JPH067361B2 - Curved surface generation method - Google Patents

Description

TECHNICAL FIELD The present invention relates to a curved surface generation method, and more particularly to a curved surface generation method for generating a curved surface using a number of given sectional curves.

<Background Art> A curved surface on a design drawing of a three-dimensional mold or the like is generally represented by a plurality of cross-section curves, and there is no shape data between one cross-section curve and the next cross-section curve.

By the way, in the case of numerically controlled processing, it is required to perform processing so as to smoothly connect between the above-mentioned two cross-sectional curves, although such an intermediate shape is not given. In other words, this means that a curved surface between the two cross-section curves is generated from the data of the cross-section curve, etc., and the NC for the curved surface processing is performed using the data relating to the generated curved surface.
This means that data must be created and processed based on the NC data. For this reason, various curved surface generation methods have been proposed and put to practical use in the past, but curved surfaces could not be generated by a simple method so as to connect them smoothly.

<Object of the Invention> An object of the present invention is to provide a curved surface generation method capable of generating a three-dimensional free-form surface smoothly connected to a given cross-sectional curve by a simple method.

<Summary of the Invention> The present invention moves a first given cross-section curve while changing it along two given second and third cross-section curves, and creates a curved surface formed by the movement. This is a generation method, and in this method, the step of obtaining the coordinate value of the i-th intermediate point P _{i, O} when the first sectional curve is divided into M, and the second and third sectional curves are divided into N respectively. J
The step of _obtaining the coordinate values of the respective points P _{O, j} , P _{M, j} of the th, the starting point P _{O, O} and the ending point P _{M, O of} the first section curve and the intermediate point
With P _{i, O} relationship, determining the point P _{O, j,} P _M, respectively _j start, the intermediate point P _i on the intermediate section curve end _point, intermediate point P _i that corresponds to _{O, j} All the points P _{i, j} (i = 1, 2, ... M; j = 1, 2, ...
··· N) has a step of generating a curved surface. According to this method, a curved surface surrounded by several sectional curves can be easily generated.

<Example> FIG. 1 is an explanatory view for explaining a curved surface generation method according to the present invention.
FIG. 2 is a flow chart of processing. In FIG. 1, 11 is a cross section for cutting the three-dimensional curved body, 11a is a cross-sectional curve (operation curve) when the three-dimensional curved body is cut by the cross section 11,
21 and 22 are cross sections including the starting point P _{O, O} and the end point P _{M, O} of the operation curve 11a, and 21a and 22a are cross sections 2 respectively.
It is a sectional curve (reference curve) when a three-dimensional curved body is cut by Nos. 1 and 22, and the end points of each reference curve are P _{O, N} and P _{M, N.} Reference numeral 13 includes the j-th points P _{O, j} and P _{M, j} when the reference curves 21 a and 22 a are divided into N, respectively, and includes the perpendicular foot Q drawn from the point P _{M, j} to the cross section 21. It is a cross section. 13a is an intermediate section curve generated by the method described later, and P _{i, j} is an intermediate point on the intermediate section curve.

The curved surface generation processing will be described below with reference to FIGS. 1 and 2.

(1) First, from the operation panel of a curved surface generation device (not shown), cross sections 11, 21, 22, a movement curve 11a, a reference curve 21a,
Data for specifying 22a, the division number M of the operation curve 11a, and the division number N of the reference curves 21a and 22a are input.

(2) Processors are 1 → i and 1 → j.

(3) Then, the processor sets each reference curve 21a, 22a.
J points P _{O, j} , P
Calculates the coordinate value of _{M, j} .

(4) After calculating the points P _{O, j} and P _{M, j} , the processor calculates the i-th point P _{i, O} when the operation curve 11a is divided into M parts. Incidentally, the calculation method of the points P _{O, j} , P _{M, j} , P _{i, O} is well known, for example, refer to Japanese Patent Application No. 56-54044.

(5) The cross-section 11 and the intermediate cross-section 13 have the same plane (H
-V plane ... See FIG. 3) to obtain conversion matrices M1 and M2. Then, when the cross section 11 including the operation curve 11a is converted into a predetermined plane using the conversion matrix M1, the start point P _{O, O} , the end point P _{M, O} , and the intermediate point of the operation curve
The coordinate values (x _O , y _O ), (x ₁ , y ₁ ), (x, y) of P _{i, O} are obtained respectively, and the conversion matrix M2 is used to obtain the points P _{O, j} , P
Coordinates (ξ ₀ , η ₀ ) of the points P _{O, j} and P _{M, j} when the intermediate cross section 13 including _{M, j} is converted into the predetermined plane (ξ ₁ ,
η ₁ ) is calculated.

(6) Thereafter, the coordinate value (ξ, η) of the intermediate point P _{i, j} is calculated by the following equation ξ = (-n _x ξ ₀ + m _x ξ ₁ ) / (m _x -n _x ) (1) η = ( -n _y η ₀ + m _y η ₁ ) / (m _y -n _y (2) m _x = x−x ₀ (3) n _x = x−x ₁ (4) m _y = y−y ₀ (5) n _y = y−y ₁ (6) This is calculated by the following formula x = (-n _x x ₀ + for each coordinate value of P _{O, O} , P _{M, O} and P _{i, O. m x x 1) / (m} x -n x) y = (-. n y y 0 + m y x 1) / (m y -n y) is because established above the midpoint P _{i, O} Is P _{O, O} , P
_{With the} same ratio that divides _{M and O} internally or externally, P _{O, j} ,
The coordinate value on the HV plane of the intermediate point P _{i , j} that internally or externally divides P _{M, j} is obtained.

(7) When the coordinate value (ξ, η) of the intermediate point P _{i, j} is obtained, the processor transforms the inverse matrix M2 ⁻¹ of the inverse matrix M2 ^−1.
Is used to inversely convert (ξ, η) into coordinate values on the cross section 13 to obtain the coordinate value of the point P _{i, j} and store it in the memory.

(8) Then, it is determined whether or not i = M, and if i <M, i + 1 → i is set, and the processes from step (4) are repeated.

(9) On the other hand, if i = M, it is determined whether j = N. If j <N, then i + 1 is updated by j + 1 → j, 1 → i and the processes from step (3) are repeated.

(10) If j = N in the determination in step (9), the curved surface generation processing ends, and thereafter, points P _{i, j (i} = 1,
, ... M; j = 1, 2, ... N) is used to create NC data for curved surface processing, and the curved surface is processed using the NC data.

<Effects of the Invention> As described above, according to the present invention, the first sectional curve 1
Step of obtaining the coordinate value of the i-th intermediate point P _{i, O} when 1a is divided into M, each j-th point P _{O, j} when the first and second sectional curves 21a and 22a are divided into N , P _{M, j}
In the step of obtaining the coordinate values of the points, the points P _{O, j} and P _{M, j} are defined by using the relationship between the starting point P _{O, O} and the end point P _{M, O of} the first sectional curve 11a and the intermediate point P _{i, O.} There is a step of _obtaining an intermediate point P _{i, j} corresponding to the intermediate point P _{i, O} on the intermediate cross-section curve 13a which is the start point and the end point, respectively, and all points by changing i, j
Since it is configured to generate a curved surface by P _{i, j} (i = 1, 2, ... M; j = 1, 2, ... N), it is possible to easily and smoothly slide a given cross-section curve. We were able to generate a curved surface connected to the crab.

[Brief description of drawings]

FIG. 1 is an explanatory view of a curved surface generating method according to the present invention, FIG. 2 is a flow chart of processing of the present invention, and FIG. 3 is a conversion diagram converted into an HV plane. 11, 21, 22 ... Section 11a, 21a, 22a ... Section curve 13 ... Intermediate section, 13a ... Intermediate section curve

 ─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP-A-57-211603 (JP, A) JP-A-57-169814 (JP, A) JP-A-58-149507 (JP, A)

Claims (1)

[Claims] 1. A curved surface generating method for generating a curved surface for numerical control machining while changing a first given sectional curve along two given second and third sectional curves. The first step of obtaining the coordinate value of the i-th intermediate point P _{i, O} when the sectional curve is divided into M, the j-th point P _{O, j} when the second and third sectional curves are divided into N, respectively , The second step of _obtaining the coordinate values of P _{M, j} , the starting point P _{o, o} and the end point P _{M, O of} the first sectional curve _, and the intermediate point P _{i, O}
Using the relationship of, the points P _{O, j} , P _{M, j} are the starting points,
The third step of _{obtaining the} intermediate point P _{i, j} corresponding to the intermediate point P _{i, O} on the intermediate section curve which is the end point, i, j is changed, and all points P _{i, j} (i = 1, 2,・ ・
M; j = 1, 2, ... N) fourth step of generating a curved surface for numerical control machining, all points P _{i, j} (i = 1, 2, ... M; j = 1, 2,・
..By N), create NC data for curved surface machining No. 5
And a sixth step of processing a curved surface based on the NC data, wherein the third step includes a start point, an end point and an end point of the first section curve when a section including the first section curve is converted into a predetermined plane. The coordinate values of the intermediate points P _{i, O} are (x ₀ , y ₀ ), (x ₁ , y ₁ ),
(X, y), and the coordinate values of the points P _{O, j} , P _{M, j} when the cross section including the points P _{O, j} , P _{M, j} are converted into the predetermined plane are (ξ ₀ , η ₀ ), (ξ ₁ , η ₁ ) _, the coordinate value (ξ, η) of the intermediate point P _{i, j} on the predetermined plane is given by the following equation ξ = (− n _x ξ ₀ + m _x ξ ₁ ). / (M _x −n _x ) η = (− ny _y η ₀ + my _y η ₁ ) / (m _y −n _y ) m _x = x−x ₀ n _x = x−x ₁ m _y = y−y ₀ Step of calculating by n _y = y−y ₁ , the coordinate value (ξ, η) is inversely converted into the coordinate value on the cross section including the points P _{O, j} , P _{M, j} , and the intermediate point P _{i, j} Method for generating a curved surface, the method including the step of obtaining coordinate values of.