JP3224852B2 - Curve drawing value calculation device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a drawing value calculating apparatus for calculating a drawing value of a curve connecting start and end points based on n-th approximate expression information connecting the start and end points and the start and end points.

[0002]

2. Description of the Related Art In a document creation processing system for displaying characters and figures, a set of characteristic points of outlines of characters and figures is stored. A method has been used in which a contour is developed in a bitmap memory by approximating it with an nth-order approximation formula, and thereafter, characters are displayed by filling the contour as necessary.

The following method has conventionally been used to develop a contour line into a bit map memory by approximating it with the n-th order approximation formula. Start point [a, f (a)], end point [b, f
(B)] and the approximate expression f (x) is given by f (x) = A′x ³ + B′x ² + C′x + D ′ (1), X is applied to the interval [a, b]. When f (x) is calculated from equation (1) each time, it requires a great deal of arithmetic processing. Therefore, a method of adding the increment value to the current value to obtain the next value is used. ing.

That is, in order to simplify the arithmetic processing, the x-axis of equation (1) is translated in parallel by a to obtain g (x) = Ax ³ + Bx ² + Cx + D (2), and the section [a, b] is defined as Change to the section [0, ba].

When the section [0, ba] is equally divided into M, the division value Δx in the x direction becomes Δx = (ba) / M (3), and the value x of the m-th division point _m is represented by x _m = (Δx) m (4), and the value x _{m + 1} of the ( _{m + 1} ) -th division point becomes x _{m + 1} = x _m + Δx (5), and Δx is simply added. Gives the next x value.

In the y direction, a value in the y direction corresponding to x _m is represented by y _m , and a value in the y direction corresponding to x _{m + 1} is represented by y
_{If m + 1} , then y _{m + 1} = y _m + {g (x _{m + 1} ) -g (x _m )} (6)

Therefore, the increment value represented by ｛·｝ is represented by Δ
expressed as y _m, when determining the [Delta] y _m by substituting x _{m + 1} and x _m in equation _{(2), Δy m = g} (x m + 1) -g (x m) = [3A (b-a ) ³ / M ³ ] m ² + [{3A (ba) + 2BM} (ba) ² / M ³ ] m + [{A (ba) ² + BM (ba) + CM ² } ( b−a) / M ³ ] (7)

The third term in equation (7) is not related to m, and the second term is a first-order term of m. Therefore, every time m increases, {3A (ba) + 2BM} (b -a) obtained merely by adding a ² / M ^3. Since the first term is a quadratic term of m, m ² is m ² = Σ2m−m. Therefore, the coefficient value twice the first term is added, and the sum of the coefficients of the first term is obtained from the addition result. Is easily obtained by subtracting

[0009]

As described above, the conventional drawing value calculation apparatus for drawing a curve calculates the increment value in the calculation of the drawing value in the y-axis direction by using the Δ calculated by the equation (7).
y _m is set as an increment value, and the result of adding to the previous drawing value is output as a drawing value.

These arithmetic processings are performed using a processor. In the processing of the processor, the equation (7) is used.
Since the coefficients of the first to third terms represented by are divided by M ³ to become real numbers, the processing is performed by the floating-point method. For this reason, Δy is obtained from the first to third terms of equation (7).
Calculating _m results in the addition of a real number expressed in the floating-point system, which requires a longer processing time than the addition between integers, and it takes a long time to calculate the drawing value of the curve drawing. .

An object of the present invention is to provide a curve drawing value calculation device improved so as to shorten the drawing value calculation processing time.

[0012]

Before describing the means for solving the problems of the present invention, the principle will be described first. When the equation (7) is transformed into the following equation, Δy _m = [A ₁ m ² + A ₂ m + A ₃ ] / M ³ (8) where A ₁ = 3 A (ba) ³ A ₂ = ｛3A (Ba) + 2BM｝ (ba) ² A ₃ = ｛ A (ba) ² + BM (ba) + CM ² ｝ (ba) (9) The coefficients A ₁ , A ₂ and A ₃ are all integer values. That is, A, B, and C are coefficients of the approximate expression, all given as integer values, and a and b are addresses corresponding to the start point and the end point of the bit-up memory, and are integer values. M is the number of divisions and is an integer value.

The calculation of A ₁ m ^{2 in} the first term of equation (8)
_{Since 1} m ² is represented by A ₁ m ² = A ₁ Σ (2m−1) = Σ (Σ2A ₁ ) −ΣA ₁ (10), the first term of equation (10) is calculated as m increases. obtained by adding the addition value obtained by adding 2A _1, the second term is obtained as an addition value obtained by adding the a ₁ to every increase of m.

A ₂ m in the second term of the equation (8) is obtained as an added value obtained by adding A ₂ every time m increases. Further, A _{3 in} the third term of the equation (8) is a term not related to m. A ₁ m ² , A ₂ m and A ₃ calculated as described above are added to the data value stored in the register AA to calculate an increase value. _{That, AA = AA + A 1 m} 2 + A 2 m + A 3 ... (11) comprising performing a calculation.

Assuming that the integer part obtained by dividing the left side of the equation (11) by M ³ is ΔY and the remainder is ΔR, AA / M ³ = ΔY + ΔR (12) It is output as an increment value in the y-axis direction, and the remainder ΔR is stored in the original register A. That is, AA = ΔR (13) is performed.

The calculation of ΔY on the right side of equation (12) is obtained by dividing AA of equation (11) by M ^3.
If is made larger than M ³ is subtracted M ³ from AA, the subtraction number as [Delta] Y, can be carried out all processing integer addition and subtraction processing only by.

The present invention is based on this principle, and is a curve drawing value calculation device for calculating a drawing value of a curve connecting start and end points based on n-th approximate expression information connecting the start point, end point and start and end points. An increase coefficient calculating section for calculating an increase coefficient from the start point, the end point and the approximate expression information and the number of divisions M between the start point and the end point; and an increase coefficient and a dividing point m calculated by the increase coefficient calculating section. And an increase value calculation unit for calculating an increase value of the division point m from the value of the division point m, and the increase value calculated by the increase value calculation unit for the division point m-1 stored in the register.
Divided by M ⁿ is added to that remainder value, and outputs the integer part of the division result as the increment value, and increment calculation unit that stores a remainder value in the register, the increment in the drawing values of the division points m-1 Arithmetic
Add the increment value calculated by the output section to the division point m.
And an output unit for outputting as a drawing value .

[0018]

The division number calculation section calculates the division number M for dividing the start and end points and calculating the drawing value of the curve from the start point, end point and approximate expression information. The increase value coefficient calculation unit calculates a coefficient of the increase value based on the start point, the end point, and the nth-order approximate expression information. That is, the coefficient A of the increase value represented by the equation (9)
Calculating the _1, A ₂ and A _3.

The increase value calculation section calculates the increase value from the coefficient calculated by the increase value coefficient calculation section. That is, equation (1)
The increase value shown in 1) is calculated. The increment value calculating unit divides the increment value calculated by the increment value calculating unit by M ⁿ to divide it into an integer part and a remainder, outputs the integer part as an increment value, and stores the remainder in an addition register. That is, the arithmetic processing of equations (12) and (13) is performed.

As described above, the increase value coefficient is calculated based on the start point, end point and n-th approximate expression information and the number of divisions M,
Since the increase value and the increase value are calculated from the increase value coefficient, all the arithmetic processing can be performed by integer arithmetic processing, and the arithmetic processing time can be reduced.

[0021]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A first embodiment of the present invention will be described with reference to FIGS. FIG. 1 is a block diagram of an embodiment of the present invention, and FIG. 2 is an operation flowchart of the first embodiment. In FIG. 1, reference numeral 1 denotes a curve drawing information memory, which stores start and end points of a curve to be drawn and approximate expression information.

Reference numeral 2 denotes a division number calculation unit.
The number of divisions of a given section is calculated by a method described in -66863 "Curve Drawing Apparatus" or the like. 3
Is an increase value coefficient calculation unit, which calculates a coefficient of the increase value from the start point, the end point, the n-th order approximate expression and the number of divisions.

Reference numeral 4 denotes an increase value calculation unit, which calculates an increase value from the increase value coefficient calculated by the increase value coefficient calculation unit 3.
Reference numeral 5 denotes an increment value calculation unit, which calculates an increment value for curve drawing from the increment value calculated by the increment value calculation unit 6, 6 denotes a bitmap memory, 7 denotes a display unit, and 8 denotes a data input / output interface (I / O) and 9 are processors (CP
U).

Next, the operation of the first embodiment will be described with reference to FIG. Process S1 In process S1, the start point, the end point, and the approximate expression information stored in the curve drawing information memory 1 are read.

Processing S2 In processing S2, the division number calculation unit 2 calculates the division number M between the start point and the end point. Processing S3 In processing S3, a register X (not shown) and a
(O), 1 is set to m, and 0 is set to AA.

Process S4 In process S4, the increase value coefficient calculation unit 3 calculates the increase value coefficient from the start point, end point and approximate expression information read from the curve drawing information memory 1 and the division number M calculated by the division number calculation unit 2. . That is, the increase value coefficients A ₁ , A
Calculating the ₂ and A _3.

Process S5 In process S5, the increase value calculation unit 4 calculates an increase value for the (m + 1) th curve drawing value from the increase value coefficient calculated in the process S4. That is, A ₁ m ² and A ₂ m are calculated, and an arithmetic process represented by the equation (11) for adding to the addition register AA is performed to calculate an increase value.

Process S6 In the process S6, the increment value calculating section 5 calculates the increment value from the increase value calculated in the process S5. That is, equation (1)
As shown in 2), the increment value AA is divided into an integer part ΔY and a remainder ΔR using M ³ as a quotient, and the integer part ΔY is output as an increment value, and the remainder is stored in the addition register AA.

Process S7: The divided value Δx in the x-axis direction is added to the X register, and the increment value in the y-axis direction, that is, the increment value ΔY calculated in the process S6, is added to the Y register and sent to the bit map memory 6. .

Processing S8 and S9 It is determined whether or not the numerical value m of the m register is equal to the number of divisions M. If NO, the value of the m register is incremented by 1 in processing S9, and the processing shifts to processing S5. Is repeated. If YES, the process ends.

Next, a second embodiment will be described. Previous
In the first embodiment described above, the coefficient A of the increase value₁, A_Twoand
A_ThreeIs calculated by the arithmetic processing shown in Expression (9), and the increase value and
The increment value was calculated. On the other hand, these operations
The processor that performs processing is, for example, 8 bits or 16
Processing is performed in data units such as bits. But
Therefore, when the division number M of the section becomes large, M ^ThreeIs the binary number 8
Bit or 16 bits,
Is required to perform processing with quadruple precision, which is
It took time. The second embodiment solves this drawback.
It is for.

In the second embodiment, when equation (8) is modified, Δy _m = [A ₁ / M ² m ² + A ₂ / M ² m + A ₃ / M ² ] / M (14)

Therefore, the integer parts obtained by dividing A ₁ , A ₂ and A ₃ by M ³ are I ₁ , I ₂ and I ₃ respectively, the integer part of the increase coefficient, and the remainders R ₁ , R ₂ and R _3. Is represented by the remainder of the increase coefficient, the increase coefficient A ₁ / M ³ , A
₂ / M ³ and A ₃ / M ³ is expressed by ^{_{A 1 / M 2 = I 1}} + R 1 A 2 / M 2 = I 2 + R 2 A 3 / M 2 = I 3 + R 3 ... (15), Equation (14) is given by Δy _m = [(I ₁ + R ₁ / M ² ) m ² + (I ₂ + R ₂ / M ² ) m + (I ₃ + R ₃ / M ² )] / M = [(I ₁ m ² + I ₂ m + I ₃ ) + (R ₁ m ² + R ₂ m + R ₃ ) / M ² ] / M (16)

Therefore, I ₁ m ² , I ₂ m, R ₁ m ² and R ₂ m are calculated in the same manner as described in the first embodiment, and first, the data values stored in the register RR are calculated. The calculated R ₁ m ² , R ₂ m and R ₃ are added to calculate the increase value of the remainder. _{That, RR = RR + R 1 m} 2 + R 2 m + R 3 ... (17) comprising performing a calculation.

Assuming that an integer part obtained by dividing the right side of equation (17) by M ² is ΔI and a remainder is ΔRR, RR / M ² = ΔI + ΔRR (18) Store. That is, the following process is performed: RR = ΔRR (19)

Further, the calculated I ₁ m ² , I ₂ m and I ₃ and ΔI calculated by the equation (18) are added to the data value stored in the register AA to calculate an increase value. That is, AA = AA + I ₁ m ² + I ₂ m + I ₃ + ΔI (20)

Then, the increase value A calculated by the equation (20)
Assuming that an integer part obtained by dividing A by M is ΔY and a remainder is ΔR, the following equation is obtained: AA / M = ΔY + ΔR (21) ΔR is stored in the original register AA. That is, AA = ΔR (22) is performed.

Next, the operation of the second embodiment will be described with reference to FIG. In FIG. 3, processes S1 to S9 are as described in FIG. 2, and the process according to the first embodiment is performed. Process S11 In process S11, it is determined whether or not the number of divisions M calculated in process S2 is larger than a certain fixed value M ₀ , and a fixed value M ₀ is determined.
If it is smaller, the process proceeds to step S3 to execute the process according to the first embodiment. If YES, the process proceeds to step S12 to execute the process of the second embodiment.

Process S12 In process S12, a register X (not shown) and a
(O), m is set to 1, AA and RR are set to 0. Process S13 In process S13, the increase value coefficient calculator 3 calculates the increase value coefficient from the approximate expression information of the start point and the end point read from the curve drawing information memory 1 and the number of divisions calculated by the number of divisions calculator 2.
That is, I _{1 to} I ₃ and R _{1 represented} by the formula (15)
~R ₃ is calculated.

Process S14 In the process S14, the increase value calculating section 4 calculates the increase value for the (m + 1) th curve drawing value from the increase value coefficient calculated in the process S4. That is, R ₁ m ² and R
Calculating a ₂ m, it is added to the remainder portion summing register RR by performing arithmetic processing represented by the formula (17) to the outermost not a calculated remainder portion increment with R _3.

Next, the remainder increase value is divided by M ² to divide it into an integer part ΔI and a remainder ΔRR as shown in equation (18). The divided remainder ΔRR is stored in the register RR as shown in Expression (19). Next, I ₁ m ² and I ₂ m are calculated and added to the addition register AA together with ΔI and I ₃ to perform an arithmetic processing shown in Expression (20) to calculate an increase value.

Process S15 In the process S15, the increment value calculator 5 calculates the increment value from the increase value calculated in the process S14. That is, as shown in Expression (21), the increase value AA is divided by M,
It divides into an integer part ΔY and a remainder ΔR, outputs the integer part ΔY as an increment value, and stores the remainder in an addition register AA.

Processing S16 The division value Δx in the x-axis direction is added to the X register, and the increment value ΔY in the y-axis direction is added to the Y register and sent to the bit map memory 6. Processing S17 and S18 It is determined whether or not the value m of the m register is equal to the number of divisions M. If NO, the value of the m register is incremented by + in processing S18.
Then, the process proceeds to step S14, and steps S14 to S16 are repeated. If YES, the process ends.

While the embodiment of the present invention has been described above, the present invention is not limited to this embodiment, and various modifications in accordance with the gist of the invention are possible.

[0045]

As described above, according to the present invention, the following effects can be obtained. The increase value coefficient is calculated based on the start point, end point, n-th approximate expression information and the number of divisions M, and the increase value and the increase value are calculated from the increase value coefficient. The repeatedly calculated increment value and increment value can be performed by addition processing, and the calculation processing time can be shortened. The increment value coefficient divided by M ^q of the division number M, due to so as to calculate the increment value and increment is divided into an integer part and a remainder portion, it is possible to perform processing with less digits.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an embodiment of the present invention.

FIG. 2 is an operation flowchart of the first embodiment.

FIG. 3 is an operation flowchart of the second embodiment.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Curve drawing information memory 2 Division number calculation part 3 Increase value coefficient calculation part 4 Increase value calculation part 5 Increment value calculation part 6 Bitmap memory 7 Display part 8 Interface (I / O) 9 Processor (CPU)

Claims (3)

(57) [Claims] 1. A curve drawing value calculation device for calculating a drawing value of a curve connecting start and end points based on n-th approximate expression information connecting a start point, an end point, and a start and end point, wherein the start point, the end point, and the approximate expression An increase coefficient calculating section for calculating an increase coefficient from the information and the number of divisions M between the start point and the end point; and dividing the increase coefficient according to the increase coefficient calculated by the increase coefficient calculating section and the value of the dividing point m. An increase value calculation unit for calculating an increase value of the point m; and adding the increase value calculated by the increase value calculation unit to a remainder value for the division point m-1 stored in the register to obtain M ⁿ
, And outputs the integer part of the division result as an increment value , and stores the remainder value in the register. The increment value calculation section calculates the drawing value of the division point m-1 by the increment value calculation section.
The increment value is added to output as a drawing value for the division point m.
A drawing output value calculation device, comprising: 2. An increment coefficient integer part and an increment coefficient remainder part by dividing the increment coefficient calculated by the increment coefficient calculation unit by the number of divisions M raised to the power of n−q (1 ≦ q <n). And the increase value calculation unit calculates the increase value coefficient remainder part and the division point m.
, And calculates the remainder increase value by adding the calculated remainder increase value to the addition value stored in the remainder register.
^nq , the remainder of the division result is stored in the remainder register, and the integer part of the division result is added to the increase value calculated from the increase coefficient integer part and the value of the division point m to calculate the increment value. the increased value calculated from the increased value coefficient integer part is added to the stored value stored in said register in parts M ^q
2. The curve drawing value calculation apparatus according to claim 1, wherein an integer part of the division result is output as an increment value, and a remainder is stored in the register. 3. Before SL min when the value of the split number M is equal to or greater than a certain value claim 1 wherein from the calculation of the curve drawing values according to according to claim 2
Curve drawing value calculation device characterized in that the switched on calculation of curve drawing value by description.