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float rotate[9]; float distTwoPoint(vect2f_t a,vect2f_t b) { return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); } int mvGetPointIndex(vect2f_t *src,int nPoint,int *index,float stepx,float stepy,int isLimit) { float thet0 = PI/2,thet1 = -PI/2; float min = 4000; float initDist,dist; vect2f_t nearpoint0,nearpoint1; int i; while(1) { index[0] = rand()%nPoint; index[1] = rand()%nPoint; if(fabs(src[index[0]].x) > (stepx * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[index[0]].y) > (stepy * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[index[1]].x) > (stepx * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[index[1]].y) > (stepy * HOMOGRAPHY_RANGE_POINT_NUM)) { if(isLimit) continue; } initDist = distTwoPoint(src[index[0]],src[index[1]]); if(initDist > 10.0f && initDist < 70.0f) break; } //index[0] = 0; //index[1] = 2; nearpoint0.x = -(src[index[1]].y - src[index[0]].y)*sin(thet0) + src[index[0]].x; nearpoint0.y = (src[index[1]].x - src[index[0]].x)*sin(thet0) + src[index[0]].y; nearpoint1.x = -(src[index[1]].y - src[index[0]].y)*sin(thet1) + src[index[0]].x; nearpoint1.y = (src[index[1]].x - src[index[0]].x)*sin(thet1) + src[index[0]].y; for( i = 0; i < nPoint; ++i ) { if(i == index[0] || i == index[1]) continue; dist = distTwoPoint(src[i],nearpoint0); if(min > dist) { index[2] = i; min = dist; } dist = distTwoPoint(src[i],nearpoint1); if(min > dist) { index[2] = i; min = dist; } } nearpoint0.x = -(src[index[0]].y - src[index[2]].y)*sin(thet0) + src[index[2]].x; nearpoint0.y = (src[index[0]].x - src[index[2]].x)*sin(thet0) + src[index[2]].y; nearpoint1.x = -(src[index[0]].y - src[index[2]].y)*sin(thet1) + src[index[2]].x; nearpoint1.y = (src[index[0]].x - src[index[2]].x)*sin(thet1) + src[index[2]].y; min = 4000; for( i = 0; i < nPoint; ++i ) { if(i == index[0] || i == index[1]|| i == index[2]) continue; dist = distTwoPoint(src[i],nearpoint0); if(min > dist) { index[3] = i; min = dist; } dist = distTwoPoint(src[i],nearpoint1); if(min > dist) { index[3] = i; min = dist; } } dist = distTwoPoint(src[index[0]],src[index[1]]); //printf("%f ",dist); if(dist < 10.0f || dist > 110.0f) return 0; dist = distTwoPoint(src[index[1]],src[index[2]]); //printf("%f ",dist); if(dist < 1.0f|| dist > 110.0f) return 0; dist = distTwoPoint(src[index[2]],src[index[3]]); //printf("%f ",dist); if(dist < 1.0f|| dist > 110.0f) return 0; dist = distTwoPoint(src[index[0]],src[index[2]]); //printf("%f ",dist); if(dist < 1.0f || dist > 110.0f) return 0; dist = distTwoPoint(src[index[3]],src[index[1]]); //printf("%f ",dist); if(dist < 1.0f || dist > 110.0f) return 0; dist = distTwoPoint(src[index[0]],src[index[3]]); //printf("%f\n",dist); if(dist < 1.0f || dist > 110.0f) return 0; return 1; }
float getErrHomography(vect2f_t *src,vect2f_t *dst,float *R,int nPoint,float stepx,float stepy) { int j; float errSum = 0.0f; float x1,y1; int count = 0; for(j = 0;j < nPoint;j++) { if(fabs(src[j].x) > (stepx * HOMOGRAPHY_RANGE_POINT_NUM) || fabs(src[j].y) > (stepy * HOMOGRAPHY_RANGE_POINT_NUM)) { continue; } x1 = (R[0] * src[j].x + R[1] * src[j].y + R[2])/(R[6] * src[j].x + R[7] * src[j].y + R[8]); y1 = (R[3] * src[j].x + R[4] * src[j].y + R[5])/(R[6] * src[j].x + R[7] * src[j].y + R[8]); errSum += fabs(x1 - dst[j].x); errSum += fabs(y1 - dst[j].y); count++; } errSum = errSum/(2.0f *count); return errSum; } int mvFindHomographyProj2Img(vect2f_t *src,vect2f_t *dst,float *R,int nPoint, float stepx,float stepy,int iterations) { CvMat _J,_B,_JtJiJtB; float J[8][8],eB[8],JtJiJtB[8],filterJtJiJtB[8],Rf[9]; memset(R,0,32); double a[8][8]; double b[8], x[9]; CvMat A = cvMat( 8, 8, CV_64FC1, a ); CvMat B = cvMat( 8, 1, CV_64FC1, b ); CvMat X = cvMat( 8, 1, CV_64FC1, x ); int i,j,k; int index[4]; float errSum = 0.0f,minErr = 10000.0f; memset(filterJtJiJtB,0,32); for(k = 0;k < 2000;k++) { if(0 == mvGetPointIndex(src,nPoint,index,stepx,stepy,1)) continue; for( i = 0; i < 4; ++i ) { a[i + 0][0] = src[index[i]].x; a[i + 0][1] = src[index[i]].y; a[i + 0][2] = 1; a[i + 0][3] = 0; a[i + 0][4] = 0; a[i + 0][5] = 0; a[i + 0][6] = -dst[index[i]].x * src[index[i]].x; a[i + 0][7] = -dst[index[i]].x * src[index[i]].y; a[i + 4][0] = 0; a[i + 4][1] = 0; a[i + 4][2] = 0; a[i + 4][3] = src[index[i]].x; a[i + 4][4] = src[index[i]].y; a[i + 4][5] = 1; a[i + 4][6] = -dst[index[i]].y * src[index[i]].x; a[i + 4][7] = -dst[index[i]].y * src[index[i]].y; b[i + 0] = dst[index[i]].x; b[i + 4] = dst[index[i]].y; } cvSolve( &A, &B, &X, CV_SVD ); x[8] = 1; for(i = 0;i < 9;i++) { Rf[i] = (float)x[i]; } errSum = getErrHomography(src,dst,Rf,nPoint,stepx,stepy); if(errSum < 0.01f) { minErr = errSum; for(i = 0;i < 9;i++) { R[i] = (float)x[i]; } break; } if(minErr > errSum) { for(i = 0;i < 9;i++) { R[i] = (float)x[i]; } minErr = errSum; } /* printf("%f %f %f\n",x[0],x[1],x[2]); printf("%f %f %f\n",x[3],x[4],x[5]); printf("%f %f %f\n",x[6],x[7],x[8]); printf("\n"); */ } errSum = minErr; if(errSum > 1.0f) return 0; for(k = 0;k < iterations;k++) { vect2f_t _dstCalc; if(0 == mvGetPointIndex(src,nPoint,index,stepx,stepy,1)) continue; for( i = 0; i < 4; ++i ) { _dstCalc.x = (R[0] * src[index[i]].x + R[1] * src[index[i]].y + R[2])/(R[6] * src[index[i]].x + R[7] * src[index[i]].y + R[8]); _dstCalc.y = (R[3] * src[index[i]].x + R[4] * src[index[i]].y + R[5])/(R[6] * src[index[i]].x + R[7] * src[index[i]].y + R[8]); J[i + 0][0] = src[index[i]].x; J[i + 0][1] = src[index[i]].y; J[i + 0][2] = 1; J[i + 0][3] = 0; J[i + 0][4] = 0; J[i + 0][5] = 0; J[i + 0][6] = -dst[index[i]].x * src[index[i]].x; J[i + 0][7] = -dst[index[i]].x * src[index[i]].y; J[i + 4][0] = 0; J[i + 4][1] = 0; J[i + 4][2] = 0; J[i + 4][3] = src[index[i]].x; J[i + 4][4] = src[index[i]].y; J[i + 4][5] = 1; J[i + 4][6] = -dst[index[i]].y * src[index[i]].x; J[i + 4][7] = -dst[index[i]].y * src[index[i]].y; eB[i + 0] = _dstCalc.x - dst[index[i]].x; eB[i + 4] = _dstCalc.y - dst[index[i]].y; b[i + 0] = dst[index[i]].x; b[i + 4] = dst[index[i]].y; } for(i = 0;i <8;i++) { for(j = 0;j < 8;j++) { a[i][j] = (double)J[i][j]; } } cvSolve( &A, &B, &X, CV_SVD ); float errSum1 = 0.0f; for(i = 0;i < 9;i++) { Rf[i] = (float)x[i]; } errSum1 = getErrHomography(src,dst,Rf,nPoint,stepx,stepy); if(errSum1 > 0.001f) { continue; } _J = cvMat(8, 8, CV_32FC1, (float *)&J[0][0]); _JtJiJtB = cvMat(8, 1, CV_32FC1,(float *)&JtJiJtB[0]); _B = cvMat(8, 1, CV_32FC1, (float *)&eB[0]); cvSolve( &_J, &_B, &_JtJiJtB, CV_SVD ); //cvSolve(&_JtJ,&_JtB,&_JtJiJtB,CV_SVD); //mvMatrixMutl(&JtJi[0][0],8,8,JtB,1,JtJiJtB); float Rtemp[9],JtJiJtBTemp[9]; for(j = 0;j < 9;j++) { JtJiJtBTemp[j] = filterJtJiJtB[j]; Rtemp[j] = R[j]; filterJtJiJtB[j] = 0.9f * filterJtJiJtB[j] + 0.1f * JtJiJtB[j]; R[j] -= filterJtJiJtB[j]; } float errSum2 = 0.0f; errSum2 = getErrHomography(src,dst,R,nPoint,stepx,stepy); if(errSum2 > errSum) { for(j = 0;j < 9;j++) { R[j] = Rtemp[j]; filterJtJiJtB[j] = JtJiJtBTemp[j]; } } errSum2 = getErrHomography(src,dst,R,nPoint,stepx,stepy); if(errSum2 < 0.1f) { break; } } R[8] = 1.0f; return 1; } float gR[20][3][3]; void mvInitCalibCameraPointTest(const vect2f_t* objectPoints, const vect2f_t* imagePoints, int width,int hight,float stepx,float stepy,int imageCnt) { int i,j,k; vect2f_t *pObjPoint = (vect2f_t *)objectPoints,*pImgPoint = (vect2f_t *)imagePoints; vect3f_t *rotate3dAngle = (vect3f_t *)malloc(imageCnt * sizeof(vect3f_t)); vect3f_t *translation3d = (vect3f_t *)malloc(imageCnt * sizeof(vect3f_t)); float R[3][3]; float k1 = 0.010245f; float k2 = 0.001011245f; float fx = 122.0f,fy = 122.0f; float cx = 150.0f,cy = 50.0f; float lamder = 1.0f,err = 0.0f; float x,y,x1,y1,x2,y2,x3,y3; srand((unsigned) time(NULL)); //cx = (float)(rand() % 200); //cy = (float)(rand() % 200); //printf("fx,fy,cx,cy = %f,%f,%f,%f\n\n",fx,fy,cx,cy); for(i = 0;i < imageCnt;i++) { rotate3dAngle[i].x = ((float)(rand() % 90) - 45.0f) * PI/180.0f; rotate3dAngle[i].y = ((float)(rand() % 90) - 45.0f) * PI/180.0f; rotate3dAngle[i].z = ((float)(rand() % 90) - 45.0f) * PI/180.0f; translation3d[i].x = (float)(rand() % 201); translation3d[i].y = (float)(rand() % 201); translation3d[i].z = (float)(400 + (rand() % 100));//(float)(rand() % 51); //printf("z init = %f\n",translation3d[i].z); } for(i = 0;i < imageCnt;i++) { float aerf,belt,garmer; aerf = rotate3dAngle[i].z; belt = rotate3dAngle[i].x; garmer = rotate3dAngle[i].y; R[0][0] = cos(aerf) * cos(belt); R[0][1] = cos(aerf) * sin(belt)* sin(garmer) - sin(aerf) * cos(garmer); R[0][2] = cos(aerf) * sin(belt)* cos(garmer) + sin(aerf) * sin(garmer); R[1][0] = sin(aerf) * cos(belt); R[1][1] = sin(aerf) * sin(belt)* sin(garmer) + cos(aerf) * cos(garmer); R[1][2] = sin(aerf) * sin(belt)* cos(garmer) - cos(aerf) * sin(garmer); R[2][0] = -sin(belt); R[2][1] = sin(garmer) * cos(belt); R[2][2] = cos(garmer) * cos(belt); #if 0 H[0][0] = fx * R[0][0] + cx * R[2][0]; H[0][1] = fx * R[0][1] + cx * R[2][1]; H[0][2] = fx * R[0][2] + cx * R[2][2]; H[0][3] = fx * translation3d[i].x + cx * translation3d[i].z; H[1][0] = fy * R[1][0] + cy * R[2][0]; H[1][1] = fy * R[1][1] + cy * R[2][1]; H[1][2] = fy * R[1][2] + cy * R[2][2]; H[1][3] = fy * translation3d[i].y + cx * translation3d[i].z; H[2][0] = R[2][0]; H[2][1] = R[2][1]; H[2][2] = R[2][2]; H[2][3] = translation3d[i].z; //printf("%f ",R[0][0] * R[0][0] + R[1][0] * R[1][0] + R[2][0] * R[2][0]); //printf("%f ",R[0][1] * R[0][1] + R[1][1] * R[1][1] + R[2][1] * R[2][1]); //printf("%f\n",R[0][2] * R[0][2] + R[1][2] * R[1][2] + R[2][2] * R[2][2]); R[0][0] = H[0][0]; R[0][1] = H[0][1]; R[0][2] = H[0][3]; R[1][0] = H[1][0]; R[1][1] = H[1][1]; R[1][2] = H[1][3]; R[2][0] = H[2][0]; R[2][1] = H[2][1]; R[2][2] = H[2][3]; gR[i][0][0] = H[0][0]; gR[i][0][1] = H[0][1]; gR[i][0][2] = H[0][3]; gR[i][1][0] = H[1][0]; gR[i][1][1] = H[1][1]; gR[i][1][2] = H[1][3]; gR[i][2][0] = H[2][0]; gR[i][2][1] = H[2][1]; gR[i][2][2] = H[2][3]; #else gR[i][0][0] = (float)(fx * R[0][0] + cx * R[2][0]); gR[i][0][1] = (float)(fx * R[0][1] + cx * R[2][1]); gR[i][0][2] = (float)(fx * translation3d[i].x + cx * translation3d[i].z); gR[i][1][0] = (float)(fy * R[1][0] + cy * R[2][0]); gR[i][1][1] = (float)(fy * R[1][1] + cy * R[2][1]); gR[i][1][2] = (float)(fy * translation3d[i].y + cx * translation3d[i].z); gR[i][2][0] = (float)R[2][0]; gR[i][2][1] = (float)R[2][1]; gR[i][2][2] = (float)(translation3d[i].z); R[0][2] = translation3d[i].x; R[1][2] = translation3d[i].y; R[2][2] = translation3d[i].z; #endif for(j = 0;j < hight;j++) { for(k = 0;k < width;k++) { pObjPoint[j * width + k].x = stepx * (k + 1); pObjPoint[j * width + k].y = stepy * (j + 1); x = stepx * (k + 1); y = stepy * (j + 1); x1 = (R[0][0] * x + R[0][1] * y + R[0][2])/(R[2][0] * x + R[2][1] * y + R[2][2]); y1 = (R[1][0] * x + R[1][1] * y + R[1][2])/(R[2][0] * x + R[2][1] * y + R[2][2]); double x2y2square = x1 * x1 + y1 * y1; double square2 = x2y2square * x2y2square; double square3 = x2y2square * x2y2square * x2y2square; double square4 = x2y2square * x2y2square * x2y2square * x2y2square; double scalek1 = k1 * square2; double scalek2 = k2 * square4; x2 = x1 * (1 + k1 * (float)square2 + k2 * (float)square4); y2 = y1 * (1 + k1 * (float)square2 + k2 * (float)square4); x3 = fx * x2 + cx; y3 = fy * y2 + cy; pImgPoint[(j) * width + k].x = (float)x3; pImgPoint[(j) * width + k].y = (float)y3; } } //float estR[9]; //mvFindHomography(pObjPoint,pImgPoint,estR,(width - 1) * (hight - 1),200); //printf("%f %f %f\n",estR[0],estR[1],estR[2]); //printf("%f %f %f\n",estR[3],estR[4],estR[5]); //printf("%f %f %f\n",estR[6],estR[7],estR[8]); //printf("\n\n"); pObjPoint += width * hight; pImgPoint += width * hight; } } int mvCalibCameraParams(const vect2f_t* objectPoints, const vect2f_t* imagePoints, int width,int hight,int imageCnt,float stepx,float stepy, matrix_t* A) { int hcount = 0; int i,j,k,m,n,p; int homographyCnt = width * hight; float mHt[3][3],**gHt; vect2f_t *pObjPoint = 0,*pImgPoint = 0; double h11,h12,h13,h21,h22,h23; double err = 0.0f; float fx = 0.0f,fy = 0.0f,cx = 0.0f,cy = 0.0f; float maxPoint = 0.0f,minPoint = 100000.0f; float *x0Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float)); float *x1Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float)); float *y0Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float)); float *y1Param = (float *)malloc((imageCnt * imageCnt * imageCnt * imageCnt * imageCnt) * sizeof(float)); double *k1k2 = (double *)malloc(4 * homographyCnt * imageCnt * sizeof(double)); double *pd = (double *)malloc(2 * homographyCnt * imageCnt * sizeof(double)); int *validImage = (int *)malloc(4 * imageCnt); gHt = (float **)malloc(imageCnt * sizeof(*gHt)); if(gHt == NULL) return 0; for(i = 0;i < imageCnt;i++) { gHt[i] = (float *)malloc(9 * sizeof(float)); if(gHt[i] == NULL) return 0; } if(width < 2 || hight < 2 || imageCnt < 10) { return 0; } if(objectPoints == NULL || imagePoints == NULL || A == NULL) return 0; /* double mfx = 1.22f,mfy = 1.22f; double mcx = 13.0f,mcy = 12.0f; double mlamder = 0.2f; float mi[9],mit[9],mtim[9]; mi[0] = 1/mfx; mi[1] = 0; mi[2] = -mcx/mfx; mi[3] = 0; mi[4] = 1/mfy; mi[5] = -mcy/mfy; mi[6] = 0; mi[7] = 0; mi[8] = 1; mit[0] = 1/mfx; mit[1] = 0; mit[2] = 0; mit[3] = 0; mit[4] = 1/mfy; mit[5] = 0; mit[6] = -mcx/mfx; mit[7] = -mcy/mfy; mit[8] = 1; mvMatrixMutl(mit,3,3,mi,3,mtim); b[0] = 1/(mfx * mfx); b[1] = 0.0f; b[2] = 1/(mfy * mfy); b[3] = -mcx/(mfx * mfx); b[4] = -mcy/(mfy * mfy); b[5] = (mcx/mfx) * (mcx/mfx) + (mcy/mfy) * (mcy/mfy); fx = sqrt(fabs(1.0f/b[0])); fy = sqrt(fabs(1.0f/b[2])); cx = -b[3] * fx * fx; cy = -b[4] * fy * fy; float b[7] = {mtim[0],mtim[1],mtim[4],mtim[6],mtim[7],mtim[8],1.0f}; */ pObjPoint = (vect2f_t *)objectPoints; pImgPoint = (vect2f_t *)imagePoints; CvMat _pt1, _pt2,_mHt; double Hdata[7][7],Bb[7],Bres[7]; int count = 0,failFalg = 0; for(i = 0;i < imageCnt;i++) { float *pGht = gHt[i]; /* printf("%f %f %f\n",gR[i][0][0],gR[i][0][1],gR[i][0][2]); printf("%f %f %f\n",gR[i][1][0],gR[i][1][1],gR[i][1][2]); printf("%f %f %f\n",gR[i][2][0],gR[i][2][1],gR[i][2][2]); */ validImage[i] = mvFindHomographyProj2Img(&pObjPoint[i * homographyCnt], &pImgPoint[i * homographyCnt],pGht,homographyCnt,stepx,stepy,200); if(validImage[i] == 0) { printf("i falid %d\n",i); continue; } /* if(fabs(gR[i][0][0] - pGht[0]) > 1.0f || fabs(gR[i][0][1] - pGht[1]) > 1.0f) { printf("\n"); printf("%f %f %f\n",gR[i][0][0],gR[i][0][1],gR[i][0][2]); printf("%f %f %f\n",gR[i][1][0],gR[i][1][1],gR[i][1][2]); printf("%f %f %f\n",gR[i][2][0],gR[i][2][1],gR[i][2][2]); printf("\n"); printf("%f %f %f\n",pGht[0],pGht[1],pGht[2]); printf("%f %f %f\n",pGht[3],pGht[4],pGht[5]); printf("%f %f %f\n",pGht[6],pGht[7],pGht[8]); printf("\n\n"); } */ } for(p = 0;p < (imageCnt - 2);p++) { for(k = p + 1;k < (imageCnt - 1);k++) { for(m = k + 1;m < imageCnt;m++) { failFalg = 0; int index[3] = {p,k,m}; if(validImage[p] == 0) continue; if(validImage[k] == 0) continue; if(validImage[m] == 0) continue; for(n = 0;n < 3;n++) { //float estR[9]; //cvFindHomography(&_pt1,&_pt2,&_mHt); float *pGht = gHt[index[n]]; mHt[0][0] = pGht[0]; mHt[0][1] = pGht[1]; mHt[0][2] = pGht[2]; mHt[1][0] = pGht[3]; mHt[1][1] = pGht[4]; mHt[1][2] = pGht[5]; mHt[2][0] = pGht[6]; mHt[2][1] = pGht[7]; mHt[2][2] = pGht[8]; h11 = mHt[0][0]; h12 = mHt[1][0]; h13 = mHt[2][0]; h21 = mHt[0][1]; h22 = mHt[1][1]; h23 = mHt[2][1]; /* printf("\n"); printf("%f %f %f\n",mHt[0][0],mHt[0][1],mHt[0][2]); printf("%f %f %f\n",mHt[1][0],mHt[1][1],mHt[1][2]); printf("%f %f %f\n",mHt[2][0],mHt[2][1],mHt[2][2]); printf("\n"); */ /* h11 = gR[n][0][0]; h12 = gR[n][1][0]; h13 = gR[n][2][0]; h21 = gR[n][0][1]; h22 = gR[n][1][1]; h23 = gR[n][2][1]; */ double v12[7] = {h11 * h21,h11 * h22 + h12 * h21,h12 * h22,h13 * h21 + h11 * h23,h13 * h22 + h12 * h23,h13 * h23,h13 * h23}; double v11[7] = {h11 * h11,h11 * h12 + h12 * h11,h12 * h12,h13 * h11 + h11 * h13,h13 * h12 + h12 * h13,h13 * h13,h13 * h13}; double v22[7] = {h21 * h21,h21 * h22 + h22 * h21,h22 * h22,h23 * h21 + h21 * h23,h23 * h22 + h22 * h23,h23 * h23,h23 * h23}; for(i = 0;i < 6;i++) { Hdata[2 * n][i] = v12[i]; } Hdata[2 * n][6] = v12[6]; Bb[2 * n + 0] = Hdata[2 * n][0]; for(i = 0;i < 6;i++) { Hdata[2 * n + 1][i] = (v11[i] - v22[i]); } Hdata[2 * n + 1][6] = (v11[0] - v22[0]); Bb[2 * n + 1] = Hdata[2 * n + 1][0]; /* double sum0 = 0.0f, sum1 = 0.0f; for(i = 0;i < 6;i++) { sum0 += v12[i] * b[i]; sum1 += (v11[i] - v22[i]) * b[i]; } if(fabs(sum0) > 0.0001f || fabs(sum1) > 0.0001f ) { failFalg = 1; } */ } /* if(failFalg) { continue; } */ double max = -10000.0f; for(i = 0;i < 6;i++) { for(j = 0;j < 6;j++) { if(fabs(Hdata[i][j]) > max) { max = fabs(Hdata[i][j]); } } } Hdata[6][0] = 0; Hdata[6][1] = 0; Hdata[6][2] = 0; Hdata[6][3] = 0; Hdata[6][4] = 0; Hdata[6][5] = 0; Hdata[6][6] = 1; for(i = 0;i < 7;i++) { for(j = 0;j < 7;j++) { Hdata[i][j] = Hdata[i][j]/max; } } Bb[6] = 1.0f; for(i = 0;i < 7;i++) { Bb[i] = Bb[i]/max; } //mvMatrixTrans((float *)H.pdata,6,6,(float *)&Ht[0]); //mvMatrixMutl(&Ht[0],6,6,H.pdata,6,&HtH[0]); //mvJacobiEigens_32f(HtH,W,B.pdata,6,0.0001f); _pt1 = cvMat(7, 7, CV_64FC1, (double *)&Hdata[0][0] ); _pt2 = cvMat(7, 1, CV_64FC1, (double *)&Bb[0] ); _mHt = cvMat(7, 1, CV_64FC1, Bres); cvSolve( &_pt1, &_pt2, &_mHt, CV_SVD ); double B11,B12,B13,B22,B23,B33,B00,deltFx,deltFy,deltCx,deltCy; B11 = Bres[0]; B12 = Bres[1]; B13 = Bres[2]; B22 = Bres[3]; B23 = Bres[4]; B33 = Bres[5]; B00 = Bres[6]; deltFx = sqrt(fabs(1.0f/B11)); deltFy = sqrt(fabs(1.0f/B13)); deltCx = fabs(-B22 * deltFx * deltFx); deltCy = fabs(-B23 * deltFy * deltFy); double a1 = mHt[0][0] - deltCx * mHt[2][0] ; double b1 = mHt[0][1] - deltCy * mHt[2][1] ; double scale = deltFx/deltFy; deltFy = sqrt((a1 * a1 + scale * b1 * b1)/fabs(1 - mHt[2][0] * mHt[2][0])); deltFx = scale * deltFy; x0Param[count] = (float)deltCx; y0Param[count] = (float)deltCy; count++; //printf("%d:fx,fy,cx,cy = %f,%f,%f,%f\n",count,deltFx,deltFy,deltCx,deltCy); //printf("%d:fx,fy,cx,cy = %f,%f,%f,%f\n",count,fx,fy,cx,cy); } } } //fx = gR[n][0][0] - cx * gR[n][2][0] //printf("%d:fx,fy,cx,cy = %f,%f,%f,%f\n",count,fx/count,fy/count,cx/count,cy/count); cx = getBestVal(x0Param,count,4.0f); cy = getBestVal(y0Param,count,4.0f); count = 0; for(i = 0;i < imageCnt;i++) { if(validImage[i] == 0) continue; float *pGht = gHt[i]; mHt[0][0] = pGht[0]; mHt[0][1] = pGht[1]; mHt[0][2] = pGht[2]; mHt[1][0] = pGht[3]; mHt[1][1] = pGht[4]; mHt[1][2] = pGht[5]; mHt[2][0] = pGht[6]; mHt[2][1] = pGht[7]; mHt[2][2] = pGht[8]; double r31,r32; r31 = mHt[2][0]; r32 = mHt[2][1]; #if 0 deltFx = 122.0f; deltFy = 122.0f; double r11,r12,r21,r22; r31 = mHt[2][0]; r32 = mHt[2][1]; r11 = (mHt[0][0] - deltCx * r31)/deltFx; r21 = (mHt[1][0] - deltCy * r31)/deltFx; r12 = (mHt[0][1] - deltCx * r32)/deltFy; r22 = (mHt[1][1] - deltCy * r32)/deltFy; double mod0,mod1; mod0 = r11 * r11 + r21 * r21 + r31 * r31; mod1 = r12 * r12 + r22 * r22 + r32 * r32; printf("mod = %f %f\n",mod0 * 40000.0f,mod1 * 40000.0f); if(fabs(mod0 - 1.0f) > 0.1f || fabs(mod1 - 1.0f) > 0.1f) { continue; } #endif double a,b,c,d,yy; a = (mHt[0][0] - cx * r31); b = (mHt[1][0] - cy * r31); c = (mHt[0][1] - cx * r32); d = (mHt[1][1] - cy * r32); double ff = (a * c * (b * b - d * d) - d * b * (a * a - c * c)) /(a * c * (r32 * r32 - r31 * r31) + r31 * r32 * (a * a - c * c)); if(fabs(ff) < 0.001f) continue; yy = 1.0f/ff; if(ff < 0.0f) continue; fy = (float)sqrt(ff); fx = (float)sqrt((a * a - c * c)/((r32 * r32 - r31 * r31) - (b * b - d * d) * yy)); //fx = scale * deltFy; //printf("f = %f %f\n",fx,fy); x0Param[count] = fx; y0Param[count] = fy; count++; } fx = getBestVal(x0Param,count,4.0f); fy = getBestVal(y0Param,count,4.0f); printf("fx,fy,cx,cy = %f,%f,%f,%f\n",fx,fy,cx,cy); float mi[9],R[9]; mi[0] = 1/fx; mi[1] = 0; mi[2] = -cx/fx; mi[3] = 0; mi[4] = 1/fy; mi[5] = -cy/fy; mi[6] = 0; mi[7] = 0; mi[8] = 1; float k1 = 0.0f,k2 = 0.0f; int kCnt = 0; double _k[2]; for(n = 0;n < imageCnt;n++) { if(validImage[n] == 0) continue; float *pGht = gHt[n]; mvMatrixMutl(mi,3,3,pGht,3,R); //printf("%f\n",R[0] * R[0] + R[3] * R[3] + R[6] * R[6]); //printf("%f\n",R[1] * R[1] + R[4] * R[4] + R[7] * R[7]); memcpy(pGht,R,36); double *_k1k2 = &k1k2[4 * kCnt * homographyCnt]; double *d = &pd[2 * kCnt * homographyCnt]; double x1,y1,x2,y2; for(i = 0;i < homographyCnt;i++) { vect2f_t pT = pObjPoint[n * homographyCnt + i]; vect2f_t iT = pImgPoint[n * homographyCnt + i]; x1 = (R[0] * pT.x + R[1] * pT.y + R[2])/(R[6] * pT.x + R[7] * pT.y + R[8]); y1 = (R[3] * pT.x + R[4] * pT.y + R[5])/(R[6] * pT.x + R[7] * pT.y + R[8]); double x2y2square = x1 * x1 + y1 * y1; double square2 = x2y2square * x2y2square; double square3 = x2y2square * x2y2square * x2y2square; double square4 = x2y2square * x2y2square * x2y2square * x2y2square; x2 = (iT.x - cx)/fx; y2 = (iT.y - cy)/fy; _k1k2[4 * i + 0] = x1 * square2; _k1k2[4 * i + 1] = x1 * square4; d[2 * i + 0] = x2 - x1; _k1k2[4 * i + 2] = y1 * square2; _k1k2[4 * i + 3] = y1 * square4; d[2 * i + 1] = y2 - y1; } //x0Param[2 * kCnt + 0] = sqrt(1.0f/(R[0] * R[0] + R[3] * R[3] + R[6] * R[6])); //x0Param[2 * kCnt + 1] = sqrt(1.0f/(R[1] * R[1] + R[4] * R[4] + R[7] * R[7])); //printf("z0 = %f\n",sqrt(1.0f/(R[0] * R[0] + R[3] * R[3] + R[6] * R[6]))); //printf("z1 = %f\n",sqrt(1.0f/(R[1] * R[1] + R[4] * R[4] + R[7] * R[7]))); kCnt++; } _pt1 = cvMat(kCnt * homographyCnt * 2, 2, CV_64FC1, k1k2); _pt2 = cvMat(kCnt * homographyCnt * 2, 1, CV_64FC1, pd ); _mHt = cvMat(2, 1, CV_64FC1, _k); cvSolve( &_pt1, &_pt2, &_mHt, CV_SVD ); _k[0] = _k[0] * 2.0f; _k[1] = _k[1] * 1.2f; //float z = getBestVal(x0Param,kCnt * 2,4.0f); //printf("k1,k2 = %f,%f\n",_k[0],_k[1]); A->pdata[0] = fx; A->pdata[1] = 0; A->pdata[2] = cx; A->pdata[3] = 0; A->pdata[4] = fy; A->pdata[5] = cy; A->pdata[6] = 0; A->pdata[7] = 0; A->pdata[8] = 1; mvBPCalcCameraParams(objectPoints,imagePoints,validImage,width,hight,imageCnt,stepx,stepy,A,_k,gHt); for(i = 0;i < imageCnt;i++) { free(gHt[i]); } free(gHt); free(x0Param); free(x1Param); free(y0Param); free(y1Param); free(k1k2); free(pd); free(validImage); return 1; } float yt[1000]; float xt[1000]; float getBestVal(float *pVal,int count,float limit) { float maxValid = 0; int validCnt; int i,j; float validVal = 0.0f; float validSum = 0.0f; for(i = 0;i < (count - 1);i++) { validCnt = 0; for(j = i;j < count;j++) { if(fabs(pVal[i] - pVal[j]) < limit) { validCnt++; } } if(validCnt > (int)maxValid) { maxValid = (float)validCnt; validVal = pVal[i]; } } validCnt = 0; for(j = 0;j < count;j++) { if(fabs(validVal - pVal[j]) < limit) { validCnt++; validSum += pVal[j]; } } return (validSum/validCnt); } void LMTest(void) { int i,j; float a1 = 1; float b1 = 1; float c1 = 1; float d1 = 1; #define LM_SIZE 4 #define PARAM_NUM 16 for(i = 0;i < 1000;i++) { xt[i] = (i - 500) * 0.1f; float temp = 2.5f * xt[i]; yt[i] = 2.36f* temp * temp + 3.345f * temp + 4.1f; } float J[LM_SIZE][LM_SIZE],Jt[LM_SIZE][LM_SIZE],JtJ[LM_SIZE][LM_SIZE],P[LM_SIZE],e[LM_SIZE],Je[LM_SIZE],JtJi[LM_SIZE][LM_SIZE],JtJiJ[LM_SIZE][LM_SIZE]; CvMat _J, _Jt,_JtJ,_P,_e,_Je,_JtJi; _J = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&J[0][0] ); _Jt = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&Jt[0][0] ); _JtJ = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&JtJ[0][0] ); _JtJi = cvMat(LM_SIZE, LM_SIZE, CV_32FC1, (double *)&JtJi[0][0] ); _P = cvMat(LM_SIZE, 1, CV_32FC1, P); _e = cvMat(LM_SIZE, 1, CV_32FC1, e); _Je = cvMat(LM_SIZE, 1, CV_32FC1, Je); float temp; for(j = 0;j < 6000;j++) { for(i = 0;i < LM_SIZE;i++) { int idx = rand() % 1000; printf("idx = %d\n",idx); temp = d1 * xt[idx]; float ytt0 = a1 * temp * temp + b1 * temp + c1; J[i][0] = temp * temp; J[i][1] = temp; J[i][2] = 1; J[i][3] = (2.0f * a1 * temp + b1) * xt[idx]; e[i] = ytt0 - yt[idx]; } mvMatrixTrans((float *)&J[0][0],LM_SIZE,LM_SIZE,(float *)&Jt[0][0]); mvMatrixMutl((float *)&Jt[0][0],LM_SIZE,LM_SIZE,(float *)&J[0][0],LM_SIZE,(float *)&JtJ[0][0]); cvInvert(&_JtJ,&_JtJi,CV_SVD); mvMatrixMutl((float *)&JtJi[0][0],LM_SIZE,LM_SIZE,(float *)&Jt[0][0],LM_SIZE,(float *)&JtJiJ[0][0]); mvMatrixMutl((float *)&JtJiJ[0][0],LM_SIZE,LM_SIZE,(float *)e,1,(float *)&P[0]); //cvGEMM(&_J,&_e,1,NULL,1,&_Je); //cvGEMM(&_JtJi,&_Je,1,NULL,1,&_P); //cvSolve( &_J, &_e, &_P, CV_SVD ); a1 = a1 - 0.2f * P[0]; b1 = b1 - 0.2f * P[1]; c1 = c1 - 0.2f * P[2]; d1 = d1 - 0.2f * P[3]; float err = 0.0f; float ytt0; for(i = 0;i < 1000;i++) { temp = d1 * xt[i]; ytt0 = a1 * temp * temp + b1 * temp + c1; err += ytt0 - yt[i]; } printf("err = %f\n",err); } printf("a,b,c = %f,%f,%f",a1,b1,c1); } double getErrHomParams(vect2f_t *src,vect2f_t *dst,float *H,double fx, double fy,double cx,double cy,int nPoint) { double x1,y1,x3,y3; float *pGht = H; float mi[9],R[9]; int i; double errSum = 0.0f; mi[0] = (float)1/(float)fx; mi[1] = 0; mi[2] = -(float)cx/(float)fx; mi[3] = 0; mi[4] = (float)1/(float)fy; mi[5] = -(float)cy/(float)fy; mi[6] = 0; mi[7] = 0; mi[8] = 1; mvMatrixMutl(mi,3,3,H,3,R); vect2f_t *_imgPoint = src; vect2f_t *_prjPoint = dst; for(i = 0;i < nPoint;i++) { vect2f_t pT = _prjPoint[i]; x1 = (R[0] * pT.x + R[1] * pT.y + R[2])/(R[6] * pT.x + R[7] * pT.y + R[8]); y1 = (R[3] * pT.x + R[4] * pT.y + R[5])/(R[6] * pT.x + R[7] * pT.y + R[8]); /* double x2y2square = x1 * x1 + y1 * y1; double square2 = x2y2square * x2y2square; double square3 = x2y2square * x2y2square * x2y2square; double square4 = x2y2square * x2y2square * x2y2square * x2y2square; double scalek1 = k1 * square2; double scalek2 = k2 * square4; x2 = x1 * (1 + k1 * square2 + k2 * square4); y2 = y1 * (1 + k1 * square2 + k2 * square4); */ x3 = fx * x1 + cx; y3 = fy * y1 + cy; errSum += fabs(x3 - _imgPoint[i].x); errSum += fabs(y3 - _imgPoint[i].y); } errSum = errSum/(2.0f *nPoint); return errSum; } double getErrCameraParams(vect2f_t *src,vect2f_t *dst,double *param,int nPoint) { int j; double errSum = 0.0f; double x,y,x1,y1,x2,y2,x3,y3; double fx,fy,cx,cy,k1,k2,R[3][3]; fx = param[0]; fy = param[1]; cx = param[2]; cy = param[3]; k1 = param[4]; k2 = param[5]; R[0][0] = param[6]; R[0][1] = param[7]; R[0][2] = param[8]; R[1][0] = param[9]; R[1][1] = param[10]; R[1][2] = param[11]; R[2][0] = param[12]; R[2][1] = param[13]; R[2][2] = param[14]; for(j = 0;j < nPoint;j++) { x = (double)src[j].x; y = (double)src[j].y; x1 = (double)(R[0][0] * x + R[0][1] * y + R[0][2])/(R[2][0] * x + R[2][1] * y + R[2][2]); y1 = (double)(R[1][0] * x + R[1][1] * y + R[1][2])/(R[2][0] * x + R[2][1] * y + R[2][2]); double x2y2square = x1 * x1 + y1 * y1; double square2 = x2y2square * x2y2square; double square3 = x2y2square * x2y2square * x2y2square; double square4 = x2y2square * x2y2square * x2y2square * x2y2square; x2 = x1 * (1 + k1 * square2 + k2 * square4); y2 = y1 * (1 + k1 * square2 + k2 * square4); x3 = fx * x2 + cx; y3 = fy * y2 + cy; errSum += fabs(x3 - dst[j].x); errSum += fabs(y3 - dst[j].y); } errSum = errSum/(2.0f *nPoint); return errSum; } void mvBPCalcCameraParams(const vect2f_t* objectPoints, const vect2f_t* imagePoints, int *validImage,int width,int hight, int imageCnt, float stepx,float stepy,matrix_t* A,double *k,float **gHt) { double deltFx = 0.0f,deltFy = 0.0f,deltCx = 0.0f,deltCy = 0.0f,deltK1 = 0.0f,deltK2 = 0.0f; double deltR11 = 0.0f,deltR12 = 0.0f,deltTx = 0.0f; double deltR21 = 0.0f,deltR22 = 0.0f,deltTy = 0.0f; double deltR31 = 0.0f,deltR32 = 0.0f,deltTz = 0.0f; //float dFx,dFy,dCx,dCy,dK1,dK2,dR11,dR12,dR13,dR21,dR22,dR23,dR31,dR32,dR33; double J[16][15],e[16],delt[15],filterDelt[15],param[15],filterDeltTemp[15],paramTemp[15]; double k1,k2,fx,fy,cx,cy; double x,y,x1,y1,x2,y2,x3,y3; int j; float miu = 0.2f; float scale = 0.2f; double R[3][3]; int iner = 0; k1 = 0.000001f;k2 = 0.000000000001f; fx = A->pdata[0];fy = A->pdata[4];cx = A->pdata[2];cy = A->pdata[5]; //LMTest(); CvMat _pt1, _pt2,_delt; _pt1 = cvMat(16, 15, CV_64FC1, (double *)&J[0][0] ); _pt2 = cvMat(16, 1, CV_64FC1, (double *)&e[0] ); _delt = cvMat(15, 1, CV_64FC1, delt); param[0] = fx; param[1] = fy; param[2] = cx; param[3] = cy; param[4] = k[0]; param[5] = k[1]; double lastErr = 10000.0f; double gErr; for(int n = 0;n < imageCnt;n++) { vect2f_t *pObjectPoints = (vect2f_t *)&objectPoints[n * width * hight]; vect2f_t *pImagePoints = (vect2f_t *)&imagePoints[n * width * hight]; if(validImage[n] == 0) continue; memset(filterDelt,0,15 * sizeof(double)); float *pGht = gHt[n]; R[0][0] = pGht[0]; R[0][1] = pGht[1]; R[0][2] = pGht[2]; R[1][0] = pGht[3]; R[1][1] = pGht[4]; R[1][2] = pGht[5]; R[2][0] = pGht[6]; R[2][1] = pGht[7]; R[2][2] = pGht[8]; param[6] = R[0][0]; param[7] = R[0][1]; param[8] = R[0][2]; param[9] = R[1][0]; param[10] = R[1][1]; param[11] = R[1][2]; param[12] = R[2][0]; param[13] = R[2][1]; param[14] = R[2][2]; gErr = getErrCameraParams(pObjectPoints,pImagePoints,param,(width * hight)); if(gErr > lastErr) { continue; } lastErr = gErr; iner = 0; for(;;) { fx = param[0]; fy = param[1]; cx = param[2]; cy = param[3]; k1 = param[4]; k2 = param[5]; R[0][0] = param[6]; R[0][1] = param[7]; R[0][2] = param[8]; R[1][0] = param[9]; R[1][1] = param[10]; R[1][2] = param[11]; R[2][0] = param[12]; R[2][1] = param[13]; R[2][2] = param[14]; int idxrtan[8]; while(!mvGetPointIndex(pObjectPoints,width * hight,&idxrtan[0],stepx,stepy,0)); while(!mvGetPointIndex(pObjectPoints,width * hight,&idxrtan[4],stepx,stepy,0)); for(j = 0;j < 8;j++) { int idx = idxrtan[j]; x = (double)pObjectPoints[idx].x; y = (double)pObjectPoints[idx].y; x1 = (double)(R[0][0] * x + R[0][1] * y + R[0][2])/(R[2][0] * x + R[2][1] * y + R[2][2]); y1 = (double)(R[1][0] * x + R[1][1] * y + R[1][2])/(R[2][0] * x + R[2][1] * y + R[2][2]); double x2y2square = x1 * x1 + y1 * y1; double square2 = x2y2square * x2y2square; double square3 = x2y2square * x2y2square * x2y2square; double square4 = x2y2square * x2y2square * x2y2square * x2y2square; x2 = x1 * (1 + k1 * square2 + k2 * square4); y2 = y1 * (1 + k1 * square2 + k2 * square4); x3 = fx * x2 + cx; y3 = fy * y2 + cy; double dx3dx2 = fx; double dy3dy2 = fy; double dx2dx1 = 1 + k1 * x2y2square \ + 4.0f * x1 * x1 * x2y2square + k2 * square4\ + 8.0f * k2 * x1 * x1 * square3; double dy2dy1 = 1 + k1 * x2y2square \ + 4.0f * y1 * y1 * x2y2square + k2 * square4\ + 8.0f * k2 * y1 * y1 * square3; J[2 * j + 0][0] = x2; J[2 * j + 0][1] = 0; J[2 * j + 0][2] = 1; J[2 * j + 0][3] = 0; J[2 * j + 0][4] = dx3dx2 * x1 * square2; J[2 * j + 0][5] = dx3dx2 * x1 * square4; J[2 * j + 0][6] = fx * dx2dx1 * (x); J[2 * j + 0][7] = fx * dx2dx1 * (y); J[2 * j + 0][8] = fx * dx2dx1 * (1); J[2 * j + 0][9] = fx * dx2dx1 * (0); J[2 * j + 0][10] = fx * dx2dx1 * (0); J[2 * j + 0][11] = fx * dx2dx1 * (0); J[2 * j + 0][12] = fx * dx2dx1 * (-x1 * x); J[2 * j + 0][13] = fx * dx2dx1 * (-x1 * y); J[2 * j + 0][14] = fx * dx2dx1 * (x1); e[2 * j + 0] = x3 - pImagePoints[idx].x; J[2 * j + 1][0] = 0; J[2 * j + 1][1] = y2; J[2 * j + 1][2] = 0; J[2 * j + 1][3] = 1; J[2 * j + 1][4] = dy3dy2 * y1 * square2; J[2 * j + 1][5] = dy3dy2 * y1 * square4; J[2 * j + 1][6] = fy * dy2dy1 * (0); J[2 * j + 1][7] = fy * dy2dy1 * (0); J[2 * j + 1][8] = fy * dy2dy1 * (0); J[2 * j + 1][9] = fy * dy2dy1 * (x); J[2 * j + 1][10] = fy * dy2dy1 * (y); J[2 * j + 1][11] = fy * dy2dy1 * (1); J[2 * j + 1][12] = fy * dy2dy1 * (-y1 * x); J[2 * j + 1][13] = fy * dy2dy1 * (-y1 * y); J[2 * j + 1][14] = fy * dy2dy1 * (y1); e[2 * j + 1] = y3 - pImagePoints[idx].y; } cvSolve( &_pt1, &_pt2, &_delt, CV_SVD ); memcpy(filterDeltTemp,filterDelt,sizeof(filterDelt)); memcpy(paramTemp,param,sizeof(param)); for(j = 0;j < 15;j++) { filterDelt[j] = 0.8f * filterDelt[j] + 0.2f * delt[j]; } for(j = 0;j < 15;j++) { param[j] = param[j] - 0.2f * filterDelt[j]; } gErr = getErrCameraParams(pObjectPoints,pImagePoints,param,(width * hight)); if(gErr > lastErr) { memcpy(filterDelt,filterDeltTemp,sizeof(filterDelt)); memcpy(param,paramTemp,sizeof(param)); //break; } else { lastErr = gErr; } iner++; if(iner > 5000) { n = imageCnt; break; } if(gErr < 0.1f) { n = imageCnt; break; } } } k[0] = k1 * 1.2f; k[1] = k2 * 1.2f; printf("best = %f,%f,%f,%f,%f,%f\n",fx,fy,cx,cy,k1,k2); printf("ERR = %f\n",gErr); if(gErr > 0.1f) { printf("calib image failed!\n\n\n\n"); } A->pdata[0] = (float)fx; A->pdata[1] = 0; A->pdata[2] = (float)cx; A->pdata[3] = 0; A->pdata[4] = (float)fy; A->pdata[5] = (float)cy; A->pdata[6] = 0; A->pdata[7] = 0; A->pdata[8] = 1; }
你好! 这是你第一次使用 Markdown编辑器 所展示的欢迎页。如果你想学习如何使用Markdown编辑器, 可以仔细阅读这篇文章,了解一下Markdown的基本语法知识。
我们对Markdown编辑器进行了一些功能拓展与语法支持,除了标准的Markdown编辑器功能,我们增加了如下几点新功能,帮助你用它写博客:
撤销:Ctrl/Command + Z
重做:Ctrl/Command + Y
加粗:Ctrl/Command + B
斜体:Ctrl/Command + I
标题:Ctrl/Command + Shift + H
无序列表:Ctrl/Command + Shift + U
有序列表:Ctrl/Command + Shift + O
检查列表:Ctrl/Command + Shift + C
插入代码:Ctrl/Command + Shift + K
插入链接:Ctrl/Command + Shift + L
插入图片:Ctrl/Command + Shift + G
直接输入1次#,并按下space后,将生成1级标题。
输入2次#,并按下space后,将生成2级标题。
以此类推,我们支持6级标题。有助于使用TOC
语法后生成一个完美的目录。
强调文本 强调文本
加粗文本 加粗文本
标记文本
删除文本
引用文本
H2O is是液体。
210 运算结果是 1024.
链接: link.
图片:
带尺寸的图片:
居中的图片:
居中并且带尺寸的图片:
当然,我们为了让用户更加便捷,我们增加了图片拖拽功能。
去博客设置页面,选择一款你喜欢的代码片高亮样式,下面展示同样高亮的 代码片
.
// An highlighted block
var foo = 'bar';
一个简单的表格是这么创建的:
项目 | Value |
---|---|
电脑 | $1600 |
手机 | $12 |
导管 | $1 |
使用:---------:
居中
使用:----------
居左
使用----------:
居右
第一列 | 第二列 | 第三列 |
---|---|---|
第一列文本居中 | 第二列文本居右 | 第三列文本居左 |
SmartyPants将ASCII标点字符转换为“智能”印刷标点HTML实体。例如:
TYPE | ASCII | HTML |
---|---|---|
Single backticks | 'Isn't this fun?' | ‘Isn’t this fun?’ |
Quotes | "Isn't this fun?" | “Isn’t this fun?” |
Dashes | -- is en-dash, --- is em-dash | – is en-dash, — is em-dash |
一个具有注脚的文本。2
Markdown将文本转换为 HTML。
您可以使用渲染LaTeX数学表达式 KaTeX:
Gamma公式展示 Γ ( n ) = ( n − 1 ) ! ∀ n ∈ N \Gamma(n) = (n-1)!\quad\forall n\in\mathbb N Γ(n)=(n−1)!∀n∈N 是通过欧拉积分
Γ ( z ) = ∫ 0 ∞ t z − 1 e − t d t   . \Gamma(z) = \int_0^\infty t^{z-1}e^{-t}dt\,. Γ(z)=∫0∞tz−1e−tdt.
你可以找到更多关于的信息 LaTeX 数学表达式here.
可以使用UML图表进行渲染。 Mermaid. 例如下面产生的一个序列图::
这将产生一个流程图。:
我们依旧会支持flowchart的流程图:
如果你想尝试使用此编辑器, 你可以在此篇文章任意编辑。当你完成了一篇文章的写作, 在上方工具栏找到 文章导出 ,生成一个.md文件或者.html文件进行本地保存。
如果你想加载一篇你写过的.md文件,在上方工具栏可以选择导入功能进行对应扩展名的文件导入,
继续你的创作。
注脚的解释 ↩︎
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