JPH0628418A - Equal equally dividing points calculating method for b-spline curve - Google Patents

Abstract

PURPOSE:To provide the equally dividing points calculating method for a B-spline curve, which can shorten the processing time. CONSTITUTION:When a B-spline curve on a drawing is indicated from a keyboard, in S1, control point information, a NOT vector, and an equal division number N are inputted, and in S2, designated length of a given point designated as one in plural equally dividing points between a start point and an end point on the B-spline curve is calculated, and in S3, curve length to a first candidate point being a target by using a ratio of length of an actual B-spline curve to a difference of the maximum value and the minimum value of the NOT vector of fundamental data of the B-spline curve is calculated, and in S4, length of the curve length and the designated length is compared, and when they are the same, it is decided that a position of a given point being a target is derived and the processing is finished, and unless they are the same, in S5, curve length of a second candidate point is calculated so as to insert and hold the given point between its point and a first candidate point, based on a difference of the curve length being length on the curve between a first condidate point and the given point and the designated length, and in S6, a position of the given piont is calculated by a bisecting method by using the curve length of a first and a second candidate points and the processing is finished.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calculating equidistant points of a B-spline curve used for representing a curve in a CAD system.

[0002]

2. Description of the Related Art A conventional method for calculating an equal point of a B-spline curve is shown in the flow chart of the conventional equal point calculation method of FIG. 6 and has been carried out through the procedure described below.

First, when a B-spline curve on the drawing is designated in the CAD system, a step (hereinafter referred to as S) is performed.
At 31, the basic data (control point information / knot vector) of this B-spline curve and the equal division number N are fetched. Next, these input data are checked in S32, and if abnormal, the process ends as an error. If normal, the total length of the B-spline curve is calculated from this basic data in S33, and S
34 at 1 / N, 2 / N, ..., (N-1) / N of the total length
Of the total length along the curve from the start point of the B-spline curve in S35, 1 / N, 2 / N, ..., (N
The point corresponding to the length of -1) / N is obtained, and the data of the obtained point is output in S36. Here, 1 / N, 2 / N, ..., (N of the total length along the curve from the starting point performed in S35
-1) / N In order to obtain a point, the calculation is required to find the point that has moved the specified length from the point on the spline curve along the path on the curve. A procedure for calculating the designated length movement of the point will be described.

FIG. 7 is a flow chart showing a conventional procedure for calculating the designated length movement of a given point on a curve. First, in S41, the basic data of the B-spline curve and the equal division number N are input, and then in S42, the parameter t ₀ on the curve of the given point is obtained,
After the knot vector t _i larger than t ₀ is obtained in S43, the length of the curve in the section [t ₀ , t _i ] is obtained in S44. Next, it is determined whether or not the length of the curve obtained in S45 matches the designated length, and if they match, the point on the curve corresponding to the knot vector t _i is obtained in S46, and the process ends. Further, if the length of and the curve does not match the length and the specified length of the curve is less than the specified length, the t _i until the length of the curve in the interval [t _0, t _i] in S47 exceeds the specified length i is increased and the process jumps to S44, and thereafter, the same operation as described above is repeated. If the length of the curve exceeds the specified length, the larger one of the parameters t ₀ and t _i-1 is set to t _start and the knot vector t _{i is set} to t _end in S48, and the middle point is t _middle = (t _start + t _end ) ÷ 2 and find the target point by the dichotomy.

FIG. 8 is an explanatory diagram for explaining the bisection method. First, the interval [t ₀ , t
The length of the curve in [ _middle ] is calculated and compared with the specified length. If the curve length and the specified length match, the point on the curve corresponding to the parameter t _middle is calculated and the process ends. If the curve length does not match the specified length, the following process is repeated until the specified length matches.

When the curve length is smaller than the designated length as shown in FIG. 8B, the value of t _middle is substituted for t _start .

When the curve length is larger than the designated length as shown in FIG. 8C, the value of t _middle is substituted for t _end . After updating t _start (or t _end ) t _middle = (t
By updating t _middle according to the formula _start + t _end ) / 2, the state returns to the state of FIG. 8A, and the length of the curve in the section [t ₀ , t _middle ] is _calculated again, and the curve length is _calculated . The above-mentioned processing is repeated until the specified length matches the specified length.

The above is the conventional procedure for calculating the designated length movement on a curve.

[0009]

In the conventional B-spline curve equidistant point calculation method described above, since t ₀ is usually the starting point on the curve, the length equal to the length specified from the given point on the curve is used. There is a problem in that it takes time to calculate the moved point, and particularly when the number of B-spline passing points is large, the processing time is proportional to the number of passing points.

An object of the present invention is to shorten the processing time B
-To provide an equal point calculation method for a spline curve.

[0011]

SUMMARY OF THE INVENTION The B-spline curve equidistant point calculation method of the present invention comprises a plurality of equal points between a start point and an end point on a B-spline curve used to represent the curve in a CAD system. In the B-spline curve equal point calculation method for calculating the position of a given point having a designated length designated as one of the points, the maximum value and the minimum value of the knot vector of the basic data of the B-spline curve are calculated. The ratio of the length of the actual B-spline curve to the difference between the two is used to determine the curve length to the first candidate point of interest, and the length on the curve between the first candidate point and the given point. Based on the difference between the curve length and the designated length, the curve length of the second candidate point is calculated so as to sandwich the given point between the first candidate point and the first candidate point, and the curve length of the first and second candidate points is calculated. The position of the given point is calculated by the bisection method using the curve length.

In the B-spline curve equal point calculation method of the present invention, the difference between the maximum value and the minimum value in the knot vector of the basic data of the B-spline curve is divided by the length of the B-spline curve. The average change rate of the knot vector per unit length of the spline, and multiplying this average change rate by the specified length up to the target giving point gives the first candidate point of interest from the start point of the B-spline curve. May be defined as the curve length up to.

[0013]

Embodiments of the present invention will now be described with reference to the drawings.

FIG. 9 is an external view showing a hardware configuration of an embodiment of the present invention. An input / output arithmetic unit 10 for carrying out the present invention is an engineering workstation (hereinafter referred to as EWS) as a CPU that plays a role of performing a calculation such as a designated length movement calculation of a B-spline curve and notifying each device unit of the calculation result. ) 1 and a CRT display 2 for displaying and outputting elements such as curves as a CAD drawing,
A keyboard 3 used by the operator for inputting numbers such as the number of equal divisions, a tablet 4 and a stylus pen 5 used by the operator for instructing curved line elements on the screen are provided.

The procedure for carrying out the present invention using the input / output arithmetic unit 10 will be described below.

The essential point of the operation of the equal point calculation method of the B-spline curve of the present invention is that when the B-spline curve on the drawing is designated from the keyboard 3 as shown in the flow chart of FIG.
In S1, the basic data (control point information / knot vector) of this B-spline curve and the equal division number N are input, and next,
In S2, a designated length of a given point that is designated as one of a plurality of equally divided points between the start point and the end point on the B-spline curve is calculated, and in S3, the knot vector of the basic data of the B-spline curve is calculated. The ratio of the length of the actual B-spline curve to the difference between the maximum value and the minimum value is used to calculate the curve length up to the target first candidate point, and the length between the curve length and the designated length is calculated in S4. If they are the same, the position of the target addition point is determined and the process ends. If they are not the same, in S5, a given point is set between the first candidate point and the given point based on the difference between the curve length which is the length on the curve and the designated length. This is to calculate the curve length of the second candidate point so as to be sandwiched, calculate the position of the given point by the dichotomy method using the curve lengths of the first and second candidate points in S6, and end the processing.

2 to 4 are detailed flow charts of one embodiment of the present invention.

First, in step S7 of FIG. 2, the spline curve on the CAD drawing is designated by using the tablet 4, basic data such as control point coordinates and knot vectors, and the point data on the curve are input, and the area is preliminarily set. Is stored in the reserved variable area. Next, in S8, the parameter on the curve of the given point is calculated and stored in the variable p ₀ . Further S9
After calculating the total length of the spline from the Simpson method of numerical integration from the control point coordinates and the knot vector stored as the basic data in, the knot vector per unit length of the spline is obtained by applying the following formula. The average rate of change of is calculated and stored in the variable λ ₀ .

[0019] Next, in S10, the candidate parameter p ₁ of the designated length moving point is obtained from p ₀ + (target designated length) × λ ₀ , and in S11, the length L of the curve in the section [p ₀ , p ₁ ] is again determined by the Simpson method. Calculate and compare the curve length L obtained in S12 with the designated length,
If they match, the process jumps to S13 of FIG. 4, finds a point on the curve corresponding to the parameter p ₁ , outputs the result, and ends the process. If the curve length and the specified length do not match, S14
Then, this value is taken out from the storage area of the value of (designated length-L) and multiplied by λ ₀ to obtain the advance width δ _p , which is added to p ₁ . That is, a new candidate point parameter is defined by p ₁ + δ _p and stored in the variable p _new , the original p ₁ is stored in the variable p _old, and the code of (specified length −L) is stored in the variable ε ₁ in S15. To do.

Here, the operation shifts to FIG. 3, the curve length L'in the section [p ₀ , p _new ] is calculated in S16, and S17 is calculated.
Then, the curve length L'is compared with the designated length, and if the curve length L'matches the designated length, the process jumps to S13 in FIG. 4 to find the point on the curve corresponding to the parameter p _new and terminate. When the curve length L ′ does not match the designated length, the sign of (designated length−L ′) is stored in the variable ε ₂ in S18, and the variable ε is stored in S19.
The sign of ₁ and the variable ε ₂ is compared. If the signs of ε ₁ and ε ₂ match, δ _p is added to the parameter p _new in S20 to make this p _new . Next, in S21, p _new
And p ₀ are compared with each other, and if p _new takes a value larger than p ₀ , the process jumps to S16, enters the loop, stores the value of the original variable p _{new in} the variable p _old, and stores the interval [p ₀ , p If it is determined in S17 that the length L ′ of the curve in [ _new ] matches the designated length, the process jumps to S13 in FIG. 4, and even if the length does not match in S17, the sign of (designated length−L ′) is ε _{1 in} S19. If it is determined that P _new is different from p _new
When the value is ₀ or less, p _{0 is set} to p _{new in} S22, the process jumps to S23 in FIG. 4, and the parameter p _new is continuously updated until the loop from S16 to S21 is exited.

The state of exiting this loop is, as is clear from the diagram showing the state of operation of the dichotomy according to the present invention in FIG. 5, the parameters on the curve of the target designated length moving point are the parameters p _old and between p _new .

Next, the operation moves to FIG. 4, and in S23, three variables p _start , p _end and p _middle are prepared and defined as follows. That is, of the parameters p _old and p _new , the smaller one is p _start , the larger one is p _end , and p _middle
= (P _start + p _end ) / 2, which are stored as the values of the variables, and the designated length moving point is searched by the dichotomy method using these. The search for the target point by the bisection method is similar to the conventional case, and is performed as follows. In S24, the section [p ₀ ,
p _middle ] to _find the length L "of the curve by numerical integration,
In S25, a comparison is made with the designated length, and if the curve length L ″ and the designated length match, the point on the curve corresponding to the parameter p _middle is found in S13 and the processing ends. If they do not match, the next process is repeated until they match the specified length. That is, when the curve length L ″ is smaller than the designated length, the value of p _middle is stored in the value of the variable p _start in S26. Further, when the curve length is larger than the designated length, the value of p _middle in S27. _Is stored in the value of the variable p _end .
After updating _start (or p _end ), p _middle =
(P _start + p _end ) / 2 updates p _middle , and S
Returning to step 24, the length of the curve in the section [p0, pmiddle] is obtained by numerical integration, and steps S24 to S28 are repeated until the curve length L ″ matches the designated length.

The above is the procedure for calculating the designated length movement on a curve to which the invention is applied.

With this configuration, it is possible to provide a B-spline curve equidistant point calculation method that is effective in shortening the processing time especially when there are many passing points.

The following table shows an example of actual performance improvement.

[0026]

[0027]

[0028]

As described above, the present invention uses the ratio of the actual length of the B-spline curve to the difference between the maximum value and the minimum value of the knot vector of the basic data of the B-spline curve. Determines the curve length to the first candidate point of
The curve of the second candidate point so that the given point is sandwiched between the first candidate point and the given point based on the difference between the curve length that is the length on the curve and the designated length By calculating the length and calculating the position of the given point by the bisection method using the curve lengths of the first and second candidate points, it is possible to reduce the time required to calculate the equidistant points of the B-spline curve. .

[Brief description of drawings]

FIG. 1 is a flow chart for explaining the essential points of the operation of a method for calculating equal points of a B-spline curve according to the present invention.

FIG. 2 is a detailed flow chart of one embodiment of the present invention.

FIG. 3 is a detailed flowchart of one embodiment of the present invention.

FIG. 4 is a detailed flow chart of one embodiment of the present invention.

FIG. 5 is a diagram showing a calculation start state of the bisection method according to the present invention.

FIG. 6 is a flow chart of a conventional equal point calculation method.

FIG. 7 is a flow chart showing a conventional procedure for calculating a designated length movement of a given point on a curve.

FIG. 8 is an explanatory diagram for explaining the bisection method.

FIG. 9 is an external view showing a hardware configuration according to an embodiment of the present invention.

[Explanation of symbols]

 1 Engineering workstation (EWS) 2 CRT display 3 Keyboard 4 Tablet 5 Stylus pen 10 Input / output computing device

Claims (2)

[Claims] 1. A position of a given point having a designated length designated as one of a plurality of equal points between a start point and an end point on a B-spline curve used for expressing a curve in a CAD system is calculated. In the B-spline curve equal point calculation method,
The ratio of the actual length of the B-spline curve to the difference between the maximum value and the minimum value of the knot vector of the basic data of the B-spline curve is used to determine the curve length up to the first candidate point of interest, and The second candidate is arranged so as to sandwich the given point between the first candidate point and the given point based on the difference between the curve length which is the length on the curve and the designated length. A method for calculating equal points of a B-spline curve, wherein a curve length of a point is calculated, and a position of the given point is calculated by a bisection method using the curve lengths of the first and second candidate points. 2. An average of knot vectors per unit length of a spline by dividing a difference between a maximum value and a minimum value in knot vectors of basic data of a B-spline curve by the length of the B-spline curve. The rate of change is defined as a curve length from the start point of the B-spline curve to the first target candidate point, which is obtained by multiplying the average rate of change by a designated length up to the target giving point. 1. The method for calculating the equal points of the B-spline curve described in 1.