JP2000076470A - Method and device for generating curved line and storage medium storing its program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To facilitate the decision of a curved line by performing a deformation processing on a parabolic line in the state that it is displayed. SOLUTION: A curved line generating method is a method for generating a new curved line which is connected to an already decided curved line in a tangential line continuously state. A curved line segment to be connected is selected, an end point q to be connected out of the both end points of the selected curved line segment is adopted as a vertex, the parabolic line Lb with a tangential line direction passing through the end point as an x-axis is displayed at the end point q and a parameter for deciding the shape of the parabolic line is controlled so that the curved line which can be connected to the end point q in the tangential line continuity state is generated from a part of the parabolic line. Thus, since deforming processing is executed on the parabolic line in the state that it is displayed, the segment of the curved line and also its shape are easily and correctly decided.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve creation method, a curve creation device, and a storage medium storing a curve creation program suitable for use in a CAD / CAM system or the like. For details, when creating a free-form surface using a computer, display a default parabola at the end point to be connected, and determine the parabolic segment to be used as a curve while deforming the displayed parabola Thus, it is possible to easily generate a curve that is at least tangent to the end point.

[0002]

2. Description of the Related Art In the creation of a free curve used in a CAD (computer aided drawing) system or a CAM (computer aided manufacturing) system, a spline (B-spline) curve is used as a method of expressing a curve having a continuous curvature. Sometimes.

[0003] However, while the spline curve has a degree of freedom in the shape that can be expressed, when the radius of curvature and the direction of the spline curve are simultaneously displayed on the spline curve, as shown in FIG. b region), an inflection point (c region), and the like. When there is such a sharp change in curvature, for example, when designing the body of an automobile, a highlight line may be distorted or a band of the highlight line may undulate.

In order to avoid such a problem, a method of using a part of a parabola (a parabolic segment) as a new curve connected to the original curve has been considered. This is, as is well known, a clever use of the property that the curvature of the parabola is smooth and the curvature monotonically decreases as the distance from the vertex of the parabola increases.

When a parabola is used as a part of a curve, a sharp change or breakage of the curvature is unlikely to occur. Therefore, the design is an extremely important design requirement for the outer casing design of industrial products such as automobiles. It's being used.

When a part of a parabola is used for a curve, a parabola must be generated, and the following method has been conventionally considered as a method of generating the parabola.

(1.) An equation (y = ax ² ) which gives a vertex or a focal point for determining the shape of a parabola, or expresses a parabola y
Among them, a parabola is generated by a mathematical method such as giving a constant a.

(2.) A part of various parabolas is prepared as a finite number of samples such as a parabolic ruler, and a parabola is generated by a method of fitting or combining appropriate samples.

[0009]

However, such a conventional parabola generation method has the following problems.

First, in the method (1.) in which a parabola is generated by a mathematical method, it is difficult to predict what shape the parabola will be generated. It is nearly impossible to quickly and accurately determine the desired curve while keeping the tangent continuous above.

For example, when a certain curve is connected to the end point r as shown in FIG. 18A, when a constant a is given and a parabola segment of a parabola is cut and pasted as shown in FIG. It is not possible to determine what kind of curve it will be. Therefore, by repeating the constant a several times, a parabolic segment close to the curve to be obtained for the first time can be found. Further, it is impossible to imagine the state of curve connection when the shape of the parabola changes as shown in FIGS. For this reason, it can be said that when using a mathematical method, it is not suitable for a design design.

Second, in the case of the method (2.), there is a shape that cannot be expressed only by pasting or combining a finite number of samples such as a parabolic ruler.
Therefore, in this case, the design of the product to be designed is limited.

As described above, in any of the above-described methods, the designer can perform the deformation operation in accordance with the sensitivity and design intention of the designer while checking the connection between the surrounding curved shape and the parabola in real time. Because you ca n’t
There is a problem that a satisfactory design cannot be made quickly.

Therefore, the present invention solves such a conventional problem. A parabola is displayed at an end point to be connected in advance, and the parabola is deformed while visually observing the displayed parabola. Thus, a curve generation method, a curve generation device, and a storage medium storing a curve generation program for determining a parabola segment to be used are proposed.

[0015]

According to a first aspect of the present invention, there is provided a curve generating method for generating a new curve which is connected in a tangent continuous state to an already determined curve. A curve segmentation method for selecting a curve segment to be connected, an end point to be connected among the end points of the selected curve segment as a vertex, and a parabola having a tangent direction passing through the end point as an x-axis as the end point. Display,
By controlling a parameter that determines the shape of the parabola, a curve that can be connected to the end point in a tangent continuous state is generated from a part of the parabola.

According to a eleventh aspect of the present invention, there is provided a curve generation device comprising a curve generation processing unit, a monitor unit, and an input unit, wherein the curve generation processing unit includes a central processing unit constituted by a computer. A processing unit and storage means are provided, a curve segment to be connected is selected, and an end point to be connected among both end points of the selected curve segment is set as a vertex,
A parabola having a tangent direction passing through the end point as an x-axis is displayed at the end point, and by controlling a parameter for determining the shape of the parabola, a curve that can be connected to the end point in a tangent continuous state is formed from a part of the parabola. The control program to be generated is stored in the storage means.

Further, in the storage medium according to the present invention, a curve segment to be connected is selected,
The end point to be connected among the end points of the selected curve segment is set as the vertex, a parabola having the tangent direction passing through the end point as the x-axis is displayed at the end point, and a parameter for determining the shape of the parabola is controlled. A curve generating program for generating a curve that can be connected to an end point in a tangent continuous state from a part of the parabola to generate a curve is stored.

According to the present invention, a default parabola is displayed at an end point to be connected, and the designer performs a deformation operation on the parabola while visually checking. If a desired curve (parabolic segment) is obtained by this deformation operation, the parabolic segment is determined.

A part of the parabola in operation is arranged so as to be always tangent to the connecting curve, and its curvature is displayed in real time. As an auxiliary display, a parabola is extended to a symmetrical portion with the vertex interposed therebetween, and the vertex of the parabola is also displayed. This is for making it easy to understand which part of the parabola is cut out as a segment.

An auxiliary point (marker) is provided to facilitate the operation of transforming the parabola. Starting from the end point, the starting point and the end point for cutting out the parabolic segment, the apex of the parabola, the auxiliary point indicating the tangential direction of the end point for deforming the shape of the parabola, and the auxiliary point indicating the parabolic direction.

In this example, four parameters are prepared as parameters for deforming the parabola. The parameters are easy for the designer to intuitively operate,
The four parameters are a part of a parabola, (1) start point position, (2) end point position, (3) expansion and contraction in tangential direction,
(4) expansion and contraction in the normal direction. Of these, (1) and (2) determine which part of the parabola is used,
(3) and (4) determine the shape of the entire parabola. The latter determination of the shape of the entire parabola corresponds to determining the constant a in the expression representing the parabola.

By using the four parameters in this manner, an intuitive deformation operation is performed on the displayed parabola, and a parabola of any shape can be generated. Also, the parabola is connected tangentially even if the designer is not conscious, and the state of curvature change can always be grasped. In addition, it is always possible to know what part of the parabola is used.

[0023]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, an embodiment of a curve generating method, a curve generating apparatus and a storage medium storing a curve generating program according to the present invention will be described with reference to the drawings.

FIG. 1 shows a curve generator according to the present invention as a CA.
FIG. 2 is a conceptual diagram of a main part showing an embodiment when applied to a D / CAM system. This system 10 uses a curve generation device 12 to generate shape data representing a free curve constructed using a part of a parabola. The created and created shape data is converted by the tool path creating device 14 into machining data for cutting.

The processing data is downloaded to, for example, a floppy disk (FD) 16, and the downloaded floppy disk 16 is set in an NC milling machine 18. The NC milling machine 18 drives an NC milling machine (not shown) or the like based on the processing data, and creates a product die represented by the shape data.

The curve generator 12 is a central processing unit (CP)
U). Therefore, the curve creating section 20 includes a CPU 22 and a memory means (ROM) 24 for storing a program and a working memory means (RAM or hard disk device) 26 used for generating a curve. The memory means 24 stores various control programs such as a curve generation control program necessary for generating a free curve and the like.

The curve creating section 20 is provided with input means for giving a command for generating a free curve or the like. In this example, any one of the dial input means 30, the mouse input means 32, and the numerical value input means 34 using a keyboard can be arbitrarily used.

As will be described later, as parameters for deforming the parabola displayed on the screen, start and end points for determining a segment (segment) of a part of the parabola to be used, and tangential directions for determining the shape of the parabola are used. The contraction and the contraction in the radiation direction can be set freely. Therefore, the dial input means 30 is provided with four dials 30a to 30d for controlling respective parameters. When the mouse input unit 32 is used, the parameters are controlled using the auxiliary points displayed on the screen. When the keyboard 34 is used, a numerical value is directly input for each parameter.

The curve generating section 20 includes a monitor display section 36.
Are connected, and a curve is generated using the curve or parabola displayed on the display unit 36. As the display unit 36, a CRT, a liquid crystal display element, or the like can be used.

The shape data created by the curve generator 20 is supplied to the above-described tool path generator 14 and converted into machining data. A disk drive 38 is further connected to the curve generator 20 and mounted. In addition to being able to download to a recorded disk (magnetic disk, optical disk, or the like), a program for creating a curve stored in the memory means 24 can be downloaded. Thus, the control program can be installed in another CAD / CAM system or the like using the downloaded floppy disk.

Now, the curve generating apparatus 1 configured as described above.
One embodiment of a procedure for generating a free curve or the like using the method 2 will be described in detail with reference to the flowchart of FIG.

Referring to FIG. 3 and subsequent figures, an original curve for which a curve is to be generated is displayed on the screen as shown in FIG. Therefore, as shown in FIG. 3, first, a curve portion where a parabola is to be connected tangentially, that is, one segment in the curve is selected (step S01).

Next, as shown in FIG. 3, which of the two end points r and q of the selected segment is to be connected to the parabola is selected (step S02). The figure shows a case where the end point q is selected.

When the end point q is selected, a first parabola which is the default of a parabola which is deformed in the future is generated, and
It is displayed so that the vertex of the parabola is located at the end point q (FIG. 4).
reference). The parabola to be displayed is a pair, and the first parabola La has the origin at the vertex on the XY plane, the point (0, 5) as the focal point, and is defined in the range of -20 <= x <= 20. Is a parabola. This parabolic display number and its shape are merely examples.

The first parabola La is set at the end point q of the segment selected at step S02, and the end point q
Is converted into a coordinate system in which the tangent direction at is the X axis and displayed (see FIG. 4). Similarly, another parabola (second parabola Lb) is a parabola that is symmetrical with respect to the X-axis, and is converted into a coordinate system on the screen by focusing on the point (0, -5). It is displayed (see FIG. 4).

Each of the pair of parabolas La and Lb is divided into two segments on both sides of the vertex, and four parabolic segments La1, La2, and L as shown in FIG.
b1 and Lb2 are generated (step S03). And
From the four default parabola segments, one parabola segment is selected as a curve candidate (step S04).

Since each of the parabolas La and Lb is equivalent to the second-order Bezier curve represented by the equation (1),
This parabolic segment can be accurately represented by a quadratic Bezier curve.

[0038]

(Equation 1)

Before starting the transformation operation on the parabolas La and Lb, the radius of curvature and the direction of both the entire existing curve including the segment selected in step S01 and the parabola segment Lb2 selected in step S04 are shown in FIG. (Step S05). Radius of curvature is 1/5 of actual
Display up to about length. By displaying the radius of curvature and the direction, the parabola L can be displayed while referring to the state of curvature continuity.
a or Lb can be entered.

Similarly, as shown in FIG. 5, the selected parabola segment Lb2 is displayed by extending the parabola to a symmetrical portion with the vertex in between (step S06).
When this extended display is performed, it becomes clear at a glance which part of the parabola is used as a line segment.

Now, the selected parabolic segment Lb2
As described above, four parameter values are designated using any of the dial, mouse drag, and numerical value input methods (step S07).

Referring again to the four parameters, FIG.
As shown in (1), there are four starting point positions, ending point positions, expansion and contraction in the tangential direction, and expansion and contraction in the normal direction. The meaning of each parameter value is as follows.

(1) The “start point position” is used to determine where in the parabola the end is to be used as a parabola segment. The given value is the parameter value t of the quadratic Bezier curve
And the initial value is 0.

(2) The "end point position" is used to determine a part of the parabola to be used as a parabola segment. The given value is the parameter value t of the quadratic Bezier curve
And the initial value is 1.

(3) "Expansion and contraction in the tangential direction" refers to scaling the parabolic segment in the tangential direction. The numerical value is given as a scaling factor, and the initial value is 1.

(4) "Expansion and shrinkage in the normal direction" is to scale the parabola segment in the normal direction. The numerical value is given as a scaling factor, and the initial value is 1.

The dial input means 30 is an input means which can obtain the rotation amount of the dial as an integer value in real time, and divides the obtained numerical value by an appropriate number of digits to obtain an arbitrary precision. it can. When the dial input means 30 is used, the above-described parameters are assigned to the four dial input means 30a to 30d, respectively, and each parameter can be changed independently and in real time.

When the mouse input means 32 is used, four auxiliary points (markers) indicated by ■ shown in FIG. 6 are used. By picking and dragging these auxiliary points, the same deformation operation as that of the dial input unit 30 can be performed. In the case of numerical input using the keyboard 34, a parabolic deformation operation is performed by directly inputting four parameter values.

Here, since the parabola is equivalent to the quadratic Bezier curve, the parabolic deformation operation can be replaced by a quadratic Bezier curve deformation operation. Various deformation operations can be easily and accurately performed by replacing the quadratic Bezier curve.

First, the change of the start point position and the end point position is realized by segmentation of the Bezier curve (step S0).
8). Assuming that the parameter values for the start point position and the end point position given in step S07 are s and t, respectively, these become the parameters used when segmenting the quadratic Bezier curve.

Using the parameters s and t, a new start point (a control point in the Bezier curve, the same applies hereinafter) Q0 and a new end point Q2
Is calculated. Control points including the original start point are P0, P1, P
Assuming that 2, the relationship between the original control point P and the new control point Q is as shown in FIG. 7, and the new control point Q has the parameters s, t
The control point Q can be calculated by the following equation (2).
Given the parameters t and s, the new start and end points can be changed simultaneously.

[0052]

(Equation 2)

Here, if the start point position is changed, the new start point Q0 is separated from the end point q selected in step S02, so that it is conventionally known that the start point Q0 is connected again to the end point q in a tangent continuous manner. Rearrange using the method.

FIGS. 8 to 12 show how the start point / end point position is changed by the segmentation. FIG. 8 shows the relationship between a parabola segment and a parabola when the starting point is moved to the right from FIG. As is apparent from this figure, the entire parabola Lb appears to rotate leftward about the start point.

FIG. 9 shows an example in which the starting point is moved to the left from the case of FIG. In this case, it looks as if the entire parabola Lb has rotated to the right. FIG. 10 is a display example when the starting point is moved further to the left than in FIG.

FIG. 11 shows an example in which the end point position is changed.
It can be seen that the shape of the parabola Lb does not change, but only the tip extends. FIG. 12 shows a case where the end point position is shorter than that in FIG. 10, and the parabolic shape does not change.

Next, expansion and contraction in the tangential and normal directions, that is, scaling is performed (step S09). Assuming that the parameter values for scaling in the tangential direction and the normal direction given in step S07 are x and y, respectively, these become the magnifications as they are. The control point P of the quadratic Bezier curve is multiplied by a transformation matrix as shown in Expression (3) using the parameters x and y to perform scaling and rearrangement to a tangent continuous position.

[0058]

(Equation 3)

Here, the matrix Ma is a matrix for performing coordinate conversion such that the control point P0 is the origin and the tangent direction at the control point P0 coincides with the x-axis. Matrix Mb
Is a matrix for scaling. The matrix Mc is a matrix for returning to the original position.

FIG. 13 shows an example of scaling in the tangential direction, where P0 to P2 are control points of a quadratic Bezier curve, and Q0 to Q2
Is the new control point after scaling. FIG. 14 shows an example of scaling in the radiation direction.

FIGS. 14 and 15 show the manner in which expansion / contraction in the tangential direction / normal direction is performed by scaling. FIG. 14 shows an example in which the parabola is extended in the tangential direction. At this time, the parabola segment Lb2 has a shape close to a straight line. Accordingly, the shape of the entire parabola is also deformed to a shape as if the constant a was small. FIG. 12 shows a case where the parabola is extended in the parabolic direction. Since the parabolic segment Lb1 has a more curved shape, the shape of the entire parabola is also greatly deformed.

When the transformation of the parabolic segment is completed, the parameter tv of the quadratic Bezier curve at the position corresponding to the vertex of the parabola, which will be used in a later step, is calculated (step S10). Since the vertex of the parabola is a point at which the length of the tangent vector passing through the end point is minimized, the value of the parameter can be calculated by solving equation (4).

[0063]

(Equation 4)

Then, the vertices are displayed using the parameters calculated in step S10 (step S11).
At the same time, the radius of curvature and the direction of curvature of the parabolic segment after deformation are displayed (step S12).

By displaying the radius of curvature and the direction, it becomes easy to connect and connect the parabolic segment to the end point in a state where the curvature is continuous with respect to q.

By specifying the positions of the vertices of the parabola, it is possible to check in real time which part of the parabola the currently operated parabola segment corresponds to, and the line segment cutting operation is also facilitated. Similarly, the parabola is extended and displayed symmetrically with respect to the vertex (step S13). At this time, the extension can be displayed using inconspicuous colors so that the difference from the actual segment being operated can be clearly seen.

By such an extended display, together with the above-described vertex display, it is possible to confirm in real time which part of the entire parabola the currently operated parabola segment (an intermediate result parabola segment) corresponds to.

Here, the vertices are displayed for the first time in step S10.
Since steps S13 to S13 are all intermediate processes, the vertices, the radius of curvature / direction, and the like are displayed at the same time as the other auxiliary points during the segmentation process.

The extended display of the parabola actually means that new segments are connected and displayed.
At this time, the parameter t of the end point of the new segment can be calculated using the following equation (5). When tv <0.5 t = 2tv-1 When tv = 0.5 No extended display When tv> 0.5 t = 2tv (5) where tv is the vertex of the parabola calculated in step S10. Is the same as the parameter.

The above-described real-time deformation operation using the dial and the mouse is repeated until the "OK" key is selected, and when the "OK" key is selected, the process of generating the parabolic segment ends (steps S14 and S1).
5).

The curve data thus generated is stored in the memory means 26 as shape data. In this case, the curve data other than the start point and the end point used in the deformation operation are not used as the shape data.

If a free curve formed by using the above-described parabola is used, a free-form surface can be created in a short time and in a state where tangents and / or curvatures are continuous. By combining the four free curves generated as described above, a mesh (patch) as a constituent unit of a free-form surface
Is formed.

[0073]

As described above, according to the present invention, the following effects can be obtained.

1. In addition to using a parabola, a parabola segment is determined while performing a transformation operation on the parabola displayed on the screen. By controlling parameters such as a start point and an end point in real time, a part of the parabola can be used by an intuitive operation. In addition, if an intermediate display that shows the shape of the entire parabola is performed in real time, it is possible to always know which part of the parabola is being used, so that it is easy to generate a tangent continuous curve. .

2. By controlling a parameter for a parabolic deformation operation, a parabola of any shape can be generated, so that a tangent continuous curve can be generated for any curve.

3. By making the operating parabola always tangent to the connecting curve and displaying the radius of curvature / direction, the designer can check the connection between the surrounding curve shape and the parabola in real time, Deformation operation can be performed according to the designer's sensitivity and design intention.

Therefore, the present invention is extremely suitable for application to a CAD / CAM system for generating a free curve such as an automobile as described above.

[Brief description of the drawings]

FIG. 1 is a system diagram of a main part showing an embodiment when a curve generation device according to the present invention is applied to a CAD / CAM system.

FIG. 2 is a flowchart showing an embodiment for explaining an algorithm of the present invention.

FIG. 3 is an explanatory diagram of a segment connecting a parabola and an end point;

FIG. 4 is a diagram illustrating an example of a default parabola displayed at an end point;

FIG. 5 is a diagram when one segment of a parabola is selected, with the display of the radius of curvature / direction and the extended display of the parabola.

FIG. 6 is an explanatory diagram of parameters used to control the shape of a parabola.

FIG. 7 is an explanatory diagram of end point segmentation of a quadratic Bezier curve.

FIG. 8 is a diagram showing a change state of a parabolic segment when the start point is operated rightward.

FIG. 9 is a diagram illustrating a change state of a parabolic segment when the start point position is operated to the left.

FIG. 10 is a diagram showing a changing state of a parabolic segment when the start point position is further moved leftward.

FIG. 11 is a diagram showing a change state of a parabolic segment when the end point position is further lengthened.

FIG. 12 is a diagram illustrating a change state of a parabolic segment when an end point position is shortened.

FIG. 13 is an explanatory diagram when scaling in the tangential direction.

FIG. 14 is an explanatory diagram when scaling is performed in the radiation direction.

FIG. 15 is a diagram showing a state where a parabolic segment is extended in a tangential direction.

FIG. 16 is a diagram showing a state when a parabolic segment is extended in a normal direction.

FIG. 17 is a diagram showing a spline curve in which a change in curvature is not smooth.

FIG. 18 is a diagram showing a relationship between an existing curve and a parabola connected thereto.

[Explanation of symbols]

10 ··· system, 12 ··· curve generator, 20 ·
..Curve creation unit, 30 dial input means, 32
..Mouse input means, 34 ... keyboard for numerical value input, 36 ... display unit, 38 ... disk drive device, La, Lb ... parabolic, La1-Lb2 ... parabolic segment

Claims (14)

[Claims] 1. A curve generating method for generating a new curve connected to a predetermined curve in a tangent continuous state, wherein a curve segment to be connected is selected, and a curve segment is selected from both end points of the selected curve segment. The end point to be connected is defined as the vertex, and a parabola having the tangent direction passing through the end point as the x-axis is displayed at the end point. By controlling the parameters that determine the shape of the parabola, the end point is connected in a tangent continuous state to the end point A curve generation method, wherein a curve that can be generated is generated from a part of the parabola. 2. A parameter for determining the shape of the parabola, wherein a start point position and an end point position of a parabolic segment used as a part of the curve, expansion and contraction in a tangential direction and an expansion and contraction in a normal direction with respect to the end point are used. The curve generating method according to claim 1, wherein 3. The curve generating method according to claim 1, wherein said parameters can be independently controlled in real time. 4. The curve generating method according to claim 1, wherein said parabolic segment is connected to said end point with a continuous curvature. 5. The curve generation method according to claim 1, wherein a parabola other than the designated parabola segment is displayed at the same time. 6. The curve generating method according to claim 1, wherein the display of the designated parabolic segment and the display of the other parabola are changed. 7. The curve generating method according to claim 1, wherein auxiliary points are simultaneously displayed on the parabola to facilitate the parameter control. 8. The method according to claim 7, wherein the auxiliary point is an end point, a start point, an end point, a point indicating a tangential direction, a point indicating a normal direction, or all or a part of a vertex of the parabola. Curve generation method. 9. The curve generating method according to claim 1, wherein, when the parabola is displayed, a radius of curvature and a curvature direction of the original curve and the parabola to be connected are displayed. 10. When displaying a parabola of an intermediate result,
2. The curve generation method according to claim 1, wherein a portion where the parabola is extended symmetrically with respect to the vertex is displayed. 11. A curve generation processing unit, a monitor unit, and an input unit, wherein the curve generation processing unit is provided with a central processing unit constituted by a computer and a storage means, and is to be connected. A curve segment is selected, an end point to be connected is set as a vertex at an end point to be connected among both end points of the selected curve segment, and a parabola having a tangent direction passing through the end point as an x-axis is displayed at the end point, and a parameter for determining a shape of the parabola is displayed. A curve generating apparatus, wherein a control program for generating a curve that can be connected to the end point in a tangent continuous state from a part of the parabola is stored in the storage means. 12. The curve generating device according to claim 11, wherein the input unit is configured by any one or all of a dial input unit, a mouse input unit, and a numerical value input unit. 13. Selecting a curve segment to be connected,
The end point to be connected among the end points of the selected curve segment is defined as a vertex, a parabola having a tangent direction passing through the end point as an x-axis is displayed at the end point, and a parameter for determining the shape of the parabola is controlled. A storage medium storing a curve generation program for generating a curve that can be connected in a tangent continuous state to an end point from a part of the parabola to generate a curve composed of a parabola. 14. The storage medium according to claim 13, wherein the storage medium is a tape storage medium or a disk storage medium.