JP2001052039A - Device and method for processing information, device and method for display and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To highly accurately generate a smooth curve by detecting the degree of influences of respective points to the previously expected vibrations of the smooth curve, determining a weight for each point and generating the smooth curve while using these respective weights. SOLUTION: A CPU 2 fetches the respective positional data of a plurality of measuring points from the outside, sorts the measurement points in a order according to the stream of time and executes density uniformization processing to the provided sequence of the measurement points for making uniform the spatial density of the measurement points. Concerning one partial point sequence among individual partial point sequences, the CPU 2 calculates a prescribed straight line. Subsequently, concerning individual measurement points forming that partial sequence of points, the CPU 2 calculates the distance from the calculated straight line as the degree of influence, and on the basis of the calculated result, the values of weight constants to the individual measurement points are calculated. Thus, on the basis of the positional data of individual measurement points for which the values of weight constants are calculated, the CPU 2 generates the smoothing curve for approximately smoothing the sequence of measurement points while utilizing a natural spline function.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an information processing apparatus and method, a display apparatus and method, and a recording medium.
It is suitable for application to an AD (Computer Aided Design) device.

[0002]

2. Description of the Related Art In recent years, in the field of shape design of industrial products and the like, the surface shape of a mock-up made as a prototype is measured by a three-dimensional measuring device, and CAD data is obtained based on positional information of a plurality of measurement points obtained. Generating design data has been done.

[0003] In this case, such CAD design data includes a curve (hereinafter referred to as a curve) obtained by smoothly approximating a sequence of points formed by these measurement points using a natural spline function based on positional information of each measurement point. (Referred to as a smoothing curve).

[0004]

In the process of generating design data, when a smoothing curve is generated by using a natural spline function as described above, the smoothing curve for each measurement point is calculated for each measurement point. The magnitude of the weight for determining the degree of approximation can be set.

[0005] However, since the importance of each measurement point in generating the smoothed curve is not generally known until the smoothed curve is actually generated, the weights of the measured points are all set to the same value. are doing.

For this reason, for example, when there is a measurement point having a large measurement error in the measurement point group, the smoothed curve is generated so as to be attracted to the measured point. There was a problem of generating unnecessary vibration.

One method for solving this problem is to increase the parameter value for determining the degree of smoothing of the generated smoothing curve in the natural spline function. There is a problem that the curve moves away from every measurement point, and the closeness of the smoothed curve to the measurement point sequence decreases.

The present invention has been made in view of the above points, and it is an object of the present invention to propose an information processing apparatus and method, a display apparatus and a method, and a recording medium capable of generating a smoothed curve for smoothly approximating a point sequence. Is what you do.

[0009]

According to the present invention, there is provided an information processing apparatus, comprising: detecting means for detecting the degree of influence of each point on vibration of a smoothing curve expected in advance; And weight generating means for determining the weight of each point on the basis of the detection result, and curve generating means for generating a smoothing curve using the determined weight of each point.

As a result, in this information processing apparatus, the weight can be determined to an appropriate size for each point in accordance with the degree of influence of the smoothing curve on the vibration. Vibration can be reduced without lowering.

Further, in the present invention, in the information processing method, a first step of detecting an influence of each point on a vibration of a smoothing curve expected in advance, and a step of detecting each influence based on the detected influence of each point. A second step of determining the weight of each point and a third step of generating a smoothed curve using the determined weight of each point are provided.

As a result, according to this information processing method, the weight can be determined to an appropriate size for each point in accordance with the degree of influence of the smoothed curve on the vibration. Vibration can be reduced without lowering the performance.

Further, in the present invention, in the display device, detecting means for respectively detecting the degree of influence of each point on the expected vibration of the smoothing curve, and determining the weight for each point based on the detection result. Weight determining means, a curve generating means for generating a smoothed curve using the determined weight of each point, and a display means for displaying the generated curve.

As a result, in this display device, the weight can be determined to an appropriate size for each point according to the degree of influence of the smoothing curve on the vibration, so that the approximation of the generated smoothing curve is reduced. The vibration can be reduced without causing the vibration.

Further, in the present invention, in the display method, a first step of detecting the influence of each point on the vibration of the smoothing curve in advance, and a weight for each point based on the detected influence of each point. , A third step of generating a smoothed curve using the determined weights of the points, and a fourth step of displaying the generated smoothed curve.

As a result, according to this display method, the weight can be determined to an appropriate size for each point according to the degree of influence of the smoothed curve on the vibration. Vibration can be reduced without lowering the vibration.

Further, in the present invention, in the recording medium, a first step of detecting the influence of each point on the vibration of the smoothing curve in advance, and a weight for each point based on the detected influence of each point. Are recorded, and a program for executing information processing including a third step of generating a smooth approximated curve using the determined weight of each point is recorded.

As a result, according to the program recorded on the recording medium, the weight can be determined to an appropriate size for each point according to the degree of influence of the smoothing curve on the vibration. The vibration can be reduced without lowering the approximation of the curve.

[0019]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below in detail with reference to the drawings.

(1) Configuration of CAD apparatus according to the present embodiment In FIG. 1, reference numeral 1 denotes a CA as a whole according to the present embodiment.
D device, CPU (Central Processing Unit)
2. ROM (Read Only Me) in which various programs are stored
mory) 3, RAM (Ra) as work memory of CPU2
ndom Access Memory) 4 and an input / output interface circuit 5 are mutually connected via a CPU bus 6, and the input / output interface circuit 5 is connected to a CRT (Cathode-Ray Tube).
7, a keyboard 8 and a mouse 9 are connected.

In this case, the CPU 2 fetches the position data D1 of a plurality of measurement points representing the edge position of the three-dimensional object provided from the three-dimensional measuring device as an external device into the RAM 4 via the input / output interface circuit 5.

The CPU 2 performs smooth approximation of the edge of the three-dimensional object based on the position data D1 of each measurement point taken into the RAM 4 in accordance with the smoothing curve generation processing procedure RT1 shown in FIG. 2 based on the program stored in the ROM 3. The generated B-spline curve is displayed on the CRT 7.

A series of processes of the CPU 2 will be described below.

(2) Processing by CPU (2-1) Sorting processing (step SP2) When the CPU 2 receives each position data D1 of a plurality of measurement points given from the outside, the CPU 2 executes a smoothing curve generation processing procedure RT1.
Is started in step SP1, and the following step SP2
In (2), the measurement points are sorted in order according to the spatial flow.

That is, the position data D1 of each measurement point provided from the three-dimensional measurement device is not always input in the order of the measurement points along the flow of the edge of the three-dimensional object. Therefore, the CPU 2 sorts the measurement points in order according to the spatial flow using, for example, a method disclosed in Japanese Patent Application No. 10-140997.

(2-2) Density Equalization Processing (Step SP)
3) Subsequently, the CPU 2 executes a density equalization process for equalizing the spatial density of the measurement points for the measurement point sequence obtained by sorting the measurement points as described above. The meaning of such a density uniformization process will be described.

Generally, as a method of generating a curve (smoothness) that minimizes the vibration (similarity) while minimizing the distance between each point with respect to a point sequence on a plane, an appropriate order (2m−
1) A method using the following natural spline function is widely used.

In this case, the natural spline function f (x) is
where a _i and c _i are constants,

[0029]

(Equation 1)

The following equation that satisfies

[0031]

(Equation 2)

Is defined as

In the method of generating a smoothing curve using a natural spline function, a point sequence is divided into a plurality of parts (for example, a point sequence is divided into one point), and a smoothing curve is calculated for each divided part. As a whole, a curve obtained by smoothing the point sequence as a whole is generated. In the expressions (1) and (2), x _i is the so-called x-coordinate of a node at this time. Incidentally, in the following, each point of the point sequence is assumed to be a node.

The last term on the right side of the equation (2) is

[0035]

(Equation 3)

Represents a function called a truncated power function defined by

Here, a sequence of points {P _i } (=
(X _i , y _i ), (0 ≦ i ≦ N−1)), the following expression that can be differentiated by the mth order as a smoothing function to be obtained:

[0038]

(Equation 4)

Given the natural spline function given by

[0040]

(Equation 5)

In order to minimize and improve the smoothness, the following equation is used.

[0042]

(Equation 6)

Should be minimized.

In the actual calculation, the following equation using a positive weighting constant w _i (0 ≦ i ≦ N−1) set by the user in accordance with the degree of demand for approximation and smoothness, and a positive constant g

[0045]

(Equation 7)

The minimization of the linear sum of the equations (5) and (6) is performed. That is, in the equation (7), g represents a weight constant relating to the vibration of the curve, and w _i represents a weight constant relating to the closeness of the smoothed curve to the corresponding point P _i . In the following, σ expressed by equation (7) is referred to as an objective function relating to smoothness.

Here, in general,

[0048]

(Equation 8)

It is clear that the natural spline function f (x) when satisfying the condition is an approximate function that minimizes the objective function σ.

Therefore, (N + m) coefficients a _i (0 ≦ i ≦ m) of the natural spline function f (x) given by the equation (2)
-1) and the values of c _i (0 ≦ i ≦ m−1) are formed from the first-order m equations (1) with respect to these coefficients a _i and c _i , and the N equations The desired natural spline function f (x) can be obtained by obtaining from the following equation (8) and substituting these into (2). Then, as described above, the coefficients a _i and c are obtained from the equations (1) and (8).
_{Determining i} can be performed by ordinary matrix calculation.

However, as described above, the edge of the three-dimensional object is divided into a plurality of measurement points p _i (= (x _i , y _i , z _i ), (0 ≦
There are several problems in the case of detecting as the position data of i ≦ N−1)) and generating the smoothed curve using the natural spline function based on the position data of each of the measurement points p _i .

As one of the problems, for example, FIG.
As shown in FIG. 5, there is a case where the measurement points p _i have a spatially non-uniform density. In such a case, generally, in the generation of a smoothing curve applying a natural spline function, the smoothing curve is generated so as to approach each measurement point p _i evenly. There is a problem that the point p _i is biased toward a place with a high spatial density.

Therefore, in the case of the CAD apparatus 1, the CPU 2
Makes the spatial density of the measurement points p _i in the measurement point sequence S uniform in step SP3 of the smoothing curve generation processing procedure RT1.

In practice, the CPU 2 sorts the sequence of measurement points S obtained by first sorting the measurement points p _i according to the density uniformization procedure RT2 shown in FIG. A suitable number n (eg, 1
0), a plurality of partial point sequences S _j (1 ≦ j) composed of measurement points p _i
≦ m) (step SP11).

Next, the CPU 2 calculates the spatial density d _j (1 ≦ j ≦ m) of the measurement point p _i for each partial point sequence S _j (step SP12).

Specifically, as shown in FIG.
Each measurement point p _i (k ≦ i ≦ k + 1) in the partial point sequence S _j
0) the minimum value of each of the x, y and z coordinates is min
X, and min Y and min Z, x, and set the y and each max X each maximum value of the z coordinate, max Y and max Z smallest rectangular solid 10 _j containing the partial point sequence S _j as, after this next formula

[0057]

(Equation 9)

The cube of the diagonal length l _j of the rectangular parallelepiped 10 _j calculated by the above is used as the volume V of the occupied space of the partial point sequence S _j.
j (1 ≦ j ≦ m) and the following equation

[0059]

(Equation 10)

The spatial density d _j of the partial sequence S _j is obtained by calculating

[0061] Note that as the volume V _j of space occupied portions point sequence S _j, cuboid 10 volume which is normally considered (i.e. vertical parallelepiped 10 _j, the product of the transverse and height) did not adopted is calculated _This is to prevent the volume of _{j from} largely changing due to a difference in the direction of the partial point sequence S _j with respect to the xyz coordinate axis.

That is, the volume V of the occupied space of the partial sequence of points S _j
When employing the volume of the rectangular parallelepiped 10 _j as _j, for example be a partial point sequence space sequence shown in FIG. 5 S _j same parts point sequence S _j and 'as shown in FIG. 6, since the orientation with respect to the coordinate axes are different In addition, the size of the smallest rectangular parallelepiped 10 _j ′ including the same differs from the size of the rectangular parallelepiped 10 _j shown in FIG. 5, and as a result, the volume V _j of each rectangular parallelepiped 10 _j , 10 _j ′ naturally becomes
A large difference also occurs in V _j ′.

On the other hand, as is clear from FIGS. 5 and 6, the diagonal lengths l _j , l _{j of the} rectangular parallelepipeds 10 _j , 10 _j ′ are
_j ′ has substantially the same size without being affected so much by the difference in the orientation of the partial point sequences S _j , S _j ′. By defining the volume V _j of space occupied cubed portions point sequence S _j of the diagonal length l _j of the smallest rectangular solid 10 _j including partial point sequence S _j as described above Therefore, the partial point sequence S _j A fair density calculation can be performed without being affected by the orientation.

[0064] Based on such a principle CPU2, for each partial point sequence S _j, and calculates the spatial density d _i of the measurement point p _i by sequentially performing operations shown in each (10).

Thereafter, the CPU 2 selects the lowest value from the spatial densities d _i of the measurement points p _i in each of the partial point sequences S _j obtained in this manner, and all the partial point sequences S _j
Unnecessary number of measurement points p _i for other partial point sequences S _j are deleted at random so that the spatial density d _i of this is matched (identified) to this value (step SP13).

Specifically, the CPU 2 calculates the minimum spatial density detected in step SP12 as d _k (1 ≦ k ≦ m),
Let n _{j be} the number of ideal measurement points p _{i in} the space occupied by S _j to make the space density of a certain partial point sequence S _j d _k .
Next formula

[0067]

[Equation 11]

Is calculated to obtain the partial point sequence S _j
Calculate the number DEL _j of the measurement points p _i to be deleted for
Thereafter, DEL _j measurement points p _i are selected from the measurement points p _i included in the partial point sequence S _j using random numbers, and are deleted.

Similarly, the CPU 2 deletes DEL _j measurement points p _i for the other partial point sequences S _j , thereby obtaining the spatial density of the measurement points p _i in the measurement point sequence S. As shown in FIG. 3 (C), the whole is made uniform.

(2-3) Weighting Optimization Process (Step SP4) On the other hand, as described above, the edge of the three-dimensional object is detected as position data of a plurality of measurement points p _i , and the position data of each of these measurement points p _i is detected. Another problem in the case of generating a smoothed curve using a natural spline function on the basis of the above is an error caused by the shape accuracy of a three-dimensional object or the measurement accuracy of a three-dimensional measuring device.

That is, in the generation of a smoothed curve using a natural spline function, as described above, a smoothed curve is generated so as to uniformly approach each measurement point p _i . For this reason, when there is a measurement point p _i having a large error, there is a problem that the generated smoothed curve is unnecessarily vibrated due to the influence of the measurement point p _i .

For example, in FIG. 7, the smoothing curve obtained through the weighting optimization processing according to the present embodiment described later becomes the curve K1, whereas the conventional method measures the measurement points p _{k + 1} , p _k Due to the influence of _{k + 3} , p _{k + 7} and p _{k + 11} , the smoothed curve is generated in a state of oscillating like the curve K2.

[0073] As one method for solving such a problem, a weight constant g in the smoothness of the representative (7) of natural spline function as described above, is set larger method of relative weight constant w _i thought Can be However, according to this method, there is a problem that the generated smoothed curve departs from every measurement point p _i and the approximation is reduced.

Therefore, in this embodiment, each partial point sequence S _j that has been subjected to the above-mentioned density uniformization processing (step SP3)
(Hereinafter, these are respectively referred to as a partial point sequence S _j ′), the degree of influence of each measurement point p _{i on} the expected vibration of the smoothed curve is predicted, and the degree of influence on the vibration is determined based on the prediction result. by the large value of the weight constant w _i of the measurement point p _i of smaller than the value of the weight constant w _i with respect to other measurement points p _i, thereby suppressing the vibration of the smoothing curve.

Here, as a method for predicting the degree of influence of each measurement point p _i on the vibration of the smoothing curve, a straight line L _j (1 ≦ j ≦ m) approximating the expected smoothing curve is used. A method is used in which each point sequence S _j ′ is calculated, and based on the distance from each measurement point p _i to the corresponding straight line L _j , the greater the distance between the measurement points p _{i, the} greater the influence on vibration. Can be. And such a straight line L
_j can be obtained as follows.

That is, when a point cloud is defined in a three-dimensional space, the spatial flow (correlation) of the point cloud is divided into a plurality of small spaces, and a linear multiple regression model That is, it can be represented by a plane on which the sum of the squares of the distances to each point is minimum.

In particular, when the point group is arranged so as to follow a curve in a three-dimensional space, the point group in each small space can be obtained by changing the viewpoint (phenomenon variable) as shown in FIG. Can be obtained as the intersection of the linear multiple regression model obtained.

Specifically, {(x _i , y _i , z _i )}
(1 ≦ i ≦ n) is a spatial point group, x and y are explanatory variables, z
Is a regression plane _Sz with

[0079]

(Equation 12)

Is given as

Here, the regression coefficients α and β are given by the following equations.

[0082]

(Equation 13)

Can be calculated as the solution of the simultaneous equations given by The regression constant K is given by

[0084]

[Equation 14]

As described above, the average values x _AV , y of x _i , y _i , and z _i (1 ≦ i ≦ n) are respectively _assigned to x, y, and z of S _z.
It can be obtained by substituting _AV, the z _AV.

Similarly, for example, y and z are explained functions, x
Is a regression plane S _x with

[0087]

(Equation 15)

Is as follows. And the regression coefficients β ', γ
Can be obtained as a solution of a simultaneous equation similar to the equation (13), and the regression constant K 'can be obtained from an equation similar to the equation (14).

Here, if the point group is arranged in a curved line near a straight line in space, it can be approximated by any of different regression planes generated by changes in different viewpoints (phenomenon functions or explanatory functions). It is thought that. That is, it is considered that the straight line L for predicting the spatial arrangement of such a point group is obtained as the intersection line S _x ∩S _z of the regression plane from different viewpoints.

Therefore, such a straight line L is expressed by the following equation.

[0091]

(Equation 16)

Can be calculated as (16)
In the equation, θ _{1 to} θ ₄ are as follows:

[0093]

[Equation 17]

Can be calculated as

Based on such a principle, the CPU 2 determines in FIG. 9 in step SP4 of the smoothing curve generation processing procedure RT1.
Accordance weighting optimization procedure RT3 shown in, First, the 'one partial point sequence S _j of the' respective parts point sequence S _j, calculates (16) the straight line L given by formula (= L _j) (step SP21).

Subsequently, as shown in FIG. 9, the CPU 2 calculates the distance q _i from the straight line L (= L _j ) calculated in step SP21 for each measurement point p _i forming the partial point sequence S _j ′. calculated as above influence, respectively calculates the value of the weight constant w _i with respect to the respective measurement points p _i based on the calculation result (step SP22).

In this case, the weighting constant w _i needs to be smaller as the measurement point p _i is farther from the straight line L (= L _j ).

[0098]

(Equation 18)

As described above, the value of the weight constant w _i for each measurement point p _i is calculated.

Then, the CPU 2 performs the same processing for the other partial point sequence S _j '(step SP21 and step S21).
P22), and a sequence of measurement points S ′ (FIG. 3 (c)) composed of the sequence of measurement points S subjected to the density uniformization process.
The values of the weight constants w _i are determined to be appropriate values for all the measurement points p _i .

(2-4) Smoothing Curve Generation Process (Step SP5) Subsequently, the CPU 2 calculates the value of the weighting constant w _i as described above based on the position data D1 of each measurement point p _i . Using a natural spline function, a sequence of measurement points S ′
Is generated. This will be described.

In general, the natural spline function f (x) is
As described above, it is defined as Expression (2) that satisfies Expression (1). However, the natural spline function f (x) defined in this way has the following two restrictions.

That is, as a first constraint, in the equation (2), an equation cannot be established unless the value of y is uniquely determined for the value of x in the natural spline function f (x) defining the curve. Therefore, y depends on how to set the coordinate axes that define the curve.
F (x) cannot be calculated for a multi-valued function that takes a plurality of values.

As a second restriction, when the point sequence is not on a plane, the smoothing curve does not always have to be on a plane.
Equation (2) cannot represent such a curve.

Therefore, in the case of the CAD apparatus 1, the 2
A smoothing curve is generated using the method disclosed in Japanese Patent Application No. 11-72612 in order to escape the two constraints. That is, this C
The AD device 1 expresses the natural spline function as a vector with the same parameters for each of the x, y, and z coordinates (hereinafter, such a natural spline function is referred to as a parametric natural spline function), and the x, y
, And each parametric natural spline function of the z coordinate is determined independently so as to minimize the respective objective function.

In this case, expressing the natural spline function as a vector with the same parameters for each of the x, y and z coordinates means that the natural spline function is expressed as x, y and z.
expressed using a parameter t independent of y, and z
It means to expand on a three-dimensional space including the axis.

As a result, the natural spline function defined by the above equations (1) and (2) is

[0108]

[Equation 19]

The following equation that satisfies

[0110]

(Equation 20)

It is rewritten as follows. This (19)
In the expression and the expression (20), ^t (*) means the transposed matrix or transposed vector of the matrix or vector (*), and the same applies to the following.

Determining the parametric natural spline functions f (t) of the x, y and z coordinates independently so as to minimize the respective objective functions means that the desired parametric natural spline function f (t) is Optimal value,
This means that it can be solved by minimizing each objective function of x, y and z coordinates independently. Here, each objective function of x, y and z coordinates is expressed by the following equation.

[0113]

(Equation 21)

Is σ defined by

Then, the parametric natural spline function f (t) for the point sequence {(P _i )} on the three-dimensional space is
By simply minimizing each of the objective functions σ (= ^t (σ _x , σ _y , σ _z )), it is possible to define a curve that satisfies approximation and smoothness for the point sequence {(P _i )}. Yes (Japanese Patent Application
11-72612).

The expression form of the parametric natural spline function f (t) is the same as that of a non-parametric natural spline function. Therefore, the objective function σ (= ^t
(Σ _x , σ _y , σ _z )) is the minimum of the objective function σ represented by the expression (7) of the natural spline function f (x) given by the expression (2) which is not parametric. Similarly to the case where the values are realized by the coefficients a _i and c _i obtained as the solutions of the simultaneous equations given by the equations (1) and (8),

[0117]

(Equation 22)

Can be calculated.

Accordingly, the parametric natural spline function f (t) for the x, y, and z coordinates for the point sequence {(P _i )} is obtained by combining the equations (19) and (22) to obtain the coefficient groups a _i , c It can be obtained by finding the value of _i and substituting this into equation (20).

In practice, each of the coefficients a _i and c _i
The value of

[0121]

(Equation 23)

Since the above holds, theoretically, the inverse matrix M ^-1 of the matrix M on the left side is obtained and multiplied by the matrix Q on the right side. You can ask.

[0123] CPU2 Based on such principle, calculated in the step SP5 of the smoothing curve generation procedure RT1, the measurement point sequence S ', the position data D1 of each measurement point p _i, each weighting optimization process (step SP4) The values of the coefficients a _i and c _i are obtained based on the weight constant w _i of each of the measured points p _i and equation (23), and are substituted into equation (20) to obtain x, y and z. parametric natural spline function f _x for the coordinate _{(t), f y (t} ), f
_z (t) is obtained.

[0124] (2-5) conversion processing (step SP6) Subsequently CPU2, each parametric natural spline function f of the obtained x, y and z-coordinate in the step SP5 (t) (= f _x (t), f _y (t), f _z
(T)) is converted into a parametric natural spline function (hereinafter, referred to as an s parametric function) using the curve length s as a parameter. The meaning will be described.

As described above, the edges of the three-dimensional object are detected as the positions of the plurality of measurement points p _i , and a smoothing curve is generated using the natural spline function based on the position data D1 of these measurement points p _i. In this case, even if the density equalization process (step SP3) and the weighting optimization process (step SP4) as described above are performed in advance, the generated smoothed curve has finely divided vibrations (hereinafter referred to as noise). )
Occurs.

As a method for removing such noise, for example, as shown in FIG. 11, the “section where inflection points frequently occur” in the smoothing curve K3 is defined as the section where noise is generated (hereinafter referred to as “noise section”). section referred to as a _N) and to define and locate such noise interval a _N in smooth curves K3, modify the curve shape of the noise interval a _N a smooth curve shape as shown by a one-dot chain line in FIG. 11 A method of performing a noise removal process is considered.

As a technique for detecting the “section where inflection points frequently occur” in the smoothed curve, the smoothed curve K
3, a “curve section in which an inflection point sequence in which the distance to an adjacent inflection point is sufficiently short” may be found.

However, even if the parametric natural spline function f (t) defined by the equation (20) is subjected to the analysis processing (for example, the calculus processing for the parameter t), the vibration frequency and the curve length of the smoothed curve are obtained. Cannot be calculated based on the distance concept.

Thus, in the case of this embodiment,
The parametric natural spline function f (t) defined by the equation (20) is converted into an s parametric function using a curve length (distance) s from one end of a smoothed curve represented by the parametric natural spline function f (t) as a parameter. To be redefined as

By doing so, it is possible to extract the characteristic amount of the smoothed curve based on the distance concept,
For example, it is possible to easily find out, for example, a “curve section in which an inflection point sequence in which the distance to an adjacent inflection point is sufficiently short” exists.

Here, the ordinal numbers of the n nodes 0, 1,...
The (2m-1) -dimensional parametric natural spline function f (t) represented by the parameter t having n-1 as a value at the node can be defined by the equation (20) as described above.

The parametric natural spline function f (t) is expressed by the following equation using the curve length s as a parameter.

[0133]

(Equation 24)

The s parametric function f represented by
^* Can be converted to (s). Note that a ₀ and c _i in the equation (24) are the property of the equation (24) as a natural spline function (equation (1)) and n nodes (in this embodiment, the measurement point sequence S ′ Measurement points p _i )
Can be determined from passing through.

The s parametric function f
^* The curve length s from the start node (t = 0) of (s) to any point t is given by

[0136]

(Equation 25)

It can be defined as a function of the parameter t as shown below.

Here, in order to actually perform such an integral calculation and to improve the calculation efficiency of the curve length s at each node,
A curve length s from the start node to an arbitrary parameter value t (i-1 <t ≦ i) in an arbitrary node section [i-1, i].
The formula for calculating (t, i-1, i) is

[0139]

(Equation 26)

Rewrite as shown below. The integrand Δs (t, i−1, i) in equation (26) represents the differential quotient of the curve length s.

Here, when calculating the curve length s at a plurality of points, it is assumed that the calculation is performed in order from the closest to the start node.
Part of the first term on the right side of the first equation of equation (6) can be reduced in calculation because it has been obtained by the calculation of the previous node, and the second term on the right side of the first equation of the equation (26) is Since the integration is performed within the adjacent node section, the integrand Δs (t, i−1,
i) can be expanded to a polynomial of a power function without a cutting condition. Actually, Δs (t, i−1, i) is given by the following equation.

[0142]

[Equation 27]

It can be obtained as follows.

The first-order derivative D1 ⁽¹⁾ Δs (t, i) for the parameter t in Δs (t, i−1, i)
−1, i) and the second-order derivative D1 ⁽²⁾ Δs (t, i−
1, i) are given by

[0145]

[Equation 28]

[0146]

(Equation 29)

Is as follows.

Then, Δs (t, i−1, i) is calculated by using the equations (28) and (29) to obtain the interval (i−1, i−1, i).
At any point h in 1), the following equation

[0149]

[Equation 30]

A quadratic approximation function Δs ^* (t,
i-1, i, h). Note that Δs (t,
Since i−1, i) is a substantially quadratic function with respect to the parameter t, a polynomial approximation of order 3 or higher is meaningless.

The approximation function Δs ^* (t, i−1,
By using (i, h), the integration procedure (calculation of the coefficient of the cubic function) can be set in advance, and can be described by an ordinary programming language.

However, since the accuracy of the polynomial approximation decreases as the distance from the vicinity of the expansion reference point h decreases, the node section [i−1,
When calculating the curve length in [i], it is necessary to calculate and integrate an approximation function at a sufficient number of division points. That is, the curve length s (i-1, i) in the node section [i-1, i] is given by the following equation.

[0153]

(Equation 31)

Approximate calculation is possible.

Further, using this equation (31), as shown in equation (20), each node p _i (= (x _i , y _i , z _i ), i =
The curve length s _i up to 0, 1, 2,...

[0156]

(Equation 32)

Can be calculated by

The resulting curve length s _{i of the} node is
S ₀ , s ₁ ,..., S _n−1 are connected to nodes (x _i , y _i , z
_i ), i = 0, 1,..., n−1, and a natural spline function that passes through all these nodes (degree of approximation = 1) is calculated by a conventional natural spline function calculation procedure. The parametric natural spline function f (t) given by the original equation (20) can be converted into an s parametric function using the curve length s as a parameter.

[0159] CPU2 based on such principles, (32) sequentially obtains the curve length s _i to each node, each made at the measurement point p _i on the basis of the equation, the column of the curve length s _i of the obtained node s _0, s _1, ......, a s _n-1 as the data string of the nodes of the curve length s, passes all of these nodes a (w _i = 1) to s parametric function f ^* (s) calculation method of conventional natural spline function Is calculated using

(2-6) Noise Removal Processing (Step SP)
7) Subsequently, the CPU 2 performs the above-described conversion processing (step SP6).
In accordance with the noise removal processing procedure RT4 shown in FIG. 12, unnecessary noise generated in the smoothing curve represented by the s parametric function f ^* (s) is removed from the s parametric function f ^* (s) obtained in. To remove noise. This will be described below along the procedure.

In the following, s-parametric functions f ^* _x (s), f ^* _{y for} x, y and z coordinates
Since the processing for (s) and f ^* _z (s) is the same,
S parametric function f ^* _x (s), f ^* _y
(S) and f ^* _z (s) are represented as D0 (s).

(2-6-1) Noise Section Detection Processing (Step SP31) First, the CPU 2 analyzes the s parametric function D0 (s) obtained by the conversion processing (step SP6) to obtain “adjacent inflections”. A noise section A _N (FIG. 13A), which is a curve section in which an inflection point sequence having a sufficiently short distance from a point exists.

In this case, as a method of detecting such a noise section A _N , analysis processing using differentiation can be applied. That is, when the smoothing curve K10 as shown in FIG. 13A is represented by the s-parametric function D0 (s), the first-order derivative D1 (s) of the s-parametric function D0 (s) is represented by FIG. Curve K as shown in B)
11 is a function representing

[0164]

[Equation 33]

The derivative D2 (s) of the second order given by
When = 2, it is a function representing a polygonal line K12 as shown in FIG.

Here, the intersection of the broken line K12 in FIG. 13C and the horizontal axis corresponds to each inflection point in the smoothed curve K10 in FIG. 13A. Therefore, this broken line K
By sequentially detecting the coordinates of the intersection of the intersection 12 and the horizontal axis, based on the coordinates of each of these intersections, the “curve where there is an inflection point sequence whose distance to an adjacent inflection point is sufficiently short” exists. Section ”can be detected.

Based on this principle, the CPU 2 calculates the first-order derivative D1 (s) and the second-order derivative D2 (s) of the s-parametric function D0 (s) obtained by the conversion process (step SP6). At the same time, the value of the parameter s at which the value of the obtained second-order derivative D2 (s) becomes “0” is sequentially detected.

Based on the value of the parameter s thus obtained, the CPU 2 determines the “section in which the inflection point sequence whose distance to the adjacent inflection point is sufficiently short” exists in the noise section A. Detect as _N.

(2-6-2) New Second Derivative Function Generation Processing (Step SP32) Subsequently, the CPU 2 removes the noise in each noise section A _N while preserving the original smoothed curve K10 as much as possible. Generate a new second derivative D2a (s) for elimination. This will be described below.

First, if the noise section A _N can be detected as described above, the second-order derivative D2 (s) is set so that the number of inflection points in this noise section A _N is set to “0”. )
Starting point of the noise interval A _N in (s _st, D2
(S _st )) and a new second-order derivative D2a (s) as shown in FIG. 13D by replacing the end point (s _ed , D2 (s _ed )) with a straight line, etc. By performing a double integration process on this, a new s-parametric function D0a (s) from which noise has been removed as shown in FIG.
Can be obtained. Actually, also in the present embodiment, the noise removal processing is performed according to such a procedure as described later.

However, for example, each value D2 of the second derivative D2 (s) at the start point and end point of the noise section A _N
When 2 (s _st ) and D2 (s _ed ) have different codes, in order to preserve as much as possible the original curve shape for the portion other than the noise section A _N in the s parametric function D0 (s), the noise section it is necessary to present a meaningful inflection point one in a _N.

Therefore, a policy for generating a new second-order derivative D2a (s) (hereinafter referred to as an improvement policy) is as follows for each noise section A _{N at} the start point and end point thereof. Each value D2 of the derivative D2 (s) of the order
(S _st ) and D2 (s _ed )
2 (s _st ) and D2 (s _ed ) have the same sign, the number of inflection points in the noise section A _N is set to “0”, and D2
When (s _st ) and D2 (s _ed ) have different codes, it can be seen that the number of inflection points in the noise section A _N may be set to “1”.

As a method for setting the number of inflection points included in the noise section A _N to “0” or “1” as described above,
A method of replacing the noise section A _N in the derivative D2 (s) of the order with a function of some straight line is conceivable.

However, if the noise section A _N in the second-order derivative D2 (s) is replaced with an appropriate straight line function without considering the functions before and after it, the smoothed curve K10 has a portion other than the noise section A _N. An adverse effect occurs and the noise section A _N
There is a problem that the original curve shape cannot be preserved in portions other than.

In the embodiment of the present invention, a new second-order derivative D2a (s) is generated by the following method in order to remove noise while preserving the original smoothed curve K10 as much as possible. To do it.

[0176] That value D2 (s _st) and D2 the (s _ed) as the variables α and β at the start and end points of the noise interval A _N of second derivative D2 (s), the noise interval A _N New second-order derivative D2a before and after
(S) is

[0177]

(Equation 34)

The function is defined as shown in FIG.

In the equation (34), ε is the distance from the outside of the noise section A _N to a region where the second-order derivative D2 (s) is not changed. In this case, to remove noise as a smooth curve from the original smoothed curve K10, a new second-order derivative D2a
Since (s) also needs to be a (smooth) continuous function that does not change abruptly, it is necessary to set ε to a value that does not significantly increase the range of curve shape conversion and at the same time, sets a certain size. is there.

The s parametric function D0a expressing a new noise-removed new smoothing curve K10 'by double integrating the new second-order derivative D2a (s) defined as in equation (34). In the case of generating (s), in order to preserve the curve shape of the original smoothed curve K10 as much as possible, at s = _sed + ε and s = _sst− ε, the original s
The parametric function D0 (s) completely matches the new s-parametric function D0a (s), and the first-order derivative D1 (s) of the original s-parametric function D0 (s)
What is necessary is that the first order derivative D1a (s) of the new s-parametric function D0 (s) also completely match.

When such a condition is satisfied, D
From the last condition of the definition of 2a (s),

[0182]

(Equation 35)

The simultaneous equations are established, and the values of the variables α and β can be obtained from the simultaneous equations. Accordingly, by solving the simultaneous equations of equation (35) to obtain α and β, and substituting these into equation (34), a new second-order derivative D2a (s) can be obtained.

In this case, however, it is necessary to determine whether α and β obtained by solving the simultaneous equations of equation (35) are in accordance with the above-described improvement policy.

[0185] Such determination is made by determining α and β obtained by solving the simultaneous equations of equation (35) as follows:

[0186]

[Equation 36]

Can be determined by determining whether or not the condition is satisfied.

If α and β do not satisfy the expression (36), the range of the noise section A _N is gradually increased within a range allowable as the amount of deformation of the curve shape.
When the values of α and β satisfying the expression (36) are obtained, the values are substituted into the expression (34) to obtain a desired new 2
The derivative of the order D2a (s) can be obtained.

On the basis of this principle, the CPU 2 first sets a new second-order derivative D2a (s) for one noise section A _{N in} equation (34) in step SP32 of the noise removal processing procedure RT4 (FIG. 12). Define
Α and β are obtained by solving the simultaneous equations of equation (35).

Further, the CPU 2 determines that α and β are (36)
It is determined whether or not the expression is satisfied, and if a positive result is obtained, a new second-order derivative D2a (s) is determined by substituting α and β into Expression (34).

On the other hand, when a negative result is obtained, the CPU 2 slightly decreases the value s _st of the value s _st at the start point of the noise section A _N and slightly increases the value s s of the value s _ed at the end point. So that the noise section A _N is expanded.

Then, the CPU 2 obtains α and β by solving the equation (35) again.
And β satisfy the equation (36). Then, the CPU 2 repeats the same processing as long as α and β satisfying the expression (36) are obtained within a range allowable as the amount of deformation of the curved shape.

Then, the CPU 2 obtains α and β satisfying the expression (36) within this range, and then obtains α and β.
Into the equation (34), thereby generating a new second-order derivative D2a (s) for the noise section A _N.
The CPU2, if not got to α and β satisfying the expression (36) within this range, stops the noise removal processing for the noise interval A _N.

Further, the CPU 2 sequentially executes the same processing for the other noise sections A _N , thereby generating new second-order derivatives D2a (s) for each noise section A _N.

(2-6-3) New Curve Generation Processing (Step SP33) Subsequently, for each noise section A _N , the CPU 2 calculates the new second-order derivative D2a (s) obtained as described above. By performing double integration processing, the s parametric function D0 (s) shown in FIG. 13 (F) is obtained by removing noise from the original s parametric function D0 (s) shown in FIG. 13 (A).
0a (s) is generated.

In this case, a new second-order derivative D2a (s)
S parametric function D0 among the primitive functions of
(S) and the first derivative D1a (s) of the same new s-parametric function D0a (s) except for the noise section A _N
Is, of course, completely identical to the original first-order derivative D1 (s).

[0197]

(37)

It can be defined as follows.

Since the new s-parametric function D0a (s) identical to the original curve except for the noise section A _N naturally completely matches the original s-parametric function D0 (s), the following equation is obtained.

[0200]

(38)

Are defined as follows.

On the basis of this principle, the CPU 2 substitutes the new first-order derivative D2a (s) defined by the equation (34) into the equation (37) in step SP34 to thereby obtain a new first-order derivative. D1a (s) is obtained and further substituted into the equation (38) to calculate the s-parametric function D0a (s).

[0203] (2-6-4) Specific examples of the noise removal processing noted below, a series of steps as described above after the detection of the noise interval A _N (step SP32 and step SP3
A specific example of the noise removal processing according to 3) will be described.

Here, in this example, in order to simplify the processing, three restrictions are provided: a restriction on the order of the s-parametric function D0 (s), a restriction on the curve length s _i between nodes, and a restriction on the noise section A _N. Shall be.

That is, the s parametric function D0 (s)
Is set to 3 as a limit of the order of. In this case, degree 3
Is the minimum order of the spline function that can control the curvature of the curve. By setting the order to 3, s
Second order derivative D2 of parametric function D0 (s)
(S) becomes a polygonal line K12 as shown in FIG. 13 (C), and the presence or absence of an inflection point can be determined only by the sign determination of the value of the second-order derivative D2 (s) at the node.

[0206] As limitations on the curve length s _i between nodes, it is assumed the curve length s _i between each node are equal. Further, the distance [s _n -s _n-1 ] between arbitrary nodes is set to ε.

Further, as a restriction on the noise section A _N , it is assumed that nodes are both end points. In addition, the distance ε to the curve part where the curve shape is stored is set to one node.

As a result of such a restriction, the second-order derivative values α and β at the end points of the noise section A _N [s _st , s _ed ] from which noise has been removed as described above are expressed by the following equations, respectively.

[0209]

[Equation 39]

[0210]

(Equation 40)

The following is obtained.

Here, κ ₁ to κ ₄ are represented by the following equations, respectively.

[0213]

[Equation 41]

[0214]

(Equation 42)

[0215]

[Equation 43]

[0216]

[Equation 44]

Is given by Ε is the length of the curve between equally spaced nodes.

Then, the equations (41) to (44) are replaced by the equation (39).
Α and β obtained by substituting into equations (40)
Satisfies the equation (36), a new s from which noise is removed
The parametric function D0a (s) is expressed by the following equation using α and β.

[0219]

[Equation 45]

The following is obtained.

Note that ν _{1 to} ν ₁₂ are represented by the following equations, respectively.

[0222]

[Equation 46]

[0223]

[Equation 47]

[0224]

[Equation 48]

[0225]

[Equation 49]

[0226]

[Equation 50]

[0227]

(Equation 51)

[0228]

(Equation 52)

[0229]

(Equation 53)

[0230]

(Equation 54)

[0231]

[Equation 55]

[0232]

[Equation 56]

[0233]

[Equation 57]

Are represented by

It should be noted here that equation (45) is effective only when α and β calculated from equations (39) and (40) satisfy equation (36). It is.
If the expression (36) is not satisfied, the noise section A _N may be extended by a distance ε on the right and left sides within an appropriate range.
By using the equations (46) to (57) while taking such incidental considerations into account, the noise-removed smoothing curve K1
0 'can be generated.

Actually, when the above-described noise removal processing is performed on the s parametric function D0 (s) expressing the curve K20 as shown in FIG. 14A on the xy plane, for example, a new s obtained is obtained. Parametric function D0a (s)
A curve K20 'as shown in FIG.

Therefore, FIGS. 14A and 14B
As is clear from the above, it was confirmed that by performing the above-described noise removal processing, a curve as an improved version in which noise was removed from the original smoothed curve could be generated.

(2-7) B-Spline Curve Generation Processing (Step SP8) Subsequently, in step SP8 of the smoothing curve generation processing procedure RT1, the CPU 2 performs the noise removal processing generated as described above. S for the, y and z coordinates
Based on the parametric function D0a (s), the coordinates of auxiliary points between each measurement point (node) p _i on the smoothed curve K10 ′ expressed by the s parametric function D0a (s) are randomly determined, and these are determined. B- passing over the auxiliary point
Calculate the spline curve.

Then, the CPU 2 calculates such a B-spline curve for each measurement point p _i ,
After displaying each of the obtained B-spline curves on the CRT 7, the process proceeds to step SP9, where the smoothed curve generation processing procedure RT1 is completed.

(3) Operation and Effect of the Embodiment In the above configuration, the CPU 2 of the CAD device 1
Based from an external device 3 dimensional measuring device in the position data D1 of each measurement point p _i representing the edges of a three-dimensional object supplied, firstly to sort each measurement point p _i along the spatial stream (step SP2).

Subsequently, the CPU 2 equalizes the spatial density of the measurement points p _{i in} the obtained measurement point sequence S (step S).
Together with P3), the value of the weighting constant w _i corresponding to the position of each measurement point p _i of the measurement point sequence S ′ thus obtained is calculated (step SP4), and thereafter the position of each measurement point p _i is calculated. data, based on the value or the like of the weight constant w _i,
A parametric natural spline function f (t) is calculated using t as a parameter that smoothly approximates the measurement point sequence S ′ (step SP5).

Next, the CPU 2 converts the parametric natural spline function f (t) into an s parametric function f ^* (s) using the curve length s of the smoothed curve as a parameter (step SP6).

Further, the CPU 2 thereafter performs a noise removal process for removing a noise component from the s parametric function f ^* (s) (step SP7), and performs B-B based on the obtained new s parametric function. A spline function is calculated, and a curve based on the B-spline function is displayed on the CRT 7 as a curve obtained by smoothing the edge measured by the three-dimensional measuring device (step SP
8).

In generating the smoothing curve, the CAD apparatus 1 detects the degree of influence of the expected smoothing curve on the vibration at each measurement point p _i as described above, and based on the detection result. The values of the weight constants w _i of the respective measurement points p _i are determined so that the smoothed curve does not oscillate,
Since the smoothing curve is generated using the weighting constants w _i of these determined measurement points p _i , it is possible to effectively reduce the vibration without lowering the smoothness of the generated smoothing curve. it can.

According to the above arrangement, the degree of influence of the expected smoothing curve on the vibration is detected for each measurement point p _i , and each measurement point is prevented from vibrating based on the detection result. the value of the weight constant w _i of p _i respectively determined, by which is adapted to generate a smoothed curve using the weight constant w _i of each measurement point p _i that these decisions, smoothing of the smoothed curve generated Thus, it is possible to effectively reduce the vibration without deteriorating the performance, and thus to realize a CAD apparatus capable of accurately generating a curve that approximates a point sequence smoothly.

(4) Other Embodiments In the above-described embodiment, a case has been described in which the present invention is applied to the CAD apparatus 1. However, the present invention is not limited to this. The present invention can be widely applied to various other information processing devices, display devices, and the like configured to generate a smoothed curve of a point sequence based on position information of each point forming the sequence. In this case, the position information of each point in the point sequence may be provided from an external device other than the three-dimensional measuring device.

In the above-described embodiment, when the smoothing curve is generated, the detecting means for detecting the degree of influence of each measurement point p _{i on} the expected vibration of the smoothing curve, and the detection result Weight determining means for determining a weight constant w _i for each measurement point p _i based on
Has dealt with the case where the curve generating means for generating a smoothed curve using determined weighting constant w _i of each measurement point p _i was configured from the single CPU2, the present invention is not limited to this, These detecting means, weight determining means and curve generating means may be constructed by separate CPUs.

[0248] Furthermore, in the above-described embodiment, it has dealt with the case of determining calculated using the weight constant w _i for each measurement point p _i (18) wherein the present invention is not limited to this, In short, if the measurement point p _i can be made smaller as it is farther than the straight line _Lj , each measurement point p _i
An arithmetic expression other than Expression (18) may be used as an arithmetic expression for calculating the weight constant w _i with respect to, or may be determined using a table or the like.

Further, in the above embodiment, the case where the degree of influence of each measurement point p _i on the vibration of the smoothed curve is defined as the distance q _i from the corresponding straight line L _j has been described. The distance q _i from the straight line L _{j is} not limited to this.
Other parameters may be defined as the degree of influence of the measurement point p _i on the vibration of the smoothing curve.

[0250] In this case, to define the impact of the measurement point p _i to vibration of the smoothing curve distance from a straight line or a curve approximating a straight line L measurement point sequence other than _j S or partial point sequence S _j You may do it.

Further, in the above-described embodiment, the recording medium for recording the program according to the present invention is an RO medium.
Although the case where the M3 is applied has been described, the present invention is not limited to this, and various other recording media such as a disk-shaped recording medium such as a hard disk and a CD-ROM, and a tape-shaped recording medium such as a magnetic tape. Can be widely applied.

[0252]

As described above, according to the present invention, when an information processing apparatus and method generate a smoothed curve,
The degree of influence of each point on the expected vibration of the smoothing curve is detected in advance, the weight of each point is determined based on the detection result, and a smoothing curve is generated using the determined weight of each point. By doing so, it is possible to determine an appropriate weight for each point according to the degree of influence of the smoothing curve on the vibration. Thus, the vibration can be reduced without lowering the approximation of the smoothed curve generated, and an information processing apparatus and method capable of accurately generating the smoothed curve can be realized.

In the display device and method, when generating a smoothing curve, the degree of influence of each point on the expected vibration of the smoothing curve is detected in advance, and the weight of each point is determined based on the detection result. Determined, a smoothing curve is generated using the determined weight of each point, and the generated smoothing curve is displayed, so that the weight of each point is determined according to the degree of influence of the smoothing curve on the vibration. Can be determined to an appropriate size. Thus, the vibration can be reduced without lowering the approximation of the smoothed curve generated, and a display device and a method capable of accurately generating and displaying the smoothed curve can be realized.

In the recording medium, a first step of detecting the degree of influence of each point on the expected vibration of the smoothing curve when generating the smoothing curve,
A second step of determining a weight for each point based on the detection result; and a third step of generating a smoothed curve using the determined weight for each point. By recording the program, the weight can be determined to an appropriate size for each point according to the degree of influence of the smoothing curve on the vibration based on the program. Thus, it is possible to reduce the vibration without lowering the approximation of the smoothing curve generated, thereby realizing a recording medium capable of generating the smoothing curve with high accuracy.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of an image processing apparatus according to an embodiment.

FIG. 2 is a flowchart illustrating a smoothing curve generation processing procedure;

FIG. 3 is a schematic diagram used for describing a density equalization process.

FIG. 4 is a flowchart illustrating a procedure of a density equalization process.

FIG. 5 is a schematic diagram used for describing a density equalization process.

FIG. 6 is a schematic diagram used for explaining a density uniformization process.

FIG. 7 is a schematic diagram for explaining a weighting optimization process;

FIG. 8 is a conceptual diagram for explaining a method of generating a predicted straight line from a multiple regression model.

FIG. 9 is a flowchart illustrating a weighting optimization process procedure;

FIG. 10 is a schematic diagram for explaining a weighting optimization process;

FIG. 11 is a schematic diagram used for describing noise removal processing.

FIG. 12 is a flowchart illustrating a noise removal processing procedure.

FIG. 13 is a graph showing shapes of curves and polygonal lines represented by functions and derivatives.

FIG. 14 is a schematic diagram illustrating a specific example of noise removal.

[Explanation of symbols]

1 CAD apparatus, 2 CPU, 3 ROM, 10
_j: rectangular parallelepiped, A _N: noise section, D1: position data, d _j: spatial density, K10: smoothed curve, g:
Weight constant, p _i ... Measurement point, S... Measurement point sequence, S _j.
Partial point sequence, s, s _i ... Curve length, w _i.
T1... Smoothing curve generation processing procedure, RT2... Density uniformization processing procedure, RT3... Weighting optimization processing procedure, RT
4. Noise removal processing procedure.

Claims (10)

[Claims] An information processing apparatus for generating a smoothing curve for smoothing and approximating a point sequence based on position information of each point forming the point sequence. Detecting means for respectively detecting the degree of influence of each of the points on the vibration of the smoothed curve; based on the detection result of the detecting means, the weight of each of the points for determining the degree of approximation of the smoothed curve to each of the points; An information processing apparatus comprising: weight determining means for determining each; and curve generating means for generating the smoothed curve using the determined weights of the points. 2. The detecting means divides the point sequence into a plurality of partial point sequences, and for each of the partial point sequences, a curve or a straight line approximating the partial point sequence is used as the position information of each of the points. 2. The information processing apparatus according to claim 1, wherein the information is generated based on the distance and the distance from each point to the curve or the straight line is detected as the degree of influence of the point on the vibration of the smoothed curve. 3. An information processing method for generating a smoothing curve for smoothing and approximating a point sequence based on position information of each point forming a point sequence. A first step of detecting the degree of influence of each of the points on the vibration of the smoothed curve, and determining the degree of approximation of the smoothed curve to each of the points based on the detected degree of influence of each of the points. An information processing method, comprising: a second step of determining a weight for each point; and a third step of generating the smoothed curve using the determined weight of each of the points. 4. In the first step, the point sequence is divided into a plurality of partial point sequences, and for each of the partial point sequences, a curve or a straight line approximating the partial point sequence is set to the position of each point. 4. The information processing method according to claim 3, wherein the information is generated based on information, and a distance from each point to the curve or the straight line is detected as the degree of influence of the point on the vibration of the smoothed curve. . 5. A display device for generating a smoothing curve for smoothly approximating a point sequence based on position information of each point forming a point sequence and displaying the generated smoothing curve, wherein the smoothing curve is When generating, the detecting means for detecting the degree of influence of each of the points on the vibration of the smoothing curve in advance, and determining the degree of approximation of the smoothing curve to each of the points based on the detection result of the detecting means. Weight determining means for determining the weight of each point, curve generating means for generating the smoothed curve using the determined weight of each point, and display means for displaying the generated curve. A display device comprising: 6. The detecting means divides the point sequence into a plurality of partial point sequences, and, for each of the partial point sequences, a curve or a straight line approximating the partial point sequence as the position information of each point. 6. The display device according to claim 5, wherein the display device is generated based on the distance, and a distance from each point to the curve or the straight line is detected as the degree of influence of the point on the vibration of the smoothed curve. 7. A display method for generating a smoothed curve for smoothing and approximating the point sequence based on position information of each point forming the point sequence and displaying the generated smoothed curve, A first step of detecting the degree of influence of each of the points on the vibration of the smoothing curve in advance, and generating the smoothed curve of each of the points based on the degree of influence of each of the detected points. A second step of determining a weight for each point that determines the degree of approximation; a third step of generating the smoothing curve using the determined weight of each point; and the generated smoothing A fourth step of displaying a curve. 8. In the first step, the point sequence is divided into a plurality of partial point sequences, and for each of the partial point sequences, a curve or a straight line approximating the partial point sequence is set at the position of each of the points. 8. The display method according to claim 7, wherein the display method is generated based on information, and a distance from each point to the curve or the straight line is detected as the degree of influence of the point on the vibration of the smoothed curve. 9. When generating a smoothed curve of a point sequence based on positional information of each point forming the point sequence, the degree of influence of each point on the expected vibration of the smoothed curve is detected. A first step of determining the degree of approximation of the smoothing curve to each point based on the detected degree of influence of each point; and a second step of determining the weight of each point. And a third step of generating the smoothed curve by using the weights of the respective points described above. 10. In the first step, the point sequence is divided into a plurality of partial point sequences, and for each of the partial point sequences, a curve or a straight line approximating the partial point sequence is converted to the position of each point. The recording medium according to claim 9, wherein the recording medium is generated based on information, and a distance from each point to the curve or the straight line is detected as the degree of influence of the point on the vibration of the smoothing curve.