JPH06150016A - Graphic display device - Google Patents

Abstract

PURPOSE:To provide the graphic display device, which accelerates processing by simplifying the judgement of crossing between a surface of the second order and a ray, concerning the graphic display device for displaying the surface of the second order while erasing hidden surfaces. CONSTITUTION:This device is provided with a ray generation part 1 for generating vectors directed from a viewpoint arbitrarily set inside a three-dimensional space toward respective passing picture elements on a screen as rays, cross range decision part 2 for dividing an entire picture element, where the ray is passed, into picture element groups composed of plural picture elements and for calculating the range of a cross picture element group, which is one part of this divided picture element group and composed of the picture elements to pass the ray crossing the surface of the second order inside the three-dimensional space, for each divided picture element group, intersection calculation part 3 for calculating the coordinate of an intersection with the surface of the second order concerning the ray to pass the respective picture elements inside the cross picture element group, and luminance setting part 4 for setting luminance of the intersection coordinate corresponding to the color of the intersection to the picture element to pass the ray crossing the intersection coordinate.

Description

Detailed Description of the Invention

[0001]

This invention relates to computer aided design (CA
The present invention relates to a three-dimensional figure used for D) and the like, and more particularly to a figure display device for displaying a quadric surface after hidden surface removal processing. In general,
When displaying a three-dimensional figure on a cathode ray tube (CRT) such as an electronic computer, the pixels covered by the three-dimensional figure are selected on the display screen, and the pixels overlap each other in the depth direction when viewed from the viewpoint. It is necessary to perform a hidden surface removal process of determining the front-back relationship of graphics and selecting and displaying the graphic closest to the viewpoint.

A ray tracing method is known as a typical method for erasing hidden surfaces. Ray tracing method is 3
A screen is set between the three-dimensional figure installed in the three-dimensional space and the viewpoint, and a half-ray ray that passes through each pixel that divides the screen into vertical and horizontal resolutions is generated from the viewpoint. FIG. 6 is an explanatory diagram showing the generation of rays, and a ray is a vector from the viewpoint to each passing pixel.

Then, the graphic element of the three-dimensional graphic on the ray is searched, and the graphic element closest to the viewpoint is selected from the graphic elements searched on the ray. In the hidden surface removal processing by the ray tracing method, rays corresponding to the number of pixels which pass through the screen within the range of the viewpoint to the field of view are generated, and the presence or absence of the figure element of the three-dimensional figure is searched for on each ray. The determination whether an element covers a pixel is called intersection determination.

The intersection determination is performed by the following method. A quadric surface is defined as a set of points in a three-dimensional space that satisfies the following quadratic equation.

[0005]

[Equation 1] This can be expressed in matrix form as follows.

[0006]

[Equation 2] However, Q is a coefficient matrix showing a quadric surface. The ray is expressed by the following equation using the parameter t.

[0007]

[Equation 3] Substituting Ray's equation 2 into the surface equation 1 of the quadratic surface, t
Find a quadratic equation for.

[0008]

[Equation 4] However, the coefficients a, b, and c satisfy the following equation.

[0009]

[Equation 5] If the quadratic equation 3 has a real number solution, the ray intersects the quadric surface, so the condition of the intersection is the discriminant D of the quadratic equation 3 described above.
But,

[0010]

[Equation 6] Is to be satisfied. In the intersection determination, it is determined whether or not each ray intersects according to the intersection condition.

[0011]

2. Description of the Related Art FIG. 9 is a system configuration diagram of a hidden surface erasing process of a figure by a conventional ray tracing method. The system of the hidden surface removal processing of the figure
The intersection calculation unit 6 and the brightness setting unit 7 are included.

The ray generation unit 5 inputs viewpoint information and generates rays that pass through the screen within the range of the field of view for the number of pixels. The intersection determination / intersection calculation unit 6 selects an intersecting figure by the intersection determination of each ray, and when there are a plurality of intersecting figures, extracts the closest intersecting figure to the viewpoint. And
If necessary, obtain the coordinates of the intersection and the normal vector at the intersection.

The brightness setting unit 7 inputs the intersection coordinates and intersection normals calculated by the intersection determination / intersection calculation unit 6, gives each ray a color according to the intersecting figure, and passes the ray. The process of setting the pixel is performed. Here, the processing in the intersection determination / intersection calculation unit 6 will be described. Figure 10
6 is a configuration diagram of an intersection determination / intersection calculation unit 6. FIG.

The intersection determination / intersection calculation unit 6 further includes an intersection determination unit 61, an intersection position calculation unit 62, a hidden surface removal unit 63, and an intersection coordinate calculation unit 64. In the intersection determination unit 61, when the ray direction vector and the ray base point coordinates are input as the ray data and the matrix Q representing the quadric surface is input as the graphic data, the quadratic equation relating to t obtained as described above. The coefficients a, b, c of 3 and the value of the discriminant D are calculated to determine whether or not there is an intersection.

In the intersection position calculation unit 62, the intersection determination unit 61
The real solution of quadratic equation 3 with respect to t from the values of a, b, and D found in

[0016]

[Equation 7] To calculate. In the hidden surface removal unit 63, when the value 4 of the real number solution t obtained by the intersection position calculation unit 62 has two real number solutions (D> 0), and when the two real number solutions are both positive (a), Since the solution having the larger value out of the two positive solutions is the intersection on the back side of the quadric surface and cannot be seen from the viewpoint, the smallest real number solution of the values of t is adopted.

When one of the two real number solutions is positive and the other is negative (b), the negative solution is outside the field of view because it corresponds to the intersection point on the rear side of the viewpoint, and the value of t Adopt a positive real number solution. Also, when both of the two real number solutions are negative (c), neither is adopted. FIG. 11 is a diagram showing the positional relationship between the quadric surface and the viewpoint of the ray and how to select the intersection.

In the intersection point coordinate calculation unit 64, the hidden surface removal unit 63
The value 4 of the real number solution t obtained in step 1 is substituted into the ray equation 2 to calculate the coordinates of the intersection. Further, the normal vector at the intersection is calculated as necessary. As described above, by performing the processing in the intersection determination / intersection calculation unit 6 on the ray passing through each pixel, the display graphic element is determined for each ray.

[0019]

However, in the conventional hidden surface erasing processing system, t is set for each ray.
Since the quadratic equation 3 is created to determine the intersection, there is a problem that it takes time to determine the intersection.
Therefore, according to the present invention, the intersection of the quadric surface and the ray is not determined for each ray, but the range of the intersecting pixel group including the pixels through which the ray intersecting the quadric surface passes is obtained. An object of the present invention is to provide a graphic display device that simplifies intersection determination and speeds up processing.

[0020]

In the present invention, the means for solving the above-mentioned problems is, as shown in FIG. 1, from each viewpoint arbitrarily set in the three-dimensional space to each passing pixel on the screen. A ray generation unit 1 that generates a vector toward a ray and an entire pixel through which the ray passes is divided into a pixel group including a plurality of pixels, and each divided pixel group is a part of the pixel group, and An intersection range determination unit 2 that obtains a range of an intersection pixel group including pixels through which a ray intersects a quadric surface in a three-dimensional space, and a quadric surface for a ray that passes through each pixel in the intersection pixel group. And a brightness setting unit 4 that sets the brightness corresponding to the color of the intersection of the intersection coordinates to the pixel through which the ray passing through the intersection coordinates passes. That is what I did.

In addition to this, in the intersection range determining unit 2, the base point coordinates A and the direction vector B of the ray passing through the reference first pixel P in the pixel group, and the first pixel P. Different from the base point coordinates of the ray passing through the second pixel Q and the base point coordinate A of the ray passing through the first pixel P.
A base point difference vector C which is a difference value between the first pixel P and the direction vector of a ray passing through the second pixel Q;
From the direction difference vector D, which is the difference value from the direction vector B of the ray passing through, and the coefficient matrix E representing the quadric surface,
This is a graphic display device which is located on a straight line connecting the first pixel P and the second pixel Q and which obtains the range of a group of intersecting pixels arranged in a line on the screen by algebraic calculation.

Alternatively, in addition to the above, the ray generation unit 1
At the initial value F of the passing coordinate of the ray passing through the reference pixel which is the reference in the pixel group and the difference value between the initial value of the passing coordinate of the ray passing through the adjacent pixel adjacent to the reference pixel and the initial value of the passing coordinate. A passing point difference vector calculation unit 13 for obtaining a passing point difference vector G, a base point coordinate initial value H of a ray passing through the reference pixel, and a base point coordinate of a ray passing through the adjacent pixel and the base point coordinate initial value. Base point difference vector calculation unit 1 for obtaining base point difference vector I which is a difference value
4, a direction vector initial value J which is a difference value between the passing point coordinate initial value F calculated by the passing point difference vector calculation unit 13 and the base point coordinate initial value H calculated by the base point difference vector calculation unit 14, and Directional difference vector calculation unit 1 for obtaining a direction vector difference value K which is a difference value between the passage point difference vector G obtained by the passage point difference vector calculation unit 13 and the base point difference vector I obtained by the base point difference vector calculation unit 14.
5 and 5.

[0023]

According to the present invention, the range of the intersecting pixel group consisting of the pixels through which the ray intersecting the quadric surface passes is first obtained. Therefore, for the pixels within the range of the intersecting pixel group, the intersection determination for each ray is performed. Is unnecessary, and the subsequent intersection position calculation and hidden surface removal processing can be significantly speeded up.

Further, for the pixels outside the range of the intersecting pixel group, it is not necessary to process the ray for each pixel, so that the intersecting determination process can be greatly simplified.

[0025]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 2 is a configuration diagram showing the configuration of the ray generation unit 1 which is an embodiment of the present invention. In FIG. 2, the ray generation unit 1
Is a screen setting unit 11, a loop counter 12,
It includes a passing point difference vector calculation unit 13, a base point difference vector calculation unit 14, and a direction difference vector calculation unit 15.

The screen setting unit 11 sets the visual field such as the visual point, the gazing point, and the visual angle on the screen arranged in the three-dimensional space according to the input visual point data, and calculates the positions of the four corners of the screen. To do. Then, the screen is divided vertically and horizontally by the resolution of the cathode ray tube, and each of the divided partitions is a pixel having a certain area.

Further, the position where the ray passes is fixed to the center of the pixel, and the position coordinate of each pixel is represented by the pass point coordinate of the ray passing the pixel. The loop counter 12 divides the pixels covering the screen into pixel groups arranged in a line in the horizontal direction, and sequentially selects each pixel group as a scan line that is a target of intersection determination.

FIG. 7 is an explanatory diagram showing scan lines on the screen. The passing point difference vector calculation unit 13 sets an arbitrary scan line selected by the loop counter 12, for example, an arbitrary pixel on the upper scanning line, for example, a leftmost pixel as a reference pixel, and passes through the passing point coordinates of the reference pixel. It is calculated as the initial point coordinate value.

Next, a pixel to the right of the reference pixel is set as an adjacent pixel, and a difference value obtained by subtracting the initial value of the passing point coordinate from the passing point coordinate of the adjacent pixel is calculated as a passing point coordinate difference value. The base point difference vector calculation unit 14 calculates the base point coordinates [b0] of the ray passing through the reference pixel as the base point coordinate initial value.

Next, a difference value [d] obtained by subtracting the initial value of the base point coordinate from the base point coordinate of the ray passing through the adjacent pixel.
b] is calculated as the base point coordinate difference value. The direction difference vector calculation unit 15 calculates a difference value [a0] obtained by subtracting the base point coordinate initial value from the passing point coordinate initial value as the direction vector initial value. Next, a difference value [da] obtained by subtracting the base point coordinate difference value from the passing point coordinate difference value is calculated as a direction vector difference value.

In the ray generating section 1 configured as described above, the direction vector initial value [a0], the direction vector difference value [da], the base point coordinate initial value [b0], and the base point coordinate difference value [db] are respectively set.

[0032]

[Equation 8] The intersection range determination unit 2 is calculated as ray data.
Is output to. In the loop counter 12, as shown in FIG. 7, the scan line which is the object of the intersection determination is in the horizontal direction, but a pixel group arranged in a line in the vertical direction may be used as the scan line.

Next, the processing in the intersection range determination unit will be described. FIG. 8 is an explanatory diagram showing pixels arranged in a line. In FIG. 8, for all rays for each pixel having an area covering the screen, the ray equation passing through an arbitrary pixel P is used as a parameter t when the ray passing position is fixed at the center of the pixel. hand

[0034]

[Equation 9] And the ray equation passing through the pixel Q adjacent to the pixel P is

[0035]

[Equation 10] And the difference component

[0036]

[Equation 11] Then the equation of the ray passing through the pixel R moved i-th direction from the pixel P in the pixel Q direction is

[0037]

[Equation 12] Represented by In order for the ray passing through the pixel R to intersect the quadric surface, the equation 5 for the ray passing through the pixel R is
It suffices that the value of the discriminant of the quadratic equation regarding t obtained by substituting it into the curved surface equation 1 representing the quadric surface is positive.

Therefore, the range of i in which the value of the discriminant is positive is obtained, and the range of the pixel group consisting of the pixels passing through the ray intersecting the quadric surface is obtained from the pixel groups arranged in a line.
Further, details of calculation of the intersection range will be described below. The variables and the ray and the coefficient representing the quadric surface are defined by the following equation.

[0039]

[Equation 13] When variables and coefficients are defined as described above, a quadratic equation expressing a quadric surface is expressed by the following equation.

[0040]

[Equation 14] The ray equation passing through the pixel R is expressed by the following equation.

[0041]

[Equation 15] When the ray equation 7 passing through the pixel R is substituted into the curved surface equation 6 of the quadric surface, the following equation is obtained.

[0042]

[Equation 16] [Db] for perspective projection in which the base point of the ray is concentrated at one point
Since is a zero vector, when the equation 8 is expanded, the coefficients a, b, and c of the quadratic equation 3 with respect to t can be obtained as follows.

[0043]

[Equation 17] Further, in case of parallel projection in which all rays are parallel, [da] is a zero vector. Therefore, when the above equation 8 is expanded, each coefficient a, b, c of the quadratic equation 3 with respect to t is obtained by the following equation.

[0044]

[Equation 18] Then, the discriminant D of the quadratic equation with respect to t is obtained as follows using the coefficients a, b and c.

[0045]

[Formula 19] However, when the discriminant D is rewritten as a quadratic equation for i, the coefficients α, β, γ are

[0046]

[Equation 20] In case of parallel projection

[0047]

[Equation 21] Is. The range of i for which the discriminant value, which is the value of the discriminant D, is positive is the range of pixels through which the ray intersecting the quadric surface passes. FIG. 4 is a diagram showing a range of i in which the discriminant value D is positive.

That is, 1) In the case where the secondary term α = 0 of i and the primary term β = 0 (the zero-order expression of i) γ> 0, the intersecting ray is from the first ray to the final ray γ When <0, there is no crossing ray. 2) When the secondary term α = 0 of i, the primary term β ≠ 0 (first-order expression of i) When β> 0, the intersecting ray is −γ / (2β ) Th ray to the last ray, when β <0, the intersecting ray is −γ / (2
β) Up to the th ray 3) When the discriminant D has no real root (quadratic equation of i) When α> 0, the intersecting ray is from the first ray to the final ray When α <0, there is no intersecting ray 4 ) When the discriminant D has a real root (a quadratic expression of i), when α> 0, the intersecting rays are from the first ray to the ray of the smallest real root of the two real roots and to the ray of the largest real root of the two real roots. When α <0 to the ray, the intersecting ray is from the ray of the smallest real root of the two real roots to the ray of the largest real root of the two real roots, where the first ray is the ray passing through the first pixel of the pixels lined up in a row, The final ray is a ray that passes through the last pixel of the pixels arranged in a line.

As described above, the rays passing through the pixels within the obtained range of i intersect the quadric surface, and the rays passing through the pixels outside the range do not intersect the quadric surface. FIG. 3 is a configuration diagram showing the configurations of the intersection range determination unit 2 and the intersection calculation unit 3 according to an embodiment of the present invention. In FIG. 3, the intersection range determination unit 2
Is composed of a matrix product calculation unit 21, a discriminant coefficient calculation unit 22, and an intersection range calculation unit 23.

Further, the intersection calculation unit 3 is composed of the intersection position calculation unit 3
1, a hidden surface removal unit 32, and an intersection point coordinate calculation unit 33. The matrix product calculation unit 21 outputs the ray data [a0], [d] for one scan line output from the ray generation unit 1.
a], [b0], [db] and the parameter [Q] of the quadric surface as the graphic data, the coefficients a, b, c of the quadratic equation 3 with respect to t are calculated by the following matrix calculation.
A parameter giving

[0051]

[Equation 22] Ask for. However, the coefficients a, b, and c are given by the following equations.

[0052]

[Equation 23] In the case of perspective projection in which the base points of rays are concentrated at one point, [db] is a zero vector, and therefore the following relationship holds.

[0053]

[Equation 24] In the case of parallel projection in which all rays are parallel, since [da] is a zero vector, the following relationship holds.

[0054]

[Equation 25] In the discriminant coefficient calculation unit 22, the discriminant D of the quadratic equation 3 relating to t

[0055]

[Equation 26] In the above equation, a second-order coefficient α of i, a first-order coefficient β of i, and a zero-order coefficient γ of i are calculated. However, the coefficients α, β, γ are given by the following equations.

[0056]

[Equation 27] Here, according to the relational expression 9 or 10, the term of (ab × cb) among the quaternary coefficient of i, the cubic coefficient of i, and the quadratic coefficient of i in the discriminant D is equal to 0. Is used. In the intersection range calculation unit 23, the coefficient α of the discriminant D,
The range of i that satisfies D ≧ 0 is calculated using β and γ.

Next, the range of the pixel group consisting of the pixels through which the intersecting ray passes is made into a real number from the calculated range of i, and the portion exceeding the pixel range of 0 to horizontal resolution -1 is excluded. FIG. 5 is a diagram showing an intersecting state of a ray and a quadric surface. Specifically, when the calculated value of i is 0 or less, the value of i is set to -0.5.

When the calculated value of i is equal to or greater than the horizontal resolution -1, the value of i is set to the horizontal resolution -0.5. The ray number s at which the intersection starts is a value obtained by rounding up the fractional part of the calculated value of i. Ray number e at the end of the intersection
Is a value obtained by cutting off the decimal part of the calculated value of i.

The position calculation unit 31 calculates the parameter t of the intersection position of the quadric surface and the ray for the ray determined to intersect by the intersection range calculation unit 23 as follows. Expression that substitutes Ray's equation 7 intersecting the quadric surface into the quadric surface equation 6

[0060]

[Equation 28] Quadratic equation for t obtained from

[0061]

[Equation 29] Solve However, the coefficients S, T and U are given by the following equations.

[0062]

[Equation 30] When S = 0, the quadratic equation 11 becomes a linear equation of t,

[0063]

[Equation 31] Is calculated as a parameter of the intersection position. When S ≠ 0, the quadratic equation 11 becomes a quadratic equation of t, and when S> 0 as a parameter of the intersection point position,

[0064]

[Equation 32] When S <0

[0065]

[Expression 33] Is calculated. If t0 is positive, t0 is used as the parameter of the intersection point, and if t0 is negative and t1 is positive, then t1
Is the intersection point parameter. If t0 and t1 are negative, the quadric surface is on the opposite side of the screen with respect to the base point, so no intersection position is set.

The hidden surface erasing unit 32 selects the graphic element located on the viewpoint side by comparing the crossing position calculated by the crossing position calculating unit 31 with the crossing position with respect to other graphic elements calculated up to that point, Find the intersection figure ID. When the hidden surface removal unit 32 determines that the intersection position of the quadric surface and the ray is closest to the viewpoint, the intersection seat calculation unit 33 calculates the intersection coordinates and the normal vector of the intersection position.

The intersection point coordinates (ix, iy, iz) are obtained by substituting the parameter t of the intersection point position into the ray equation 7 as follows.

[0068]

[Equation 34] The normal vector (nx, ny, nz) of the intersection is obtained from the following equation.

[0069]

[Equation 35] The processing in the intersection range determination unit 2 and the intersection calculation unit 3 described above,
The scan line divided by the ray generation unit 1 is sequentially scanned, and the obtained intersection coordinates, intersection normal vector, and intersection figure ID are output to the brightness setting unit 4 shown in FIG. The brightness setting unit 4 determines the brightness for each pixel, but the process is the same as the operation performed in the conventional graphic display device by the ray tracing hidden surface elimination method.

[0070]

According to the present invention, the presence or absence of intersection of a quadric surface and a ray is not judged for each ray individually, but for pixels passing by a ray intersecting the quadric surface. Since the range of the pixel group consisting of is first determined, the intersection determination for each ray passing through the pixels in the range of the pixel group becomes unnecessary, and subsequent intersection position calculation and hidden surface removal processing can be performed immediately. The intersection determination processing can be speeded up.

Further, since it is not necessary to process the ray for each pixel with respect to the pixels outside the range of the pixel group, the processing in the ray tracing can be efficiently performed and the graphic display can be speeded up. There is an effect.

[Brief description of drawings]

FIG. 1 is a block diagram of the principle of the present invention.

FIG. 2 is a configuration diagram of a ray generation unit according to an embodiment of the present invention.

FIG. 3 is a configuration diagram of an intersection range determination unit / intersection calculation unit according to an embodiment of the present invention.

FIG. 4 is a diagram showing a range of i in which the discriminant value D in the intersection determination of the present invention is positive.

FIG. 5 is a diagram showing an intersecting state of a ray and a quadric surface according to an embodiment of the present invention.

FIG. 6 is an explanatory diagram showing generation of rays.

FIG. 7 is an explanatory diagram showing scan lines on the screen.

FIG. 8 is an explanatory diagram showing pixels arranged in a line.

FIG. 9 is a block diagram of a conventional ray tracing system.

FIG. 10 is a block diagram of a conventional intersection determination / intersection calculation unit.

FIG. 11 is a diagram showing a positional relationship between a quadric surface and a viewpoint.

[Explanation of symbols]

 1 ... Ray generation unit 2 ... Intersection range determination unit 3 ... Intersection calculation unit 4 ... Luminance setting unit

Claims (3)

[Claims] 1. In a graphic display device for displaying a quadric surface by the ray tracing method, a ray generation unit () for generating a vector from each arbitrarily set viewpoint in a three-dimensional space to each passing pixel on the screen as a ray ( 1) and dividing the entire pixels through which the rays generated by the ray generation unit (1) pass into a pixel group composed of a plurality of pixels, and
An intersection range determination unit (2) that obtains, for each of the divided pixel groups, a range of an intersection pixel group that is a part of the pixel group and that passes through a ray that intersects a quadric surface in a three-dimensional space. An intersection calculation unit (3) for calculating coordinates of an intersection with the quadric surface for a ray passing through each pixel within the range of the intersection pixel group obtained by the intersection range determination unit (2); A brightness setting unit (4) for setting the brightness corresponding to the color of the intersection of the intersection coordinates calculated by the intersection calculation unit (3) to a pixel through which a ray passing through the intersection coordinates passes. Graphic display device. 2. The intersection range determination unit (2) includes a base point coordinate (A) and a direction vector (B) of a ray passing through a reference first pixel (P) in a pixel group, Base point difference which is a difference value between the base point coordinates of a ray passing through the second pixel (Q) different from the first pixel (P) and the base point coordinates (A) of the ray passing through the first pixel (P). A vector (C) and a direction difference vector (which is a difference value between a direction vector of a ray passing through the second pixel (Q) and a direction vector (B) of a ray passing through the first pixel (P). D) and the coefficient matrix (E) representing the quadric surface are located on a straight line connecting the first pixel (P) and the second pixel (Q), and are arranged in a line on the screen. The graphic display device according to claim 1, wherein the range of the intersecting pixel group is obtained by algebraic calculation. 3. The ray generation unit (1) is configured such that a ray passing initial value (F) of a ray passing through a reference pixel serving as a reference in a pixel group and a ray passing through an adjacent pixel adjacent to the reference pixel. Passing point difference vector calculation unit (13) for obtaining a passing point difference vector (G) that is a difference value between the passing coordinate of the ray and the passing coordinate initial value, and a base point coordinate initial value (H) of the ray passing through the reference pixel. And a base point difference vector calculation unit (14) for obtaining a base point difference vector (I) that is a difference value between the base point coordinates of a ray passing through the adjacent pixel and the base point coordinate initial value, and the passing point difference vector calculation unit ( 13) initial value (F) of pass point coordinates obtained in 13) and the base point difference vector calculation unit (1
4) The direction vector initial value (J) which is the difference value with the base point coordinate initial value (H) obtained in 4), the passing point difference vector (G) obtained in the passing point difference vector calculation unit (13) and the starting point A directional difference vector calculation unit (15) for obtaining a directional vector difference value (K) that is a difference value with respect to the base point difference vector (I) obtained by the difference vector calculation unit (14). The graphic display device according to 1 or 2.