EP2686957A1

EP2686957A1 - Optoelectronic rotary encoder

Info

Publication number: EP2686957A1
Application number: EP12712066.5A
Authority: EP
Inventors: Gerd Reime
Original assignee: Individual
Current assignee: Individual
Priority date: 2011-03-17
Filing date: 2012-03-14
Publication date: 2014-01-22
Also published as: DE102011014374B3; WO2012123104A1; US20140001349A1

Abstract

An optoelectronic rotary encoder for setting or regulating parameters comprises a first measuring arrangement having a plurality of first light sources (2.41, 2.43), which are arranged on an imaginary closed line and emit light beams in a clocked manner, time-sequentially, and a first receiver (2.3) for receiving a first light beam emitted by at least one of the first light sources and reflected by an object. An evaluation device evaluates the light received by the receiver (2.3) and converted into electrical signals and determines therefrom a position of the object relative to the rotary encoder. A further measuring arrangement is provided for the identification of additional information likewise by means of the evaluation device. The further measuring arrangement has a further light source (2.5) and a further receiver (2.7) for receiving a further light beam emitted by the further light source (2.5) and reflected at the object. A shading element (2.2, 2.10, 2.11) permits the passage of the first light beams of the first measuring arrangement to and from a first location (1.3) - assigned to the imaginary closed line - of an operating surface (1.2) and passage of the further light beams of the further measuring arrangement to and from a further location (1.4) of the operating surface (1.2) in each case with reflection of the light beams into the receivers (2.3, 2.7). A simple and expedient rotary encoder is thus provided which can also be used in safety-relevant areas.

Description

Optoelectronic encoder

RELATED APPLICATIONS The present application claims priority of German Patent Application 10 2011 014 374.2, filed on Mar. 17, 2011, the disclosure of which is hereby expressly made the subject of the present application.

Field of the invention

The invention relates to an optoelectronic rotary encoder for setting or regulating parameters according to the preamble of claim 1.

State of the art

Such a rotary encoder is known from EP 1 435 509 B1, wherein three light sources are operated in series as LEDs, wherein two of the three light sources emit light as transmitters in two light paths, while the third light source is connected as a receiver. If a clock is terminated in this arrangement, the receiver is used again as the transmitter in the next clock, with one of the previous transmitters becoming the receiver, and so on. At the receiver, the incoming light signals are converted into electrical signals, which are then evaluated in order to detect a rotating object moving in front of the rotary encoder with respect to its angular position.

For evaluation purposes, a measuring system known from EP 0 706 648 B1 is used there, in which light sources emit light alternately so that a direct light signal without clock-synchronized alternating light components is applied to a receiver. Are e.g. provided two light sources and a receiver, an object located above the optoelectronic elements reflects light to the receiver. The circuit is designed so that extraneous light has no influence and light signals can be clearly perceived, the e.g. come from the light source and the receiver existing light paths. An optical transmission

CONFIRMATION COPY transmission from a light source to a receiver is fundamentally dependent on the position and nature of the object reflecting the light. In the principle known from EP 0 706 648 B1, however, both light sources are regulated in their intensity so that the receiver sees them with the same intensity. The ratio of the necessary currents corresponds to the ratio of the optical transmission of the two routes. The control always controls the operating currents of the two light sources in opposite directions, so that a compensation of the received signals to zero takes place. Thus, the control signal is proportional to the ratio of one of the two optical transmission factors to the total transmission. Thus, without knowledge of the transfer factors, it is possible to recognize their equality and thus the middle position of the object. This means that, regardless of the type of object, a position having equal distances from the light sources can be surely detected. From US Pat. No. 5,103,085 A, an arrangement is known in the case of an optical proximity detector, in which light is channeled outward via a shading element through a glass layer. If there is an object, such as a finger, light is reflected back into the measuring device and the approach is evaluated. From DE 103 00 223 B3, an optical rotary encoder is known in which a plurality of arranged on an imaginary circular line light sources are operated alternately as a receiver and light emitter. In parallel, external light compensation takes place via an independent light source assigned to the receiver, which light source is adjustable in amplitude and sign. Shading is not provided.

From DE 100 24 156 A1 a device for the optoelectronic position determination of an object is known in which light is emitted alternately by two transmitters in the direction of a common receiver through a medium such as a glass sheet. The emitted, clocked signal is received by a common receiver and decomposed back into its components assigned to the individual light sources. The receiver receives on the one hand a reflection of the light rays on the glass plate, on the other hand when approaching an object corresponding signals which are evaluated in an evaluation unit. Based on the output value of the evaluation unit and a specific angle curve of the object with respect to the radiation Lungsquellen with known spatial relationship of the radiation sources to each other, position and / or movement of the object are detected.

From DE 10 2006 020 570 A1 an optoelectronic device for detecting the position and / or movement of an object with a plurality of light transmitters is known, which build up a multi-dimensional light field. The movement of an object in the light field is detected. In addition, the light beams can be redirected to a receiver via a bulge or click dome. As a result, a clear operability of additional functions is possible in addition to the position detection.

From EP 0 809 120 A2 an optical position sensor is known in which two optical sensors with sensor-active areas are provided. The sensor-active regions of the sensors overlap, so that the position can be determined by determining an angular position within the entire sensor region as a function of the received light.

A preferred field of use for rotary encoders may be the entry of PIN codes e.g. at ATMs in terms of a numbered dial. Security issues with entering PIN codes so far rely on the use of standard 12-key padlocks that are easy to spy on. The same principle applies to an analog dial. However, if the dial could be designed so that it is not specified with digits, but an arbitrary input position is detected and from there starting from a rotary movement a counter displays the numbers zero to nine, this could realize an increased safety standard.

Object of the invention

Based on this prior art, the present invention has the object to provide a simple and cheap encoder that can also be used in security-related areas.

This object is achieved by an optoelectronic rotary encoder with the features of claim 1. On the one hand, the optoelectronic rotary encoder is able to determine an angular position of an object based on at least one light beam reflected by an object. In addition, a further measurement order can also recognize additional additional information, such as a confirmation of a selected value. Both measuring arrangements are operated opto-electronically, that is to say by means of light source and receiver. In order to obtain an unambiguous assignment, locations are provided by means of at least one shading element on an operating surface, at which a passage of the light emitted by the light sources is possible so that it can be reflected back into the respective receiver. As a result, only a very specific signal can be reliably evaluated which makes it possible to detect a maximum value of the reflection even of light sources operated in succession. Upon movement of the object, a shift of the maximum value and its addition to the light sources known with regard to their position is thus detected so that the direction of rotation of the object and also a relative angle of rotation can be determined. From this it is possible to determine information which, for example, corresponds to the selection of a specific number of a PIN code. At the same time, for example, confirmation of the selected numbers can be recognized by additional measuring arrangement as additional information. Preferably, a plurality of groups of synchronized and at the same angular distance from each other arranged light sources, preferably LEDs, are provided, which are operated clocked by a clock control. In the case of a sequential evaluation, it can be assigned by the clock of the clock control, from which group of light sources a maximum value of radiant power at the receiver enters, so that the position of the object, such as a serving hand, can be recognized on the control surface. Based on this, the further position relative to a previous position can then be determined during a further movement of the object, which makes it possible to determine the direction of rotation and the relative angle of rotation.

Preferably compensation light sources are used in the measuring arrangements. These compensation light sources are controlled by a device for controlling the intensity of the compensation light source and / or the first light source so that the receiver both light inputs, ie that of the first light source as well perceives the light originating from the compensation light source with the same intensity. The currents to be supplied to the first light source and to the compensation light source can be set in relation to obtain the desired information about the angular position or the actuation of the confirmation key.

Further advantages emerge from the dependent claims and the following description of an embodiment. Brief description of the figures

In the following the invention will be explained in more detail with reference to an embodiment. Show it:

1 is a perspective view of an operating element,

2 shows a cross section through the operating element according to FIG. 1.

3 is a plan view of the operating element,

4 shows a course of the light beams when operating the annular control element,

FIG. 5 control values R during operation of the operating element according to FIG. 4, FIG.

6 shows the course of the light beams when the central operating element is operated, FIG. 7 shows a control value when operating the central operating element, FIG.

8 shows a block circuit for operating the operating element,

9 shows a timing in the signal processing.

Detailed description of preferred embodiments

The invention will now be described by way of example with reference to the accompanying drawings. However, the embodiments are only examples that are not intended to limit the inventive concept to a particular arrangement. Before the invention is described in detail, it should be noted that it is not limited to the respective components of the device and the respective method steps, since these components and methods vary can. The terms used herein are intended only to describe particular embodiments and are not intended to be limiting. In addition, if singular or indefinite articles are used in the specification or claims, this also applies to the majority of these elements unless the overall context clearly makes otherwise clear.

The figures show an optoelectronic rotary encoder for setting or regulating parameters. A preferred area of use is e.g. the entry of PIN codes e.g. at ATMs. Such a solution may be provided at an ATM, e.g. 1, that is, on a closed line, which in the exemplary embodiment has a circular shape, found on a control surface 1.2, a first point 1.3, which are operated by an object 1.1 as the serving hand as a dial of an analog phone can. This first point 1.3 of the operating surface 1.2 surrounds a central punctiform further point 1.4 of the operating surface. During operation, the hand can be guided in a circle along the first position 1.3, wherein a first measuring arrangement assigned to this first position detects the movement of the object and detects therefrom the position of the object relative to the rotary encoder and optionally the direction of rotation or rotational speed. Regardless of the placement of the object on the first location 1.3 of the operating surface 1.2, which corresponds to a detected maximum of reflection, there may e.g. start a counter for the numbers zero to nine. If, during the rotary movement, which is intuitive to operate like an analog dial, then a certain number is reached by the user, he can confirm this at the further point 1.4 of the control surface 1.1 by a corresponding operation. It goes without saying, however, that the rotary encoder can also be used to determine data other than PIN codes, such as e.g. when entering coordinates or angle data on measuring instruments, machines or the like.

The optoelectronic rotary encoder can be seen with regard to its arrangement from FIGS. 2 and 3. A first measuring arrangement comprises a plurality of first light sources 2.41, 2.42, 2.43, 2.44, 3.11, 3.14, 3.21, .. 3.24 arranged on an imaginary, closed line. In the exemplary embodiment, these first light sources comprise a plurality of groups of light sources which are the same, namely the first group 2.41, 2.42, 2.43 and 2.44, the second group 3.11, 3.12, 3.13 and 3.14, and the third group 3.21, 3.22, 3.23 and 3.24. It goes without saying that more or fewer groups can be provided depending on the desired resolution. As backlight 3.3 for this first measuring arrangement, which is actively switched, for example, when approaching an object, LEDs are provided. The other light sources can preferably be designed as LEDs.

These first light sources emit light-clocked, time-sequentially and are driven by an IC according to FIG. 8 (for example Type 909.06 from Elmos Semiconduc tor AG), which will be discussed further below. The first light sources is at least a first receiver 2.3, in the embodiment exactly one receiver for receiving one of at least one of the first light sources 2.41, 2.42, 2.43, 2.44, 3.11, .. 3.14, 3.21, .. 3.24 emitted and reflected by an object 1.1 Light beam in the form eg a photodiode provided. The receiver 2.3 is assigned a compensation light source 2.12. An evaluation device 8.1 in the form of the IC is provided for evaluating the light beams converted by the receiver 2.3 into electrical signals and for determining a position of the object relative to the rotary encoder, wherein the position in conjunction with the known location of the first light sources and the movement during the movement Time also rotation angle, direction of rotation and rotation speed can be determined.

For detecting additional information, a further measuring arrangement is provided which, in the exemplary embodiment, contains the output 8.4 of the key confirmation, that is to say the confirmation of the selected digit as additional information in the case of a PIN code. The further measuring arrangement has at least one further light source 2.5 and as receiver the at least one first receiver 2.3 or at least one further receiver 2.7, wherein in the exemplary embodiment exactly one further light source 2.5 and exactly one additional receiver 2.7 are provided. The receiver 2.7, which is likewise formed by a photodiode, serves to receive the further light beam emitted by the further light source 2.5 and reflected by an object 1.1, as shown in FIG. The further receiver 2.7 is also assigned an LED as a further compensation light source 2.13. 2, the first light sources 2.41 and 2.43 emit a light beam without an object 2.9 up through the control 1.2 from. Likewise, the further light source radiates toward the further point 1.4 of the control surface 1.2 a light beam 2.8. To illuminate the further point 1.4, an LED 2.14 can be provided. While the backlight 3.3 and the LED 2.14 emit visible light, for the first light sources 2.41, 2.42, 2.43, 2.44, 3.11, 3.14, 3.21, 3.24 and the further light source 2.5 preferably light in the non-visible region such as in Infrared area used.

In order to detect a reflection increase or decrease of the emitted light in the presence of an object 1.1, at least one shading element 2.2, 2.10, 2.11 is provided which, in the case of an imaginary circular closed line on which the first light sources 2.41, 2.42, 2.43, 2.44, 3.11, .. 3.14, 3.21, .. 3.24 are arranged, preferably substantially rotationally symmetrical, which then regularly leads to a circular first point 1.3 of FIG. The shading elements are suitable in the first measuring arrangement according to FIG. 4 via the passage openings arranged above the light sources for the passage of the light beams 2.9 of e.g. allow the first light source 2.41 to the first position 1.3 of the control surface 1.2. From there, in the presence of an object 1.1, the light beam 4.1 reflected by the object reaches the first receiver 2.3 via the corresponding passage opening. On the other hand, for the further measuring arrangement according to FIG. 6, the shading elements permit a passage of the light beam 2.8 coming from the further light source 2.5 up to the further location 1.4 of the operating surface. From there, in the presence of the object 1.1, light reflected by the object as light beam 6.1 passes in the direction of the receiver 2.7 through the shading elements. The passage openings are arranged by the shading elements so that a reflection of the emitted light takes place in the region of the existing object 1.1.

Fig. 3 illustrates that the first light sources 2.41, 2.42, 2.43, 2.44, 3.11, .. 3.14, 3.21, .. 3.24 are arranged in the individual groups at the same angular distance from each other. These groups of light sources are clocked, time-sequentially operated, as shown for example in FIG. 8. In Fig. 8, the IC 8.1 to on the top left side three outputs 8.6, 8.7 and 8.8, over which the groups first Light sources are controlled clocked. With this clock, the further light source 2.5 in Fig. 8 on the left bottom is controlled via a fourth output 8.10 of the IC 8.1. The compensation light sources 2.12 and 2.13 assigned to the receivers 2.3 and 2.7 are also actuated in a clocked manner via the compensation output 8.9. To the input channels 8.12 of the IC 8.1, the first receiver 2.3 and possibly the second receiver 2.7 are connected, which can be selected via an internal switch 8.11.

The first and / or the further measuring arrangement have at least one compensation light source 2.12 or 2.13 assigned to the first receiver 2.3 or the further receiver 2.7, which emits light to the first or further receiver.

In IC 8.1, a device known per se from EP 0 706 648 B1 for regulating the intensity of the emitted light emitted by the at least one first light source 2.41, 2.42, 2.43, 2.44, 3.11, 3.14, 3.21, .. 3.24, provided at the first receiver 2.3 incoming light and of the first compensation light source 2.12 emitted, the first receiver 2.3 incoming light by means of a control value. The intensity of the light is controlled so that the receiver 2.3 perceives the at least one first light source and the first compensation light source 2.12 with the same intensity. The evaluation device then uses this control value 5.11 5.32, which results in perception with the same intensity, simultaneously to detect the position and / or direction of rotation of the object 1.1 relative to the rotary encoder during operation of the light sources operated in turn. Since the lighting conditions change with each movement of the object 1.1, a constant readjustment takes place so that the position of the object can also be determined over time. Due to the changing position, the direction of rotation and the relative angular position and in conjunction with the time the rotational speed along the circular first point 1.3 of the control panel 1.2 can be calculated. Likewise, the confirmation of the further location 1.4 is thus recognized when approaching the object 1.1 and during the subsequent removal of the object. To reinforce the reflection can, but not on the above the at least one shading element 2.2, 2.10, 2.11 arranged control surface 1.2 at the first position 1.3 and at the other point 1. 4, the reflection of the light beams supporting depressions or elevations according to FIG. 2 are provided.

In a movement of the object e.g. along the first position 1.3 of the control panel 1.2 beginning above the first light source 2.4.1 in Fig. 3 left on the 9 o'clock position clockwise over the first light sources 3.11, 3.21, 2.42, 3.12, 3.22, etc. results in an image shown in FIG 5. In Fig. 5, the abscissa represents the angular position W and the ordinate represents the control value R. When the object 1.1 approaches from the bottom left of the first light source, the control value 5.11 belonging to this first light source 2.41 gradually rises to its maximum value, which in the exemplary embodiment is set equal to the angular position of 0 degrees. If the object is continued via the further light sources, then this control value 5.11 decreases again, but first the control value 5.21 for the adjacent first light source 3.11 increases and then the control value 5.31 for the further light source 5.21 and the control value 5.12 successively continue the movement for the first light source 2.42, while the previous ones fall off again. However, since the position of the first light sources is known, it is thus also possible to deduce the position of the object in relation to the rotary encoder or relative to the position at the maximum value at the first light source 2.41. Through software, the first impact of the object can then be defined as a zero-angle position, so that the further movement then successively releases in the control, in a PIN-code entry, digits which are selected by the operator at a suitable location, e.g. within 1.3. Offsetting position and time can then be used on output channels of the IC 8.1 to provide information such as e.g. on the output channel 8.2 the direction of rotation, on the output channel 8.3 the turning steps are tapped.

In principle, the further measuring arrangement according to FIGS. 6 and 7 is designed analogously to the first measuring arrangement. Here, too, a compensation takes place via a device for controlling the intensity to the effect that the light emitted by the further light source 2.5 and reflected at the object 1.1, that of the other receiver 2.7 - or in an embodiment not shown in the drawing Also received by the first receiver 2.3 - and converted into electrical signals is perceived there with the same intensity as the radiated from the other compensation light source 2.13 in the receiver light. From this, a control value is likewise determined which, when the object 1.1 approaches the time T, plots approximately the course shown in FIG. 7. Without applied finger results in the control value 7.2, but if the finger is placed, the result is the control value 7.1, so that an approach and an actuation of the other point 1.4 can be reliably detected. From this process, the keystroke is output on the IC 8.1 on the output channel 8.4 and the approach of the object 1.1 on the output channel 8.5.

FIG. 9 shows the timing during signal processing during operation of the control panel. For simplicity, only a few clock pulses are shown in the figures. In practice, e.g. each used about 40 clock changes. In this case, one cycle in each case comprises an activation of the first light sources or of the further light source as well as an associated compensation cycle in which the compensation light sources are effectively switched. The compensation light sources are always controlled in accordance with the timing for the compensation output 8.9 gap to the effective switching of the light sources. According to FIG. 9, there are two time ranges 9.1 and 9.2. In the time domain 9.1, the three groups of first light sources 2.41, 2.42, 2.43, 2.44, 3.11, 3.14, 3.21, .. 3.24 are activated in succession via the outputs 8.6, 8.7 and 8.8, while in this time range the further measuring arrangement is inactive , as shown by the control for the internal switch 8.11. If the changeover switch 8.11 is actuated, the further time range 9.2, via which the output 8.10 for the further light source 2.5 is now activated, starts, so that in this time period the further point 1.4 of the control panel 1.2 is activated. In the time range 9.1 so that the relative angular position and the rotational movement can be detected, in the time range 9.2 the operation of the other point 1.4 in the middle of the field of operation.

It will be understood that this description is susceptible of various modifications, changes and adaptations, ranging from equivalents to the appended claims. LIST OF REFERENCE NUMBERS

1.1 object

1.2 Control surface

1.3 First annular control surface

1.4 Additional central control surface

2.1 board

2.2 second annular shading element

2.3 first receiver / central photodiode

2.5 additional light source / LED for 1.4

2.6 Lighting / LED for visible light

2.7 further receiver / photodiode for 1.4

2.8 Beam of 2.5

2.9 Beam of 2.41 and 2.43 respectively

2.10 first shading element

2.11 third shading element

2.12 first compensation light source / LED

2.13 further compensation light source / LED

2.14 visible light from 2.6

2.41, ... 2.44 first light sources / first group of four LEDs in parallel 3.11, .., 3.14 first light sources / second group of four LEDs in parallel 3.21, .., 3.24 first light sources / third group of four LEDs connected in the same way

3.3 LED for backlight

.1 Light beam reflected at finger 1.1

5.11 Control value when sweeping the LED 2.41

5.12 Control value when sweeping the LED 2.42

5.13 Control value when passing the LED 2.43

5.14 Control value when sweeping LED 2.44

5.21 Control value when sweeping the LED 3.11

5.22 Control value when sweeping the LED 3.12

5.31 Control value when sweeping the LED 3.21

5.32 Control value when sweeping the LED 3.22

.1 reflected light beam of 2.5 at the finger

7.1 Control value with finger applied

7.2 Control value without applied fingers

.1 evaluation device / IC

.2 Output of the direction of rotation

.3 Output of the turning steps

.4 Output of the operation of 1.3

.5 Output of approach to 1.3

.6 First output of the IC

.7 Second output of the IC

.8 Third output of the IC

.9 Compensation output of the IC

.10 Fourth output of the IC

.11 Internal switch for input channel selection

.12 input channels of the IC

.1 time range

.2 time range

Claims

Patent claims

1. Optoelectronic rotary encoder for setting or controlling parameters

- comprising a first measuring arrangement

- several first light sources (2.41, 2.42, 2.43, 2.44, 3.11,..3.14, 3.21,..3.24) arranged on an imaginary closed line, which emit light beams in a clocked, time-sequenced manner,

- at least one first receiver (2.3) for receiving a first light beam (4.1) emitted by at least one of the first light sources and reflected by an object (1.1),

- wherein an evaluation device (8.1) is provided for evaluating a light received by the receiver (2.3) and converted into electrical signals and for determining a position of the object (1.1) relative to the rotary encoder,

- and with a further measuring arrangement for detecting additional information (8.4), also by means of the evaluation device (8.1),

characterized in that the further measuring arrangement has at least one further light source (2.5) and the at least one receiver (2.3) or at least one further receiver (2.7), each for receiving a light emitted by the further light source (2.5) and reflected on an object (1.1). further light beam (6.1), and

in that at least one shading element (2.2, 2.10, 2.11) is provided, which is suitable for allowing first light rays (4.1) of the first measuring arrangement to pass through to and from a first point (1.3) of a control surface (1.2) assigned to the imaginary closed lines, with reflection of the emitted first light rays (4.1) into the first receiver (2.3) and a passage of further light rays (6.1) of the further measuring arrangement to and from a further point (1.4) of the control surface (1.2) with reflection of the emitted further light rays (6.1) in the first receiver (2.3) or in the further receiver (2.7).

2. Rotary encoder according to claim 1, characterized in that the first digit

(1.3) of the control surface (1.2) is the central point-shaped additional point in a ring

(1.4) . the control surface (1.2).

3. Rotary encoder according to claim 1 or 2, characterized in that the first light sources (2.41, 2.42, 2.43, 2.44, 3.11, ..3.14, 3.21, ..3.24) several groups of synchronized, in turn on a circular line forming the closed line arranged light sources, the light sources within a group being arranged at the same angular distance from one another and the groups of light sources being operated in a clocked, time-sequenced manner.

4. Rotary encoder according to one of the preceding claims, characterized in that the first light sources (2.41, 2.42, 2.43, 2.44, 3.11, ..3.14,

3.21, ..3.24) exactly one receiver (2.3) is assigned.

5. Rotary encoder according to one of the preceding claims, characterized in that the first measuring arrangement and / or the further measuring arrangement has at least one compensation light source (2.12, 2.13) assigned to the first receiver (2.3) or the further receiver (2.7) for emitting light to the first or subsequent recipient.

6. Rotary encoder according to claim 5, characterized in that a device for regulating the light intensity of the at least one first light source (2.41, 2.42, 2.43, 2.44, 3.11, ..3.14, 3.21, ..3.24) emitted at the first receiver (2.3) incoming light and / or the light emitted by the first compensation light source (2.12) and arriving at the first receiver (2.3) to form a control value is provided in such a way that the first receiver (2.3) has the at least one first light source and the first compensation light source with the same intensity, the evaluation device (8.1) evaluating the control value (5.11 5.32) resulting from the perception with the same intensity when the first light sources, which are operated in turn, are operated to detect the angular position and / or direction of rotation of the object (1.1) relative to the rotary encoder.

7. Rotary encoder according to one of the preceding claims, characterized in that the control surface (1.2) arranged above the at least one shading element (2.2, 2.10, 2.11) at the first point (1.3) or at the further point (1.4) the total reflection of the Has depressions or elevations that support light rays.

8. Rotary encoder according to one of the preceding claims, characterized in that computing means are provided which, when an object (1.1) approaches, perceive a maximum reflection of the first light rays (4.1) as the starting point and, based on this, when the object moves and thus the maximum determine a relative angular position to the starting point by reflection along the imaginary line.