JPH04153695A - Curve approximating method - Google Patents

Abstract

PURPOSE:To shorten a time required to generate an outline font by storing values of parameter functions of a curve expression previously, and finding the value of the curve expression by using only a necessary number of parameter functions. CONSTITUTION:A microprocessor CPU 0 controls the whole hardware. Then a RAM 1 is stored previously with the values of parameters of the curve expression determined as to (n) parameter values of the curve expression. According to a curve to be represented, the value of the curve expression is found from the values of parameter functions as to only (m) (m<n) out of the (n) parameter values and division points determined corresponding to the (m) parameter values are connected by straight lines. Consequently, the time required to generate the outline font is shortened.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method of approximating a curve in an outline font.

[Prior Art] In recent years, outline fonts have become rapidly popular as a means of representing curved lines in characters, figures, etc.

Conventionally, when actually displaying a curve using an outline font, the curve is approximately represented by sequentially dividing the curve until adjacent dividing points degenerate to the same point, and sequentially connecting each dividing point with a straight line.

[Problems to be Solved] The conventional method described above has the problem that a large amount of calculation processing is required each time curve data of an outline font is generated, and it takes a large amount of time to generate an outline font.

An object of the present invention is to reduce the time required to generate outline fonts.

[Means for Solving the Problems] The present invention represents a curve based on a parametric curve formula using two anchor points and at least one control point, and divides this curve into a plurality of parts. In a method of approximately representing a curve by connecting adjacent dividing points with straight lines, the values of the parameter functions of the curve formula that are determined for each of the n parameter values of the curve formula are stored in advance, and the curve to be expressed is Accordingly, the values of the curve formula are determined based on the values of the Paran-Ri function only for m of the n parameter values (m < n), and the dividing points determined corresponding to the m parameter values are determined. It is connected with a straight line.

E Example] Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

In the embodiments described below, unless otherwise specified, cubic curves such as cubic Bezier curves and cubic spline curves are used as curves representing outline fonts. Parametric representation of these curves is as follows.

Q - W A x P A + W B x P B + WC x PC + WD x PD - CI) Here, WA, WB, WC and WD are the parameters "t"
For example, in the case of a cubic Hezier curve, it is expressed as follows.

WA= (1-t) 3-(2a) WB-3t
(1-t)2...(2b)WC-3t (
1-t)...(2C)WD-t"
... (2d) (0≦t≦1) PASPBSPC and PD determine the shape of the curve
-The coordinates on the Y plane are as follows.

PA (x, y): Anchor point PB (x, y): Control point PC (x, y
): Control point PD (x, y): Anchor point Here, considering equation (1), the parameter function WA
, WB, WC, and WD are uniquely determined by the type of cubic curve, for example, as shown in equations (2a) to (2d), and PA, PB.

PC and PD are predetermined according to the shape of the curve. Therefore, the parameter functions WA, WB, W
Regarding C and WD, the parameter "t" is subdivided as shown in FIG.
It is possible to calculate the values of B, WC and WD and store the calculation results in a data table. PASPB
The coordinates (x, y) of SPC and PD are also set in advance.
can be stored in a data table. By storing each data in the data table in this way and performing hardware calculation based on equation (1) using a multiplier and an adder, curve data can be generated at high speed. That is, as shown in FIG. 5, t (0
≦t≦1) is divided into 256 parts, and a parameter function WA is applied to each part in advance.

By determining WB, WC, and WD and performing hardware calculations based on equation (1), it is possible to determine the coordinates of a total of 257 points on the curve. By sequentially connecting these coordinates with straight lines, a curve can be approximated.

By the way, in the above example, the curve would be divided into 256 parts to approximate it. For example, for a curve with a small curvature,
It is possible to express an approximate curve with sufficient viscosity without increasing the number of divisions. This is illustrated in Figures 3 and 4 (A
) and FIG. 4(B). The curve shown in FIG. 3 is composed of a total of 14 small curves 01 to C14.

That is, each of the small curves C1 to C14 is expressed by equation (1) using different anchor points and control points. Figure 4 (A
) and FIG. 4(B) show the small curves C1 and C2 shown in FIG. 3, respectively. The small curve C1 is divided into 16 parts as shown in FIG. 4(A), and approximately represented by 17 points QO20 to QO,16 on the small curve C1. Therefore, in the example of Figure 5, n=0.16.32,...
・・・・・・ Set n by 16 steps (such as 256)
256/16-16) and perform calculations only for these n. The small curve C2 is shown in Figure 4 (B)
The QO is divided into 32 parts as shown in 33 points on the small curve C2.
Approximately expressed as 10 to Q O, 32. Therefore, in the example in Figure 5, increase n by 8 steps (256/32-8), such as n-0, 8, 161, -... 256, and calculate only for these n. Just go. In this way, by determining an appropriate number of divisions in advance according to the curve and performing only the calculations for that number, it is possible to further speed up the hardware calculations. Note that a specific method for determining the number of divisions will be described later.

With reference to the above, a method of approximating the curve shown in FIG. 3 will be described below.

FIG. 1 is a block diagram showing hardware used to approximate the curve shown in FIG. 3.

CPU0 is a microprocessor that controls the entire l\-ware.

ROM O is a read-only memory that stores programs for various processes performed by the microprocessor CPU0.

RAM O is a random access memory, and stores various data described below in advance. R.A.M.O.
stores data related to various curves, such as data related to cubic spline curves in addition to data related to cubic Bezier curves, and these data are sent to RAMI, RAM2, and RAM3, which will be described later, as necessary.

RAM M1 is a random access memory that stores the values of the parameter functions WA, WB, WC, and WD shown in FIG. These data WAO~WA
25B, WBO~W825B, WCO~WC25G
, WDO to WD 258 are sent from RAM O, and are sent from RAM I as shown in FIG.
stored within.

RAM2 is a random access memory, and stores coordinate data of anchor points PA and PD, control points PB and PC for each of the small curves C1 to C14 shown in FIG. Each of these coordinate data is sent from RAM0 and is stored in RA Nl 2 as shown in FIG. In Fig. 7, PAXO to PDXO are the respective X coordinates of the anchor point and control point in the small curve C1, P
AYO to PDYO are the respective X coordinates of these points, FAXI to PDX1 are the respective X coordinates of these points in the small curve C2, and PAYI to PDYI are the respective X coordinates of these points.

RAM 3 is a random access memory that stores in advance data corresponding to the number of divisions of each of the short curves C1 to C14 shown in FIG. 3 for each of the short curves C1 to C14. The data corresponding to the number of divisions may be the number of divisions itself or the number of steps n shown in FIG. In this embodiment, random access memory RA
As shown in FIG. 8, M3 stores the number of steps n, that is, the increment Δn of n. In FIG. 8, Δn
1, Δn2, . . . are the numbers of steps stored corresponding to the small curves C1, C2, . . . shown in FIG. 3, respectively. These data Δn1,
.DELTA.n2, . . . are sent from RAM0 and are stored in RAMB as shown in FIG.

RA kl 4 is random access memory, (1
) The result of the hardware calculation based on the formula is the coordinate data Q (x,
y). These coordinate data Q(x
, y) are stored in RAM 4 as shown in FIG. In FIG. 9, data X010 to XO,1
6 and YO10 to YO,le are the X and X coordinates of points QO,0 to Q0,1B on the small curve C1 in FIG. 4(A), respectively, and the data X1,0 to X1,32 and Yl, 0 to Yl, 32 are the small curve C2 in FIG. 4(B)
X and X of the upper points Q 1.0 to Q 1, 32, respectively
It is a coordinate.

PNTI is an address pointer for RAM1, and an independent address pointer PNTIA%PNTIB.

It is composed of PNTIC and PNTID.

PNTIASPNTIB, PNTIC and PNTID
is the data WAO to WA25 stored in RAMI
B, WBO~W825B, WCO~WC256, W
It specifies the addresses of DO to WD25B (see FIG. 6), respectively.

PNT2 is the address pointer of RAM2, and RA
This designates the address of each coordinate data (see FIG. 7) of the anchor point and control point stored in M2.

PNT3 is the address pointer of RAM3,
The number of steps Δn1, Δn2, . . .
. . . (see FIG. 8).

PNT4 is an address pointer of RAM4, and coordinate data XO20~X obtained by hardware calculation
O, 16 and YO10 to Y0, 16, etc. (see Figure 9)
This specifies the address of .

STP is a latch circuit that latches the number of steps Δn1, Δn2, . . . (see FIG. 8) stored in the RAM 3.

ADD is an adder circuit, which indicates the currently selected address pointer (PNTIASPNTIB.

PNTIC or PNTID) value and latch circuit S
TP value and sends the addition result to the currently selected address pointer.

In other words, the number of steps Δn1, Δn2, etc. in which the value of the address pointer is latched in the latch circuit STP
...It will play a role of increasing the number of people.

MLT is a multiplier circuit that combines the data stored in RAM 1 shown in FIG. 6 and R shown in FIG.
This is to perform multiplication with the data stored in A M2. In other words, the multiplication in equation (1) (for example, WA
XPA) part will be calculated.

ALU is an arithmetic logic circuit, and multiplier circuit ML
This is to add the multiplied value of T and the value of an accumulator ACC, which will be described later.

ACC is an accumulator that holds the operation result of the arithmetic logic circuit ALU and sends this operation result to one input of the arithmetic logic circuit ALU. In other words, the arithmetic logic circuit ALU and the accumulator ACC perform the calculation of the addition part in equation (1).

C0NT is a control circuit that receives instructions from the microprocessor CPU0 and controls each of the arithmetic operations described above. This control circuit C0NT includes microprograms for each of the arithmetic operations described above.

Next, the operation of the circuit shown in FIG. 1 will be explained with reference to the flowcharts shown in FIGS. 2(A), (B), and (C).

First, initial settings are performed based on a signal from the microprocessor CPU0.

(a): Data corresponding to each t of the parameter functions WASWB, WC, and WD shown in Fig. 5 is sent from RAM0 to RAMI, and these data are stored in RAM1 as shown in Fig. 6. be done. RAM0 to RAM
2, coordinate data of anchor points and control points are sent for each of the small curves 01 to C14 shown in FIG. 3, and these data are stored in RAM 2 (this The step number data Δn1, Δn2, and Δn2 for each of the small curves C1 to C14 are stored in RAM O to RAM3, corresponding to the number of divisions of each of the small curves C1 to C14 shown in FIG. . . . are sent, and these data are stored in RAM B (2S) as shown in FIG.

(b), address pointers PNT2, PNT3, PNT
As a result, the address where the data PAXO shown in FIG.
The address where the data Δn1 shown in the figure is stored is the 9th address.
The addresses for storing the data X0.0 shown in the figure are each designated.

Initial settings are completed as described above, and then calculation processing is performed on the short curve C1 shown in FIGS. 3 and 4 (A).

(C) Near address pointer PNTIA is set to "O," address pointer PNTIB is set to "257," address pointer PNTIC is set to "514," and address pointer PNTID is set to "771." That is, as shown in FIG.
The addresses where OSWCO and WDO are stored are respectively specified. The latch circuit STP has
Data M [PNT
3] is latched. That is, the number of steps Δnl shown in FIG. 8 (the number of steps "16" corresponding to the number of divisions of the short curve C1 shown in FIG. 4(A)) is latched.

(d): Next, the calculation routine shown in FIG. 2(B) is performed as follows.

First, in order to find the X coordinate of point QO10 shown in FIG. 4(A),
xPC+WDxPD” is calculated as follows.

(dl): Accumulator ACC is cleared and “0”
or is set.

(d2) R specified by near address pointer PNTIA
Data M [PNTIA] or “WAO” stored at address “0000” of AMI (see Figure 6)
Or it is sent to the “X” power of the multiplier circuit MLT. Data M [PN
T2] or PAXO” (see FIG. 7) is sent to the “Y” input of the multiplier circuit MLT.

(d3): The product-sum calculation shown in FIG. 2(C) is performed as follows.

(dlol): Multiplier circuit MLT's “X” human power value “WAO” and “Y′ large input value “PAXOo” product “WA”
OXPAXO” is “Z” of the multiplier circuit MLT
is output to. In other words, “WA x P A in equation (1)
A calculation corresponding to `` is performed.The calculation result is sent to the ``71 input'' of the arithmetic logic circuit ALU, while data ``0'' of the accumulator ACC is sent to the ``X° large input'' of the arithmetic logic circuit ALU.

(d]02) - The sum of the "X" human power value of the arithmetic logic circuit ALU and the "Y" human power value of the arithmetic logic circuit ALU is calculated,
This calculation result is sent to accumulator ACC. As a result, “WAOxPAXO” is stored in accumulator ACC.
The value will be retained.

(d103) The value of address pointer PNT2 is “1”.
” is added, and as a result, the pointer value becomes “0001°”.

(d4) R specified by near address pointer PNTIB
The data M[PNTIB, that is, "WBO" (see FIG. 6) stored at address "0257" of A M1 is sent to the "X' input of the multiplier circuit MLT. It is designated by the address pointer PNT2. R A
Data M[PNT2] stored at address “0001” of M2, that is, “PBXO” (Fig. 7)
J light) is sent to the "Y" power of the multiplier circuit MLT.

(d5): The product-sum calculation shown in FIG. 2(C) is performed. The basic operation is the same as described in (d3) above.

In the multiplier circuit MLT, “WB” shown in FIG.
The product “WBOxP” of Oo and “PBXO” shown in Figure 7
BXO", that is, the calculation corresponding to "WB
The sum with the value "WAOXPAXO" held in C is calculated. This calculation result “W A Ox P A
O+WBOxPBXO” is held in the accumulator ACC.In other words, “WAxPA+” in equation (1) is
A calculation corresponding to "WBXPB" is performed.

(d6) R specified by near address pointer PNTIC
The data M[PNTIC or "WCO" (see FIG. 6) stored at address "0514°" of AMI is sent to the "X" input of the multiplier circuit MLT.

Data M[ stored at address "0002" of RAM2 specified by address pointer PNT2
PNT2] or "PCXO" (see FIG. 7) is sent to the "Y" input of the multiplier circuit MLT.

(d7): The product-sum calculation shown in FIG. 2(C) is performed. The basic operation is the same as that described in (d3) above.

In the multiplier circuit MLT, “WC
The product “WCOxP” of “O” and “Pcxo” shown in FIG.
CXO”, that is, “wc x p c” in equation (1)
A calculation corresponding to is performed. In the arithmetic logic circuit ALU,
This calculation result “wcoxpcxo” and accumulator A
The value held in CC “WAOxPAXO+WBOx
PBXO” is calculated.The result of this calculation is “WAO
XPAXO+WBOXPBXO+WCOxPcXO° is held in accumulator ACC. That is, here, "WAXPA + WBxPB + WCxPC" in equation (1)
A calculation corresponding to is performed.

(d8) R specified by near address pointer PNTID
Data M[PNTID], ie, WDO" (see FIG. 6) stored at address "0771" of AMI is sent to the "X° large input" of multiplier circuit MLT. Data M[ stored at address “0 (103”) of RAM2 specified by address pointer PNT2
PNT2], that is, "PDXO" (see FIG. 7), or the "Y" large input of the multiplier circuit MLT.

(d9): The product-sum calculation shown in FIG. 2(C) is performed. The basic operation is the same as that described in (d3) above.

The multiplier circuit MLT is the “WD” shown in FIG.
The product “WDOxP” of “O” and “PDXO” shown in FIG.
DXO", that is, the calculation corresponding to "WDxPD" in equation (1) is performed. In the arithmetic logic circuit ALU, this calculation result "WDOxPDXO° and the value held in the accumulator ACC "W A Ox P A X O + W
The sum of “B OXPBXO+WCOxPCXO” is calculated.The result of this calculation is “W A OX P A X O+
W B OxP B X O+ W COx P C
X O+ W D Ox P D X O.

is held in accumulator ACC. That is, here, equation (1) (7) - WAXPA + WBXPB + WCx
A calculation equivalent to PC+WDXPD° can be performed.

(dlO): In the above manner, the X coordinate of the point QO10 shown in FIG. 4(A) is calculated. The above calculation result held in the accumulator ACC is stored at address "0000" of RAM 4 designated by address pointer PNT4. This stored data M[PN
T4] is represented as X010° in FIG.

(dll) "1" is added to the value of the near address pointer PNT4, and as a result, the pointer value becomes "0001".

(d12) to (d21): Next, in order to find the X coordinate of point QO10 shown in FIG. 4(A), use the above (dl)
The processes (d12) to (d21) shown in FIG. 2(B) are performed in the same way as the processes (d10). The obtained calculation result “WAOxPAYO+W B Ox P
B Y O+ W COx P CY O+ W D
QxPDYOo is stored at address "0001" of RAM4 specified by address pointer PNT4. This stored data M [PNT4] is “Y” in FIG.
It is expressed as 0,0''.

(d22), 11' is added to the value of the address pointer PNT4, and as a result, the pointer value becomes "0002".

Cd2B) 8 is subtracted from the value of the nearest pointer PNT2, and as a result, the pointer value becomes "oooo".

As described above, the calculation routine shown in FIG. 2(A) is completed, and the X coordinate of point Q O,0 shown in FIG. 4(A) is
X010° and the X coordinates "yo, o" are stored in the RAM 4 (see FIG. 9).

(e) Nearest pointer PNTIA, PNTIB, P
The number of steps Δn1 (the number of steps "16" corresponding to the number of divisions of the small curve C1 shown in FIG. 4(A)) latched in the latch circuit STP is added to the values of NTIC and PNTID. Therefore, address pointer P
The pointer values of NTIA, PNTIB, PNTICSPNTID are “16”273° (257+1
6), “530” (514+16), “787”
(771 + 16).

(f) Value of near address pointer PNTIA &“256
If the force is greater than ') II is cut off.

The current value of address pointer PNTIA (yo “001B”)
Therefore, the processing power is transferred to the calculation routine (d), and the processing power is increased (
The same processing power as that described in d) is performed. As a result, the X coordinate of point QO11 shown in FIG. 4(A) is "X011".
and the X coordinate "YO21" force) are stored in the RAM 41 (see FIG. 9). The specific data number, “Xo, 1’ is “WA16xPAXO+WB16XPBXO+WC16
xPCXO+WD16xPDxo” and “YQ, l
” is “WA16xPAYO+WB16XPBYO+WC
16XPCYO+WD16xPDYO" (see FIGS. 6 and 7).

As described above, similar processing is performed until the value of the address pointer PNTIA becomes thicker than 256". As a result, as shown in FIG.
1B's X coordinates "xo, o" ~ "Xo, 16" and X coordinates "Yo, 0" ~ "Y O, 16" Force, 1@order R
AM4 (see FIG. 9).

(g) The value of near address pointer PNTIA is “256”
If the value is larger than , the following processing is performed. 8 is added to the value of address pointer PNT2, and as a result, the pointer value becomes "0008" (see FIG. 7). 1 is added to the value of address pointer PNT3, and as a result, the pointer value becomes "0001" (see FIG. 8).

In this manner, the processing for the short curve C1 shown in FIGS. 3 and 4(A) is completed.

(h), it is determined whether the value of the address pointer PNT3 has become "14".This value "14" is the third
This corresponds to the number of divisions of the curve shown in the figure, and this value is appropriately selected for each curve.

Since the current value of address pointer PNT3 is "0001", processing moves to calculation routine (C), and the above (C) to (
Processing similar to that described in g) is performed. the result,
The X coordinates of points Q1,0 to Q1,32 shown in FIG. 4(B) are "Xl,0" to "X 1.32" and the
(1' to "Y1,32" are sequentially stored in the RAM 4 (see FIG. 9).

As above, the value of address pointer PNT3 is determined.
The same process is performed for the small curves C] to C14 shown in FIG. 3 until reaching 14'. Address pointer PN73
When the value of becomes "14'," the small curves C1 to C shown in FIG.
Processing power for 14: It is determined that the process has ended.

As mentioned above, the appropriate number of divisions can be selected for each small curve depending on its curvature, etc., and if the optimal number of divisions is selected for each small curve, the software calculation can be performed easily. It is possible to increase the speed. General (1) When the curvature is small, an approximate curve can be expressed accurately even with a small number of divisions.

Therefore, a method for determining the optimal number of divisions of a small curve will be described below.

The first method will now be explained with reference to FIG.

In FIG. 10, PA and PD are anchor points of the short curve CV1, and PB and PC are control points of the short curve CV1. Lab.

L bc, L cd, and L da are the lengths of straight line segments connecting PA and PB, PB and pc, PC and PD, and PD and PA, respectively. Generally, the lengths of the line segments Lab and Led are longer as the CVIO curvature is smaller or larger. Therefore, using the following evaluation formula, the small curve CVI
It is possible to find the optimal number of divisions "N".

ΔL-(Lab+Lbc+Led-Lda)+1-(3
)N-2flog(a) ΔL'-(4)2≦
a≦8 (“a-” is the base) The base “a” is selected as appropriate depending on the accuracy of the approximation of the curve, and the number of divisions “N” shown in equation (4) or the data table Number of divisions (“25” in the example in Figure 6)
6”).

An example of calculating the number of divisions using the above evaluation formula (in the case of "a-3") is shown in Figure 11.
This figure shows an example in which the y coordinates of B and PC are sequentially reduced, that is, the curvature of the small curve is sequentially reduced.

Note that the "step" shown in Figure 11 is "256/N".
is the value of step number data Δn1 shown in FIG.
This corresponds to Δn2, . . . . As shown in Figure 11, when the above evaluation formula is used,
It can be seen that the smaller the curvature of the small curve, the fewer the number of divisions.

Note that in equation (3), the values of each line segment may be used as they are, or values obtained by squaring the lengths of these line segments may be used.

Next, the second method will be explained with reference to FIGS. 12 and 13.

In FIG. 12, PA and PD are anchor points of the short curve CV2, and PB and PC are control points of the short curve CV2. Sl is the above point PA, P
This is the area of a rectangle formed when BSPC and PD are successively connected with straight lines. Generally, the area of the above rectangle S1
becomes larger as the curvature of the small curve CV2 becomes larger. Therefore, the optimal number of divisions of the short curve CV2 is determined by the following evaluation formula.
You can find N.

N-2(I o g (a) S 1 t,
,, (5) 2≦a≦8 (“a” is the base) The base “a” is selected as appropriate depending on the approximation accuracy of the curve, and the number of divisions “N” shown in equation (5) is the number of divisions in the data table (in the example in Figure 6, it is “25”)
6").

In FIG. 13, PA and PD are the anchor points of the short curve C3, and PB and PC are the control points of the short curve CV3. S2 is the above point PA, P
S3 is the area of a triangle formed when points B and PD are sequentially connected with straight lines, and S3 is the area of a triangle formed when the points PA, PC, and PD are sequentially connected with straight lines.

Generally, the sum "S2+53" of the areas of the triangles S2 and S3 increases as the curvature of the small curve CV3 increases. Therefore, the optimum number of divisions "N" of the short curve CV3 can be determined using the following evaluation formula.

N=2 flog(a)(S2+53)l ,,, (
6) 2≦a≦8 (“a” is the base) The base “a” is selected as appropriate depending on the approximation accuracy of the curve, and the number of divisions “N” shown in equation (6) or the data Number of divisions in the table (“25” in the example in Figure 6)
6”).

Note that in equations (5) and (6), the values of each area are used as they are, but values obtained by squaring these areas may also be used.

Next, the third method will be explained with reference to FIG.

In FIG. 14, PA and PD are the anchor points of the short curve C■0, and PB and PC are the control points of the short curve C■0. Dl is the first on the small curve CVD
, and is a point other than anchor points PA and PD. Specifically, the value of WA-WD is obtained by setting t-1/2 in equations (2a) to (2d), and these values are substituted into equation (1). In addition, the small curve C
(2) Among 0, the curve between the point PD and the first dividing point D1 is called the first dividing curve. DB is a second division point on the short curve CVD located between PD and Dl, and is a point other than PD and D1. Specifically, (2a)-(2d)
The value of WA-WD is obtained by setting t-3/4 (-1/2+1c) in Equation 1, and these values are substituted into Equation (1). It should be noted that among the small curves C■0, the one between the point PD and the second dividing point D2 is referred to as a second dividing curve. Similarly, t −7/8 (=1/2+
DB (not shown), t-15/I6 (-1/
2+I74+l/8+1/16) small curve CV
The fourth dividing point on D is set as D4 (not shown), and so on, dividing points Dn (not shown) on the small curve C■0 are determined one after another. Note that when the first to nth division points D1 to Dn are determined in this manner, they can be determined at high speed by using the data table shown in FIG. Ll is the length of the line segment connecting points PA and PD with a straight line, L2 is the point P
The length of the line segment connecting A and the first dividing point D1 with a straight line, L
3 is the length of the line segment connecting the point PD and the first dividing point D1 with a straight line, L4 is the length of the line segment connecting the first dividing point D1 and the second dividing point D2 with a straight line, L5 is the length of a line segment connecting the point PD and the second division point D2 with a straight line.

The operation of determining the number of divisions will be described below with reference to FIG.

After determining the first division point D1, the lengths of the line segments L1, L2, and L3 are determined, and the following difference pig is calculated.

ΔLl−L2+L3−Ll−(7a) It is determined whether the first difference data ΔL1 satisfies the following conditions.

ΔL1 × ΔLO (7b) where ΔLO is a predetermined constant. When the first difference data ΔL1 satisfies the condition of equation (7b), the number of divisions of the short curve CVO in FIG. 14 is "1". When the first difference data ΔL1 does not satisfy the condition of equation (7b), after determining the second dividing point D2, the lengths of the line segments L4 and L5 are determined, and the following calculations are performed.

ΔL2-L4+L5-L3 (8B) Determine whether the second difference data ΔL2 satisfies the following conditions.

ΔL2<ΔLO...(8b) When the second difference data ΔL2 satisfies the condition of equation (8b), the number of divisions of the short curve Cvo in FIG. 14 is "2".
'. When the second difference data ΔL2 does not satisfy the condition of equation (8b), division is performed in the same manner as above, and the division points DB, D4, . . . Dn are sequentially divided.
and difference data ΔL3, ΔL4,... ΔL
Find n. It is determined whether the nth difference data ΔLn satisfies the following conditions.

ΔLn<ΔLO−(9b) When the nth difference data ΔLn satisfies the condition of equation (9b), the number of divisions of the small curve cVo in FIG. 14 is “2”.
°−1'.

Note that in the fourth method described above, (2a) to (2d)
In the formula, t = 1/2, t -3/4 (s/
2+1/4) t=7/8 (-1/2+1/4+
l#), t -15/1B(-1/2+1/4+1/
8 + 1/1B) ...... to find each division point, for example, t -1/2, t -1/4 (
-1/2-1c), t = 3/8 (-1/2-1/
4+1/8) t =5/16 (-1/2-1/
4+1/8-1/16) , . . . and each dividing point may be obtained. In short, when finding the th division point, n at the (k-1)th division point
You may add or subtract "1/2" to the value of +-1.

[Effects] According to the present invention, the values of the parameter functions of the curve formula are stored in advance and the values of the curve formula are determined using only the necessary number of parameter functions. No arithmetic processing is required, and the time required to generate an outline font can be significantly reduced.

[Brief explanation of the drawing]

Figures 1 to 14 all illustrate embodiments of the present invention, with Figure 1 being a block diagram and Figure 2 (A)
, FIG. 2(B) and FIG. 2(C) are flowcharts showing the operation of FIG. 1, FIG. 3, FIG. 4(A), and FIG.
Figure (C) is an explanatory diagram of the outline font, Figure 5 is a conceptual diagram of the data table, Figures 6 to 9 are the address maps of each pig stored in the RAM, and Figure 10 is the number of divisions of the small curve. An explanatory diagram of the first method of determining the number of divisions. Figure 11 is a diagram showing a specific example of determining the number of divisions using the first method. Figures 12 and 13 are diagrams of the second method of determining the number of divisions of a small curve. FIG. 14 is an explanatory diagram regarding the third method of determining the number of divisions of a small curve. PA, PD・・・Anchor point PB, PC・
...Applicant for control points and above Seikosha Co., Ltd.

Claims (1)

[Claims] A curve is expressed based on a parametric curve formula using two anchor points and at least one control point, and the curve is divided into a plurality of parts and adjacent dividing points are defined. In the method of approximately representing the above-mentioned curve by connecting them with straight lines, the values of the parameter functions of the above-mentioned curve equation, which are determined for each of the n parameter values of the above-mentioned curve equation, are stored in advance, and depending on the curve to be expressed, For m of the above n parameter values (m<n), find the value of the above curve formula based on the value of the above parameter function, and connect the division points determined corresponding to the above m parameter values with a straight line. A curve approximation method characterized by: