TWI709894B - Gesture feature processing method and touch control module using the same - Google Patents
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Abstract
一種手勢特徵處理方法,適用於一觸控模組,其中該觸控模組包括一觸控螢幕、一感測單元以及一計算單元,該感測單元電性連接該觸控螢幕,且該計算單元電性連接該感測單元,該手勢特徵處理方法包括:該感測單元偵測一使用者的一手指接觸該觸控螢幕的一起始座標;該計算單元執行一方向紀錄步驟以得到一方向資料組;該感測單元偵測該手指離開該觸控螢幕的一終點座標;以及該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別。 A method for processing gesture features is applicable to a touch module, wherein the touch module includes a touch screen, a sensing unit, and a calculation unit. The sensing unit is electrically connected to the touch screen, and the calculation The unit is electrically connected to the sensing unit, and the gesture feature processing method includes: the sensing unit detects an initial coordinate of a user's finger touching the touch screen; the calculation unit executes a direction recording step to obtain a direction Data set; the sensing unit detects an end coordinate where the finger leaves the touch screen; and the calculation unit performs gesture recognition based on the start coordinate, the direction data set and the end coordinate.
Description
本發明係關於一種適用於觸控模組的手勢特徵處理方法,尤指一種透過劃線方向強化識別特徵的手勢特徵處理方法。The present invention relates to a gesture feature processing method suitable for a touch module, and in particular to a gesture feature processing method that strengthens recognition features through the scribing direction.
目前觸控裝置所使用的手勢識別模型演算法,主要依靠方向碼的匹配以及計算以識別使用者輸入的手勢,而上述方向碼則根據當前觸控點以及過去觸控點之間的劃線方向為基礎,因此方向碼與劃線方向的判定具有著極大的相關性。然而,由於一般觸控模組的劃線方向分類較為粗略,僅能判定出最基本的上、下、左、右等四個方向,這容易導致對使用者所輸入的手勢的方向變化解析不夠精細,而將實際上不同方向的筆劃皆判定為同一方向;另一方面,對於一些轉折方向相同卻由於筆劃長度不同而隸屬於不同文字或圖樣的手勢,目前過於粗略的識別模型演算法也會將其判定為相同的方向組合。The current gesture recognition model algorithm used in touch devices mainly relies on the matching and calculation of the direction code to recognize the gesture input by the user, and the above direction code is based on the current touch point and the line direction between the past touch points As a basis, the direction code and the determination of the marking direction have a great correlation. However, due to the rough classification of scribing directions of general touch modules, only the most basic four directions of up, down, left, and right can be determined, which easily leads to insufficient analysis of the direction changes of the gestures input by the user Fine, and actually judge the strokes in different directions as the same direction; on the other hand, for some gestures that have the same turning direction but belong to different characters or patterns due to different stroke lengths, the current recognition model algorithms that are too rough will also It is judged as the same direction combination.
為解決上述問題,本領域亟需一種新穎的手勢特徵處理方法。In order to solve the above problems, a novel gesture feature processing method is urgently needed in the art.
本發明之一目的在於揭露一種適用於觸控模組的手勢特徵處理方法,其可將劃線方向紀錄至方向資料組,進而能強化手勢識別的相關特徵。One purpose of the present invention is to disclose a gesture feature processing method suitable for a touch module, which can record the scribing direction to the direction data set, thereby enhancing the related features of gesture recognition.
本發明之另一目的在於揭露一種觸控模組,其可可將劃線方向紀錄至方向資料組,進而能強化手勢識別的相關特徵。Another object of the present invention is to disclose a touch module, which can record the scribing direction to the direction data set, thereby enhancing the related features of gesture recognition.
為達上述目的,一種適用於一觸控模組的手勢特徵處理方法乃被提出,該觸控模組包括一觸控螢幕、一感測單元以及一計算單元,該感測單元電性連接該觸控螢幕,且該計算單元電性連接該感測單元,該手勢特徵處理方法包括:To achieve the above objective, a gesture feature processing method suitable for a touch module is proposed. The touch module includes a touch screen, a sensing unit, and a calculation unit. The sensing unit is electrically connected to the The touch screen is touched, and the computing unit is electrically connected to the sensing unit, and the gesture feature processing method includes:
該感測單元偵測一使用者的一手指接觸該觸控螢幕的一起始座標;The sensing unit detects an initial coordinate of a user's finger touching the touch screen;
該計算單元執行一方向紀錄步驟以得到一方向資料組;The calculation unit executes a direction recording step to obtain a direction data set;
該感測單元偵測該手指離開該觸控螢幕的一終點座標;以及The sensing unit detects an end point where the finger leaves the touch screen; and
該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別;The calculation unit performs gesture recognition according to the start coordinates, the direction data set, and the end coordinates;
其中,該方向紀錄步驟包括:Among them, the direction recording steps include:
獲得一先前座標以及一當下座標,其中該先前座標為該當下座標一時距前該手指於該觸控螢幕上的座標;Obtaining a previous coordinate and a current coordinate, where the previous coordinate is the coordinate of the finger on the touch screen before the current coordinate by one hour;
根據該先前座標以及該當下座標計算得出一水平變化向量以及一鉛直變化向量;Calculate a horizontal change vector and a vertical change vector based on the previous coordinates and the current coordinates;
根據該水平變化向量以及該鉛直變化向量計算得出一角度變化向量;Calculate an angle change vector based on the horizontal change vector and the vertical change vector;
根據該角度變化向量判定該當下座標的一劃線方向;以及Determine the direction of a line of the current coordinate according to the angle change vector; and
將該劃線方向紀錄至該方向資料組。Record the line direction to the direction data group.
在一實施例中,該劃線方向為上、下、左、右、左上、左下、右上以及右下的其中之一。In an embodiment, the scribing direction is one of up, down, left, right, top left, bottom left, top right, and bottom right.
在一實施例中,該方向紀錄步驟更包括:In one embodiment, the direction recording step further includes:
獲得一轉向座標,其中該轉向座標為該當下座標該時距後該手指於該觸控螢幕上的座標;Obtain a steering coordinate, where the steering coordinate is the coordinate of the finger on the touch screen after the current coordinate and the time interval;
判斷該轉向座標至該先前座標以及該當下座標連線的一距離是否大於一閾值;以及Determine whether a distance from the steering coordinate to the previous coordinate and the current coordinate line is greater than a threshold; and
判斷該轉向座標是否等於該終點座標;Determine whether the steering coordinate is equal to the end point coordinate;
其中,當該距離大於該閾值時,該計算單元根據由該當下座標前進至該轉向座標的一轉向向量判定該當下座標的一轉向方向,並將該轉向方向紀錄至該方向資料組;Wherein, when the distance is greater than the threshold, the calculation unit determines a steering direction of the current coordinate according to a steering vector from the current coordinate to the steering coordinate, and records the steering direction in the direction data set;
其中,當該轉向座標不等於該終點座標時,該計算單元在該時距後更新該轉向座標。Wherein, when the steering coordinate is not equal to the end point coordinate, the calculation unit updates the steering coordinate after the time interval.
在一實施例中,該轉向方向為上、下、左、右、左上、左下、右上以及右下的其中之一。In an embodiment, the steering direction is one of up, down, left, right, top left, bottom left, top right, and bottom right.
在一實施例中,該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別包括對該方向資料組以及一字符資料庫執行相似度演算法。In one embodiment, the calculation unit performing gesture recognition based on the start coordinates, the direction data set, and the end coordinates includes executing a similarity algorithm on the direction data set and a character database.
為達上述目的,本發明進一步提出一種觸控模組,其包括一觸控螢幕、一感測單元及一計算單元以執行一手勢特徵處理方法,其中該感測單元電性連接該觸控螢幕,且該計算單元電性連接該感測單元,該手勢特徵處理方法包括:To achieve the above objective, the present invention further provides a touch module, which includes a touch screen, a sensing unit, and a calculation unit to perform a gesture feature processing method, wherein the sensing unit is electrically connected to the touch screen And the computing unit is electrically connected to the sensing unit, and the gesture feature processing method includes:
該感測單元偵測一使用者的一手指接觸該觸控螢幕的一起始座標;The sensing unit detects an initial coordinate of a user's finger touching the touch screen;
該計算單元執行一方向紀錄步驟以得到一方向資料組;The calculation unit executes a direction recording step to obtain a direction data set;
該感測單元偵測該手指離開該觸控螢幕的一終點座標;以及The sensing unit detects an end point where the finger leaves the touch screen; and
該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別;The calculation unit performs gesture recognition according to the start coordinates, the direction data set, and the end coordinates;
其中,該方向紀錄步驟包括:Among them, the direction recording steps include:
獲得一先前座標以及一當下座標,其中該先前座標為該當下座標一時距前該手指於該觸控螢幕上的座標;Obtaining a previous coordinate and a current coordinate, where the previous coordinate is the coordinate of the finger on the touch screen before the current coordinate by one hour;
根據該先前座標以及該當下座標計算得出一水平變化向量以及一鉛直變化向量;Calculate a horizontal change vector and a vertical change vector based on the previous coordinates and the current coordinates;
根據該水平變化向量以及該鉛直變化向量計算得出一角度變化向量;Calculate an angle change vector based on the horizontal change vector and the vertical change vector;
根據該角度變化向量判定該當下座標的一劃線方向;以及Determine the direction of a line of the current coordinate according to the angle change vector; and
將該劃線方向紀錄至該方向資料組。Record the line direction to the direction data group.
在一實施例中,該劃線方向為上、下、左、右、左上、左下、右上以及右下的其中之一。In an embodiment, the scribing direction is one of up, down, left, right, top left, bottom left, top right, and bottom right.
在一實施例中,該方向紀錄步驟更包括:In one embodiment, the direction recording step further includes:
獲得一轉向座標,其中該轉向座標為該當下座標該時距後該手指於該觸控螢幕上的座標;Obtain a steering coordinate, where the steering coordinate is the coordinate of the finger on the touch screen after the current coordinate and the time interval;
判斷該轉向座標至該先前座標以及該當下座標連線的一距離是否大於一閾值;以及Determine whether a distance from the steering coordinate to the previous coordinate and the current coordinate line is greater than a threshold; and
判斷該當下座標或該轉向座標是否等於該終點座標;Determine whether the current coordinate or the steering coordinate is equal to the end coordinate;
其中,當該距離大於該閾值時,該計算單元根據由該當下座標前進至該轉向座標的一轉向向量判定該當下座標的一轉向方向,並將該轉向方向紀錄至該方向資料組;Wherein, when the distance is greater than the threshold, the calculation unit determines a steering direction of the current coordinate according to a steering vector from the current coordinate to the steering coordinate, and records the steering direction in the direction data set;
其中,當該當下座標以及該轉向座標均不等於該終點座標時,該計算單元在該時距後更新該先前座標、該當下座標以及該轉向座標。Wherein, when the current coordinates and the steering coordinates are not equal to the end coordinates, the calculation unit updates the previous coordinates, the current coordinates, and the steering coordinates after the time interval.
在一實施例中,該轉向方向為上、下、左、右、左上、左下、右上以及右下的其中之一。In an embodiment, the steering direction is one of up, down, left, right, top left, bottom left, top right, and bottom right.
在一實施例中,該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別包括對該方向資料組以及一字符資料庫執行相似度演算法。In one embodiment, the calculation unit performing gesture recognition based on the start coordinates, the direction data set, and the end coordinates includes executing a similarity algorithm on the direction data set and a character database.
為使 貴審查委員能進一步瞭解本發明之結構、特徵及其目的,茲附以圖式及較佳具體實施例之詳細說明如後。In order to enable your reviewer to further understand the structure, features and purpose of the present invention, the drawings and detailed descriptions of preferred specific embodiments are attached as follows.
請參考圖1及圖2,圖1繪示本發明之觸控模組之一實施例的方塊圖,圖2則繪示本發明之手勢特徵處理方法之一實施例的流程圖。本發明提供的觸控模組1包括一觸控螢幕11、一感測單元12以及一計算單元13,其中該感測單元電性12連接該觸控螢幕11,且該計算單元13電性連接該感測單元12,且該手勢特徵處理方法包括:該感測單元12偵測一使用者的一手指接觸該觸控螢幕11的一起始座標(步驟a);該計算單元執行一方向紀錄步驟以得到一方向資料組(步驟b);該感測單元12偵測該手指離開該觸控螢幕11的一終點座標(步驟c);以及該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別(步驟d)。Please refer to FIGS. 1 and 2. FIG. 1 is a block diagram of an embodiment of the touch module of the present invention, and FIG. 2 is a flowchart of an embodiment of a gesture feature processing method of the present invention. The
具體而言,當該觸控模組1啟動且該使用者欲執行手勢識別時,該感測單元12會偵測該使用者的該手指接觸該觸控螢幕11的最初位置,並將其定義為起始座標。為了進一步獲得該手勢的其它特徵資料,該計算單元13會繼續執行該方向紀錄步驟。Specifically, when the
請參考圖3,其繪示該方向紀錄步驟之一實施例的流程圖,其包括:獲得一先前座標以及一當下座標(步驟b1);根據該先前座標以及該當下座標計算得出一水平變化向量以及一鉛直變化向量(步驟b2);根據該水平變化向量以及該鉛直變化向量計算得出一角度變化向量(步驟b3);根據該角度變化向量判定該當下座標的一劃線方向(步驟b4);將該劃線方向紀錄至該方向資料組(步驟b5);獲得一轉向座標(步驟b6);判斷該轉向座標至該先前座標以及該當下座標連線的一距離是否大於一閾值(步驟b7);根據由該當下座標前進至該轉向座標的一轉向向量判定該當下座標的一轉向方向,並將該轉向方向紀錄至該方向資料組(步驟b8);以及判斷該當下座標或該轉向座標是否等於該終點座標(步驟b9)。Please refer to FIG. 3, which shows a flowchart of an embodiment of the direction recording step, which includes: obtaining a previous coordinate and a current coordinate (step b1); calculating a level change based on the previous coordinate and the current coordinate Vector and a vertical change vector (step b2); calculate an angle change vector based on the horizontal change vector and the vertical change vector (step b3); determine a line direction of the current coordinate based on the angle change vector (step b4) ); Record the line direction to the direction data set (step b5); obtain a steering coordinate (step b6); determine whether a distance from the steering coordinate to the previous coordinate and the current coordinate line is greater than a threshold (step b7); Determine a steering direction of the current coordinate based on a steering vector from the current coordinate to the steering coordinate, and record the steering direction to the direction data set (step b8); and determine the current coordinate or the steering Whether the coordinates are equal to the end point coordinates (step b9).
具體而言,該計算單元13透過該感測單元12獲得該手指於當下時間點於該觸控螢幕上的座標,並將其定義為當下座標;此外,該計算單元13透過該感測單元12獲得該當下座標一時距(例如是一幀)前該手指於該觸控螢幕上的座標,並將其定義為先前座標。Specifically, the
得到該先前座標以及該當下座標後,即可計算出由該先前座標前進至該當下座標的一水平變化向量Δx以及一鉛直變化向量Δy,在得到該水平變化向量Δx以及該鉛直變化向量Δy後,該計算單元13即可藉由該鉛直變化向量Δy以及該水平變化向量Δx,計算出一角度變化向量Δθ。After obtaining the previous coordinate and the current coordinate, a horizontal change vector Δx and a vertical change vector Δy from the previous coordinate to the current coordinate can be calculated. After obtaining the horizontal change vector Δx and the vertical change vector Δy , The
詳細而言,該角度變化向量Δθ、該該水平變化向量Δx以及該鉛直變化向量Δy的關係可以用下列式子表達: In detail, the relationship between the angle change vector Δθ, the horizontal change vector Δx, and the vertical change vector Δy can be expressed by the following formula:
此時,根據該鉛直變化向量Δy以及該水平變化向量Δx的正負號以及該角度變化向量Δθ的範圍,可以將該當下座標的劃線方向分類為上、下、左、右、左上、左下、右上以及右下的其中之一,具體分類依據請參考下表:
表一 劃線方向
值得一提的是,上表中的角度範圍僅為本實施例的參考值,並不用以限定本發明,根據實際上辨識方向的需要,使用者或設計者可將上述的角度上下界調整至符合該方向的範圍。在劃線方向成功判定後,該計算單元13會將該劃線方向紀錄至該方向資料組,作為之後手勢辨別時的特徵依據。It is worth mentioning that the angle range in the above table is only the reference value of this embodiment, and is not used to limit the present invention. According to the actual needs of identifying the direction, the user or designer can adjust the upper and lower limits of the angle to Meet the range of the direction. After the scribing direction is successfully determined, the
另一方面,當觸控過程中手指移動到與該先前座標以及該當下座標連線以外的位置,則有可能是手勢方向改變,此時為了要確定是該手勢的必要轉向亦或是使用者的書寫習慣而導致的偏折,該計算單元13會將該當下座標該時距(例如是一幀)後該手指於該觸控螢幕上遠離該先前座標以及該當下座標連線的座標定義為一轉向座標,並且計算該轉向座標至該先前座標以及該當下座標連線的一距離是否大於一閾值。倘若該距離小於該閾值,則表示此時手指的移動可能是使用者的書寫習慣而導致的偏折,並非手勢本身的轉折點,因此無需紀錄此轉向動作;倘若該距離大於該閾值,則代表該筆劃應為有效筆劃,此時該計算單元將會根據由該當下座標前進至該轉向座標的一轉向向量判定該當下座標的一轉向方向。詳細而言,該轉向向量同樣可分解出水平變化向量以及鉛直變化向量,並藉由該鉛直變化向量以及該水平變化向量的正負號以及比值,得出該轉向方向並分類為上、下、左、右、左上、左下、右上以及右下的其中之一,由於此處與上述得到劃線方向的方式類似,在此不加以贅述。在得到該轉向方向後,該計算單元13會將該轉向方向紀錄至該方向資料組。On the other hand, when the finger moves to a position other than the previous coordinate and the current coordinate during the touch, the gesture direction may change. At this time, in order to determine whether it is the necessary steering of the gesture or the user Deflection caused by the writing habit of, the
在執行完畢劃線方向以及轉向方向的判斷及紀錄後,該計算單元13會透過該感測單元12偵測該使用者的該手指是否離開該觸控螢幕11,也就是該當下座標或該轉向座標是否等於該終點座標。若是,則代表當前階段的方向紀錄步驟暫時結束;若否,則代表該使用者仍然在書寫過程中,該計算單元13將在該時距(例如是一幀)後更新該先前座標、該當下座標以及該轉向座標,也就是在該時距後重新獲得一次先前座標、當下座標以及轉向座標,透過新的先前座標、當下座標以及轉向座標得到新的水平變化向量Δx、鉛直變化向量Δy以及角度變化向量Δθ,並進一步得到新的劃線方向以及可能存在的轉向座標以及轉向方向,將其紀錄到該方向資料組內。After the determination and recording of the scribing direction and the turning direction are performed, the
當使用者的該手指離開該觸控螢幕11時,該感測單元12會偵測該手指離開該觸控螢幕11的最終位置,並將其定義為終點座標。之後,該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別。When the user's finger leaves the
詳細而言,由於在方向資料組中各個劃線方向以及轉向方向皆被依序紀錄,且同時被細分為上、下、左、右、左上、左下、右上以及右下的其中之一。因此,在進行手勢特徵辨識時,可以在忽略筆劃本身的情況下,對該方向資料組以及一字符資料庫執行相似度演算法,只要手勢本身的劃線方向以及轉向方向排列組合與字符資料庫中的方向排列相似度達到標準,即可判定為該字符。除此之外,此方法還可另外結合筆劃長度、轉折點位置等其它特徵識別,更加提高手勢辨別的成功率以及正確性。In detail, since each scribing direction and turning direction in the direction data group are sequentially recorded, and are simultaneously subdivided into one of up, down, left, right, top left, bottom left, top right, and bottom right. Therefore, when performing gesture feature recognition, the similarity algorithm can be performed on the direction data group and a character database while ignoring the stroke itself, as long as the stroke direction and turning direction arrangement combination of the gesture itself and the character database If the similarity of the arrangement in the direction reaches the standard, it can be judged as the character. In addition, this method can additionally combine stroke length, turning point position and other feature recognition, which further improves the success rate and accuracy of gesture recognition.
本案所揭示者,乃較佳實施例,舉凡局部之變更或修飾而源於本案之技術思想而為熟習該項技藝之人所易於推知者,俱不脫本案之專利權範疇。The disclosure in this case is a preferred embodiment, and any partial changes or modifications that are derived from the technical ideas of the case and can be easily inferred by those who are familiar with the art do not deviate from the scope of the patent right of the case.
綜上所陳,本案無論目的、手段與功效,皆顯示其迥異於習知技術,且其首先發明合於實用,確實符合發明之專利要件,懇請 貴審查委員明察,並早日賜予專利俾嘉惠社會,是為至禱。In summary, regardless of the purpose, means and effect of this case, it is shown that it is very different from the conventional technology, and its first invention is suitable for practicality, and it does meet the patent requirements of the invention. I implore the examiner to investigate and grant the patent as soon as possible. Society is for the best prayer.
步驟a:該感測單元偵測一使用者的一手指接觸該觸控螢幕的一起始座標 步驟b:該計算單元執行一方向紀錄步驟以得到一方向資料組 步驟b1:獲得一先前座標以及一當下座標 步驟b2:根據該先前座標以及該當下座標計算得出一水平變化向量以及一鉛直變化向量 步驟b3:根據該水平變化向量以及該鉛直變化向量計算得出一角度變化向量 步驟b4:根據該角度變化向量判定該當下座標的一劃線方向 步驟b5:將該劃線方向紀錄至該方向資料組 步驟b6:獲得一轉向座標 步驟b7:判斷該轉向座標至該先前座標以及該當下座標連線的一距離是否大於一閾值 步驟b8:根據由該當下座標前進至該轉向座標的一轉向向量判定該當下座標的一轉向方向,並將該轉向方向紀錄至該方向資料組 步驟b9:判斷該當下座標或該轉向座標是否等於該終點座標 步驟c:該感測單元偵測該手指離開該觸控螢幕的一終點座標 步驟d:該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別 1:觸控模組 11:觸控螢幕 12:感測單元 13:計算單元Step a: The sensing unit detects that a finger of a user touches an initial coordinate of the touch screen Step b: The computing unit performs a direction recording step to obtain a direction data set Step b1: Obtain a previous coordinate and a current coordinate Step b2: Calculate a horizontal change vector and a vertical change vector based on the previous coordinates and the current coordinates Step b3: Calculate an angle change vector based on the level change vector and the vertical change vector Step b4: Determine the direction of a line of the current coordinate according to the angle change vector Step b5: Record the line direction to the direction data group Step b6: Obtain a steering coordinate Step b7: Determine whether a distance from the steering coordinate to the previous coordinate and the current coordinate line is greater than a threshold Step b8: Determine a steering direction of the current coordinate based on a steering vector that advances from the current coordinate to the steering coordinate, and record the steering direction in the direction data set Step b9: Determine whether the current coordinate or the steering coordinate is equal to the end coordinate Step c: The sensing unit detects an end point where the finger leaves the touch screen Step d: The calculation unit performs gesture recognition according to the start coordinates, the direction data set, and the end coordinates 1: Touch module 11: Touch screen 12: Sensing unit 13: Computing unit
圖1繪示本發明之觸控模組之一實施例的方塊圖。 圖2繪示本發明之手勢特徵處理方法之一實施例的流程圖。 圖3繪示圖2中方向紀錄步驟之一實施例的流程圖。 FIG. 1 shows a block diagram of an embodiment of the touch module of the present invention. FIG. 2 shows a flowchart of an embodiment of the gesture feature processing method of the present invention. FIG. 3 is a flowchart of an embodiment of the direction recording step in FIG. 2.
步驟a:該感測單元偵測一使用者的一手指接觸該觸控螢幕的一起始座標 Step a: The sensing unit detects that a finger of a user touches an initial coordinate of the touch screen
步驟b:計算單元執行一方向紀錄步驟以得到一方向資料組 Step b: The computing unit performs a direction recording step to obtain a direction data set
步驟c:該感測單元偵測該手指離開該觸控螢幕的一終點座標 Step c: The sensing unit detects an end point where the finger leaves the touch screen
步驟d:該計算單元根據該起始座標、該方向資料組以及該終點座標進行手勢識別 Step d: The calculation unit performs gesture recognition according to the start coordinates, the direction data set, and the end coordinates
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