倒車軌跡理論實現(xiàn)方法

1、倒車軌跡理論實現(xiàn)方法                   帥文  王文梁關(guān)鍵字：倒車軌跡  視角轉(zhuǎn)換 前言：倒車軌跡是近兩年部分國產(chǎn)汽車導(dǎo)航設(shè)備上新消滅的一個功能，其借助方向盤轉(zhuǎn)角信息將汽車可能的后退路線疊加到后視攝像頭的輸出上并標(biāo)注出距離，以直觀形象化的形式幫忙駕駛?cè)藛T調(diào)整選擇倒車路線，削減駕駛?cè)藛T特殊是新手的誤推斷，對使用者是一個不錯的有用功能。倒車軌跡

2、在智能倒車領(lǐng)域內(nèi)屬于幫助倒車系統(tǒng)中的一種，雖然其還無法達(dá)到智能化倒車，但是其有用性和幫助性上對汽車智能化單元技術(shù)方面是一個有效的補(bǔ)充。本文將基于使用為目的，從閱歷角度并結(jié)合基本數(shù)學(xué)推導(dǎo)分析倒車軌跡的原理、實現(xiàn)過程并給出實際使用過程中需要的操作點。由于本文非側(cè)重于數(shù)學(xué)理論，對部分?jǐn)?shù)學(xué)細(xì)節(jié)在不影響實際結(jié)論狀況下不做深化探討。一 倒車軌跡的基本原理  從日常閱歷可知，以自行車為例，假如前輪有肯定轉(zhuǎn)角，在維持轉(zhuǎn)角不變狀態(tài)和無軸向移動前提下自行車走過的路徑將會以某個圓點為中心旋轉(zhuǎn)，同樣的狀態(tài)也會消滅在汽車上。其走過路徑如圖1。圖中假設(shè)車輪不會消滅軸向移動，故假如保持車輪轉(zhuǎn)角

3、不變的狀況下，每個車輪只能沿著垂直其車軸的方向行進(jìn)，這里取前后輪的軸心作為軌跡跟蹤點（實際過程中兩個前輪軸心不會消滅平行），則軌跡應(yīng)當(dāng)是以前后輪軸向線的焦點為圓心的圓。圖中為為前輪同水平方向的夾角，記前后輪軸距為L，后輪軸長為W，后輪距離車尾的距離為D，從幾何關(guān)系可知，后輪軸心的運動軌跡可以描述為以半徑Lcot()的圓周運動。兩個后輪的軌跡分別為Lcot()-W/2和Lcot()+W/2的圓。這里的推導(dǎo)過程接受閱歷法結(jié)合幾何推算，完全從數(shù)學(xué)角度的推算過程請參考資料1。圖中的x方向和y方向不同于一般習(xí)慣主要是考慮后面的視角變換。從等式可以看到，當(dāng)接近0度時候行進(jìn)軌跡近似直線，接近90度時半徑呈縮

4、小趨勢，符合我們?nèi)粘ｉ啔v值。二 視角轉(zhuǎn)換   從倒車公式推導(dǎo)出的路線圖為行進(jìn)路線的俯視圖，實際顯示給操作者的路線應(yīng)當(dāng)是從車內(nèi)觀看點觀看到的軌跡，駕駛?cè)藛T看到的運動軌跡實際為以車尾攝像頭為中心點坐標(biāo)的圖像描述（圖一中車尾位置的原點）。將攝像頭位置定為坐標(biāo)零點，則軌跡上的任意點位置公式為：（x+Lcot()）2+(y+D)2=(Lcot()2     （1）上面推導(dǎo)的軌跡仍舊是基于俯視條件下的軌跡，看到的應(yīng)當(dāng)為處于肯定視角觀看的軌跡，故需要進(jìn)行肯定角度的轉(zhuǎn)換才能切換到實際觀看到的圖像。假設(shè)攝像頭的可視角范圍為

5、2，攝像頭距離地面h，攝像頭中心線同水平面的夾角為，輸出屏幕的高度為H，這里假設(shè)攝像頭相對于屏幕為一個點，會造成實際計算結(jié)果的肯定偏差，關(guān)于偏差的細(xì)節(jié)數(shù)學(xué)計算不屬本文爭辯的重點。我們實際觀看到的Yr為地面y在顯示屏H上的投影，y方向的轉(zhuǎn)換過程如圖二：上圖中為了便于計算，將經(jīng)過攝像頭采集后輸出的顯示器直接投影到同一個圖中，這和實際輸出沒有區(qū)分。上圖中的虛線為水平線，點線為屏幕的中心點到攝像頭的連線，為中心線和水平線的夾角將上圖進(jìn)行簡化可轉(zhuǎn)為下列數(shù)學(xué)問題，等腰三角形中同頂點成已知角度所對應(yīng)的邊長，簡化后的計算如圖三。Yr對應(yīng)的角度為+-，其中=arctg(h/y) 通過幾何運算可得：三&

6、#160;計算軌跡的條件從以上計算我們可以看到，需要計算出軌跡，必需供應(yīng)以下參數(shù)：1 攝像頭的可視角范圍2a2 攝像頭距離地面距離h3 攝像頭中心線同水平面的夾角4 輸出屏幕的高度H和寬帶W5 汽車前后輪軸距L6 汽車軸長W，后輪距離車尾的距離D7 前輪同水平方向的夾角以上參數(shù)中除轉(zhuǎn)角外對于固定的車型和安裝方式都已經(jīng)固定，轉(zhuǎn)角的獵取可以有兩種方式：1 對于有方向盤角度信息的車型可以直接通過輸出接口如can總線獵取。2外加角度傳感器獵取角度信息。兩種方式都需要對采集的信息作肯定的校正。 四 驗證  將上面公

7、式的2和3帶入1，可推導(dǎo)出顯示屏幕上的實際軌跡圖像。我們用vc實現(xiàn)了過程模擬，程序流程圖四，模擬結(jié)果如圖五。在真實的嵌入式平臺上實現(xiàn)需要該平臺支持圖像疊加功能，目前很多多媒體soc芯片都能具備硬件融合功能，可以便利的將描繪出的軌跡疊加到攝像頭的輸入信號上，對于角度信息的采集，則要求平臺有can總線接口（部分車型可以輸出角度信息）或外加角度傳感器接口獵取車輪轉(zhuǎn)角。五  結(jié)論：從驗證狀況看，結(jié)果和閱歷吻合，證明算法的主要正確性。一些細(xì)節(jié)信息需要針對具體的實現(xiàn)平臺進(jìn)行微調(diào)。以上算法對于下列場景無法解決，假如路面有斜坡由于整個系統(tǒng)無法感知而導(dǎo)致疊加圖像有誤，當(dāng)?shù)管囁俣冗^快（如漂移）

8、會造成上述公式整體失效，但是對于一般用戶場景-低速、路面相對平整還是主要場合，故將參數(shù)校準(zhǔn)后會有較好的參考價值。/ BackTrack.h: interface for the CBackTrack class. / / #if !defined(AFX_BACKTRACK_H_EAF4E3A8_3691_44DA_A864_72658056A1D9_INCLUDED_) #define AFX_BACKTRACK_H_EAF4E3A8_3691_44DA_A864_72658056A1D9_INCLUDED_ #if _MSC_VER > 1000 #pragma once #endi

9、f / _MSC_VER > 1000 #include "RearCalibration.h" /* struct Mypoint int x; int y; ; typedef struct Mypoint MyPoint; */ class CBackTrack public: bool InitObject(CRearCalibration *pCali, float fAngle,float fAxleDist,float fWheelDist,int lWidth, int lHeight); void DrawExtendSpot(unsigned ch

10、ar *lpDIBBits, int lWidth, int lHeight, bool bInverse=false); void DrawExtendTrack(unsigned char *lpDIBBits, int lWidth, int lHeight); void DrawBackSpot(unsigned char *lpDIBBits, int lWidth, int lHeight); void DrawBackTrack(unsigned char *lpDIBBits, int lWidth, int lHeight, bool bInverse=false); /*

11、void Way2_Back_Track_Draw(char *lpDIBBits, int lWidth, int lHeight); void Back_Track_Draw(char *lpDIBBits, int lWidth, int lHeight); void Calibration_Track_Draw(CRearCalibration *pCali,char *lpDIBBits, int lWidth, int lHeight); void GetBackTrackDraw(CRearCalibration *pCali,char *lpDIBBits, int lWidt

12、h, int lHeight, float fAngle); */ void DrawTrack(unsigned char *lpDIBBits, int lWidth, int lHeight); CBackTrack(); virtual CBackTrack(); private: void InverseBmp(unsigned char *lpDIBBits, int lWidth, int lHeight); CRearCalibration *m_pCali; float m_fAngle; float m_VBack; int m_iTlong; int m_step; vo

13、id GetExtendUV(); void ComputerExtendXY(); void GetTfromView(int lWidth, int lHeight); void ComputerXY(); void ComputerUV(); CPoint GetUfromVofExtend(short v); CPoint GetUfromV(short v); void GetMarkXU(); short RelationYV(short v); int m_iNT; int m_iFT; float m_fLX40; float m_fLY40; float m_fRX40; f

14、loat m_fRY40; float m_fLeX40; float m_fLeY40; float m_fReX40; float m_fReY40; int m_iLU40; int m_iLV40; int m_iRU40; int m_iRV40; int m_iLeU40; int m_iLeV40; int m_iReU40; int m_iReV40; float m_LRearAxle; float m_LRearWheel; int m_U1288,m_U2288; ; #endif / !defined(AFX_BACKTRACK_H_EAF4E3A8_3691_44DA

15、_A864_72658056A1D9_INCLUDED_) / BackTrack.cpp: implementation of the CBackTrack class. / / #include "stdafx.h" #include "BackTrack.h" #include "math.h" #ifdef _DEBUG #undef THIS_FILE static char THIS_FILE=_FILE_; #define new DEBUG_NEW #endif / / Construction/Destruction

16、 / CBackTrack:CBackTrack() m_VBack = 0.1f; m_LRearAxle = 0; m_LRearWheel = 0; m_iTlong = 0; GetMarkXU(); CBackTrack:CBackTrack() / /分步驟進(jìn)行編程 /* void CBackTrack:GetTfromView() /float VBack = 138.9; / 相機(jī)視野的最近點和最遠(yuǎn)點距離汽車后軸的距離，Ny要大于100，由于現(xiàn)在假定相機(jī)安裝在后軸中心，故先付值100 int Ny,Fy; Ny = 100; Fy = 330; / 中間變量 float a,b

17、; int t; /推斷分母中為零的項，a不行能為零，由于前軸中心的轉(zhuǎn)向角永久小于50度 if( sin(m_fAngle) != 0 ) a = m_LRearAxle / (float)(tan (m_fAngle) - m_LRearWheel / 2; b = m_LRearAxle / m_VBack / (float)(sin (m_fAngle); m_iNT = (int)(b * (float)(asin ( Ny / a) + 0.5f); m_iFT = (int)(b * (float)(asin ( Fy / a) + 0.5f); /當(dāng)這兩項為零時，車輛沒有倒車，因

18、此可以只把后輪的延長線畫出 else m_iNT = (int)(Ny/m_VBack + 0.5f); m_iFT = (int)(Fy/m_VBack + 0.5f); / computer time jump step m_step = (m_iFT - m_iNT) / 30; m_iTlong = 0; for( t = m_iNT; t m_iFT; t = t + m_step) m_iTlong + ; */ void CBackTrack:GetTfromView(int lWidth, int lHeight) /float VBack = 138.9; / 相機(jī)視野的最近

19、點和最遠(yuǎn)點距離汽車后軸的距離，Ny要大于100，由于現(xiàn)在假定相機(jī)安裝在后軸中心，故先付值100 int Ny,Fy; Ny = 100; Fy = 380; / 中間變量 /float a,b; int t; CPoint pl,pr; m_iNT = (int)(Ny/m_VBack + 0.5f); m_iFT = (int)(Fy/m_VBack + 0.5f); /* float a,b; a = m_LRearAxle / (float)tan (m_fAngle); b = m_LRearAxle / m_VBack / (float)sin (m_fAngle); do m_fL

20、X0 = -(a - m_LRearWheel / 2) * (float)(cos(m_iNT / b) + a; m_fLY0 = (a- m_LRearWheel / 2) * (float)(sin(m_iNT / b); pl = m_pCali->GetUVfromXY( m_fLX0, m_fLY0); m_fRX0 = -(a+m_LRearWheel / 2) * (float)(cos(m_iNT / b) + a; m_fRY0 = (a+ m_LRearWheel / 2)* (float)(sin(m_iNT / b); pr = m_pCali->Get

21、UVfromXY( m_fRX0, m_fRY0); m_iNT +; while( pl.x 1 | pl.y 1 | pr.x 1 | pr.y 1); do m_fLX0 = -(a - m_LRearWheel / 2) * (float)(cos(m_iFT / b) + a; m_fLY0 = (a- m_LRearWheel / 2) * (float)(sin(m_iFT / b); pl = m_pCali->GetUVfromXY( m_fLX0, m_fLY0); m_fRX0 = -(a+m_LRearWheel / 2) * (float)(cos(m_iFT

22、/ b) + a; m_fRY0 = (a+ m_LRearWheel / 2)* (float)(sin(m_iFT / b); pr = m_pCali->GetUVfromXY( m_fRX0, m_fRY0); m_iFT -; while( pl.x > lWidth | pl.y > lHeight | pr.x > lWidth | pr.y > lHeight); */ / computer time jump step m_step = (m_iFT - m_iNT) / 38; m_iTlong = 0; for( t = m_iNT; t m

23、_iFT; t = t + m_step) m_iTlong + ; /* ComputerXY() 計算倒車軌跡點 參數(shù)是方向盤轉(zhuǎn)角，此處暫為前軸中心點的轉(zhuǎn)角 */ void CBackTrack:ComputerXY() float a,b; a = m_LRearAxle / (float)(tan (m_fAngle); b = m_VBack * (float)(sin (m_fAngle) / m_LRearAxle; int t; int l = 0; for ( t = m_iNT ; t m_iFT ; t = t + m_step) / left rear wheel ba

24、ck track m_fLX l = - ( a - m_LRearWheel / 2) * (float)(cos ( b * t ) + a; m_fLY l = ( a - m_LRearWheel / 2) * (float)(sin( b * t ); / right rear wheel back track m_fRX l = - ( a + m_LRearWheel / 2) * (float)(cos ( b * t ) + a; m_fRY l = ( a + m_LRearWheel / 2) * (float)(sin( b * t ); l+; /* 車輛后輪延長線，

25、無論方向盤轉(zhuǎn)角等參數(shù)如何變， 延長線上的點是不變的，因此可分開來寫，尤其是當(dāng)前軸 中心點的轉(zhuǎn)角為零時，在圖像上只顯示后輪延長線，因此需要 單獨寫出來 */ void CBackTrack:ComputerExtendXY() int t; int l = 0; for(t = m_iNT ; t m_iFT ; t = t + m_step) / left rear wheel extend m_fLeX l = m_LRearWheel / 2; m_fLeY l = t*m_VBack; / right rear wheel extend m_fReX l = - m_LRearWheel

26、 / 2; m_fReY l = m_fLeY l ; l+; void CBackTrack:ComputerUV() int t; int l = 0; CPoint p; for( t = m_iNT ; t m_iFT ; t = t + m_step) / left rear wheel back track in image p = m_pCali->GetUVfromXY( m_fLXl, m_fLYl); m_iLUl = p.x; m_iLVl = p.y; /right rear wheel back track in image p = m_pCali->Ge

27、tUVfromXY( m_fRXl, m_fRYl); m_iRUl = p.x; m_iRVl = p.y; l+; void CBackTrack:GetExtendUV() int t; int l = 0; CPoint p; for( t = m_iNT ; t m_iFT ; t = t + m_step) / left rear wheel extend in image p = m_pCali->GetUVfromXY( m_fLeXl, m_fLeYl); m_iLeUl = p.x; m_iLeVl = p.y; / right rear wheel extend i

28、n image p = m_pCali->GetUVfromXY( m_fReXl, m_fReYl); m_iReUl = p.x; m_iReVl = p.y; l+; void CBackTrack:DrawBackSpot(unsigned char *lpDIBBits, int lWidth, int lHeight) int t ; long lLineBytes = WIDTHBYTES(lWidth * 8); for( t = 0 ; t m_iTlong ; t +) / left wheel track spot *(unsigned char *)lpDIBBi

29、ts + lLineBytes * m_iLVt + m_iLUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iLVt -1) + m_iLUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iLVt +1) + m_iLUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * m_iLVt + m_iLUt -1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * m

30、_iLVt + m_iLUt + 1) = 255; / right wheel track spot *(unsigned char *)lpDIBBits + lLineBytes * m_iRVt + m_iRUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iRVt -1) + m_iRUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iRVt +1) + m_iRUt) = 255; *(unsigned char *)lpDIBBits + lLineBy

31、tes * m_iRVt + m_iRUt -1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * m_iRVt + m_iRUt + 1) = 255; void CBackTrack:DrawExtendSpot(unsigned char *lpDIBBits, int lWidth, int lHeight, bool bInverse) if(bInverse) InverseBmp(lpDIBBits,lWidth,lHeight); int t ; long lLineBytes = WIDTHBYTES(lWidth * 8)

32、; for( t = 0 ; t m_iTlong ; t +) / left wheel track spot *(unsigned char *)lpDIBBits + lLineBytes * m_iLeVt + m_iLeUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iLeVt -1) + m_iLeUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iLeVt +1) + m_iLeUt) = 255; *(unsigned char *)lpDIBBit

33、s + lLineBytes * m_iLeVt + m_iLeUt -1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * m_iLeVt + m_iLeUt + 1) = 255; / right wheel track spot *(unsigned char *)lpDIBBits + lLineBytes * m_iReVt + m_iReUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (m_iReVt -1) + m_iReUt) = 255; *(unsigned ch

34、ar *)lpDIBBits + lLineBytes * (m_iReVt +1) + m_iReUt) = 255; *(unsigned char *)lpDIBBits + lLineBytes * m_iReVt + m_iReUt -1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * m_iReVt + m_iReUt + 1) = 255; if(bInverse) InverseBmp(lpDIBBits,lWidth,lHeight); void CBackTrack:DrawBackTrack(unsigned char

35、 *lpDIBBits, int lWidth, int lHeight, bool bInverse) if(bInverse) InverseBmp(lpDIBBits,lWidth,lHeight); int t,tj ; float k ; int U,offset; long lLineBytes = WIDTHBYTES(lWidth * 8); for( t = 0 ; t m_iTlong - 1 ; t +) / draw left wheel back track k = (float) ( m_iLU t - m_iLU t + 1 ) / (float) ( m_iLV

36、 t - m_iLV t + 1 ); if( m_iLV t m_iLV t + 1 ) for ( tj = m_iLV t ; tj m_iLV t + 1 ; tj+) offset = lLineBytes * tj; U = (int) (m_iLU t - k * (m_iLV t - tj); if( U lWidth - 1 && tj lHeight - 1 && tj >1 && U >1 ) *(unsigned char *)lpDIBBits + offset + U) = 255; *(unsigned

37、char *)lpDIBBits + offset - lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset + lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset + U +1) = 255; *(unsigned char *)lpDIBBits + offset + U -1) = 255; else if( m_iLV t > m_iLV t + 1 ) for ( tj = m_iLV t ; tj > m_iLV t + 1 ; tj-)

38、 offset = lLineBytes * tj; U = (int) (m_iLU t - k * (m_iLV t - tj); if( U lWidth - 1 && tj lHeight - 1 && tj >1 && U >1 ) *(unsigned char *)lpDIBBits + offset + U) = 255; *(unsigned char *)lpDIBBits + offset - lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset

39、+ lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset + U +1) = 255; *(unsigned char *)lpDIBBits + offset + U -1) = 255; / draw right wheel back track k = (float) ( m_iRU t - m_iRU t + 1 ) / (float) ( m_iRV t - m_iRV t + 1 ); if( m_iRV t m_iRV t + 1 ) for ( tj = m_iRV t ; tj m_iRV t + 1 ; tj

40、+) offset = lLineBytes * tj; U = (int) (m_iRU t - k * (m_iRV t - tj); if( U lWidth - 1 && tj lHeight - 1 && tj >1 && U >1 ) *(unsigned char *)lpDIBBits + offset + U) = 255; *(unsigned char *)lpDIBBits + offset - lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offse

41、t + lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset + U +1) = 255; *(unsigned char *)lpDIBBits + offset + U -1) = 255; else if( m_iRV t > m_iRV t + 1 ) for ( tj = m_iRV t ; tj > m_iRV t + 1 ; tj-) offset = lLineBytes * tj; U = (int) (m_iRU t - k * (m_iRV t - tj); if( U lWidth - 1 &

42、amp;& tj lHeight - 1 && tj >1 && U >1 ) *(unsigned char *)lpDIBBits + offset + U) = 255; *(unsigned char *)lpDIBBits + offset - lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset + lLineBytes + U) = 255; *(unsigned char *)lpDIBBits + offset + U +1) = 255; *(unsigne

43、d char *)lpDIBBits + offset + U -1) = 255; if(bInverse) InverseBmp(lpDIBBits,lWidth,lHeight); void CBackTrack:DrawExtendTrack(unsigned char *lpDIBBits, int lWidth, int lHeight) int t ,tj; float k ; int V; long lLineBytes = WIDTHBYTES(lWidth * 8); for( t = 0 ; t m_iTlong - 1 ; t +) / draw left wheel

44、extend track if( m_iLeU t > m_iLeU t + 1 ) for ( tj = m_iLeU t ; tj > m_iLeU t + 1 ; tj-) k = (float) ( m_iLeV t - m_iLeV t + 1 ) / (float) ( m_iLeU t - m_iLeU t + 1 ); V = (int) ( k * tj + m_iLeV t - k * m_iLeU t ); if( tj lWidth - 1 && V lHeight - 1 && tj >1 && V &

45、gt;1 ) *(unsigned char *)lpDIBBits + lLineBytes * V + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * ( V - 1 ) + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (V + 1) + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * V + tj +1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * V

46、 + tj -1) = 255; else for ( tj = m_iLeU t ; tj m_iLeU t + 1 ; tj+) k = (float) ( m_iLeV t - m_iLeV t + 1 ) / (float) ( m_iLeU t - m_iLeU t + 1 ); V = (int) ( k * tj + m_iLeV t - k * m_iLeU t ); if( tj lWidth - 1 && V lHeight - 1 && tj >1 && V >1 ) *(unsigned char *)lpDI

47、BBits + lLineBytes * V + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * ( V - 1 ) + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (V + 1) + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * V + tj +1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * V + tj -1) = 255; / draw right

48、 wheel extend track if( m_iReU t > m_iReU t + 1 ) for ( tj = m_iReU t ; tj > m_iReU t + 1 ; tj-) k = (float) ( m_iReV t - m_iReV t + 1 ) / (float) ( m_iReU t - m_iReU t + 1 ); V = (int) ( k * tj + m_iReV t - k * m_iReU t ); if( tj lWidth - 1 && V lHeight - 1 && tj >1 &&a

49、mp; V >1 ) *(unsigned char *)lpDIBBits + lLineBytes * V + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * ( V - 1 ) + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * (V + 1) + tj) = 255; *(unsigned char *)lpDIBBits + lLineBytes * V + tj +1) = 255; *(unsigned char *)lpDIBBits + lLineBytes * V + tj -1) = 255; else for ( tj = m_iReU t ; tj m_iReU t + 1 ; tj+) k = (float) ( m_iReV t - m_iReV t + 1