the intersection points of the three planes according to the intersection points of the planes, wherein the coordinates of the intersection points of the three planes are p7= [ plane0, pl3 and plB ], the coordinates of the intersection points of the three planes are p0= [ plane0, pl4 and pl C ], and the coordinates of p1 to p5 are obtained through mirror images.
3. The method for generating a ship-shaped diamond cutting model according to claim 1, wherein the method for calculating coordinates of the crescent plane vertices p144 to p153 in the step (6) on three-dimensional coordinate axes comprises the following steps:
(6.1) obtaining a plane M1 from lower lumbar vertex coordinates p132, p136 and a moon inclination moonfacetAngle; obtaining a plane M2 by using lower waist vertex coordinates p136 and p140 and a lunar inclination moonfacetAngle; obtaining a plane M3 by using lower waist vertex coordinates p140 and p80 and a lunar inclination moonfacetAngle; obtaining a plane M4 by using lower waist vertex coordinates p80 and p84 and a lunar inclination moonfacetAngle; obtaining a plane M5 by using lower waist vertex coordinates p84 and p88 and a lunar inclination moonfacetAngle; obtaining a plane M6 by using lower waist vertex coordinates p88 and p92 and a lunar inclination moonfacetAngle;
(6.2) from the lower lumbar apex coordinates p92, p132 and the lunar transverse angle moonRotateangle, a lunar cross-sectional plane plM can be found;
(6.3) obtaining coordinates of a three-plane intersection point according to the plane intersection point, wherein the coordinates are p 152= [ M1, M2, plM ]; p152= [ M1, M2, plM ] coordinates of the three-plane intersection point; p153= [ M2, M3, plM ] coordinates of the three-plane intersection point; p 144= [ M3, M4, plM ] coordinates of the three-plane intersection point; the coordinates of p145 to p151 are then found by mirroring.
4. The method for generating a ship-shaped diamond cutting model according to claim 1, wherein the method for calculating coordinates of the bottom peak point p162 and pavilion peaks p154 to p161 in the step (7) on three-dimensional coordinate axes comprises the steps of:
(7.1), bottom spike point coordinates p162=vector 3 (0, 0, -pavilion height);
(7.2) obtaining plane2 in which p154 to p161 are located from normal vector (0, 1) and fixed point (0, -pavilion rate x pavilion height);
(7.3) obtaining a coordinate p160= [ line (p 162, p 128), plane2] according to the intersection point of the line and the plane, wherein the line (p 162, p 128) is a straight line passing through two points of the p162 and the p 128; p159= [ line (p 162, p 151), plane2] straight line intersects with the plane, wherein line (p 162, p 151) is a straight line passing through both points p162 and p 151; p158= [ line (p 162, p 149), plane2] straight line intersects with the plane, wherein line (p 162, p 149) is a straight line passing through two points of p162 and p149, and coordinates of p157, p156, p155, p154 and p161 are obtained by mirroring.
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