JPS60242311A - Three-dimensional reflector for recognizing form of body andmeasuring device for position and form of body - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a reflector or optical sensor having a three-dimensional structure for object shape recognition.

The three-dimensional reflector according to the present invention represents the position of the reflector in the observation system, the distance from the reflector to the irradiation and detection point, the coordinate system representing the reflector, and the irradiation and detection point. It is a book about the response of a light source to irradiation with the information necessary to derive the three parameters of the angular difference between the coordinate system.

Since the response of the reflector is completely different from the background noise, the response of the reflector can be checked separately from the background noise.

In the present invention, the response of a reflector to illumination is indicative of the arrangement of singularities of the projection on a plane on a curved surface and the position of the singularities with respect to the light source, depending on the geometry of the reflector.

Further, the reflector according to the present invention has periodicity spatially or locally, and specifically is composed of a periodic reflecting surface due to the movement of emitted waves or the depiction of a certain geometric shape.

When such a reflector is illuminated by a scanning beam or by firing an overall illumination beam by a transmitter, if the beam is directed to a point on the reflector that is coincident with the normal to the reflector surface, then The reflected light received by a detector installed near a beam emitting point of a transmitter or the like is reflected in the direction of the transmitter and forms an image object. The geometrical arrangement of reflection points obtained by the image object is the location of points perpendicular to the reflector traveling towards the image object.

Whenever the transmitter and detector are not close together, the configuration of reflection points obtained at the detector will result in a reflection that coincides with the bisector of the angle formed by the direction connecting the detector and transmitter positions. Corresponds to the placement of points perpendicular to the vessel.

The present invention also relates to a device for measuring the shape and position of objects, and in particular to certain devices in the use of three-dimensional reflectors for object shape recognition.

Prior Art French Painting Patent No. 1,57 filed on June 10, 1968
0,810 presented a wave-shaped reflector with concentric undulations.

This reflector is used as a driving mirror for a car, and conventionally converts the image of the car's lights into groups of linearly arranged light spots.

Problems to be Solved by the Invention The above-mentioned conventional invention cannot determine the position of a point perpendicular to the conventional car's light on the mirror, and the mirror cannot be used to recognize the shape of an object.

Means and Actions for Solving the Problem The singularity of a reflector that is illuminated and detected by its image object passes through the center of the reflector and passes through the equatorial plane of one spherical reflector or the equatorial plane of a flat reflector. Spread out in a straight line or in a line of curves through the projection of an image object on a surface.

A reflector with a concentric wave pattern, a reflector with a wave pattern that spreads out radially from the center, a reflector with a radial wave pattern and two circles, and a reflector with a hyperbolic wave pattern. The vessel is expressed as follows.

Depending on the type of reflector, the singularity obtained by the detector can be linear,
Spread out in a circle, both straight and circular, or in an equilateral hyperbola.

We also describe a spherical reflector in which the position of the reflector surface obtained by the detector is projected onto a spherical equatorial plane along the diameter on the equatorial plane.

According to the present invention, the shape and distance parameters of the object are
at least two reflectors having a group of corrugations, or two
one reflector with two groups of waveforms, and if the detector and transmitter of the luminescence are integral, the detector projection on the reflector surface, and if the detector and transmitter of the luminescence are integral. Otherwise, an array of at least two light spots directed towards the detector through the projection of the midpoint of the line segment connecting the emitter and the detector is detected by the reflector.

Therefore, the reflective surface is established by the coordinates for the detector, and the reflector surface is located perpendicular to the straight line from the detector to the projection point.

First, we will discuss the equation for the surface of the reflector.

In the general case, the transmitter E and the detector are not integrated.

First, -2-1 axis is the coordinate of transmitter E's knee mark XDI VD l zD is the detector's coordinate! +3'
Let r z be the coordinates of the traveling point P of the reflector.

And NCx*ytz)=o is the equation of the reflector at the center of the reflector's coordinate system, ie at the origin 0 of the x+3'*z coordinate.

For the P point obtained by the detector, the following conditions must be satisfied.

Here, nXI+ is the norm of vector x in Euclidean linear space, and λ is a real number.

Equation (1) can be considered in the following two cases.

First, the first case is when the transmitter E and the detector E are close to each other, and this can be written as follows.

IPD ll= II pi It = e Therefore equation (1) becomes:

Next, the second case is when the transmitter E and the detector E are integrated, and this can be written as follows.

11PEIl= l1pI) II= eMoreover, stroke=”D=”x:”x=(”K+XD)
/27, = yI) = )'l: )'lmi(yB
+ yD) /2”n = zD=”I : zx=
(zP+zD)/2 holds, and therefore equation (1) becomes as follows.

By eliminating the 2λe term from equation (3)), we obtain the first example: When the reflector equation is expressed as N (x
,y,z)=Z−f(ρ)=0 (5) Therefore, we obtain equations (4) and (7).

The projection of the singularity obtained by the image object is the reflector x =
y = center P of Q. passes through the beam and the projection of the image object on the reflector surface and lies on a straight line.

This P. The point is also the origin 0.

When transmitter E and detector are close but do not match, X
□ and y□ are (XB×Xp)/2 and (7B
+ )'p) /2 In other words, the image object can be expressed as the midpoint of the line segment connecting the transmitter and the detector.

Second example When the reflector equation is expressed as N(x,
y, z) to Z-f(θ) = 0 (9) If θ= ta −' (y/x), by substituting the numerical values of the formula, the following can be obtained.

Here, ρz = (xf+y1'') '2 This equation (b) indicates a circle with radius ρk/2 passing through the origin, and the point (xl + 3'I) is the image on the reflector surface. It is the projection point of the body.

Third example: When the equation of the reflector is expressed as 6 as follows, N (
XI)'IZ) :=Z-f (x'-y') ==□
Hwhere, =xt, fi d, Equation (4) K By substituting the numerical values of equation (6), is obtained.

This equation α◆ indicates a hyperbola that passes through the origin, and is: Point (゛...yl)''i 0 projection point of the image object on the reflector surface.

Regarding the fourth example, Figure 7, the sphere is Xm 3' according to Cartesian coordinates.
* It can be expressed using Z as well as using polar coordinates ψ, ψ, 2.

The radius R of the sphere is a periodic latitude function D(ψ).

When the equation for a spherical reflector is shown as: N(X
I)'IZ)=X17+Z-D2 (ψ)=0(g)ψ
is a function of 2 and ψ=7/R.

1/ R = (x 10 y) shall be.

The partial derivative of N can be expressed as follows.

These three partial derivatives must satisfy equation (2) for the case where the transmitter and detector are in close proximity.

therefore, is given.

This means that in the plane of z = o, the projection of the singular point by the image object is arranged on a straight line passing through the center of the reflector and passing through the midpoint of the line segment connecting the transmitter and detector. means.

When the transmitter and detector coincide, the linear array is z=O
passes through the projection of the image object on the plane of .

Embodiment Referring to FIG. 1, block E is a light transmitter such as a laser source, and block D is a detector such as a photodetector or a camera. P represents a running point on the surface N of the reflector 1o. Point P can be detected by a detector if the normal line erected to surface N at point P bisects angle EPD.

If so, the derivative of N(x, y+z) with respect to the coordinates satisfies equation (1).

In FIG. 2, the transmitter E and the detector are integrated as (ED). In this case, if the normal to the surface N passes through (ED), the illuminated point P will be captured by the detector.

For simplicity, the example below is for the case where the undulations of the reflector are distributed with a single period.

First Example (Figure 3) The formula for the reflector is given by z=Acos(2πρ/λ). Here, A
and λ are constants I, ρ=(2+, * > ”/2.

The cross section of the reflector lO on the X02 plane is a cosine curve 11. Using the spatial period λ, z = A ax(2πX/λ
). The surface of the reflector is made of a cosine curve with an axis of 0°. It forms a circular relief 12. The relief at the center is not a valley, and if the generatrix were a sine curve instead of a cosine curve, there would be a sharp point or a hole at the base point of the center. The position of the plane z=zo, which is restricted to the rear plane, is arbitrary.

FIG. 3 shows the projection J of the image object (ED), and the position of the point detected by the detector is represented by a straight line 13 connecting one point and the center point P of the reflector 0.

J is a point on the uncertain straight line 13. The reflector 10 alone does not function to recognize the shape.

The formula for the reflector of the second embodiment (FIGS. 4, 5A and 5B) is given by Z = A cos kθ.

Here A and K are constants. The reliefs 14 are no longer concentric as in FIG. 3, but radial.

The cross section of the reflector cut by the tube 14.15 concentric with the axis Oz is a curve 24.25 (Fig. 5A) which changes with a sinusoidal waveform.
and Figure 5B), and 1 The peaks of the peaks and valleys of these curves are the origin P. They are lined up. The point 16 captured by the detector is the projection of the image/body (ED) on the reflector surface and the origin P.

They are arranged in a circle 17 whose diameter is the length connecting the points.

One point is an uncertain point on the circle 17 on the opposite side of the diameter direction from point Po.

Third embodiment (Fig. 6) In Fig. 6, the reflector formula #'iZ = Aaya (2yr
u/λ), where u=l−y2. undulations 18
The two asymptote lines bisect each other to form a hyperbolic shape, and the ups and downs are parallel.

The points captured by the detector are distributed in a hyperbola parallel to the coordinate axes with an asymptote. This hyperbola 19 is the center P of the reflector. and passes through the projection J of the image object on the reflector surface.

One point in FIG. 6 is a constant point. It is the point P with respect to the defect of the asymptote of the trajectory of the illuminated point. It is symmetrical.

The fourth embodiment, FIG. 7, has already been discussed. The radius of the sphere is a periodic function of latitude and is established by equation (g).

FIG. 7 shows a latitudinal relief 21 on a sphere 20, which is 0. The plurality of tops and grooves form a circle with the axis as the axis. The projections of points captured by the detector on the xOy plane are distributed on a straight line 22 passing through the five projection points of the Po point and the image object (ED) on the xOy plane. This straight line is the diameter of the sphere. On the sphere, the points captured by the detector lie in a large circle 23. The most significant advantage of the spherical reflector is that the apparent length of the straight line formed by the bright spot captured by the detector remains essentially constant, no matter how tilted the light beam is with respect to the axis of the spherical reflector. It is in.

A reflector embodying the invention makes it possible to determine the distance or attitude of an object based on the alignment of straight lines or curves with respect to a framework of theoretical constructs that can be calculated.

Moreover, the non-periodic distribution of undulations makes it possible to encode the distribution of singular points along said alignment for discrimination between several reflectors.

FIG. 9 shows an aperiodic reflector derived from the reflector of FIG. 3, the undulations of which are not periodic. The contoured line 24 is made by repeating a sinusoidal curve with a constant thickness. The inconspicuous thin lines 25 which are the tops of the undulations are the recesses of the undulations. They appear in FIG. 9 as three groups 26, 27, 28 with five undulations each. The relief is spatially periodic in each group, but it is different from one group to another.

FIG. 10 shows an aperiodic reflector derived from the reflector of FIG. 4, the undulations of which are not periodic. The clear l529 is the top of the undulations created by repeating sinusoidal curves on a piece of constant thickness, and is inconspicuous and thin, 1li30.
are the concavities of those undulations. They appear in FIG. 10 as three groups 31, 32° 33 with 3,6°8 undulations each. The relief is spatially periodic in each group, but it is different from one group to another.

The reflector of FIG. 11 has elements of both the concentrically undulating reflector of FIG. 3 and the ray-like undulating reflector of FIG. It has elements.

As a result, K if the illumination point detected by the detector lies on both a straight line and a circle that intersect the center of the reflector and the projection J of the image object on the reflector surface.

Five points are therefore determined by one reflector.

To obtain the reflector of FIG. 11, the following surfaces are constructed.

2, = A (2πρ/λ) α and Z, = A (2) π/9 (to) If zl and 2. If both are positive, leave the larger of the two. If zl and 22 are both negative, leave the smaller of the two.

If Zl is positive and z is negative, leave zI. If Zl is negative and z is positive, leave z. 1st
In Figure 1, the shading on the reflector indicates the locations where zI is positive and the locations where z2 is positive.These are distinguished by separate @ marks. The double shaded area is 2. and 2. are simultaneously positive (area 41
). The blank 42 on the left is where zI and z have opposite signs (the positive one is left), and 43 is where zl and z
2 are both negative (the smaller one is left behind). Area 42 was not raised as a problem, area 4
3 is treated like area 41.

In Fig. 11, radius '/4 + "'/4,...
・・・・・・・・・λ (2P-1) /,,・・・・・・・・・・・・(2P
+1)'/, the circle is distinguished by a directional straight line when zf is zero.

Since K=12, FIG. 12 shows circles 44 and 45 forming part of the reflector.

ρ= (2P-1), and ρ=(2P+3)"/
2 and by straight lines 47 and 48, θ= (2P-1)π44 and θ= (2P+3)
π/24 In addition, circle 46 is plotted ρ = (2P+1)π/2 As straight @49, θ = (2P+1)π/24 Circles 44, 45 and 46 are plotted at Z=0 and -iL, plane xOy exist.

FIG. 12 AFi includes circular channels 50 and 51;
The former is raised and the latter is depressed.

Circles 44.45 and 46 and straight lines 47.48 and 49
is shown in FIG. 12 BIC. Straight lines 47° 48 and 49 coincide with Z=0 and exist in the plane xoy. Figure 12B is
It includes two straight channels 52 and 53, the former being raised and the latter being recessed.

To make Figure 12C, the larger of zl and 21 is left.

When zl and z are equal, ρ=λ (θ/2π) ■ Equation) indicates an Archimedean spiral. This is (2P+
1) (π/2k), and ρ= (2g+1)(
λ/4).

The spiral is a circle with ρ = (2P + 1) λ/4 and θ = (2g
+i) It can be seen that it passes through the point where the straight line intersects π/2.

In Figure 13, P changes from 0 to 7, and g changes from O to 1 engineering. In each area instructions are given for the problem of raising the larger of the spirals z1 or zl within it.

FIG. 14 depicts a first embodiment of the pose and position determination scheme according to the present invention.

Three reflectors 101, 102. of the type shown in FIG.
103 are arranged on the same plane at the corners of an equilateral triangle. When the reflector is irradiated with light, straight rays 131, 132
．． 133 reaches the detector. These rays intersect at five points, and a straight line IJ (I detector) runs perpendicular to the reflector plane. When the reflectors are placed at equilateral or other triangular corners, additional instructions are given to the foregoing description. It should be noted that one point on the perpendicular line from the construction is an uncertain point in Figure 3. Therefore, for attitude recognition, at least two reflectors of the type shown in Figure 3 are required.
pcs are required.

FIG. 16 shows a cross-sectional view of the reflector 101 in FIG. 14, taken along a plane that includes the perpendicular line and reaches one point. straight line 1
Both ends 1 and 2 of the diameter r of the reflector arranged along 31 are captured by the detector at angles .theta.1, .theta. with the vertical n.

And the distance d-IJ is given by the following formula.

FIG. 16 shows a second embodiment of the pose and position determination scheme.

Three reflectors 201, 202, 203 of the type shown in FIG. 4 are arranged in the same plane and at the corners of an equilateral triangle. When these reflectors are irradiated, they emit circular emission lines 171,
172 and 173 are reflected to the detector. Those rays are 1
They intersect at a point, and the straight line IJ (I, detector) runs perpendicular to the reflective surface. When the reflectors are placed at equilateral or other triangular corners, additional instructions are given to the foregoing description. A notable advantage of the spherical reflector of Figure 8 is that
Regardless of the orientation of the detector (one point) at a distance with respect to the center of the reflector, the apparent length of the line segment formed by the point captured by the detector remains substantially constant. Become.

FIG. 17 shows a planar reflector 1 with concentric circular waveforms.
15th except that 01 was replaced by a spherical reflector.
Similar to the figure. α is the angle at which the spherical reflector is viewed from the detector, and R is the radius of this reflector. And the distance d is given by:

It can be seen that only the position of the target object is determined. Therefore, one spherical reflector is sufficient.

The arrangement of the three concentric wave reflectors and the radial wave reflector can also be devised with the other types of reflectors described above.

Such an arrangement is easily conceivable. And it doesn't make much sense to express it clearly.

It should be noted that when two or more emission lines are straight, two reflectors are sufficient to determine one point. If the emission curve is more than one circle, three reflectors are required to make it clear that the two circles intersect in two places. After all, one reflector is sufficient for one straight line and one circle as far as the emission line is concerned.

So far, we have assumed that the light source and detector are combined. Figures 18 and 19 are cases in which these two things are separated. In Fig. 18, the light source E is the reflector 1o.
A vertical axis exists above the center of the plane. The projection of the detector on a single point or reflective surface is concentrated on a straight line for a landmark such as 131.

! In FIG. 19, the detector 1 is positioned vertically over the center of the reflector 1o. Then, on a landmark line such as 131, point H, the projection of the light source falling on the reflector surface, is concentrated.

The previous case of FIG. 18 is particularly interesting because it allows the reflector and light source to be moved and the detector to be fixed.

Applying an automatic guidance device for a self-propelled vehicle such as a truck to the attitude and distance determination system embodying the present invention is as follows:
This will be described in conjunction with FIGS. 19 and 20. The necessary circuit calculation blocks lead to the detector.

The detector consists of a charge coupled device (CCK) camera. FIG. 20 shows the algorithm of the device.

140... Image collection 141... Limit and contour detection 142... Direction determination of point J where straight lines 131, 132, 133 are converged 143... Each Calculate d using equation 21 by measuring θ and θ at reflectors 101-103. Calculation of deviation 145... Distance calculation between the image object and the point Effect of the invention As described above, the present invention uses a reflector having a large number of adjacent undulations consisting of periodic peaks and valleys. , it is possible to reliably recognize not only the position of an object but also the shape of the object, and the position measurement accuracy is high, and the detector and transmitter can be placed close together or integrated, so it can be used as a self-propelled vehicle, etc. It can be used with high reliability.

[Brief explanation of the drawing]

The invention is illustrated in detail in the accompanying drawings, in which FIG. 1 shows a reflector of an embodiment embodying the invention being irradiated from a transmitter and received by a detector provided separately from the transmitter. FIG. 3 is a geometrical diagram showing the state of a scanning beam. FIG. 2 also shows an embodiment of a reflector which satisfies the present invention and which is adapted to be emitted from a transmitter and received by a detector merging with the transmitter.
FIG. 3 is a geometrical diagram showing the state of the emitted scanning light beam. Further, FIG. 3 is a perspective view showing a planar reflector in which points detected by the detector are distributed on seven straight lines. Also, Figures 4 and 5A
and FIG. 5B is a perspective view showing a planar reflector in which the points detected by the detector are distributed on a circle. Further, FIG. 6 shows a planar reflector in which the points detected by the detector are distributed on an equal hyperbola. 7 and 8 also represent spherical reflectors whose radius is periodically determined by latitude. 9 and 10 represent reflectors derived from FIGS. 3 and 4, respectively, which have concentric circular (FIG. 3) and radial straight (FIG. 4) undulations. It is distributed with different spatial periods in its group reliefs. Also the 11th
The figure represents a reflector with both radial and concentric undulations. In addition, Fig. 12 A1 Fig. 12 B and Fig. 12 C are
12 is a diagram illustrating the geometric process that allows the reflectors of FIGS. 3 and 4 to be adjusted to the reflector differences of FIG. 11; FIG. Moreover, FIG. 13 is a diagram further explaining the structure of the reflector of FIG. 11, which is based on the reflectors of FIGS. 3 and 4. FIG. 14 also shows a first embodiment of a method for determining attitude and distance using the reflector of FIG. Further, FIG. 15 explains how to determine the distance between the detector and the reflector in the case of the reflector of the type shown in FIG. 3. Figure 16 also shows the second method for determining attitude and distance using the reflector in Figure 4.
This shows an embodiment of the invention. Further, FIG. 17 explains how to determine the distance between the detector and the reflector in the case of the reflector of the type shown in FIG. 8. Furthermore, FIGS. 18 and 19 show a case in which the transmitter and detector that emit light are not integrated as a system of the present invention. FIG. 20 exemplifies a method for processing data collected by the detector. D......Detector E...Transmitter P...Irradiation point J...Projection N...・・・・・・Reflector surface lO・・・Reflector Applicant's Office Nacional Detude Nido Recierge Aerospatiale Agent (A itη 1 word (no change in content) Fig. 2 7 Figure 5B Figure 6 Figure 8 Figure 9 Figure 10 Figure 111!l Figure 12A Figure 4S Figure 12C Figure 13 Figure 16 Figure 15 Figure 17 Figure 20 Procedure Amendment Book January 1985 28th, Manabu Shiga, Commissioner of the Japan Patent Office1, Indication of the case, Patent Application No. 274180 of 1982, Name of the invention, Three-dimensional reflector for object shape recognition and object position and shape measuring device 3, Person who makes corrections case Relationship with Patent Applicant France 92320 Châtaillon-Apennu de la Division Leclerc 29 Office National détude Ni de Resiercié Aeros Bassials Representative Vinyl Trouba Nationality 7 Reims 4, Agent 〒105 5. Date of amendment order Self-initiated 6. Full text of the specification to be amended, drawings, and translation of the power of attorney 7. Contents of the amendment As shown in the attached document (no changes to the content of the full description and drawings) Regarding the translation of the power of attorney, the title of the invention will be corrected.

Claims (1)

[Claims] (1) In response to the irradiation of the light source, light spots arranged in a unique arrangement are aligned along a trajectory and detected by the detection means. , has a wavy surface formed by a large number of adjacent undulations consisting of spatially periodic peaks and valleys that are symmetrical and parallel to the center, and each of the undulations has a trajectory passing through the center of symmetry. A reflector for recognizing the shape of an object, characterized in that the foot of a perpendicular line descending from the detection means is on the surface, and this foot is the point that determines the trajectory. (2) The relief is radial straight about the center of symmetry,
A patent claim in which the locus of the light spot is a circle passing through the center of symmetry), and the leg of the perpendicular line descending from the detection means to the reflector surface is a point on the opposite side of the circle in the diametrical direction from the center of symmetry. A three-dimensional reflector for object shape recognition according to item 1. (3) The undulations are substantially hyperbolic in shape with their center at the center of symmetry of the reflector, and the locus of the light spot is another hyperbolic shape passing through the center of symmetry, so that the undulations extend from the detection means to the reflector. The three-dimensional reflector for object shape recognition according to claim 1, wherein the foot of the perpendicular line descending to the surface is in a symmetrical relationship with the center of symmetry of the reflector, which is the intersection of the asymptotes of the hyperbola. (4) The wave-shaped surface of the reflector is substantially spherical, and the undulations appear substantially in the form of grooves in the latitudinal direction on the spherical surface, and the locus of the light spot is directed at the equator where the diameter is the largest. A three-dimensional object shape recognition device according to claim 1, wherein a foot of a perpendicular line projected in a great circle onto the nearby spherical surface and descended from the detection means to the reflector surface is a point on the straight line. reflector. (5) in response to the illumination of the light source, on which a peculiar array of light spots is aligned along a trajectory, whose position with respect to the light source and the detection means to be detected is characteristic, and centered It has a wave-shaped surface formed by a number of adjacent undulations, each having parallel and spatially periodic peaks and troughs that are symmetrical and parallel to the other, and each of the undulations has a trajectory passing through the center of symmetry. A three-dimensional reflector for object shape recognition, characterized in that the foot of a perpendicular line descending from the midpoint of a line segment connecting a light source and a detection means is on the surface, and the foot is a point that determines the trajectory. (6) A three-dimensional reflector for object shape recognition according to claim 1, wherein the adjacent parallel undulations have spatially different periodicities at different positions on the reflector surface. (7) Concentric undulations about the center of symmetry of the reflector;
A three-dimensional reflector for recognizing the shape of an object according to claim 1, which also has straight radial undulations about the center of symmetry, and the two intersect at right angles. (8) A light transmitting means, a detector for detecting light from the light transmitting means, and a reflector coplanar with the object and having a surface having a plurality of wavy uniform patterns, the reflecting means being a detector. It emits luminescent points with a distribution along the marking alignment in the form of a wavy pattern in the direction of , and has means for determining at least two or more concentrated points of said alignment, and said concentrated points are said to be A device for measuring the position and shape of an object, characterized in that it is an image projected onto a device surface. (9) The reflecting means has a concentric waveform and is composed of at least two or more, and the marking alignment of the reflecting means is a straight line that is a collection of the feet of perpendicular lines drawn from the image object to the surface of the reflecting means. A device for measuring the position and shape of an object according to scope 8. The αq reflecting means has a waveform radial with respect to the center, and there are at least three circular marking alignments intersecting the legs of a perpendicular line descending from the image object to the surface of the reflecting means. A device for measuring the position and shape of objects. συ The reflecting means is a sphere having an equatorial plane, and the groove surface of the spherical surface is parallel to the above equatorial plane, and the alignment for marking where the feet of the perpendicular line descending from the image object to the equatorial plane of the reflecting means is as follows. Claim 8 which is two or more straight lines
Device for measuring the position and shape of the object described in Section 1. (2) means for determining the normal line to the surface of the reflecting means, a straight line connecting both ends of the diameter of the image object and the reflecting means, and an angle formed by these and the normal; 9. An apparatus for measuring the position and shape of an object according to claim 8, comprising means for calculating . (2) Determine the angle at which the spherical reflecting means obtained by the detecting means faces from the detecting means, and calculate the distance from the detector to the center of the spherical reflecting means based on this angle and the radius of the spherical reflecting means. Claim 8 having the means
Device for measuring the position and shape of the object described in Section 1.