JPH04500877A - System for performing linear interpolation - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention] System for performing linear interpolation field of invention The present invention relates generally to computer systems and, more particularly, to interpolation between known data points. It is concerned with the calculation system for performing.

Background of the invention In many applications in the fields of computation and numerical analysis, it is necessary to The value of the function must be approximated from the known values of the function at other points in the region. Must be. − As an example, the air pressure (function) makes up a set of locations (regions) on Earth. ``Locations can be known, and from these known pressures, people may wish to determine the value of pressure at other locations. This is a linear complement. It can be completed by any method in between.

In linear interpolation, a function is defined by each region coordinate value for which the function value is known. It is assumed to be piecewise linear between adjacent points in the region to be identified. Ru. Therefore, the interpolated value at the target point of the region, i.e. the function value should be interpolated. The area coordinate value of a point in the area where the area is The relationship for the function value is (1) the relative distance of the desired area coordinates from the known point; and (2) the difference between the values of the function at two adjacent known points. ing. Expressed mathematically, in the -dimensional domain, this is . Here, f is an interpolation function, and X and X are the domain coordinate values of points whose function values are known. , and Xd is the area coordinate value where the function value is interpolated.

In the prior art, interpolation calculations have been performed by electronic calculation systems.

In these systems, function values for known points are stored in a single electronic storage device. is stored in For each interpolation, this storage stores the For each of two known points whose region coordinates are adjacent to the region coordinates It must be accessed twice, once to get the value.

Summary of the invention The present invention provides a new and improved system for generating interpolated values.

Briefly summarizing, the invention provides, in aspects: - generating an interpolated value in response to an input value; Provides an interpolation system to generate. This interpolation system A function consisting of multiple function value storage tables for storing function values for area coordinate values of Equipped with value storage. The address generator responds to the input value and stores it in the function value storage table. The function value storage table can be used to send function values in parallel. generates an address signal. The interpolator is a function sent in parallel by a function value storage table. It receives values and input values and generates interpolated values in response thereto. In another aspect , this invention stores function values for every other area coordinate value in the area. The stage of preparing multiple function value storage tables for the function, and identifying the storage locations in the function value storage tables. and the address signal that allows the function value storage table to send function values in parallel. generating stages and receiving function values and input values sent in parallel by the function value storage table. the interpolated values in response to the input values. Provides a way to generate intermediate values.

Brief description of the drawing The invention is pointed out with particularity in the appended claims and in conjunction with the accompanying drawings. It will be further understood that by referring to the following explanation given, In the drawing, FIG. 1 shows a functional block diagram of a linear interpolation system according to the present invention, and FIG. 1 shows a block diagram of an effective address generator in the system shown in FIG. FIG. 3 shows a block diagram of an interpolation device effective for the system shown in FIG. 1, and FIG. and 4B show three-dimensional areas useful for understanding multidimensional interpolation according to the present invention. Or, again Figure 5 shows the functional configuration of a linear interpolation system that performs linear interpolation in a two-dimensional domain. The figure shows.

FIG. 1 shows an exemplary embodiment of a linear interpolation system according to the invention. In Figure 1 As can be seen, the interpolator 70 stores function values for known points. There are two optical storage devices 30 and 32. Each of these optical storage devices has an address ADRS ODD odd address signal from generator 38 ADRS EVEN even Address signals the known function values to interpolator 36 along lines 34 and 35. feed the column. Address generator 38 indicates the target point, i.e. at which interpolation is to be performed. Defines the high-order region coordinate values of a point in a certain region. XI along line 12 In response to the high-order part of the N signal, the known ADRS ODD odd address signal A that identifies the storage location for the point function value DRS EVEN (j%7 Generates the address signal. In addition, the address generator 38 is coupled to interpolator 36 by line 40 and thereby Generates a SEL selection signal that is used to

The interpolator 36 extracts a low X-factor on the line 14 that defines the low region coordinate value of the target point. 1. signals and existing signals from optical storage devices 3o and 32 on lines 34 and 35, respectively. Knowledge point i1C function value, 2! Interpolation device 3 6 uses these signals as inputs 1-2 to calculate the region identified by XIN Shinshichi. The interpolation function value f(XIN) for the coordinate value is subtracted.

In one embodiment, as shown in FIG. 1, the notation tl! Recorded in devices 30 and 32 181 values of stored known points are prepared for each integer domain coordinate value. Table 30 The function values stored in are related to all integer domain coordinate values, and are also stored in Table 32. The function values determined are those associated with even integer region coordinate values. Each optical storage device 30 and 32 consecutive memory locations] values are their respective associated area coordinate values. are stored in ascending order of values, so the address of each function value in optical storage is The numbers correspond directly to the integer part of the area coordinates of each known point.

5 above, the function value for a known point is stored between the two optical storage devices 3o and 32. It is distributed. As you may have guessed, the function value for odd coordinate values is optical memory. Function values stored in the device 30 and for even coordinate values are stored in the optical storage device 32. During interpolation, the function values for two adjacent area coordinates are not recorded optically. One from each of storage devices 30 and 32. Two optical storage devices 3° and and 32 are prepared so that the function values can be obtained from the two optical storage devices simultaneously. be able to. As a result, the configuration shown in Prisoner 1 uses a single optical storage device. function values for known points can be obtained in less time than conventional systems.

That is, the optical storage device 30 has Function value for all area coordinate values closest to the target point, as identified by the signal on the line 34, and the optical storage 32 provides the area coordinates identified by the XIN signal. The function value for the even area coordinate value closest to the value is given on the line 35. explained below As such, the SEL selection signal is set to the function value given by the memory devices 3o and 32. The area coordinate values for the at lines 34 and 35 as explained below, indicating whether Controls the use of the signal by interpolator 36. More specifically, referring to Equation 1, , SEL selection signal 1! ADR8ODD odd 7 dos L/S signal again i! ADR8EVEN Whether the even address address signal corresponds to the area coordinate values X and x2 is determined by optical memory. Which of the values represented by the signals sent by devices 30 and 32 is the function value f( XI) and f(xt).

An exemplary embodiment of address generator 38 is shown in FIG. address generator 38 ADRS OD to identify storage locations in two optical storage devices, respectively Generates D odd address signal ADRS EVEN even 7 dos 1/s signal. In addition , address generator 38 generates the SEL selection signal used by interpolator 36. Ru. In the address generator 38 shown in FIG. 2, the function values should be interpolated. High order for the XIN signal that identifies the integer part of the region coordinate value of a point in a region The portion is coupled along line 12 to address generator 38. Integer part of XIN signal The least significant bit of the binary representation of the Determine what value you have. Therefore, the least significant bit of the high part of the XIN signal indicates that the area coordinate values of the target point in the area where the function values are to be interpolated are even or odd. It indicates which integer region coordinate value is immediately above the coordinate value of and is coupled to line 40.

ADRS ODD odd 7 dress signal and ADRS EVE) J4%7 dress signal I It is a function of the integer part of the X engineering N signal in Jfi12. More specifically, the address Both signals are an integral part of the XIN signal, except for the lower order signal that provides the SEL selection signal. It is a function of several parts. Each optical storage device 30 and 32 stores an integer domain coordinate value, i.e. Since the area coordinate values for which numerical values are known and the function values for 1/02 are memorized, A DRSODD odd 7 donce signal and AD RS E V E N even address signal The value of is the largest integer half of the integer part of the area coordinates represented by the X engineering and N signals. It is a function.

More specifically, referring to FIG. 1, optical storage devices 3o and 32 having the same address For storage locations in , the resulting output has all integer domain coordinate values. If a known point in a region has a higher region locus than a point in a region with an even abundance region value, Therefore, on lines 50 and 52, the address generator is The address signal generated by If the area coordinates of a point are directly above an even integer coordinate, they should represent the same value. Ru. The area coordinate values of the points in the area where the function values are to be interpolated. is immediately above all integer area coordinate values, the table storage device 32 stores ADRS OD. The address of the location identified in the D-odd address signal table storage device fi30. ADRS that identifies the location with the next higher address response signal should be eliminated. Address generator 38 satisfies these bases. Generates ADRS ODD odd 7 donce signal and ADRS EVEN even 7 dress signal do.

As mentioned above, the lowest integer part of the area coordinates of the desired point is the lower area coordinate. Whether a known point in a region with a value has an even or odd region coordinate value Show that. Therefore, this bit also applies to the ADR8ODD odd7donce signal and the ADR8ODD S EVEN Even 7 address signals occupy the same storage location in optical storage devices 30 and 32 Indicates whether it is identified. As shown in address generator 38 of FIG. The least significant bit of the integer part of the XIN signal that defines the area coordinate value of the target value is sent to the binary adder 4. 6VC carry input and here B INF addition input terminal to adder 46 receives the binary value 0 on line 48, and the A INP addition input terminal receives the integer value of the XIN signal. The upper bit of the part is received. Alternatively, the least significant bit of the integer part of the desired point simply the least significant bit carried by line 48 at the B INP summation input terminal. can be controlled.

The output of adder 46 is ADRS EVEN generated by address generator 38. even address address signal, which is used as an address for optical storage device 32; Ru. The upper bit of the area coordinates of the desired point carried by line 42 is also The ADRS ODD odd address signal is used in the optical storage device 30. is the address for. As noted by those skilled in the art, this form In the ADRS ODD odd address signal, the SEL signal is negated. When ADRS　EVEN even address address signal is equal. SEL selection signal is low ADRS EVEN even address address signal ADRS ODD odd address one larger than the door address signal. These results are listed in the table at the bottom of Table 2. It is. As can be seen from the above, these are the optical storage devices 30 and 32. Give the necessary address for.

A functional block diagram of the supplementary I%11 device 36 is illustrated at 93. It was shown in Figure 3. Similarly, interpolator 36 extracts functions from optical storage devices 30 and 32 along lines 34 and 35. receive value. Line 34 indicates optical storage 3 containing function values for all area coordinate values. It is labeled "odd" to indicate that it carries a function value from 0. ing. Similarly, the line 35 represents the function value for the even area index from the optical storage device 32. It is labeled "even J" to indicate that it is carrying . Lines 34 and 35 connect to two multiplexers 20 and 22, both of which The multiplexers 20 are controlled in concert by the SEL selection signal, and the multiplexers 20 If the target value is immediately above that of the target point identified by the The function value of the knowledge point is coupled to the line 37, and the multiplexer 22 connects the function value of the knowledge point to the target What is the function value of the known point just below the point? Connect to fj39.

Further circuitry including a subtracter 24, a multiplier 26 and a second adder 28 is connected to lines 37 and and the function value represented by the signal at line 39 and the XIN signal at line 14. Using the low part of the X engineering N signal, we show the fractional part of A value is generated. As noted above, a known point lies in an integer domain coordinate value; This simplifies interpolation calculations. Specifically, referring to the equation at the bottom of Figure 3, The difference between the area coordinates of known points, i.e. the value of “(x　i41　x　i　)　J, is Since the area coordinate values of known points are always sequential integer area coordinates, it is always equal to "1" K. stomach. Furthermore, for the same reason, the area coordinates of the desired point and the expression r in the equation ( The difference between the area coordinates of the lower known point indicated by is equal to the fractional part of the area coordinate value of the gauge point, and this is equal to the fractional part of the XIN signal at line 14. It corresponds to the lower part.

In this way, the subtracter 24, multiplier 26 and adder 28 in the interpolator 36 The calculation circuit section converts the equation in the interpolation equation shown in the lower right corner of Figure 3 into a numerical value. calculate. Specifically, the subtractor 24 is defined by the expression marked 24 in the equation. This gives the difference between the function values at known points, as shown below. Multiplier 26 uses this difference (on line 14) as shown by the expression labeled 26 in Eq. Multiply by the fractional component of the area coordinate value of the target point (represented by the signal carried by) do. Finally, adder 28 combines the product produced by multiplier 26 and the The lower region coordinates in the region as indicated by the formula labeled 28 give the sum of the function value at a known point with the value, and this gives the XIN signal Therefore, give interpolated values for the nine target points expressed.

Alternative! j+! In the fifth example, the value for the known point 1 is the content addressable storage The data can be stored in the computer memory (CAM).

In this case, optical storage devices 30 and 32 store area coordinate values and functions for known points. Remember both values. The function value for the known point is then calculated using the area coordinate value of the desired point. can be accessed. The benefits of using CAM are (1) the known points; (2) the difference between the area coordinate values; and (2) the difference between the area coordinate values; It does not need to be uniform. Although the difference between the area coordinate values is uniform, If not “1”, the adder 28 (FIG. 3) of the interpolator 36 generates values such that n is divided by their difference to produce the actual interpolated value. . On the other hand, if the difference is not uniform, the optical storage device uses the area coordinate values for the division. It may be coupled to an interpolator f36 capable of determining the difference to be made.

Statement: A system according to the present invention for performing linear interpolation in a multidimensional coordinate domain It is explained according to 94 people to 5.

]9 As shown in Figure 4, in a two-dimensional interpolation system, the function value is known. The location of the point in the region is in the two-dimensional region indicated by the axes X and y. form a two-dimensional lattice. The value of the function at the target point is the square where the target point is. Completion from the function values at the four nearest known points forming the corners of the grid “window” The decision will be made due to busy schedules.

As seen in Figure 4A, the target point Sd is determined by a grid of points whose function values are known. It is projected onto two of the defined lines 26. The resulting projected point is point e Identified as S,l and S,2. These projection points S, Y and “I)2 The value for the function aK at is the pair of known points S11 and Lx l S21 and S22. Using a one-dimensional interpolation system such as that described above in connection with Figure 1. can be calculated by the system.

As shown in FIG. 4B, two projection points S1 and 5p21! ,point. , exists Ru, sh Prisoner 5 identifies the area coordinate values along the X and y axes for the target point, respectively. interpolation in a two-dimensional coordinate domain according to the present invention in connection with the It shows the circuit for doing this. This circuit includes two one-dimensional interpolation blocks 70 ( ODD) and 70 (EVEN), both of which are interpolated books 70 (Fig. ) corresponds to ℃. Each block 70 (ODD) and 70 (EVEN) has its optical record. A storage device (not shown) is provided along every other line 26 as shown in FIG. 4A. Store the function value for a known point in the coordinate area. The times shown in Figure 5 The integer parts of the fractional signals XIN and YIN are processed using a one-dimensional interpolation block 7. ゜, and each of this block also has a projection point for one of □ and s, 2. Gives the function value. The outputs of the two one-dimensional blocks 70 are combined with the fractional portion of the YIN signal. is coupled to an interpolator 36, which also provides a function value for the target point.

To accomplish this, the two one-dimensional interpolation blocks 7o are An optical storage device (not shown in Figure 5) provides the function value for every other point on the line. There is). That is, parallel to the X axis and parallel to the y axis as shown in Figure 4A. Suppose that a function value is given along a parallel line that intersects the y-axis along an integer point along The -dimensional interpolation block 70 (ODD) includes a y-dimensional interpolation block 70 (ODD) that intersects the y-axis at odd points along the y-axis. The light corresponding to the optical storage devices 3o and 32 (FIG. 1) gives the function value along the line where There is a storage device, and the other interpolation block 70 (EVEN) has y4+11VC Also an optical storage device 3o gives function values along the line that intersects the y-axis at even points along the There are optical storage devices corresponding to .

The optical storage devices 3o and 32 in the interpolation block 70 (ODD) memorize the function value at a known point along the line stored in it at the stored memory location. Then, the function values along successive lines are recorded in successive sets in each memory. It is stored in a memory location. Optical storage device 3o in interpolation block 70 (ODD) and 32 are parts of both the integer part of the XIN input signal and the integer part of the YIN input signal. In response, 7 dons are given. Specifically, the address signal is an address generator 38(x) for generating an address signal, and in response to a Y/N signal; This signal is generated by an address generator 38(y) which generates an address signal. Both address generators 38 (x) and 38 (y) are address generators 38 ((il It is the same as l). Each of address generators 38(x) and 38(y) Generate even and odd set address signals. In detail, the address generator 38 (x ) are both address signals along the X axis, X ADR3ODD odd address Signal X ADR8EVEN even address address signal and address generator 38 (y) is the 7 dress signal both along the y-axis, Y ADR3ODD odd add Generates response signal Y ADR3EVEN even 7 donce signal.

Optical storage device 3o and interpolation block 70 (ODD) and 70 (EVEN) 32 is X generated by address generators 38 (x) and 38 (y) ADR3ODD, X ADRS EVEN, Y ADR8ODD, and Y AD Address signals formed by various combinations of R3EVEN signals be dressed. In detail, along consecutive lines with odd y-axis coordinate values, An interpolation block that stores function values at successive points with odd X-axis coordinates. 70 (ODD) K Okel table memory device fl30 (see Figure 1) l! ,X AD R8ODD odd X-axis address signal to Y ADR8ODD odd y-axis address signal low Addressed by an address signal formed by tying to the end. Y ADR8ODD: A specific line in the Fry axis address signal area, therefore optical recording. Identifying a particular set of function values stored in storage device 3 (see FIG. 1), and The DR8ODD odd X-axis address signal is a specific point on the line, and therefore a function for this point. Y ADR8ODD odd y-axis address signal that stores the value was identified. Identify a specific memory location in a collection.

Similarly, along consecutive lines with odd y-axis coordinates, lines with even x-axis coordinates In the interpolation block 70 (ODD) which stores the function values at consecutive points The optical storage device (see Figure 1) uses the XADR3EVEN even X-axis address signal as YAD RS ODD formed by connecting to the low end of the odd y-axis address signal Addressed by an address signal. Y ADR3ODD odd y-axis address signal represents a particular line in the region and therefore a particular collection of function values stored in optical storage 32. and X ADR8EVEN (identification in the Ax axis element address signal line). Y ADR8ODD odd y-axis that stores the point, and therefore the function value for this point. 7. Identify the specific location in the set 9 identified by the Dong signal.

Along a continuous line with an even y-axis coordinate value, have an odd x@ coordinate value ℃・ru In the interpolation block 70 (EVEN), which stores the function values at consecutive points. The optical storage device 30 (see FIG. 1) converts the XADR3ODD odd X-axis address signal into Y ADR8EVEN formed by tying to the low end of the y-axis address signal. The 7-dress signal is applied to the 7-dress signal. Y ADR3EVEN even y-axis 7don The signal is stored on a particular line in the area and thus in the optical storage device 130 (see FIG. 1). ADR8ODD Odd X-Axis 7 Dress Signal YADRS stores a specific point on the line and therefore the function value for this point. 1i1'VEN A specific location in the set identified by the y-axis address signal. identify

Finally, the even χ-axis coordinate i is divided into continuous lines with I'C1 even y-axis coordinate value. Interpolation block 70 (EVEN) that stores function values at consecutive points that have The optical storage device 32 (see FIG. 1) in Connect the l/s signal to the low end of the Y ADRS EVENg4y-axis address signal. 7 is addressed by the address signal formed by. Y ADRS EVEN'Ay axis 7 dress signal is a specific line in the area, thus the optical storage device 3 2 (see FIG. 1), and The EVEN signal stores a particular point on the line and therefore the function value for this point. Y ADRS EVEN% Characteristic in the set identified by the y-axis address signal identify a specific location.

In this way, as described above, the X ADRS ODD odd X-axis address signal, R8EVENg4x-axis address signal, Y ADRS ODD odd y-axis address signal , and Y ADRS EVEN even generated by the combination of the y-axis address signals. The four sets of address signals are assigned to the region closest to the target point for which the function value is known. Identify four points at . - for performing interpolation in a dimensional domain, as shown in Figure 1. As in the embodiment shown, address generators 38(x) and 38(y) The area coordinate values of odd values and false values are expressed by the X and YIN signals, respectively. 5ELx indicating whether it is thicker or smaller than the area coordinate value of the target point such as and generates a 5ELy selection signal.

As noted above, interpolation blocks 70 (ODD) and 70 (EVEN) are projected Interpolation for points S1 and Sp2 ([generates 1, same as shown in Fig. 3 The interpolator 36 which is Receive the interpolated value and use it with the 5ELy selection signal and the fractional part of the YIN signal. Then, an interpolated value for the target point is generated. As you may have guessed, the 5ELy selection The selection signal indicates which of the projection points S and Sp2 are interpolation blocks 70 (ODD) and 70 ( EVEL N) shows whether it is related to the interpolated value generated by the process.

The invention can be extended in a similar manner to provide interpolated values for higher dimensional regions. can be For example, a three-dimensional region defined by orthogonal, y and z axes In order to perform interpolation, the coordinates XIN, YIN and ZIN are defined by The target point is first located along a line parallel to the Z-axis, e.g. at an integer position along the Z-axis. It will be understood that projection onto two parallel planes is sufficient. of these planes each defines a set of lines parallel to the y-axis that intersect the y-axis at integer positions along the y-axis. and each line is located at an integer position along the y-axis where the function value is known. Contains points that can be placed. The interpolator has two quadratic circuits similar to the one shown in Figure 5. There is an original interpolation block, and each of the optical storage devices has a block for each of the planes. There is an additional set of storage locations, so these storage devices are also included in the ZINM issue! I: Address generation substantially similar to address generator 38 (FIG. 2) in response to several parts. Z ADRS ODD odd two-axis address signal and Z AD given by generator R8EVEN Even 2-axis address signal is used to address 7. What is shown in Figure 3 An interpolator similar to represents the interpolated values in each of the planes parallel to the two axes. The interpolated values from each of the two-dimensional interpolation blocks are received, and the ZIN signal is The fractional part of 5ELT and the selection signal are used to generate an interpolated value. higher dimensional Interpolation in a region is completed by similar extensions from successive lower dimensional regions. can be

This invention has been described through the use of specific embodiments. For other examples, please refer to the attached documents. It is within the range of the requested term. For example, the interpolation method can be columnar coordinates, radial coordinates or any other coordinate system can be used. Also, the known points do not need to be arranged in a grid; On the contrary, it can be distributed arbitrarily. - In a dimensional system, a point need not be equally spaced. In an n-dimensional system, the set of co-pass points is There is no need to form parallel lines or planes.

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Claims (17)

[Claims] 1. An interpolation system for generating an interpolated value in response to an input value, the interpolation system comprising:A. region Multiple function value records for storing function values for every other region coordinate value in B. a function value store containing a memory table; B. in the function value storage table in response to the input value. Generates an address signal that identifies the location and allows the function value storage table to send function values in parallel. an address generator to enable C. Receives and responds to function values and input values sent in parallel by function value storage table An interpolation system that includes an interpolator, for generating interpolated values. 2. The function value storage includes two function value storage tables, each of which address is associated with each region coordinate value. Multiple addressable for storing function values for every other region coordinate value Claim for generating interpolated values in a one-dimensional domain, comprising a storage location. 1. The interpolation system described in 1. 3. The input value is represented by multiple input signals with high and low parts. the address generator receives the high part and responsively addresses the function value storage table. 3. The interpolation system of claim 2, wherein the interpolation system generates an address signal for scanning. 4. The function value memory table consists of an even function value memory table and an odd function value memory table. An even address signal and an odd function value memory table for the address generator to address the even function value storage table. 4. The interpolation system of claim 3, wherein the interpolation system generates an odd address signal for addressing the memory table. stem. 5. The function value storage table stores function values for integer area coordinate values, and Even address signals and odd addresses that identify addresses whose generators differ by at most 1 5. The interpolation system of claim 4, wherein the interpolation system generates a signal. 6. The address generator converts the most significant bit set of the high-order part of the input signal into an odd address signal. and also the most significant bit set of the high-order part of the address signal and the high level of the address signal. 6. The sum of the least significant bits of the digit parts is combined as an odd address signal. interpolation system. 7. The interpolator A. in response to the function values sent by the even function value storage device and the odd function value storage device. a subtractor part for generating a difference value, B. the difference value generated by the subtractor section and the product value in response to the lower part of the input signal. a multiplier section for generating C. The product value generated by the multiplier part and the sum of the function values sent by one of the even function value stores and the odd function value store. 6. The interpolation system of claim 5, comprising an adder section for generating. 8. The address signal generated by the address generator is in the area above and below the input value. After identifying the coordinate values, the address generator further identifies the even address signal or the odd address signal. Input that identifies which represent area coordinate values greater than and less than the input value 5. The interpolation system of claim 4, wherein the selection signal is generated in response to a high-order portion of the signal. 9. interpolator, A. Receives function values from the even function value storage device and the odd function value storage device and sends them as a selective signal. B. selector for combining the order of each region coordinate value in response to a signal; B. selector a subtractor portion for generating a difference value in response to ordered function values from C. Subtractor section for generating a product value in response to the difference value generated by the minute and the low portion of the input signal. D. Product value and even function value storage generated by the multiplier part to generate a sum with the function value sent by the device and one of the odd function value stores. 9. The interpolation system of claim 8, comprising an adder portion of. 10. The interpolator in Section M above is A. a subtractor for generating a difference value in response to a function value sent by a function value storage device; calculator part, B. for generating a product value in response to the difference value and input value generated by the subtractor section. the second multiplier part, and C. The product value generated by the multiplier section and the function sent by the function value storage An interpolation system according to claim 1, comprising an adder section for generating a sum with a value. stem. 11. The function value storage device contains a function value storage table for each dimension that makes up the area. And for each of these, the address is related to each area coordinate value. For every other region coordinate value in each dimension that constitutes the region in the storage location where contains multiple sets of addressable storage locations for storing function values , an interpolation system according to claim 1 for generating interpolated values in a multidimensional domain. . 12. The input value is divided into high-order parts and low-order parts for each dimension that makes up the region. The address generator is represented by multiple input signals with multiple dimensions. It consists of an address generator, each of which corresponds to the relevant dimension in the domain. for receiving and responsive to the high-order portion of the input signal to address the function value storage table. each dimension address in the function value storage table. Addressed by selected combinations of address signals generated by the generator 12. The interpolation system of claim 11. 13. The above function value storage table has a continuous even dimension for each continuous dimension in the domain. Contains an original function value storage table and an odd-dimensional function value storage table, with an even-dimensional function value storage table for each continuous dimension. An original function value storage table and an odd-dimensional function value storage table are provided for each position of the preceding dimension in continuous dimensions. Contains the function value for the interleaved coordinate values of the relevant dimension in combination with the reference value. 13. The interpolation system of claim 12. 14. Each dimension address generator selects the highest part of the input signal for its associated dimension. the upper bit set as the odd address signal, and also the top of the high part of the address signal. The odd address signal is the sum of the bit set and the least significant bit of the high-order part of the address signal. 14. The interpolation system of claim 13, wherein the interpolation system combines as: 15. The above interpolator has a plurality of successive interpolation stages, each stage having successive dimensions. Perform interpolation at each stage, and each stage becomes A. by the selected pair of the even-dimensional function value storage table and the odd-dimensional function value storage table. a subtractor portion for generating a difference value in response to the sent function value; B. in the subtracter part the difference value thus generated, and in response to the lower part of the input signal for the relevant dimension. a multiplier section for generating a product value; and C. The product generated by the multiplier part value and sent by one of the even-dimensional function value storage table and the odd-dimensional function value storage table described above. an adder part for generating the sum with the function value, 14. The interpolator of claim 13, comprising at least one interpolator block consisting of: system. 16. The address signals generated by each of the dimensional address generators are Identifies the region coordinate values above and below the input value in the region, and the dimensional address generator updates Which of the even address signal or the odd address signal is larger and smaller than the input value? Select a signal in response to the high-order portion of the input signal that identifies which represents the region coordinate value. each interpolation block further includes an even function value storage device and an odd function value storage device. receives the function value from a selector for coupling to said subtracter section and said adder section; An interpolation system according to claim 15. 17. A. to store the function value for every other region coordinate value in the region. preparing a plurality of function value storage tables; B. Identify locations in the function value storage table so that the function value storage table can send function values in parallel. C. generating an address signal to enable the C. Function value storage table It receives function values and input values sent in parallel and generates interpolated values in response. stage, A method of generating interpolated values in response to input values containing .