JPH10320583A - Method for compressing and expanding data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for compressing and expanding data that can deal with a three-dimensional basic primitive shape as a circumscribed rectangular parallelepiped information which reduces the amount of data. SOLUTION: Taking the shape of primitive P as information on a circumscribed rectangular parallelepiped CR of a rectangular parallelepiped or a cylinder, this circumscribed rectangular parallelepiped information compresses data by calculating a reference point B of a vertex coordinate of each vertex's coordinate of the circumscribed rectangular parallelepiped and three vectors that indicate from each vertex coordinate the width (w), the height (h) and the depth (d) and expands the data by calculating each vertex coordinate information from the reference point and the three vectors.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for compressing and expanding data of a three-dimensional basic primitive shape using circumscribed cuboid information in three-dimensional computer graphics (3DCG).

[0002]

2. Description of the Related Art With the improvement of graphics processing performance of computers, various three-dimensional simulation systems using three-dimensional computer graphics have begun to be applied to industry. In a three-dimensional simulation system,
Model a real or imaginary object (three-dimensional CAD) and simulate space (virtual space)
They are placed on top.

Further, by setting a viewpoint of a camera or the like in a simulation space, an object in the simulation space viewed from the viewpoint is displayed on a display of a computer. People watching the display can simulate the model as if they were watching the reality.

[0004] A basic element constituting such a three-dimensional application is a three-dimensional model, which is often basically composed of basic primitives such as a rectangular parallelepiped, a cylinder and a sphere. That is, the object to be modeled is divided into a plurality of basic primitive shapes, and a three-dimensional primitive shape is applied to each of the basic primitives. The shape parameters of this primitive are its vertex coordinate group (set of three-dimensional coordinates).

Therefore, a three-dimensional application reads three-dimensional shape data stored as vertex coordinates and executes a three-dimensional simulation based on the vertex coordinates.

In recent years, with the development of a network environment such as an internetwork, a server-client type computer technology has become widespread. The client computer sends a request to search and acquire information to the server computer, and the result of the request is sent from the server to the client via the network. As the three-dimensional application, a type in which a three-dimensional model is placed on a computer on a server side and a client side downloads required three-dimensional data from a server has become widespread.

[0007]

When three-dimensional model data composed of basic primitive shapes is stored on a computer based on the coordinate values of its vertices, the problem is the large amount of data.

[0008] The larger the amount of data, the larger the data capacity occupied by the external storage device (usually a hard disk) of the computer in which it is stored. In an application that downloads three-dimensional model information via a network, the time required for the model data to be transmitted over the network increases, and it takes time to read the data of the three-dimensional model.

For example, the data volume of a rectangular parallelepiped is 96 bytes as follows.

Number of vertices 8 (pieces) × three-dimensional coordinate value 3 (x,
(y, z coordinates) × floating point data size 4 (bytes) = 96 bytes.

A cylinder is usually represented by a polygonal cylinder, but at least a dodecagonal prism is required to be displayed like a cylinder. When a cylinder is approximated by a dodecagon, the data amount becomes 288 bytes as follows.

Number of vertices 24 (12 × 2) × three-dimensional coordinate value 3
X Floating point data size 4 (bytes) = 288 bytes.

However, in the above example, the coordinate value is represented by a floating point number, and the data size of the floating point number is based on 4 bytes of a single precision floating point number handled by a normal computer.

In the three-dimensional model constituted by these primitive shapes, the number of constituent primitives increases as the model shape becomes more complicated. As a result, the capacity of the model data increases, the network transmission time increases, and the model data reading time increases. A vicious cycle occurs: increase → decrease in application comfort.

An object of the present invention is to provide a data compression / expansion method capable of treating a three-dimensional basic primitive shape as circumscribed cuboid information with a reduced data amount.

[0016]

SUMMARY OF THE INVENTION The present invention reduces the data capacity of a primitive shape by converting and compressing the information of the basic primitive shape to minimum circumscribed cuboid information and reconstructable minimum parameter values. And restores the original basic primitive shape from the obtained information, and is characterized by the following method.

(First Invention) In expressing an object of computer graphics as a set of primitives of a rectangular parallelepiped or a cylinder in a three-dimensional model, and treating the primitive shape as circumscribed rectangular parallelepiped or cylindrical circumscribed cuboid information, Is compressed by calculating a reference point B, which is one vertex coordinate of each vertex coordinate of the circumscribed cuboid, and three vectors indicating the width w, height h, and depth d of the circumscribed cuboid from each vertex coordinate, Data expansion is performed by calculating each vertex coordinate information from the reference point and three vectors.

[0018] The circumscribed cuboid information (second invention) rectangular parallelepiped, one vertex V ₄ of a rectangular parallelepiped of each vertex as the reference point B, the coordinate information of the other vertex V ₀ ~V ₇ that faces the reference point The data compression for calculating three vectors w, h, and d by the following equation is used as follows: B = V ₄ w = V ₇ −V ₄ h = V ₀ −V ₄ d = V ₅ −V ₄ Equation: V _i = B + δ _wi w + δ _hi h + δ _di d where δ _wi = 0 (i = 0, 1, 4, 5) 1 (i = 2, 3, 6, 7) δ _hi = 0 (i = 4, 5,6,7) 1 (i = 0,1,2,3) δ _di = 0 (i = 0,3,4,7) 1 (i = 1,2,5,6) and wherein data expansion to be converted to V _i.

(Third Invention) The circumscribed rectangular parallelepiped information of a regular n-sided prism or a cylinder other than a rectangular parallelepiped is represented by vertices V _{0 to} V _{n-1 on the} upper surface.
And each vertex of the lower surface V _n ~V reference point B from _2n-1 of the coordinate information from the following equation and the three vectors w, h, and data compression for calculating the _{d, h = C t -C b} d = 2 (V _n− C _b ) w = 2R (p / | p |) B = C _b − (w + d) / 2 where C _{b is} the center of the circumscribed circle of the regular n-gon forming the base R: positive n forming the base radius C _t prismatic circumcircle: center of regular n-sided polygon constituting the upper surface p: outer product of h and d | p |: the following formula from the magnitude circumscribed cuboid information of the vector _{p, V i = C b +} sin (2π (In) / n) w / 2 + co
s (2π (i−n) / n) d / 2 (i = n to 2n−
1) V _i = V _{i + n} + h (i = _{0 to n} −1) where Cb is the data extension that is converted into the coordinates of each vertex V _i on the bottom and top surfaces according to the center coordinates of the bottom surface.

(Fourth Invention) The circumscribed rectangular parallelepiped information of a regular n pyramid or a cone is obtained from the coordinate information of the vertex V ₀ and each of the vertices V _{1 to} V _{n on} the bottom surface by the following equation and a reference point B and three vectors w,
h = d ₀ -C _b d = 2 (V ₁ −C _b ) w = 2R (p / | p |) B = C _b − (w + d) / 2 _b : the center of the circumscribed circle of the regular n-gon forming the bottom surface R: the radius of the circumscribed circle of the regular n-gon forming the bottom surface p: the outer product of h and d | p |: the magnitude of the vector p Formula: V _i = C _b + sin (2π (i−1) / n) w / 2 + co
s (2π (i-1) / n) d / 2 (i = 1~n) V 0 = C b + h where, C _b: each vertex of the bottom surface to the center coordinates of the bottom coordinate V _i and vertex coordinates V ₀ It is characterized by data expansion to be converted.

[0021] (fifth invention) the circumscribed rectangular information of the positive n truncated pyramid or truncated cone, from the vertex V ₀ ~V _n-1 and the lower surface of the coordinate information of each vertex V _n ~V _2n-1 of the upper surface The reference point B is given by the following equation
And the three vectors w, h, d are calculated as follows: h = V ₀ −C _b d = 2 (V ₀ −C _t ) (when t ≧ 1) d = 2 (V _n −C _b ) (When t <1) w = 2R _t (p / | p |) (when t ≧ 1) w = 2R _b (p / | p |) (when t <1) B = C _t − (w + d) ) −2−h (when t ≧ 1) B = C _b − (w + d) / 2 (when t <1) where C _b : the center of a circumscribed circle of a regular n-sided polygon forming the bottom surface R _b : the bottom surface The radius of the circumscribed circle of the regular n-gon forming the upper surface C _t : the center of the circumscribed circle of the regular n-gon forming the upper surface R _t : the radius of the circumscribed circle of the regular n-gon forming the upper surface p: the outer product of h and d | p |: the magnitude of the vector p t: (for t ≧ 1) similarity ratio of regular n-sided bottom and top from the circumscribed cuboid information following equation, the vertex of the upper surface coordinate _{V i V i = C t +} sin (2πi / n ) W / 2 + cos (2π
i / n) d / 2 ( i = 0~n-1) when the vertex coordinates V _i (t ≧ 1 _{bottom) V i = C b + t} (V in -C t) (i = n~2n-1 ) Top surface vertex coordinates V _i (when t <1) V _i = C _t + t (V _{i + n} −C _b ) (i = _{0 to n} −1) Bottom surface vertex coordinates V _i (when t <1) ) V _i = C _b + sin (2π (in) / n) w / 2 + co
s (2π (in) / n) d / 2 (i = n to 2n−
1) However, C _t: center coordinates of the upper surface C _b: and wherein data expansion to be converted by the center coordinates of the bottom surface to the top surface and each vertex coordinate V _i of the bottom surface.

(Sixth invention) The circumscribed rectangular parallelepiped information of a sphere represented by a triangle and a rectangle as the number of divisions of longitude m and the number of divisions of latitude n is represented by the north pole V ₀ , south pole V _1, and other vertices V ₂ to V
Data compression for calculating a reference point B and three vectors w, h, and d from the coordinate information of _{m (n-1) according} to the following equation: h = V ₀ −V ₁ w = 2R (p / | p |) d = 2R (p / | p | ) B = C- (w + h + d) / 2 where, R: radius of the sphere C: the center of the sphere p: outer product of h and _{(V 2 -C) | p |} : vector p size From this circumscribed cuboid information, the following equation is obtained: V ₀ = B + (w + d) / 2 + h V ₁ = V ₀ −h V _{mi + j + 2} = C + cos (2πj / m) sin (2πi /
n) w / 2 + cos (2πi / n) h / 2 + sin (2
πj / m) sin (2πi / n) d / 2 (i = 0 to n−
2, j = 0 to m-1) where C is the center coordinate of the sphere, and the north pole coordinate V ₀ , the south pole coordinate V _1, and other coordinates V
_It features data decompression to convert to _{mi + j + 2} .

[0023]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First, circumscribed rectangular parallelepiped information of a primitive shape as a basis of the present invention will be described, and then an embodiment in which the present invention is applied to each basic primitive shape will be described. In the embodiment, a method of compressing data from vertex coordinates to circumscribed cuboid information and a compression ratio (compressed data capacity / original data capacity × 100) and a method of expanding data from circumscribed cuboid information to vertex information will be described in detail.

Note that the three-dimensional coordinate values shown in the embodiment use coordinate values in a right-handed coordinate system, and the data capacity of a primitive is indicated by the number of bytes occupied by the data. Further, single-precision floating-point data is used for data of a floating-point number, and the data size is 4 bytes each. For integer data, a signed integer is used and the data size is 4 bytes. Therefore, one three-dimensional coordinate value and three-dimensional vector value are composed of three floating-point elements x, y, and z, so that the data capacity is 12 bytes.

The circumscribed cuboid of the primitive is basically the one having the smallest volume value (indicated by CR) among the cuboids circumscribed to the primitive P as shown in FIG. The information amount indicating the circumscribed rectangular parallelepiped may use the vertex coordinates, but in the present invention, it is represented using one feature point and three vectors from the viewpoint of data amount reduction.

As feature points, as shown in FIG. 2, the coordinates of one vertex on the bottom surface of the circumscribed cuboid (hereinafter referred to as reference point B)
As the two vectors, vectors indicating the width, height, and depth of the circumscribed rectangular parallelepiped as shown in the figure (hereinafter, referred to as vectors w, h, and d, respectively) are defined as circumscribed rectangular parallelepiped information. Therefore,
Since the circumscribed rectangular parallelepiped information is composed of four three-dimensional parameters, its data size is 4 × 12 = 48 bytes.

In the present invention, a reference point B of a circumscribed cuboid and a vector w,
Vertex coordinate information is compressed by calculating h and d.
The vertex coordinate information is expanded by calculating the vertex coordinates of the primitive from the reference point B of the circumscribed rectangular parallelepiped and the vectors w, h, and d.

(First Embodiment) An embodiment in which the data compression / expansion method according to the present invention is applied to a rectangular parallelepiped will be described. The rectangular parallelepiped is a basic primitive in which each surface is rectangular as shown in FIG.

(4) Convert vertex coordinate information into circumscribed cuboid information
As shown in FIG. 3, the vertices of the rectangular parallelepiped are V _{0 to} V ₇
And number them. The conversion from the vertex coordinate information to the circumscribed rectangular parallelepiped information is executed by the following equation as a difference between the reference point and the vertex opposed thereto.

Reference point: B = V ₄ Width vector: w = V ₇ −V ₄ Height vector: h = V ₀ −V ₄ Depth vector: d = V ₅ −V ₄ ○ Compression ratio The number of vertices of the rectangular parallelepiped is eight. So the data capacity is 8 × 12 =
96 bytes. Since the circumscribed rectangular parallelepiped information is 48 bytes, the compressed data capacity is 48 bytes. Therefore, the compression ratio is 48 /
96 × 100 = 50%.

Conversion of circumscribed cuboid information into vertex coordinate information
The method of expanding the circumscribed cuboid information into the vertex coordinate information is based on the reference point B.
Is added to the width w, height h, and depth d for each vertex.

The vertex _{coordinates: V i = B + δ wi} w + δ hi h + δ di d _{However, δ wi = 0 (i =} 0,1,4,5) 1 (i = 2,3,6,7) δ hi = 0 ( i = 4, 5, 6, 7) 1 (i = 0, 1, 2, 3) δ _di = 0 (i = 0, 3, 4, 7) 1 (i = 1, 2, 5, 6) ( Second Embodiment An embodiment in which the data compression / expansion method according to the present invention is applied to a regular n prism (including a cylinder) other than a rectangular parallelepiped will be described. A regular n prism is a basic primitive in which a top surface and a bottom surface are congruent regular n prisms and the side surfaces are rectangular parallelepiped. FIG. 4 shows a case where n = 3 (a regular triangular prism).

Conversion of vertex coordinate information to circumscribed cuboid information
Vertices way positive n prism that compression is 2n, V ₀ ~V _n-1 each vertex numbers to top as shown in FIG. 5, Vn~V to the lower surface
Attach _2n-1 . The conversion from the vertex coordinate information to the circumscribed cuboid information is executed as follows.

The center and radius of the circumscribed circle of the equilateral n-gon forming the bottom surface are calculated by the following equations.

Center: C _b = ΣV _i / n (i = n〜2n−1) Radius: R = | V _n −C _b | (where || indicates an absolute value) A regular n-gon forming the upper surface Is calculated by the following equation.

Center: C _t = ΣV _i / n (i = 0 to n−1) The vectors h and d are calculated by the following equations.

[0037] calculating the _{h = C t -C b d =} 2 (V n -C b) the vector w by the following equation. Vector: p = h × d (where x indicates the cross product of vectors) w = 2R (p / | p |) (where || indicates the magnitude of the vector) The reference point B is calculated by the following equation .

B = C _b- (w + d) / 2 In order to restore the original regular n prism using the information on the circumscribed rectangular parallelepiped, information on the number n of the squares is necessary. Therefore, in the case of a regular n prism, the compressed information is the circumscribed rectangular parallelepiped information + the number of squares n.

Compression rate Since the number of vertices of a regular n prism is 2n, its data capacity is 2n ×
12 = 24n bytes. Since the circumscribed rectangular parallelepiped information is 48 bytes and the integer value indicating the number of corners is 4 bytes, the compressed data capacity is 52 bytes.

Therefore, the compression ratio is 52 / 24n × 100
= (216.67 / n)%. In the case of a cylinder, since the minimum value of n is usually about 12, compression of 18% or less is possible.

Conversion of circumscribed rectangular parallelepiped information to vertex coordinate information
The method of extending the information from the information of the circumscribed rectangular parallelepiped and the number of corners n to the vertex coordinate information is executed as follows.

The vertex coordinates V _i of the bottom surface (i = n〜2)
n-1) is calculated.

The center coordinates _{C b = B + (w +} d) of the bottom _{/ 2 V i = C b +} sin (2π (i-n) / n) w / 2 + co
s (2π (i−n) / n) d / 2 The vertex coordinates V _i (i = 0 to n−1) of the upper surface are calculated by the following equation.

V _i = V _{i + n} + h (Third Embodiment) An embodiment in which the data compression / expansion method according to the present invention is applied to a regular n pyramid (including a cone) will be described. A regular n pyramid is a basic primitive whose base is a regular n-gon and whose side is an isosceles triangle. In FIG. 6, n = 3
(A regular triangular pyramid).

Converting vertex coordinate information to circumscribed rectangular parallelepiped information
Vertices way regular n-sided pyramid of compression is n + 1, V ₀ the vertex to indicate each vertex number 7, the bottom surface to give a V ₁ ~V _n.
The conversion from the vertex coordinate information to the circumscribed cuboid information is executed as follows.

The center and radius of the circumscribed circle of the regular n-sided polygon forming the bottom surface are calculated by the following equations.

Center: C _b = ΣV _i / n (i = 1 to n) Radius: R = | V ₁ −C _b | (where || indicates an absolute value) Vectors h and d are calculated by the following equations. I do.

H = V ₀ −C _b d = 2 (V ₁ −C _b ) The vector w is calculated by the following equation.

Vector: p = h × d (where x indicates the cross product of vectors) w = 2R (p / | p |) (where || indicates the magnitude of the vector) Is calculated.

B = C _b- (w + d) / 2 In order to restore the original regular n pyramid using the information on the circumscribed rectangular parallelepiped, information on the number of angles n is necessary. Therefore, in the case of a regular n pyramid, the compressed information is the circumscribed rectangular parallelepiped information + the number of squares n.

Compression rate Since the number of vertices of a regular n pyramid is n + 1, its data capacity is (n
+1) x12 = 12n + 12 bytes. Since the circumscribed rectangular parallelepiped information is 48 bytes and the integer value indicating the number of corners is 4 bytes, the compressed data capacity is 52 bytes.

Therefore, the compression ratio is 52 / (12n + 1)
2) × 100 = (433.33 / (n + 1))% In the case of a cone, the minimum value of n is usually about 12,
Compression of 3.3% or less is possible.

(4) Convert the circumscribed cuboid information into vertex coordinate information
The method of extending the information from the information of the circumscribed cuboid and the number of corners n to the vertex coordinate conversion is executed as follows.

The vertex coordinates V _i of the bottom surface (i = 1 to
n) is calculated.

[0055] the center coordinates of the bottom _{C b = B + (w +} d) / 2 V i = C b + sin (2π (i-1) / n) w / 2 + co
s (2π (i−1) / n) d / 2 The vertex coordinates V ₀ are calculated by the following equation.

V ₀ = C _b + h (Fourth Embodiment) An embodiment in which the data compression / expansion method according to the present invention is applied to a regular n-frustum (including a truncated cone) will be described. The regular n-pyramidal frustum is a basic primitive having a regular n-sided shape with a similar upper surface and a lower surface and a trapezoidal shape on the side surface. FIG. 8 shows a case where n = 3 (a truncated regular triangular pyramid).

Conversion of vertex coordinate information to circumscribed cuboid information
Positive n angle frustum vertices of a method of compression is 2n, V ₀ ~V _n-1 each vertex numbers to top as shown in FIG. 9, V _n ~V to the lower surface
Attach _2n-1 . The conversion from the vertex coordinate information to the circumscribed cuboid information is executed as follows.

The center and the radius of the circumscribed circle of the regular n-gon forming the bottom surface are calculated by the following equations.

Center: C _b = ΣV _i / n (i = V _{n to} V _{2n -1} ) Radius: R _b = | V _n -C _b l (where || indicates an absolute value) The center and radius of the circumcircle of the regular n-gon are calculated by the following equation.

Center: C _t = ΣV _i / n (i = V _0-
V _n-1 ) radius: R _t = | V ₀ −C _t | (where || indicates an absolute value)
Ask for.

T = R _t / R _{b The} vectors h and d are calculated by the following equation.

When h = C _t −C _b t ≧ 1 (the upper regular n-gon is larger), d = 2
When (V ₀ −C _t ) t <1 (the regular n-gon on the bottom is larger), d = 2
(V _n -C _b) calculating a vector w by the following equation.

Vector: p = h × d (where x indicates the cross product of vectors) If t ≧ 1, w = 2R _t (p / | p |) (where |
Indicates the magnitude of the vector.) If t <1, w = 2R _b (p / | p |) The reference point B is calculated by the following equation.

When t ≧ 1, B = C _t − (w + d) / 2
In the case of −ht <1, B = C _b − (w + d) / 2 In order to restore the original frustum using the information of the circumscribed rectangular parallelepiped, the angle n and the kurtosis t I need information. Therefore, in the case of a regular n-sided pyramidal frustum, the compressed information is circumscribed rectangular parallelepiped information + the number of squares n + the kurtosis t.

Compression ratio Since the number of vertices of the regular n-frustum is 2n, the data capacity is 2n.
× 12 = 24n bytes. The circumscribed cuboid information is 48 bytes,
Since the integer value indicating the angle is 4 bytes and the floating point number indicating the kurtosis is 4 bytes, the compressed data capacity is 56 bytes.

Therefore, the compression ratio is 56 / 24n × 100
= (233.33 / n)%. In the case of a truncated cone, the minimum value of n is usually about 12, so that compression of 19.4% or less is possible.

Conversion of circumscribed rectangular parallelepiped information to vertex coordinate information
The method of extending the information from the information of the circumscribed rectangular parallelepiped and the number of corners n to the vertex coordinate information is executed as follows.

When t ≧ 1 (the upper regular n-gon is larger)
In this case, the vertex coordinates V on the upper surface are calculated by the following equation. _i(I = 0 to n-
1) is calculated.

[0069] upper surface of the center _{coordinates: C t = B + (w} + d) / 2 + h V i = C t + sin (2πi / n) w / 2 + cos (2π
i / n) d / 2 The vertex coordinates V _i (i = nｉ2n−1) of the bottom surface are calculated by the following equation.

[0070] bottom center _{coordinates: C b = C t -h V} i = C b + t (V in -C t) when t <1 for (the larger positive n rectangular bottom surface) of the bottom surface by the following equation The vertex coordinates V _i (i = n〜2n−1) are calculated.

[0071] bottom center _{coordinates: C b = B + (w} + d) / 2 V i = C b + sin (2π (i-n) / n) w / 2 + co
s (2π (in) / n) d / 2 The vertex coordinates V _i (i = 0 to n−1) of the upper surface are calculated by the following equation.

[0072] upper surface of the center coordinates: implementation of _{C t = C b + h V} i = C t + t (V i + n -C b) how the data compression and decompression according to the present invention (Fifth Embodiment) were applied to a sphere The form will be described. 3D CG
The sphere is represented by a triangle and a rectangle as shown in FIG.

Conversion of vertex coordinate information to circumscribed rectangular parallelepiped information
Compression method The number of longitude divisions (number of meridians) of a sphere is m, and the number of latitude divisions (latitude teaching)
Is n, the number of vertices of the sphere is m (n-1) +2, and each vertex number is V ₀ for the north pole, V ₁ for the south pole, and V _{2 to} V _{m ( n-1) +1} . The conversion from the vertex coordinate information to the circumscribed cuboid information is executed as follows.

The center and radius of the sphere are calculated by the following equations.

Center: C = (V ₀ + V ₁ ) / 2 Radius: R = | V ₀ -C | (where || indicates an absolute value) A vector h is obtained by the following equation.

[0076] determine the vector w by h = V ₀ -V _1-order equation.

Vector: p = h × (V ₂ −C) (where x indicates the cross product of vectors) w = 2R (p / │p│) (where | │ indicates the magnitude of the vector) The vector d is obtained by the equation.

Vector: p = w × h (where x indicates the cross product of vectors) d = 2R (p / │p│) (where | │ indicates the magnitude of the vector) Ask for.

B = C- (w + h + d) / 2 In order to restore the original sphere using the information on the circumscribed cuboid, information on the number of meridians m and the number of latitudes n is required. Therefore, in the case of a sphere, the compressed information is the circumscribed cuboid information + the number of meridians m + the number of latitude lines n.

Compression rate The number of longitude divisions (number of meridians) of a sphere is m, and the number of latitude divisions (number of latitudes)
Is n, the number of vertices of the sphere is m (n−1) +2, so its data capacity is (m (n−1) +2) × 12 = 12 (m
(N-1) +2) bytes. The circumscribed rectangular parallelepiped information is 48 bytes, and an integer value indicating the number of meridians and the number of latitude lines is 4 bytes each, and the compressed data capacity is 56 bytes.

Therefore, the compression ratio is 56/12 (m (n−
1) +2) × 100 = (466.67 / (m (n−1))
+2))%. Usually, the minimum value of m is 12, and the minimum value of n is about 6, so that compression of 7.5% or less is possible.

Conversion of circumscribed cuboid information to vertex coordinate information
The method of extending the information from the circumscribed cuboid + the number of meridians m + the number of latitude lines n to the vertex coordinate information is executed as follows.

The north pole coordinate V ₀ is calculated by the following equation.

V ₀ = B + (w + d) / 2 + h The coordinates V ₁ of the south pole are calculated by the following equation.

V ₁ = V ₀ -h Other coordinates V _{mi + j + 2} (i = 0 to n−2, j
= 0 to m-1).

Central coordinates of the sphere: C = B + (w + h + d) / 2 V _{mi + j + 2} = C + cos (2πj / m) sin (2πi /
n) w / 2 + cos (2πi / n) h / 2 + sin (2
πj / m) sin (2πi / n) d / 2

[0087]

As described above, according to the present invention, the information of the basic primitive shape is converted and compressed into the circumscribed rectangular parallelepiped information and the minimum restorable parameter value, and the original basic primitive shape is converted from the compressed information. Is restored, the data capacity of the primitive is reduced.

Further, by reducing the data capacity, (1) the external storage capacity of the computer in which the shape data is to be stored is reduced. (2) The amount of data transferred on the network is reduced.

In the data compression according to the present invention, since the compressed data is based on the circumscribed cuboid information,
Compression can be performed to a substantially constant data capacity regardless of the number of vertices of the original basic primitive.

[Brief description of the drawings]

FIG. 1 is an example of a primitive and a circumscribed cuboid.

FIG. 2 is an example of parameters of a circumscribed cuboid in the present invention.

FIG. 3 shows vertices of a rectangular parallelepiped.

FIG. 4 shows a primitive shape of a regular triangular prism.

FIG. 5 shows an example of a regular n prism and a circumscribed rectangular parallelepiped.

FIG. 6 shows a primitive shape of a regular triangular pyramid.

FIG. 7 is an example of a regular n pyramid and a circumscribed rectangular parallelepiped.

FIG. 8 shows a primitive shape of a truncated triangular pyramid.

FIG. 9 shows an example of a regular n-frustum and a circumscribed cuboid.

FIG. 10 shows a primitive shape of a sphere.

[Explanation of symbols]

 P: Primitive CR: Bounding cuboid

Claims (6)

[Claims] An object of computer graphics is represented by a three-dimensional model as a set of primitives of a rectangular parallelepiped or a cylinder, and the primitive shape is treated as circumscribed rectangular parallelepiped or cylindrical circumscribed cuboid information. The data is compressed by calculating three vectors indicating the width w, the height h, and the depth d of the circumscribed cuboid from each vertex coordinate, and the reference point B as one vertex coordinate of each vertex coordinate of A data compression / expansion method characterized by decompressing data by calculating each vertex coordinate information from three vectors. Wherein said circumscribed rectangular information cuboid, one vertex V ₄ of a rectangular parallelepiped of each vertex as the reference point B, the following equation from the coordinate information of the other vertex V ₀ ~V ₇ that faces the reference point three vectors w, h, and data compression for calculating the _{d, B = V 4 w =} V 7 -V 4 h = V 0 -V 4 d = V 5 -V 4 the following equation the circumscribed cuboid information, V _{i = B + δ wi w + δ} hi h + δ di d _{However, δ wi = 0 (i =} 0,1,4,5) 1 (i = 2,3,6,7) δ hi = 0 (i = 4,5,6, 7) conversion _{1 (i = 0,1,2,3) δ di} = 0 (i = 0,3,4,7) 1 (i = 1,2,5,6) by a rectangular vertex coordinates V _i 2. The data compression / expansion method according to claim 1, wherein the data is expanded. 3. The circumscribed rectangular parallelepiped information of a regular n-sided prism or a cylinder other than a rectangular parallelepiped is calculated from the coordinate information of each vertex V _{0 to} V _n-1 on the upper surface and each vertex V _{n to} V _{2n-1 on} the lower surface according to the following equation. Reference points B and 3
One of a vector w, h, and data compression for calculating the _{d, h = C t -C b} d = 2 (V n -C b) w = 2R (p / | p |) B = C b - (w + d) / 2 where C _b : the center of the circumscribed circle of the regular n-gon forming the bottom surface R: the radius of the circumscribed circle of the regular n-gon forming the bottom surface C _t : the center of the regular n-gon forming the top surface p: h and d cross product | p |: size following equation circumscribed cuboid information of the vector _{p, V i = C b +} sin (2π (i-n) / n) w / 2 + co
s (2π (i−n) / n) d / 2 (i = n to 2n−
_{1) V i = V i +} n + h (i = 0~n-1) where, Cb: to claim 1, wherein the data expansion to be converted by the center coordinates of the bottom surface to the bottom surface and each vertex coordinate V _i of the upper surface Data compression / expansion method described. 4. The circumscribed rectangular parallelepiped information of a regular n-pyramid or cone is obtained by calculating a reference point B and three vectors w, h, d from the coordinate information of the vertex V ₀ and the vertices V _{1 to} V _n of the bottom surface according to the following equation. and calculated data _{compression, h = V 0 -C b d} = 2 (V 1 -C b) w = 2R (p / | p |) B = C b - (w + d) / 2 where, C _b: a bottom The center of the circumscribed circle of the regular n-gon constituting R: the radius of the circumcircle of the regular n-gon constituting the base p: the outer product of h and d | p |: the magnitude of the vector p From this circumscribed cuboid information, V _i = C _b + sin (2π (i−1) / n) w / 2 + co
s (2π (i-1) / n) d / 2 (i = 1~n) V 0 = C b + h where, C _b: each vertex of the bottom surface to the center coordinates of the bottom coordinate V _i and vertex coordinates V ₀ The data compression / decompression according to claim 1, characterized in that the data to be converted is expanded.
Stretching method. 5. The circumscribed rectangular parallelepiped information of a regular n-frustum or a truncated cone includes vertices V _{0 to} V _n-1 on the upper surface and vertices V _n to V _n on the lower surface.
Data compression for calculating a reference point B and three vectors w, h, and d from the coordinate information of V _{2n -1} by the following equation: h = V ₀ −C _b d = 2 (V ₀ −C _t ) (t ≧ 1) d = 2 (V _n −C _b ) (when t <1) w = 2R _t (p / | p |) (when t ≧ 1) w = 2R _b (p / | p |) (When t <1) B = C _t − (w + d) / 2−h (when t ≧ 1) B = C _b − (w + d) / 2 (when t <1) where C _b : the bottom surface center R _b positive n-gon of the circumscribed circle constituting the radius of the regular n polygon circumscribed circle constituting the bottom C _t: center of regular n polygon circumscribed circle constituting the upper surface R _t: positive n-sided polygon constituting the upper surface The radius of the circumscribed circle of p: the outer product of h and d | p |: the magnitude of the vector p t: the similarity ratio of the regular n-gon on the bottom surface and the top surface From this circumscribed rectangular parallelepiped information, the following equation, the vertex coordinates V _i of the top surface (t ≧ 1) V _{i = C t + sin (2πi} / n) w / 2 + cos (2π
i / n) d / 2 ( i = 0~n-1) when the vertex coordinates V _i (t ≧ 1 _{bottom) V i = C b + t} (V in -C t) (i = n~2n-1 ) Top surface vertex coordinates V _i (when t <1) V _i = C _t + t (V _{i + n} −C _b ) (i = _{0 to n} −1) Bottom surface vertex coordinates V _i (when t <1) ) V _i = C _b + sin (2π (in) / n) w / 2 + co
s (2π (in) / n) d / 2 (i = n to 2n−
1) However, C _t: center coordinates of the upper surface C _b: Data compression and decompression method of claim 1, wherein the data expansion to be converted to each vertex coordinate V _i of the top and bottom surfaces to the center coordinates of the bottom surface. 6. The circumscribed rectangular parallelepiped information of a sphere represented by a triangle and a rectangle as the number m of longitude divisions and the number n of latitude divisions is the north pole V ₀ , the south pole V ₁ of the sphere, and other vertices V _{2 to} V _{m (n -1) From} the coordinate information, a reference point B and three vectors w, h, d
H = V ₀ −V ₁ w = 2R (p / | p |) d = 2R (p / | p |) B = C− (w + h + d) / 2 where R: radius of sphere C: Center of sphere p: Outer product of h and (V ₂ −C) | p |: Size of vector p From this circumscribed cuboid information, V ₀ = B + (w + d) / 2 + h V ₁ = V ₀ −h V _{mi + j + 2} = C + cos (2πj / m) sin (2πi /
n) w / 2 + cos (2πi / n) h / 2 + sin (2
πj / m) sin (2πi / n) d / 2 (i = 0 to n−
2, j = 0 to m-1) where C is the center coordinate of the sphere, and the north pole coordinate V ₀ , the south pole coordinate V _1, and other coordinates V
The data compression / expansion method according to claim 1, wherein data expansion for converting to _{mi + j + 2} is performed.