JP3665506B2 - Shape analyzer - Google Patents

Description

で算出することができる。制御装置は、このｃｏｓθが一定値（例えば逆行角度を９０度とした場合には０）以下となった場合に逆行データ（図２で言えば、ベクトルｂの先端に位置する補正データが逆行データ）と定義する。
【００１７】
図３には、補正データに対して逆行位置を特定した一例が示されている。図中矢印方向に順次補正データが配列し、途中で逆行している場合、この部分で上記のｃｏｓθが０以下となるため、逆行位置（逆行開始位置）Ｐが特定される。
【００１８】
逆行位置を特定した後、制御装置は次に特定した逆行位置の前後に存在する補正データから交点を探索する。探索する範囲は、バッファのサイズで決めることができ、あるいは予め数（例えば前後１００個のデータ）を決めておくこともできる。交点探索は、逆行位置前後に存在するベクトル群（隣接する補正データから作成されるベクトル）の組が交点を有するか否かで行う。
【００１９】
図４には、図３の補正データにおいて逆行位置の前後を探索して得られる交点Ｑが示されている。この図の場合には、逆行位置の前（矢印方向が順方向であり、逆行位置からこの矢印と反対方向が「前」となり、矢印の向きが「後」である）と後で同一交点が探索されることになる。
【００２０】
そして、交点が探索された後、制御装置は交点に相当する最初の補正データと最後の補正データとの間に存在する補正データを逆行データとみなし、削除（逆行フラグをセット）する。
【００２１】
図５には、逆行位置Ｐと交点Ｑとの間に存在する逆行データの削除の様子が示されている。交点Ｑに相当する最初の補正データと最後の補正データとの間にあるデータ（破線部分）が逆行データと特定され、削除される。（Ｂ）から分かるように、削除後のデータには従来のような途切れはなく、従って補間処理が不要である。
【００２２】
なお、逆行位置を特定し、次いでその前後に存在する交点を探索する過程で、複数の交点が得られる場合がある。この場合にも同様に処理することができる。
【００２３】
図６には逆行位置Ｐ前後の補正データを探索した結果、前に１つ、後ろに２つ交点が得られた場合が示されている。この場合、逆行位置Ｐから前に探索して得られる交点Ｑ３が最も最初の補正データ及び最後の補正データに相当するので、これらの間にある補正データを逆行データと特定する。これにより、逆行データを確実に特定し、途切れのないデータを得ることができる。
【００２４】
また、逆行角度を例えば９０度とした場合、角度が９０度に極めて近いものの９０度に達しないような場合には逆行していないと判定されてしまう場合がある。例えば、図７に示されるように、それぞれの角度が９０度より若干大きいα（α＝１８０度−θ）をなしつつループを構成するようなデータ配列の場合、本来であれば逆行データとして特定しなければならないにもかかわらずｃｏｓθが０より大きいと判定されて逆行していないと誤判定してしまうことになる。
【００２５】
そこで、このような場合にも対応すべく、逆行角度に許容値を設定し、（逆行角度＋許容値）に基づいて逆行位置を特定することもできる。例えば逆行角度を９０度、許容値を−３度とする如くである。これにより、θが８７度以上の場合には逆行位置と特定され、図７のような場合でも確実に逆行データを削除することができる。
【００２６】
なお、このように許容値を設定すると、補正データに本来、逆行が存在していないのに逆行データと誤判定してしまう場合もあり得る。例えば図８に示されるように、９０度より若干大きいβ（β＝１８０度−θ）をなすが逆行は生じていないデータ配列の場合でも、θが８７度以上であれば逆行位置と特定してしまうことになる。しかしながら、一般の形状解析装置においては図８に示されるようなデータ配列の出現確率は極めて低く、実用上問題ない。
【００２７】
さらに、補正データに逆行が存在しているが、逆行位置Ｐのみ存在し、交点が存在しない場合もあり得る。図９にはこのような場合のデータ配列の一例が示されている。逆行角度から逆行位置Ｐを特定することができるが、データ配列がループを構成していないため交点が存在していない。このような場合には逆行データを特定することができないので、従来の方法、すなわちＸ値の変化から逆行データを特定して削除することが好適である。
【００２８】
また、逆行位置及び交点は存在するものの、それだけでは全ての逆行データを特定して削除することができない場合もある。例えば、図１０に示されるような場合、逆行位置Ｐが存在し、逆行位置から後の探索で交点Ｑが存在するが、この交点に相当する最初の補正データと最後の補正データとの間の補正データを逆行データと特定して削除しても（破線部分）、交点の前と後にさらに逆行データが存在（一点鎖線）し、これを特定できないため、全ての逆行データを削除することができない。したがって、このような場合を考慮し、交点に基づいた逆行データの特定（削除）処理の後に、従来のＸ値変化による逆行データの特定（削除）処理を行うのが好適である。この処理により、図中一点鎖線の逆行データをも削除することができる（但し、この場合にはデータの途切れが生じてしまうため、後に円弧補間や自由曲線補間などの補間処理が必要となる）。
【００２９】
図１１及び図１２には、以上述べた制御装置の処理フローチャートが示されている。まず、逆行データの探索位置が補正データ範囲内であるか否かを確認し（Ｓ１０１）。補正データ範囲内である場合には、着目している補正データのベクトルａ、ｂを算出する（Ｓ１０２）。ベクトルａ、ｂを算出した後、角度定義により逆行位置を特定する（Ｓ１０３）。すなわち、２つのベクトルａ、ｂのなす角ｃｏｓθが０以下であるか否か（所定の許容値を設定した場合には、ｃｏｓθが許容値に応じた値以下であるか否か）を判定する。そして、逆行していると判定された場合には（Ｓ１０４でＹＥＳ）、逆行位置からその前後の交点を探索し、交点が存在した場合には交点内のデータ、すなわち交点に相当する最初のデータと最後のデータとの間のデータに逆行フラグをセットする（Ｓ１０５）。逆行フラグがセットされた補正データは、後のデータ処理において無視されるため、結果的に逆行データを削除したことになる（バッファメモリには逆行データは存在する）。逆行フラグをセットした後、逆行探索位置を交点位置にスキップする（Ｓ１０７）。
【００３０】
以上の処理を繰り返すことで、補正データに存在する逆行データを削除することが可能であるが、本実施形態では、さらに図９あるいは図１０のような場合に対応すべく、引き続いて従来のＸ値による逆行削除処理を行う（図９のように交点が存在しない場合には、Ｓ１０６でＮＯと判定されて従来処理に移行する）。
【００３１】
すなわち、図１２に示されるように、探索位置をＳ１０３及びＳ１０４で特定した逆行位置まで再びスキップし（Ｓ１０８）、削除されなかった補正データに対してＸ値による逆行判定を行う（Ｓ１０９）。すなわち、削除されなかった補正データのＸ値が順次増加しているかを判定し、一部Ｘ値が減少した後、減少前のＸ値に戻っている場合には、減少してから戻るまでの補正データを逆行データと判定して逆行フラグをセットする（Ｓ１１０）。
【００３２】
このように、本実施形態では、従来技術のようにＸ値の変化で逆行データを特定するのではなく、角度に基づいて逆行開始位置を特定し、この逆行開始位置を基点として交点を探索し、この交点に基づいて逆行データを削除しているので、途切れのない実面データを得ることができる。
【００３３】
なお、本実施形態では、交点に基づく逆行データの削除処理後に従来技術のＸ値による削除処理を行っているが、交点に基づく逆行データの削除処理のみを行ってもよい。
【００３４】
また、形状解析装置の解析モードとして、
モード１：交点に基づく削除処理
モード２：Ｘ値に基づく削除処理（従来方法）
モード３：交点とＸ値に基づく削除処理
の３モードを有し、ユーザが適宜選択できるように構成することも可能である。
【００３５】
また、本実施形態では、逆行データに対して逆行フラグをセットすることで結果として逆行データを削除しているが、逆行データ自身はメモリ内に存在しているので、メモリ内に存在している補正データを繰り返し使用し、最適の処理を見いだすこともできる。
【００３６】
【発明の効果】
以上説明したように、本発明によれば、補正データに存在する逆行データを確実に特定して削除し、途切れのない実面データを得ることができる。これにより、従来必要であった補間処理が不要となり、処理時間の短縮を図ることができる。
【図面の簡単な説明】
【図１】 実施形態の外観構成図である。
【図２】 ベクトル算出説明図である。
【図３】 逆行位置（逆行開始位置）の説明図である。
【図４】 交点位置の説明図である。
【図５】 逆行データの削除説明図である。
【図６】 複数交点が存在する場合の説明図である。
【図７】 角度特異例の説明図である。
【図８】 他の角度特異例の説明図である。
【図９】 交点が存在しない場合の説明図である。
【図１０】 さらに他の特異例の説明図である。
【図１１】 実施形態の処理フローチャート（その１）である。
【図１２】 実施形態の処理フローチャート（その２）である。
【図１３】 スタイラスを走査して得られる測定データの説明図である。
【図１４】 図１３の測定データを補正して得られる補正データの逆行説明図である。
【図１５】 従来の逆行データ削除説明図である。
【符号の説明】
１０ 基台、１２ 載物台、１４ ワーク、１６ 検出装置、１８ 駆動装置、２０ 支柱、２２ 表示装置。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a shape analysis apparatus and method, and more particularly to measurement data processing of an object to be measured (work) obtained by scanning with a stylus.
[0002]
[Prior art]
Conventionally, a shape analysis apparatus or a three-dimensional coordinate measuring machine that scans the surface of a workpiece with a stylus and analyzes the shape of the workpiece surface is known.
[0003]
The measurement data obtained by scanning the stylus is not the workpiece shape itself, but the workpiece surface shape via the stylus. Therefore, in order to obtain the actual workpiece surface shape data, Specifically, it is necessary to obtain data obtained by subtracting the radius data of the stylus (referred to as stylus radius correction).
[0004]
FIG. 13 shows a state in which the workpiece surface is scanned with a stylus. Detection data from a detector having a stylus is data of a one-dot chain line in the figure, and this is a probe center trajectory offset from the actual measurement plane (shown by a solid line) by the radius of the probe 100 of the stylus. Therefore, the actual data of the workpiece is obtained by offsetting this measurement data by the data processing and performing the reverse offset by the probe radius.
[0005]
However, in the actual surface data (correction data) after the stylus radius correction, as shown in FIG. 14, there is a case where backward data 200 (shown by a broken line) is generated particularly at a corner portion of the workpiece. The retrograde data is data in which data that should have been arranged in only one direction returns to the reverse direction and is arranged in the direction of the main body again. In FIG. 14, since the stylus is scanned in the direction of the arrow in the figure, the data should have been arranged in the direction of the arrow. It is returning in the direction. If such retrograde data exists, the true actual data cannot be obtained and must be removed.
[0006]
Therefore, conventionally, the correction data after the stylus radius correction is compared with the value in one direction of the correction data (specifically, the X-axis direction when scanning is performed by moving the stylus in the X-axis direction). , The data in which the X value did not increase but the X value decreased was detected and identified as retrograde data and deleted.
[0007]
[Problems to be solved by the invention]
However, in the method of identifying and deleting the retrograde data based on only the X value change in this way, the data is deleted so that the X value does not overlap, so that the corner portion is interrupted as shown in FIG. Then, interpolation processing must be performed after that, and there is a problem that processing becomes complicated.
[0008]
The present invention has been made in view of the above-described problems of the prior art, and an object of the present invention is to provide an apparatus that can reliably identify retrograde data existing in correction data and obtain actual data without interruption. There is.
[0009]
[Means for Solving the Problems]
In order to achieve the above object, the present invention corrects measurement data obtained by scanning the surface of an object to be measured with a stylus by using the stylus radius, and from the correction data, the correction data, the actual surface data of the workpiece, Is a device for analyzing the shape of the object to be measured by deleting the retrograde data that is the difference between the correction data, and means for specifying the retrograde start position that is the start position of the retrograde data based on the inter-data angle of the correction data. It is characterized by having. In the presence of retrograde, the angle between the data increases significantly. Therefore, by focusing on the inter-data angle, the reverse start position can be specified accurately.
[0010]
Here, the present invention further includes means for detecting an intersection existing at least before or after the retrograde start position, and means for identifying and deleting the retrograde data based on the intersection. When going backwards, there is often a data intersection, that is, an intersection when returning again. Therefore, an intersection point can be detected, and the range of the retrograde data can be specified based on the intersection point. Note that “deletion” includes not only physically erasing the data but also considering the data itself as unnecessary data by adding some mark without erasing the data itself.
[0011]
In addition, the present invention is characterized by further comprising means for specifying and deleting the retrograde data based on a change in the arrangement direction of the correction data. The change in the array direction is an X value change in the prior art, and the retrograde data can be deleted more reliably by using the conventional deletion process in a complementary manner.
[0012]
In the present invention, the position of the correction data at which the inter-data angle of the correction data is a predetermined value or more can be set as the retrograde start position. The predetermined value is preferably 90 degrees, and a value obtained by setting a predetermined allowable value for 90 degrees may be set as the predetermined value.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[0014]
FIG. 1 is an external configuration diagram of the shape analysis apparatus. A mounting table 12 is provided on the base 10, and a work 14 is fixed on the mounting table 12. Further, the base 10 is provided with a detection device 16 having a stylus on a support 20 by a driving device 18. The detection device 16 is driven in the X direction and Z direction in the figure by the drive device 18, the tip of the stylus is brought into contact with the surface of the work 14 by driving in the Z direction, and the unevenness on the surface of the work 14 is detected by movement in the X direction. . The detected unevenness amount is converted into an electric signal, and is supplied to and displayed on a display device 22 such as a computer display.
[0015]
When the display device 22 is a computer display, the control device of the computer main body drives and controls the drive device 18 via the communication device, and the detection signal from the detection device 16 is processed and displayed on the display device 22. it can. In addition, a control device (CPU) in the computer performs stylus radius correction on the measurement data from the detection device 16 and calculates actual surface data obtained by subtracting the probe radius of the stylus. In the process of calculating actual data, first, correction data is calculated, and then retrograde data existing in the correction data is specified and deleted. Note that “deletion” in the present embodiment does not delete the retrograde data, but sets a flag indicating that the retrograde data is set for the retrograde data, and sets the retrograde flag in the later processing. This means that it is excluded from processing (it is technically equivalent to deletion in that it is not processed. In addition, there is an advantage that the data itself can be used for other processing by leaving it unerased. ). Since the method for obtaining correction data from the measurement data, that is, the reverse offset processing of the probe radius is the same as the conventional method, a method for specifying the retrograde data from the correction data will be described below.
[0016]
2 to 10 schematically show the retrograde data specifying process in the control device according to the present embodiment. In the figure, black circles are correction data, and the control device represents changes between the correction data as vectors. In the figure, vectors a and b are shown. Then, the control device calculates the angle θ formed between the vectors by calculating the inner product of the vectors from the vectors between the correction data. Specifically, the angle formed by the vectors a and b is
[Expression 1]

Can be calculated. When the cos θ is equal to or less than a certain value (for example, 0 when the retrograde angle is 90 degrees), the control device performs retrograde data (in FIG. 2, the correction data positioned at the tip of the vector b is the retrograde data. ).
[0017]
FIG. 3 shows an example in which the retrograde position is specified for the correction data. In the case where the correction data is sequentially arranged in the direction of the arrow in the figure and reverses in the middle, the cos θ becomes 0 or less in this part, so the reverse position (reverse start position) P is specified.
[0018]
After specifying the retrograde position, the control device searches for an intersection from correction data existing before and after the specified retrograde position. The search range can be determined by the size of the buffer, or a number (for example, 100 data before and after) can be determined in advance. The intersection search is performed based on whether or not a set of vectors (vectors created from adjacent correction data) existing before and after the retrograde position has an intersection.
[0019]
FIG. 4 shows an intersection point Q obtained by searching before and after the retrograde position in the correction data of FIG. In the case of this figure, the same intersection point is present before and after the retrograde position (the arrow direction is the forward direction, the direction opposite this arrow from the retrograde position is “front”, and the direction of the arrow is “rear”). Will be explored.
[0020]
After the intersection is searched, the control device regards the correction data existing between the first correction data and the last correction data corresponding to the intersection as the backward data, and deletes (sets the backward flag).
[0021]
FIG. 5 shows how the retrograde data existing between the retrograde position P and the intersection point Q is deleted. Data (broken line portion) between the first correction data and the last correction data corresponding to the intersection point Q is identified as retrograde data and deleted. As can be seen from (B), the deleted data is not interrupted as in the prior art, and therefore no interpolation processing is required.
[0022]
A plurality of intersections may be obtained in the process of specifying the retrograde position and then searching for the intersections existing before and after that. In this case, the same processing can be performed.
[0023]
FIG. 6 shows a case where one intersection is obtained before and two intersections are obtained as a result of searching for correction data before and after the retrograde position P. In this case, since the intersection point Q3 obtained by searching before from the retrograde position P corresponds to the first correction data and the last correction data, the correction data between them is specified as the retrograde data. As a result, the retrograde data can be reliably identified and uninterrupted data can be obtained.
[0024]
Further, when the retrograde angle is set to 90 degrees, for example, it may be determined that the retrograde is not performed if the angle is very close to 90 degrees but does not reach 90 degrees. For example, as shown in FIG. 7, in the case of a data array that forms a loop with each angle forming α (α = 180 degrees−θ) slightly larger than 90 degrees, it is originally specified as retrograde data. In spite of having to do, it is determined that cos θ is larger than 0, and it is erroneously determined that it is not retrograde.
[0025]
Therefore, in order to cope with such a case, an allowable value can be set for the retrograde angle, and the retrograde position can be specified based on (retrograde angle + allowable value). For example, the retrograde angle is set to 90 degrees and the allowable value is set to -3 degrees. Thereby, when θ is 87 degrees or more, the retrograde position is specified, and the retrograde data can be surely deleted even in the case of FIG.
[0026]
If the allowable value is set in this way, there is a possibility that the correction data is erroneously determined as the retrograde data even though the retrograde does not originally exist in the correction data. For example, as shown in FIG. 8, even in the case of a data array having β (β = 180 ° −θ) slightly larger than 90 ° but no reverse is generated, if θ is 87 ° or more, the reverse position is specified. It will end up. However, in a general shape analysis apparatus, the appearance probability of a data array as shown in FIG. 8 is extremely low, and there is no practical problem.
[0027]
Further, although there is a retrograde in the correction data, there may be a case where only the retrograde position P exists and no intersection exists. FIG. 9 shows an example of the data arrangement in such a case. The retrograde position P can be specified from the retrograde angle, but there is no intersection because the data array does not form a loop. In such a case, since the retrograde data cannot be specified, it is preferable to specify and delete the retrograde data from the conventional method, that is, the change in the X value.
[0028]
In addition, although there are retrograde positions and intersections, it may not be possible to identify and delete all retrograde data by itself. For example, in the case shown in FIG. 10, there is a retrograde position P, and there is an intersection point Q in the search after the retrograde position, but between the first correction data and the last correction data corresponding to this intersection point. Even if the correction data is identified as the retrograde data and deleted (dashed line), the retrograde data still exists before and after the intersection (dashed line), and this cannot be specified, so all the retrograde data cannot be deleted. . Therefore, in consideration of such a case, it is preferable to perform the conventional process of specifying (deleting) the retrograde data by changing the X value after the process of specifying (deleting) the retrograde data based on the intersection. By this process, the reverse data of the alternate long and short dash line in the figure can also be deleted (however, in this case, the data is interrupted, so that an interpolation process such as circular interpolation or free curve interpolation is required later). .
[0029]
11 and 12 show process flowcharts of the control device described above. First, it is confirmed whether or not the search position for the retrograde data is within the correction data range (S101). If it is within the correction data range, vectors a and b of the correction data of interest are calculated (S102). After calculating the vectors a and b, the retrograde position is specified by the angle definition (S103). That is, it is determined whether or not the angle cos θ formed by the two vectors a and b is 0 or less (when a predetermined allowable value is set, whether cos θ is equal to or smaller than a value corresponding to the allowable value). . If it is determined that the vehicle is retrograde (YES in S104), the intersection point before and after the retrograde position is searched. If there is an intersection point, the data in the intersection point, that is, the first data corresponding to the intersection point A retrograde flag is set to data between the first data and the last data (S105). Since the correction data in which the retrograde flag is set is ignored in the subsequent data processing, the retrograde data is deleted as a result (the retrograde data exists in the buffer memory). After setting the retrograde flag, the retrograde search position is skipped to the intersection position (S107).
[0030]
By repeating the above processing, it is possible to delete the retrograde data existing in the correction data. However, in this embodiment, in order to cope with the case shown in FIG. 9 or FIG. A retrograde deletion process by value is performed (when there is no intersection as shown in FIG. 9, NO is determined in S106 and the process proceeds to the conventional process).
[0031]
That is, as shown in FIG. 12, the search position is skipped again to the retrograde position specified in S103 and S104 (S108), and the retrograde determination based on the X value is performed on the correction data that has not been deleted (S109). That is, it is determined whether or not the X value of the correction data that has not been deleted is sequentially increased. When the X value partially decreases and then returns to the X value before the decrease, the period from the decrease to the return The correction data is determined to be retrograde data, and the retrograde flag is set (S110).
[0032]
Thus, in this embodiment, instead of specifying the retrograde data by changing the X value as in the prior art, the retrograde start position is specified based on the angle, and the intersection point is searched using the retrograde start position as a base point. Since the retrograde data is deleted based on this intersection, actual data without interruption can be obtained.
[0033]
In this embodiment, the deletion process based on the X value of the conventional technique is performed after the deletion process of the backward data based on the intersection. However, only the backward data deletion process based on the intersection may be performed.
[0034]
In addition, as an analysis mode of the shape analyzer,
Mode 1: Deletion processing based on intersection point Mode 2: Deletion processing based on X value (conventional method)
Mode 3: It is also possible to have three modes of deletion processing based on the intersection and the X value so that the user can select as appropriate.
[0035]
In the present embodiment, the retrograde data is deleted by setting the retrograde flag for the retrograde data. However, the retrograde data itself exists in the memory, and therefore exists in the memory. The correction data can be used repeatedly to find the optimum process.
[0036]
【The invention's effect】
As described above, according to the present invention, it is possible to reliably identify and delete the retrograde data existing in the correction data and obtain actual data without interruption. As a result, the interpolation processing that has been conventionally required is not required, and the processing time can be shortened.
[Brief description of the drawings]
FIG. 1 is an external configuration diagram of an embodiment.
FIG. 2 is an explanatory diagram of vector calculation.
FIG. 3 is an explanatory diagram of a retrograde position (retrograde start position).
FIG. 4 is an explanatory diagram of intersection positions.
FIG. 5 is an explanatory diagram of deletion of retrograde data.
FIG. 6 is an explanatory diagram when a plurality of intersections exist.
FIG. 7 is an explanatory diagram of an example of an angle singularity.
FIG. 8 is an explanatory diagram of another example of angle singularity.
FIG. 9 is an explanatory diagram when no intersection exists.
FIG. 10 is an explanatory diagram of still another specific example.
FIG. 11 is a process flowchart (No. 1) according to the embodiment;
FIG. 12 is a process flowchart (2) according to the embodiment.
FIG. 13 is an explanatory diagram of measurement data obtained by scanning a stylus.
14 is a reverse explanatory view of correction data obtained by correcting the measurement data of FIG.
FIG. 15 is a diagram for explaining conventional retrograde data deletion.
[Explanation of symbols]
10 bases, 12 mounts, 14 workpieces, 16 detectors, 18 drive units, 20 struts, 22 display units.

Claims (6)

The measurement data obtained by scanning the surface of the object to be measured with a stylus is corrected using the stylus radius, and the retrograde data that is the difference between the correction data and the actual surface data of the workpiece is deleted from the correction data. An apparatus for analyzing the shape of an object to be measured,
A shape analysis apparatus comprising means for specifying a retrograde start position, which is a start position of retrograde data , based on an inter-data angle of the correction data. The apparatus of claim 1, further comprising:
Means for detecting an intersection that exists at least before or after the retrograde start position;
Means for identifying and deleting the retrograde data based on the intersection;
A shape analysis apparatus comprising: The apparatus according to claim 1, further comprising:
A shape analysis apparatus comprising: means for identifying and deleting the retrograde data based on a change in the arrangement direction of the correction data. In the apparatus in any one of Claims 1-3,
A shape analysis apparatus characterized in that a position of correction data at which an angle between data of the correction data is equal to or greater than a predetermined value is set as the retrograde start position. The apparatus of claim 4.
The shape analyzing apparatus according to claim 1, wherein the predetermined value is 90 degrees. The apparatus of claim 4.
The shape analysis apparatus according to claim 1, wherein the predetermined value is a value in which a predetermined allowable value is set for 90 degrees.

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