JPH05151319A - Curved surface generating method in cad device - Google Patents

Abstract

PURPOSE:To obtain the curved surface generating method which can generate a free curved surface for reflecting faithfully a designer's intention, on the CAD device. CONSTITUTION:This curved surface generating method consists of a data input process for inputting a border line, a reference gradual variation line 10 and a guide gradual variation line 20 of a free curved surface, a reference line side patch constitution line estimating process for estimating a reference line side patch constitution line in the direction being parallel to the reference gradual variation line 10, a reference line side patch constitution line correcting process for finding a point being the nearest from the reference line side patch constitution line, and correcting the reference line side patch constitution line so as to pass through this found point, and a guide line side calculating process for calculating a guide line side patch constitution line in the direction being parallel to the guide gradual variation line 20 so as to pass through the found point. Accordingly, with this method, a designer's intention can be reflected by the reference gradual variation line 10 and the guide gradual variation line 20.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for creating a curved surface in a CAD device. In particular, it relates to a method of creating an internal curved surface of a free curved surface from the boundary line of the free curved surface.

[0002]

2. Description of the Related Art In recent years, CAD has received a great deal of attention in society, and this technology is changing the form of conventional design and production based on drawings.

At present, one of the major problems in CAD technology is the handling of free-form curves and curved surfaces. The designer can construct a more complicated and more precise structure by handling this free curve / curved surface in all directions.

There is a cross-section line input method as one of the free curved surface input methods. This cross-section line input method is described, for example, in "Solid Modeling" (written by Hiroaki Chiyokura, published by Industrial Research Society), Chapter 6, "Input of free-form surface". In the cross-section line input method, a free-form surface is constructed by inputting a cross-section line of a free-form surface and generating a surface patch within a surface surrounded by these curves. That is, the designer inputs a boundary line of the free-form surface, and creates a free-form surface by creating a patch curved surface inside the boundary line based on the boundary line.

As described above, various methods have been proposed as a method of creating a patch curved surface forming the free curved surface from the boundary line which is the contour of the free curved surface. The text describes two conventional methods.

The first conventional method will be described. Figure 2
Shows definitions of various terms related to free-form surface creation. That is, the boundary line of the free-form surface that is the object of creation is composed of four curves, of which 2 in the vertical direction.
The curved lines are referred to as reference line 1 and reference line 2, and the two lateral curves are referred to as guide line 1 and guide line 2. Further, in FIG. 2, the contour line of the patch curved surface forming the free curved surface is also shown by a dotted line. This contour line is called a patch curved frame, or simply curved frame. As shown in the figure, the curved frame in the direction parallel to the two reference lines is called the reference line side curved frame, and the curved frame parallel to the two guide lines is called the guide line side curved frame. The portion surrounded by these curved frames is each patch curved surface forming a free curved surface.

FIG. 3 shows a flow chart and an explanatory view showing the first conventional method. This method will be described with reference to the drawings. In step 3-1, the patch structure is first determined from the number of segments of the boundary line surrounding the free curve. This is a method of simply selecting the larger number of the segments of the curves facing each other. For example, the number of segments of the reference line 1 is 2 and the number of the reference line 2 is
If the number of segments is 3, the number of patches in the vertical direction is 3. Similarly, when the number of segments of the guide line 1 is 4 and the number of segments of the guide line 2 is 2,
The number of patches in the horizontal direction is four. Then, step 3-
2, the tangent vectors at both ends of the reference line 1 and the reference line 2 are obtained. Then, in step 3-3, the tangent vectors at both ends of the frame on the reference line side are obtained by linearly interpolating the tangent vectors obtained in step 3-2. That is, as shown on the right side of FIG. 3, linear interpolation is performed between the tangent vector of the reference line 1 and the tangent vector of the reference line 2, and in the example shown in the figure, three reference line side frames are included. The tangent vectors at both ends of are required.
Next, in step 3-4, the frame on the reference line side is estimated as a curve of one segment from the tangent vector obtained in the previous step. Further, in step 3-5, the frame on the reference line side is divided based on the patch configuration determined in step 3-1. For example, in the example shown on the right side of FIG. 3, the reference line side frame is divided into three. Finally, in step 3-6, the guide line side frame is estimated by cubic spline interpolation using the division points obtained in the previous step. In this way, the patch surface forming the free-form surface is created.

FIG. 4 shows a part of a flow chart showing the second conventional method and an explanatory diagram for explanation. This conventional second method is different from the first method only in the operation of step 3-3. That is, by replacing the flow chart shown in FIG. 4 with step 3-3 of FIG. 3, the whole flow chart of the second method is obtained. Here, only the part different from the first method will be described.

The difference between the second method and the first method is how to obtain the tangent vectors at both ends of the frame on the reference line side. The method of obtaining the value will be described below with reference to the flowchart of FIG. In step 4-1, the chord vector V1 which is the direction vector of the chord connecting both ends of the reference line 1 is
The tangent vector of the guide line 1 is projected on the plane which is the normal line, and is V2. Next, the outer product of V1 and V2 is taken, and the vector is taken as V3. The vector V1 obtained in this way,
Create a polar coordinate system with V2 and V3 as the coordinate axes. In step 4-2, the coordinate angle of the tangent vector on the polar coordinates created in the previous step, that is, α _S1 and β _S1 are calculated as in the explanatory diagram shown on the right side of FIG. Step 4
Two coordinate angles are similarly obtained for the other three tangent vectors remaining at -3. And finally,
In step 4-4, the two coordinate angles of the tangent vector at both ends of the reference line side frame are obtained by linear interpolation of the two coordinate angles of the tangent vector obtained in the previous step. At this time, this linear interpolation uses linear interpolation based on the line length ratio on the guide line 1 as shown in the explanatory diagram shown on the right side of FIG. In this way, the tangent vectors at both ends of the frame on the reference line side are obtained. This second conventional method is
It is empirically known that a relatively smooth curved surface can be created as compared with the conventional first method.

[0010]

The conventional method for creating a curved surface has been constituted by the above steps. Therefore, according to the first conventional method, since the tangent vector of the reference line frame is linearly interpolated from the tangent vector of the reference line 1 and the reference line 2, there is a problem in that the curved surface created is not rounded. ..

Further, according to the second conventional method, the tangent vector of the frame on the reference line side is interpolated by the line length ratio of the guide line, so that a curved surface with a rounder shape is created as compared with the first conventional method. However, it was not possible to express an arbitrary curved surface based on the designer's intention.

The present invention has been made in view of the above problems, and an object thereof is to obtain a curved surface creation method on a CAD device capable of creating a curved surface that more faithfully reflects the designer's intention.

[0013]

In order to solve the conventional problems, the present invention is a method for creating an internal curved surface of a free-form surface on a computer-aided design apparatus, the method comprising: a boundary line of the free-form surface; Using one or more reference gradual change lines that are vertical cross-section lines inside the free-form surface and one or more guide gradual change lines that are horizontal cross-section lines inside the free-form surface, In the method of creating a curved surface in a CAD device for creating the internal curved surface by creating a patch constituent line that is a boundary line of the patch curved surface forming the free curved surface, the boundary line, the reference gradual change line, and the guide gradual change line. A reference line for estimating a reference line side patch constituent line in a direction parallel to the reference gradual change line from a data input step of inputting, and the reference gradual change line and a boundary line parallel to the reference gradual change line. Side patch component line estimation step, and It is on the id-graded line, and the reference line side patch component line estimated in the reference line side patch component line estimation step is calculated as the closest point closest to the reference line side patch component line, and is estimated so as to newly pass through the proximity point. A reference line side patch component line correction step of correcting the reference line side patch component line,
A guide line side patch constituent line calculating step of calculating a guide line side patch constituent line in a direction parallel to the guide gradual change line so as to pass through the passing point, and the reference line side patch constituent line. A curved surface creation method in a CAD device, characterized in that a curved surface is created by outputting two types of patch composition lines, which are the guide line side patch composition line.

[0014]

According to the curved surface creation method of the present invention on the CAD apparatus, first, the reference line side patch constituent line is estimated in the reference line side patch constituent line estimating step. Then, in the reference line side patch constituent line correcting step, the estimated reference line side patch constituent line is corrected so as to match the guide gradual change line, and further, the corrected reference line side patch constituent line and guide gradual change line are obtained. Based on this, the guide side patch constituent line was determined.

Therefore, it is possible to obtain each patch curved surface which constitutes a smooth free-form surface along the given reference gradual variable and guide gradual change line.

[0016]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT A preferred embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 shows a flowchart of a curved surface creating method which is an embodiment of the present invention.

The present embodiment is different from the conventional first method and second method in determining each frame of the patch curved surface forming the free curved surface and the reference gradual change line 10 and the guide gradual change line 2.
It is a method that allows the designer to input a detailed intention for the curved surface by designating the shape inside the free curved surface using 0 and. As will be described later with reference to FIG. 1, the second conventional method is internally used to estimate the tangent vectors at both ends of the frame on the reference line side.

The detailed operation of this embodiment will be described with reference to the flow chart of FIG. First, in step 1-1, the structure of a patch forming the free-form surface is determined from the number of boundary line segments surrounding the free-form surface. This is a step of selecting the larger number of the segments of the opposing curves, as in the conventional method. In this embodiment, a 4 × 3 patch configuration will be described in the same manner as described in the conventional method. Then step 1-2
In, the tangent vectors at both ends of the reference line 1 and the reference line 2 and the reference gradual change line 10 parallel to the reference line are obtained. For example, as shown in the explanatory diagram on the right side of the flowchart of FIG. 1, in this embodiment, there are two reference gradual change lines 10. As described above, there may be one or more gradual change lines. The same applies to the gradually changing guide line 20 parallel to the guide line. Then, in step 1-3, it is determined in which section the end point position of the frame on the reference line side to be obtained is located. This is, for example, which reference line and the reference gradual change line 10 the end point is, or which reference gradual change line 10 and the reference gradual change line 10 is located.
This is a step of determining whether or not For example, as shown in the explanatory diagram on the right side of FIG. 1, the frame end point a on the reference line side is between the tangent vectors T _S1 and T _S2 . Similarly, the end point b is between T _S2 and T _S3 , and the end point c is T _S3 and T _S4.
Between Then, in step 1-4, the end point a, which is determined in which section in the previous step,
Estimate the tangent vector of b and c. This is estimated using interpolation in the second conventional method. That is, the tangent vector of the end point a is T _S1 which is the end of the section to which the end point a belongs.
And the tangent vector of T _S2 . This estimation is performed according to the flowchart shown in FIG. Similarly, the tangent vector of the end point b is tangent vector T _S2 and T
_It is estimated by interpolation with _S3, and the tangent vector of the end point c is estimated by interpolation of tangent vectors T _S3 and T _S4 . Next, in step 1-5, the frame group on the reference line side is estimated from the tangent vector obtained in step 1-4. Then, in step 1-6, the point on the guide gradual change line 20 closest to the estimated frame group on the reference line side is obtained. That is,
This is a step of obtaining the closest contact point for each estimated reference line side frame on the guide gradual change line 20.

A feature of this embodiment is that the reference gradual change line 10 and the frame on the reference line side estimated based on the reference line are made to match the guide gradual change line 20. .. That is, in the next step 1-7,
That is, the corrected reference line frame is determined by performing cubic spline interpolation from the tangent vector of the closest point obtained in step 1-6 and the end point of the reference side frame. In this way, the reference gradual change line 10 and the guide gradual change line 20
It is possible to determine the frame of the patch curved surface along. Then, in step 1-8, step 1-
The corrected reference line frame is re-cut based on the patch configuration determined in 1. Then, the guide line side frame is determined from the re-cut point and the tangent vector of the end point of the guide line side frame by cubic spline interpolation as in the reference line frame.

As described above, according to this embodiment, since the reference gradual change line 10 and the reference side frame estimated based on the reference line are corrected so as to match the guide gradual change line 20, the guide gradual change line 20 is corrected. It is possible to perform smooth interpolation along both the gradual change lines of the variable line 20 and the reference gradual change line 10. In addition,
Cubic spline interpolation is the tangent vector of the end point of the line segment,
This is a method of interpolating a line segment from the coordinates of an intermediate passing point.

By the way, in the present embodiment, as shown in the explanatory view on the right side of FIG. 1, two reference gradual change lines 10 and one guide gradual change line 20 are shown. As long as the number is above, any number can be selected, and the patch configuration can be selected independently. For example, when a more detailed free-form surface is to be constructed, it is possible to use more gradual lines and make adjustments such that the gradual line is reduced for a portion with little change.

As described above, when the curved surface generating method according to the present embodiment is used, the patch curved surface that constitutes the free curved surface that more faithfully reflects the designer's intention on the CAD device is set as the boundary line and the free curved surface surrounding the free curved surface. It is possible to create from the reference gradual change line 10 and the guide gradual change line 20 representing the internal shape of the.

[0024]

As described above, according to the present invention,
Since the designer's intention is indicated by the gradual change line representing the internal shape of the free-form surface, there is an effect that the patch curved surface can be configured faithfully to the designer's intention.

Therefore, the cycle of designing and modifying the free-form surface is reduced, and the free-form surface intended by the designer can be formed at high speed.

Furthermore, since the curved surface generating method according to the present invention can faithfully prosper the designer's intention, the boundary line surrounding the free curved surface can be made relatively smaller than the conventional method. That is, since each individual free-form surface can be widened, there is an effect that the total amount of curved surface data can be reduced.

[Brief description of drawings]

FIG. 1 is a flow chart of a curved surface creating method according to an embodiment of the present invention and an explanatory diagram thereof.

FIG. 2 is an explanatory diagram for defining / explaining each curved surface frame that represents a boundary line surrounding a free-form surface and an internal shape thereof.

FIG. 3 is a flowchart of a curved surface creating method according to a first conventional method, and an explanatory diagram thereof.

FIG. 4 is a flowchart of a curved surface creating method according to a second conventional method, and an explanatory diagram thereof.

[Explanation of symbols]

 10 Standard Gradient Line 20 Guide Gradual Line

Claims (1)

[Claims] 1. A method of creating an internal curved surface of a free-form surface on a computer-aided design apparatus, comprising: a boundary line of the free-form surface and one or more vertical cross-section lines inside the free-form surface. By using a reference gradual change line and one or more guide gradual change lines that are lateral cross-section lines inside the free-form surface, a patch constituent line that is a boundary line of the patch curved surface forming the free-form surface is defined. A curved surface creating method in a CAD device for creating the internal curved surface by creating a data input step of inputting the boundary line, the reference gradual change line, and the guide gradual change line, the reference gradual change line, and From a boundary line parallel to the reference gradual change line, a reference line side patch constituent line estimating step of estimating a reference line side patch constituent line in a direction parallel to the reference gradual change line, and on the guide gradual change line, Reference line side patch component line estimation Reference line side patch component line estimated in the process,
A reference line side patch configuration line correction step of calculating the closest proximity point and correcting the estimated reference line side patch configuration line so as to newly pass through the proximity point, and so as to pass through the passing point A guide line side patch constituent line calculation step of calculating a guide line side patch constituent line in a direction parallel to the guide gradual change line, and the reference line side patch constituent line and the guide line side patch constituent line. A free-form surface is generated by outputting the two types of patch constituent lines as described above.