JP4721072B2 - Polygon data compression and decompression system - Google Patents

Description

  The present invention relates to geometric compression for reducing numerical information of vertex coordinates of polygon data.

 In recent years, digital content using 3D graphics has increased due to high performance of CPUs (Central Processing Units) and the spread of graphic boards, and platforms have diversified from game machines to mobile phones. In these, polygon data processing of tens of thousands of orders is becoming possible, but traffic through the bus often becomes a bottleneck in processing speed due to a huge amount of data transfer from the CPU to the graphic accelerator. As for this problem, a method of compressing and transferring polygon data as well as image data and audio data and decompressing it on the processing side is effective. Conventional research on polygon data is roughly divided into phase compression and geometric compression. Phase compression is distortion-free compression for vertex connection information, and includes generalized triangle strips and generalized triangular meshes. In particular, main 3D graphics libraries solve the problem of vertex duplication related to phase compression by an index buffer format.

  On the other hand, geometric compression is no distortion compression or distortion compression for numerical information of vertex coordinates, and includes scalar quantization, entropy coding, and the like. For example, scalar quantization, which is distortion compression, reduces the number of bits to be allocated by rounding the value of each component of vertex coordinates stepwise. On the other hand, for data with a certain bias such as an exponent part, a variable length code corresponding to the appearance frequency of a symbol is assigned, and distortion-free compression is used to reduce the total code amount. For example, Non-Patent Document 1 discloses a technique for compressing a floating-point exponent with an arithmetic code.

Further, Patent Document 1 discloses phase compression for an object composed of a triangular mesh and geometric compression thereof. In this geometric compression, first, the coordinates of all vertices are converted into integer values by quantization. Next, assuming that the triangle A formed by the target vertex forms a parallelogram with another triangle B adjacent thereto, the coordinates of the target vertex are predicted. The predicted coordinates are corrected based on the angle between the triangles A and B predicted from the angle between another pair of triangles adjacent to the parallelogram. Then, a residual between the corrected predicted coordinate and the actual coordinate is calculated, and entropy coding or the like is performed on the residual.
Martin Isenburg, Peter Lindstorm and Jack Soneyink, "Lossless Compression of Predicted Floating-Point Geometry" Computer-Aided Design, Volume 37, Issue 8, pp869-8778 (2005) US Pat. No. 6,167,159

  An object of the present invention is to propose a novel geometric compression method for effectively reducing numerical information of vertex coordinates of polygon data.

  1st invention has a difference vector calculation part, a local basis calculation part, a local transformation part, and a mantissa truncation part, and the compression system which performs geometric compression of polygon data for every vertex in the order of a triangle strip provide. The difference vector calculation unit expresses the first vertex to be processed by a first difference vector that is a difference from the immediately preceding second vertex. The local basis calculation unit includes a second difference vector defined by the second vertex and the third vertex immediately preceding the second vertex, and a third difference defined by the third vertex and the fourth vertex immediately preceding the third difference vector. Based on the difference vector, a three-dimensional local basis for the first difference vector is calculated. The local conversion unit locally converts the first difference vector based on the calculated local base. The mantissa truncation unit converts the first difference vector subjected to distortion compression by variably truncating the lower bits of the mantissa part in accordance with the size of the exponent part for each component of the locally converted first difference vector. Output as compressed data.

  Here, in the first invention, the local basis is a normal direction of a surface stretched by the first basis component parallel to the third difference vector and the second difference vector and the third difference vector. It is preferable to include at least one of the second base components. In addition, the local basis may include a third basis component that is a specific direction on the surface spanned by the second difference vector and the third difference vector. In this case, it is preferable that the third basis component is calculated by Gram-Schmidt orthogonalization based on the second difference vector and the third difference vector.

  In the first invention, the mantissa truncation unit may perform entropy coding on the exponent part of each component of the first difference vector subjected to local transformation.

  In the first invention, the second vertex, the second difference vector, and the third difference vector are the difference vectors restored by performing the inverse transformation of the local transformation on the difference vector that has been previously distortion-compressed. Is preferably generated based on

According to a second aspect of the present invention, in the compression system that performs geometric compression of polygon data for each vertex in the order of triangle strips, the difference vector calculation unit sets the first vertex to be processed together with the first vertex to the first The first difference vector, which is the difference from the second vertex forming one side of the triangle, is expressed by the mantissa truncation unit according to the size of the exponent part for each component of the first difference vector. Then, the lower-order bits of the mantissa part are variably rounded down so that the first difference vector is subjected to distortion compression and then output as compressed data, and the compressed data decompression unit compresses the distortion-compressed first difference vector. restoring with extending in a first differential vector before, the vertex data calculating section, by adding the first difference vector is the stretched second vertex, the first vertex That process and the repeatedly executed every vertex, the processing in the difference vector calculating unit relates vertex immediately following the first vertex, the first vertex and the second vertex of which is restored by processing in the vertex data calculating section immediately before A polygon data compression system is provided.

A third invention provides a decompression system that comprises a compressed data decompression unit, a local basis computation unit, a local inverse transform unit, and a vertex data computation unit, and decompresses compressed data of polygon data. The compressed data decompression unit supplements the lower bits of the mantissa part truncated at the time of compression for each component of the first differential vector subjected to distortion compression, and the second vertex immediately before the first vertex To the first difference vector, which is the difference of. The local basis calculation unit includes a second difference vector defined by the second vertex and the third vertex immediately preceding the second vertex, and a third difference defined by the third vertex and the fourth vertex immediately preceding the third difference vector. Based on the difference vector, a three-dimensional local basis for the first difference vector is calculated. The local inverse transform unit performs a local inverse transform, which is an inverse transform of the local transform at the time of compression, on the first difference vector based on the calculated local base. The vertex data calculation unit is subjected to the local inverse transform. The first vertex is calculated based on the first difference vector and the second vertex calculated by the previous extension.

Here, in the third invention, the local basis is a normal direction of a surface stretched by the first basis component parallel to the third difference vector and the second difference vector and the third difference vector. It is preferable to include at least one of the second base components. In addition, the local basis may include a third basis component that is a specific direction on the surface spanned by the second difference vector and the third difference vector. In this case, it is preferable that the third basis component is calculated by Gram-Schmidt orthogonalization based on the second difference vector and the third difference vector.

According to the first invention, the first vertex to be processed as well as expressed by the first differential vector, in terms of the local transformation at the local base of the three-dimensional, the low-order bits of the mantissa of each component variable truncate. Thereby, the vertex information of polygon data can be effectively compressed while suppressing distortion errors. On the other hand, according to the third invention, the data compressed by the first invention can be appropriately decompressed.

According to the second invention, when the vertices are sequentially compressed, the differential vector once compressed is restored and used in the processing of the next vertex. Thereby, when the vertices are sequentially expanded, it is possible to prevent errors due to distortion compression from accumulating along with the transition of the vertices to be processed.

[Summary of algorithm]
Prior to a specific description of the system, first, a geometric compression algorithm for polygon data according to the present embodiment will be outlined. The data targeted by this algorithm is vertex coordinates having the data format shown in FIG. As a numerical expression format of the vertex coordinates, 32-bit single precision of the IEEE 754 system, which is a standard, is used. In the IEEE754 system, a 32-bit word is divided into three parts: a sign part (S), an exponent part (Exp), and a mantissa part (Mantissa), and a numerical value is expressed. As for the distribution of the number of bits, the sign part (S) is 1 bit, the exponent part (Exp) is 8 bits, and the mantissa part (Mantissa) is 23 bits. Here, the sign part (S) indicates 0 for a positive sign and 1 for a negative sign. The exponent (Exp) is an integer value of an exponent with 2 as a radix, and takes a positive value with 127 biased. The mantissa (Mantissa) is a bit after the decimal point of a binary decimal number obtained by subtracting 1 from an actual mantissa. The normalized number is expressed by the following equation (e = Exp-127, m = 1. Mantissa).

(Normalized number)
S x 2 ^e x m

  As shown in FIG. 2, the vertex Pn to be subjected to compression processing is expressed by a difference vector dn that is a difference from the vertex Pn-1 that forms one side of the triangle T1 together with the vertex Pn. Then, distortion compression is applied to each component (x, y, z) of the difference vector dn. In this embodiment, distortion compression is realized by variably truncating the lower bits of the mantissa part of each component. As can be seen from the expression for the normalized number, the change in the value due to truncation of the mantissa (Mantissa) is smaller as the value of the exponent (Exp) is smaller. From this point of view, when the value of the exponent part is small, the influence by the truncation of the mantissa part (Mantissa) is relatively small, so the lower bits of the mantissa part are greatly rounded down. On the other hand, when the value of the exponent part is large, the influence of the change of the mantissa part is large, so that the lower bits are rounded down. Specifically, as shown in FIG. 3, in the mantissa part 23 bits, the lower (23- (ec)) bits are rounded down as the number of truncations (truncation), and the (ec) bits are significant digits. Let it be a factor (c is an adjustment factor). Thereby, e and the number of significant digits of the mantissa part have a proportional relationship, and the distortion can be reduced as a whole. Further, the precision of the floating point number and the compression ratio are adjusted by the adjustment coefficient cε [−149, 127]. The number of significant digits (factor) is rounded to 0 for negative numbers and 23 for numbers greater than 24. In this manner, the distortion-compressed difference vector dn is output as the compressed data of the vertex Pn.

  One of the features of this compression algorithm is that the vertex Pn is expressed by the difference vector dn, and the lower bits of the mantissa part are discarded. The difference vector dn is a difference based on a vertex Pn-1 that forms one side of the triangle together with the vertex Pn. In the case of a triangle strip, the difference vector dn corresponds to a difference based on the vertex Pn-1 immediately before the vertex Pn. . By expressing the vertex Pn with a difference vector, its component becomes a value smaller than the original coordinate value of the vertex Pn. Therefore, compared with the case where the coordinate value itself is cut off, it is expected that the lower bits of the mantissa part are cut off more greatly, and as a result, the compression ratio can be improved.

  Next, a method for further improving the compression ratio by improving the basic concept described above and locally transforming the difference vector dn based on a three-dimensional local basis will be described. FIG. 4 is a diagram showing the relationship between the difference vector dn to be processed and the local basis {u, v, w}. In general, a triangular polygon is a set of triangles covering a two-dimensional curved surface. Therefore, one side (vector) dn of a triangle T1 is two sides (vectors) dn-1, dn-2 of a triangle T2 adjacent to the triangle T1, as follows. It can be assumed that it has the following geometric features.

(Assumption A) One side dn of the triangle T1 is parallel to one side dn-2 of the triangle T2, and in the case of a triangular strip, the other side dn-2 corresponds to the side immediately before the side dn.
(Assumption B) One side dn of the triangle T1 is coplanar with the surface stretched by the two sides dn-1, dn-2 of the triangle T2, and in the case of a triangular strip, the other two sides dn-1, dn-2 And corresponds to the previous two sides.

  Here, the assumption A is based on regularity of polygon data artificially created by a manual or an algorithm. Assumption B is based on the possibility of approximation in the normal direction that approaches a smoother surface as the polygon model becomes finer.

  Paying attention to the correlation between such adjacent triangles T1 and T2, if the local transformation is applied to the difference vector dn expressed in the absolute coordinate system, the component can be made smaller. If the above-described mantissa part is rounded down for the locally converted difference vector dn, a higher compression ratio can be expected.

  Specifically, first, a three-dimensional local basis {u, v, w} is set based on the triangle T1 to which the vector dn belongs and the adjacent triangle T2. This local basis {u, v, w} is stretched by (1) the direction parallel to the vector dn-2 as the basis component u (from assumption 1), and (2) the vectors dn-1, dn-2. It is preferable to set the normal direction of the surface (triangle T2) as another basis component w (from assumption 2). The remaining base component v is preferably defined as a specific direction on the plane (triangle T2) spanned by the vectors dn-1 and dn-2. In this embodiment, the unit vector of the vector dn-2 is u, the unit vector obtained by subjecting the vector dn-1 to Gram-Schmidt orthogonalization for the unit vector u, v, and the outer product of these unit vectors u and v. An orthonormal basis {u, v, w} is defined with a unit vector as w.

Next, the difference vector dn (x, y, z) is locally transformed based on the local basis {u, v, w}. Each component (α, β, γ) of the converted difference vector d′ n is calculated by the inner product of the following equation.

α = | <u, dn> |
β = | <v, dn> |
γ = | <w, dn> |

  Then, the above-described difference vector dn (α, β, γ) is subjected to distortion compression by truncating the mantissa as described above. A difference vector dn (x, y, z) before conversion having an exponential component distribution as shown in FIG. 5 is obtained by local conversion using an orthonormal basis {u, v, w} as shown in FIG. It is converted into α, β, γ distribution. This distribution is such that α >> β, γ is established from Assumption A (dn // dn-2), and α, β >> γ is established from Assumption B (dn⊥w), so that α> β> γ. This is also supported by theory. As a result, truncation of the mantissa part for the α, β, and γ components is as follows, and it is expected that the truncation of the γ component will greatly contribute to the improvement of the compression ratio.

(Distortion compression after local transformation)
Exponent value Mantissa truncation bit number α component Large small β component Medium Normal γ component Small Large

  Next, a compression system that implements the above-described compression algorithm will be described. In the compression system according to this embodiment, polygon data drawn by a triangle strip is a compression target, and in principle, distortion compression is performed for each vertex while sequentially shifting the vertex in the order of the triangle strip.

  FIG. 7 is an explanatory diagram of a triangular strip. In the triangle strip, triangles are sequentially defined by two sides connected in a ladder shape from the initial vertex P0, and vertices are shared by adjacent faces. As shown in the figure, when the initial vertex P0 is designated in the order of P1, P1, P2, P3, P4, P4, P5, P0, P6, P2, P7, P4, P8, the vertex P2 is designated. Then, a triangle P0P1P2 composed of two sides P0-P1 and P1-P2 is formed. When the next vertex P3 is designated, the triangle P1P2P3 is formed, and when the vertex P4 is further designated, the triangle P2P3P4 is formed. At the vertex P4, the same vertex is designated twice, and then jumps to the vertex P5. This means that when the same vertex P4 is designated redundantly, a triangle having the side P4-P5 as one side is exceptionally not formed, and a new triangle is started with the subsequent vertex P5 as the initial vertex. . Thereafter, triangle P5P0P6 (when apex P6 is specified), triangle P0P6P2 (when apex P2 is specified), triangle P6P2P7 (when apex P7 is specified), triangle P2P7P7 (when apex P4 is specified), triangle P7P4P8 (when apex P8 is specified) ) In this order. In a 3D graphics library such as DirectX or OpenGL, a method of managing vertex connection information with an index, that is, an index buffer method is used in order to reduce the amount of data by eliminating redundant vertex redundancy. In this scheme, all vertices are listed and the three vertices of each triangle are described as the triangle strip index.

[Compression system]
FIG. 8 is a block diagram of the compression system according to this embodiment. The compression system includes a difference vector calculation unit 1, a local conversion unit 2, a mantissa truncation unit 3, a local basis calculation unit 4, a storage unit 5, a compressed data decompression unit 6, and a local basis inverse conversion unit 7. And a vertex data calculation unit 8.

  The difference vector calculation unit 1 calculates the difference between the n-th vertex data Pn (x, y, z) input as a processing target and the immediately preceding vertex data P′n−1 (x, y, z) in the triangle strip. Is calculated and output as a difference vector dn (x, y, z). The immediately preceding data P′n−1 is held in the vertex data calculation unit 8. Note that the immediately preceding vertex data P′n−1 is not the original vertex data Pn−1, but a value obtained by restoring a distortion-compressed value (“′” attached to the sign means a restored value). . The initial vertex P0 is not calculated by the difference vector calculation unit 1 but is stored in the vertex data calculation unit 8 as data necessary for calculating the difference vector d1 of the next vertex P1.

  The local conversion unit 2 performs local conversion on the difference vector dn based on the local basis B {u, v, w} calculated by the local basis calculation unit 4, and converts the difference vector dn (α, β, γ after conversion). ) Is output. Here, the α component is the inner product of the vector u and the difference vector dn, the β component is the inner product of the vector v and the difference vector dn, and the γ component is the inner product of the vector w and the difference vector dn. As described above, an orthonormal basis can be used as the local basis B {u, v, w}, and the previous difference vector d′ n−1 and the second difference vector d′ n−2 can be used. Based on the above, it is generated for each vertex. As shown in FIG. 4, the previous difference vector d′ n−1 includes a vertex Pn−1 (more precisely, a restored value P′n−1) and a vertex Pn−2 (exact Is defined by the restoration value P′n−2). In addition, the previous difference vector d′ n−2 includes a vertex Pn−2 (more precisely, a restored value P′n−2) and an immediately preceding vertex Pn−3 (more precisely, the restored value P′n−). 3) and prescribed by.

  The mantissa truncation unit 3 variably truncates the lower bits of the mantissa part according to the size of the exponent part for each component α, β, γ of the difference vector dn after local conversion. The differential vector d′ n (α ′, β ′, γ ′) subjected to distortion compression in this way is output to the outside as compressed data of the vertex data Pn and also supplied to the compressed data decompression unit 6.

  The mantissa truncation unit 3 may perform distortion-free compression by entropy coding on the exponent parts of the α, β, and γ components in parallel with the mantissa part truncation process. Since the exponent value eε [−126, 127] represented by an 8-bit fixed length always has a certain degree of bias, a compression effect by entropy coding can be expected. As entropy coding, for example, static Huffman codes can be used. In this case, the value of the exponent part is measured for each component, and a Huffman tree is constructed according to the number of appearances. Also, the number of symbols, symbols, and the number of appearances are described at the beginning of the compressed data, and a Huffman tree is reconstructed from these when decompressing.

  The compressed data decompression unit 6 compensates the lower bits of the difference vector d′ n (α ′, β ′, γ ′), and returns to the signed decimal format (simply add 0 to align the number of digits). The α, β, and γ components obtained by this expansion do not match those output from the local conversion unit 2 and include a mantissa part distortion error. Note that when the mantissa truncation unit 3 performs entropy encoding of the exponent part, decoding corresponding to this is also performed.

The local inverse transform unit 7 includes the difference vector d′ n (α ′, β ′, γ ′) expanded by the compressed data expansion unit 6 and the local basis B {u, v, and local inverse transformation based on w} is performed to calculate a difference vector d′ n (x, y, z). This inverse transformation corresponds to the inverse processing of the transformation in the local transformation unit 2. The difference vector d′ n does not coincide with the difference vector dn output from the difference vector calculation unit 1 and includes a mantissa part distortion error. The calculated difference vector d′ n is supplied to the storage unit 5 and the vertex data calculation unit 8. The difference vector d′ n supplied to the storage unit 5 is stored in the storage area d′ n−1 to be used as the previous difference vector in the processing of the next vertex Pn + 1. In addition, the data in the storage area d′ n−1 used as the previous difference vector in the processing of the current vertex Pn should be used as the previous difference vector in the processing of the next vertex Pn + 1. It is stored in the storage area d′ n−2 . Along with this, the data currently stored in the storage area d′ n−2 is discarded.

  On the other hand, the vertex data calculation unit 8 calculates a value obtained by adding the difference vector d′ n to the currently stored vertex data P′n−1 as new vertex data P′n. This new vertex data P′n is used as the previous vertex data in the processing of the next vertex Pn + 1. Thus, the reason why the data once compressed is restored and used in the processing of the next vertex Pn + 1 is to prevent accumulation of errors due to distortion compression during expansion.

  This accumulation prevention of errors will be described in detail with reference to FIG. When the processing target is the vertex P1, the difference from the vertex P0 immediately before forming one side of the triangle together with the vertex P1 is expressed as the difference vector d1, and the compression difference vector d′ 1 is calculated by distortion-compressing the difference vector d1. Is done. Then, the vertex P′1 is restored by expanding the compressed difference vector d′ 1 and adding this to the vertex P0. However, since there is an error effect due to distortion compression, a deviation occurs between the restored vertex P′1 and the original vertex P1. The original vertex can be specified on the compression side, but only the restored vertex can be specified on the decompression side. Therefore, if the difference vector is calculated starting from the original vertex at the time of compression, the deviation from the original vertex is gradually increased by the repeated processing in the order of vertices P2, P3, P4 at the time of expansion. End up. In this embodiment, in order to prevent the accumulation of such errors, in the compression process for the vertex Pn + 1 immediately after a certain vertex Pn, the vertex P′n restored by the immediately preceding processing is not the original vertex Pn. Use. Note that the present technique for preventing error accumulation is not limited to truncation of the mantissa part, and can be applied to other distortion compression.

  The above processing is repeated every time the vertex data Pn + 1, Pn + 2,. Then, with the completion of the processing of the last vertex data Plast, the compression of all the vertices constituting the polygon data is completed. If the vertex Pn to be processed matches the previous one, etc., the processing of the current vertex Pn is skipped as an exception process.

  As described above, in the compression system according to the present embodiment, the mantissa part of the α, β, γ components of the difference vector dn locally transformed by the local basis B {u, v, w} according to the size of the exponent part. The lower bits of are variably truncated. Then, the component of the difference vector d′ n that has been subjected to distortion compression by this truncation is used as compressed data. Thereby, it becomes possible to effectively compress the vertex data of the polygon data while suppressing the distortion error. In particular, if a local basis based on a triangle to which the difference vector dn belongs and an adjacent triangle is used, a higher compression rate can be secured.

[Extension system]
FIG. 10 is a block diagram of a decompression system corresponding to the compression system described above. This decompression system includes a compressed data decompression unit 11, a local inverse transform unit 12, a vertex data calculation unit 13, a local base calculation unit 14, and a storage unit 15. The data passed from the compression system to the decompression system includes the coordinate data of the initial vertex P 0 and the compression data d′ n (α ′, β ′, γ ′) (n = 1, 2, 3,...・） The correspondence between the size of the exponent part and the truncation bit of the mantissa part is determined in advance between the compression side and the expansion side. Further, the initial vertex P0 is stored in the vertex data calculation unit 13 as data necessary for calculating the next vertex P1.

  The compressed data decompression unit 11 supplements the lower-order bits truncated at the time of compression with respect to the compressed data P′n (α ′, β ′, γ ′) and returns it to the floating-point format (simply add 0 to change the number of digits. Align). When the exponent part is entropy-coded, the expansion is also performed. As a result, the difference vector d′ n, which is the difference between the vertex P′n and the immediately preceding vertex P′n−1, is expanded and restored.

The local inverse transform unit 12 includes the difference vector d′ n (α ′, β ′, γ ′) expanded by the compressed data expansion unit 11 and the local basis B {u, v, On the basis of w}, the local inverse transformation of the following equation, that is, the inverse transformation of the local transformation at the time of compression, is performed to calculate the difference vector d′ n (x, y, z). The same three-dimensional local basis B {u, v, w} as that on the compression side is used, and the previous difference vector d'n-1 (vertex P'n-1, P'n-2 Defined) and the second difference vector d′ n−2 (defined by P′n−2 and P′n−3). The calculated difference vector d′ n is supplied to the vertex data calculation unit 13 and the storage unit 15.

d′ n (x, y, z) = <u, d′ n> u + <v, d′ n> v + <w, d′ n>

  The vertex data calculation unit 13 adds the current difference vector d′ n (x, n, x) calculated by the local inverse transformation unit 12 to the currently stored vertex data P′n−1 (the one already calculated by the previous expansion). By adding (y, z), vertex data P′n (x, y, z) as output data is calculated. This new vertex data P′n is used as the previous vertex data in the processing of the next vertex Pn + 1.

Further, the difference vector d′ n supplied to the storage unit 15 is stored in the storage area d′ n−1 to be used as the previous difference vector in the processing of the next vertex Pn + 1. In addition, the data in the storage area d′ n−1 used as the previous difference vector in the processing of the current vertex Pn should be used as the previous difference vector in the processing of the next vertex Pn + 1. It is stored in the storage area d'n-2. Along with this, the data currently stored in the storage area d′ n−2 is discarded.

  The above processing is repeated every time compressed data d′ n + 1, d′ n + 2,. Then, with the completion of the processing of the last vertex data d′ last, the expansion of all the vertices constituting the polygon data is completed.

  As described above, according to the decompression system according to the present embodiment, it is possible to appropriately decompress the compressed data generated by the above-described compression system.

  In the above-described embodiment, the compression / decompression system has been described. However, a computer program that causes a computer to execute an equivalent processing procedure also constitutes another aspect of the present invention. In this case, the basic flow of the compression process is as follows (details are omitted as described above). Although the compression efficiency is reduced, the following steps 12 and 13 can be omitted and the difference vector calculated in step 11 can be directly distorted and compressed, and the present invention does not exclude such a form. .

(Compression procedure)
(Step 11) Difference vectorization of vertices to be processed (Step 12) Calculation of local basis (Step 13) Local transformation of difference vector based on local basis (Step 14) Distortion compression of difference vector after transformation

The decompression process is as follows. If local conversion is not performed in the compression process, the following steps 22 and 23 are unnecessary.
(Extension processing procedure)

(Step 21) Expansion of compressed data (Step 22) Calculation of local base (Step 23) Calculation of difference vector by local inverse transformation using local base (Step 24) Calculation of vertex data

Explanatory drawing of data format of vertex coordinates Explanatory diagram of vertices expressed by difference vector Illustration of truncation of lower bits in mantissa Diagram showing the relationship between the difference vector and the local basis Exponential component distribution map for the difference vector before conversion Exponential distribution map for the difference vector after conversion Illustration of triangle strip Block diagram of compression system Explanatory diagram of cumulative distortion error during expansion Block diagram of decompression system

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Difference vector calculation part 2 Local transformation part 3 Mantissa truncation part 4 Local base calculation part 5 Storage part 6 Compressed data decompression part 7 Local inverse transformation part 8 Vertex data calculation part 11 Compressed data decompression part 12 Local inverse transformation part 13 Vertex data Calculation unit 14 Local basis calculation unit 15 Storage unit

Claims (11)

In a compression system that performs geometric compression of polygon data for each vertex in the order of triangle strips,
A difference vector calculation unit that expresses a first vertex to be processed by a first difference vector that is a difference from the immediately preceding second vertex;
A second difference vector defined by the second vertex and the third vertex immediately preceding the second vertex, and a third difference vector defined by the third vertex and the fourth vertex immediately preceding it. A local basis calculation unit for calculating a three-dimensional local basis for the first difference vector,
Based on the calculated local basis, a local conversion unit that locally converts the first difference vector;
For each component of the first difference vector that has been locally transformed, the first difference vector that is distortion-compressed by variably truncating the lower bits of the mantissa part according to the size of the exponent part is output as compressed data. A polygon data compression system comprising a mantissa truncation unit.   The local basis is a first base component parallel to the third difference vector and a normal direction of a surface stretched by the second difference vector and the third difference vector. 2. The polygon data compression system according to claim 1, comprising at least one of base components.   3. The polygon data according to claim 2, wherein the local base includes a third base component that is a specific direction on a surface spanned by the second difference vector and the third difference vector. 4. Compression system.   The polygon data of claim 3, wherein the third basis component is calculated by Gram-Schmidt orthogonalization based on the second difference vector and the third difference vector. Compression system.   5. The polygon data according to claim 1, wherein the mantissa truncation unit performs entropy coding on an exponent part of each component of the first difference vector subjected to local transformation. 6. Compression system.   The second vertex, the second difference vector, and the third difference vector are based on a difference vector restored by performing an inverse transformation of the local transformation on a difference vector that has been previously distortion-compressed. 6. The polygon data compression system according to claim 1, wherein the polygon data compression system is generated as described above. In the compression system for performing geometric compression polygon data per vertex in the order of triangle strips, a difference vector calculating portion, the first vertex to be processed, to form one side of the first triangle with the first vertex The first difference vector, which is the difference from the second vertex, is represented by the first difference vector, and the mantissa truncation unit has, for each component of the first difference vector, a lower bit of the mantissa part according to the size of the exponent part. , The first differential vector is distorted and output as compressed data, and the compressed data decompression unit converts the first differential vector that has been compressed into the first differential vector before compression. while stretching the differential vector, vertex data calculation unit, by adding the first difference vector is the stretched to the second vertex to restore the first vertex Processing and, repeatedly executed for each vertex,
In the process in the difference vector calculation unit regarding the vertex immediately after the first vertex, the first vertex restored by the process in the immediately preceding vertex data calculation unit is used as the second vertex. Polygon data compression system. In a decompression system that decompresses compressed data of polygon data,
For each component of the first distortion-compressed difference vector, the difference between the first vertex to be processed and the second vertex immediately preceding it by supplementing the lower bits of the mantissa part truncated at the time of compression A compressed data decompression unit that decompresses the first difference vector,
A second difference vector defined by the second vertex and the third vertex immediately preceding the second vertex, and a third difference vector defined by the third vertex and the fourth vertex immediately preceding it. A local basis calculation unit for calculating a three-dimensional local basis for the first difference vector,
Based on the calculated local basis, a local inverse transform unit that performs local inverse transform on the first difference vector, which is an inverse transform of local transform at the time of compression;
A vertex data calculation unit that calculates the first vertex based on the first difference vector subjected to the local inverse transformation and the second vertex calculated by the previous extension. Polygon data expansion system.   The local basis is a first base component parallel to the third difference vector and a normal direction of a surface stretched by the second difference vector and the third difference vector. 9. The polygon data expansion system according to claim 8, comprising at least one of base components.   The polygon data according to claim 9, wherein the local base includes a third base component that is a specific direction on a surface spanned by the second difference vector and the third difference vector. Stretch system.   The polygon data of claim 10, wherein the third base component is calculated by Gram-Schmidt orthogonalization based on the second difference vector and the third difference vector. Stretch system.

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