/******************* TO DO 5 *********************
* BlendImages:
* INPUT:
* ipv: list of input images and their relative positions in the mosaic
* blendWidth: width of the blending function
* OUTPUT:
* create & return final mosaic by blending all images
* and correcting for any vertical drift
*/
CByteImage BlendImages(CImagePositionV& ipv, float blendWidth)
{
// Assume all the images are of the same shape (for now)
CByteImage& img0 = ipv[0].img;
CShape sh = img0.Shape();
int width = sh.width;
int height = sh.height;
int nBands = sh.nBands;
int dim[2] = {width, height};
// Compute the bounding box for the mosaic
int n = ipv.size();
float min_x = 0, min_y = 0;
float max_x = 0, max_y = 0;
int i;
float dy = 0;
for (i = 0; i < n; i++)
{
CTransform3x3 &pos = ipv[i].position;
CVector3 corners[4];//表示图片的4个角的坐标，分别为左下，右下，左上，右上
corners[0][0] = 0.0;
corners[0][1] = 0.0;
corners[0][2] = 1.0;
corners[1][0] = width - 1;
corners[1][1] = 0.0;
corners[1][2] = 1.0;
corners[2][0] = 0.0;
corners[2][1] = height - 1;
corners[2][2] = 1.0;
corners[3][0] = width - 1;
corners[3][1] = height - 1;
corners[3][2] = 1.0;
corners[0] = pos * corners[0];
corners[1] = pos * corners[1];
corners[2] = pos * corners[2];
corners[3] = pos * corners[3];
corners[0][0] /= corners[0][2];
corners[0][1] /= corners[0][2];
corners[1][0] /= corners[0][2];
corners[1][1] /= corners[0][2];
corners[2][0] /= corners[0][2];
corners[2][1] /= corners[0][2];
corners[3][0] /= corners[0][2];
corners[3][1] /= corners[0][2];
// *** BEGIN TODO #1 ***
// add some code here to update min_x, ..., max_y
//Use c0 and c3 to get the range of x and y.
int iminx, iminy, imaxx, imaxy;
ImageBoundingBox(img0, pos, iminx, iminy, imaxx, imaxy);
if (i == 0)
{
dy += imaxy;
}
if (i == n - 1)
{
dy -= imaxy;
}
/*if (min_x > corners[0][0])
{
min_x = corners[0][0];
}
if (max_x < corners[3][0])
{
max_x = corners[3][0];
}
if (min_y > corners[0][1])
{
min_y = corners[0][1];
}
if (max_y < corners[3][1])
{
max_y = corners[3][1];
}
*/
min_x = min(min_x, float(iminx));
min_y = min(min_y, float(iminy));
max_x = max(max_x, float(imaxx));
max_y = max(max_y, float(imaxy));
// *** END TODO #1 ***
}
// Create a floating point accumulation image
CShape mShape((int)(ceil(max_x) - floor(min_x)),
(int)(ceil(max_y) - floor(min_y)), nBands);
CFloatImage accumulator(mShape);
accumulator.ClearPixels();
double x_init, x_final;
double y_init, y_final;
// Add in all of the images
for (i = 0; i < n; i++) {
CTransform3x3 &M = ipv[i].position;
CTransform3x3 M_t = CTransform3x3::Translation(-min_x, -min_y) * M;
CByteImage& img = ipv[i].img;
// Perform the accumulation
AccumulateBlend(img, accumulator, M_t, blendWidth);
if (i == 0) {
CVector3 p;
p[0] = 0.5 * width;
p[1] = 0.0;
p[2] = 1.0;
p = M_t * p;
x_init = p[0];
y_init = p[1];
} else if (i == n - 1) {
CVector3 p;
p[0] = 0.5 * width;
p[1] = 0.0;
p[2] = 1.0;
p = M_t * p;
x_final = p[0];
y_final = p[1];
}
}
// Normalize the results
CByteImage compImage(mShape);
NormalizeBlend(accumulator, compImage);
bool debug_comp = false;
if (debug_comp)
WriteFile(compImage, "tmp_comp.tga");
// Allocate the final image shape
CShape cShape(mShape.width - width, height, nBands);
CByteImage croppedImage(cShape);
// Compute the affine deformation
CTransform3x3 A = CTransform3x3();
// *** BEGIN TODO #2 ***
// fill in the right entries in A to trim the left edge and
// to take out the vertical drift
A[0][2] = width /2;
A[1][0] = dy / (mShape.width - width);
// *** END TODO #2 ***
// Warp and crop the composite
WarpGlobal(compImage, croppedImage, A, eWarpInterpLinear);
// WarpGlobal(compImage, croppedImage, A, eWarpInterpNearest); //similar as linear
// WarpGlobal(compImage, croppedImage, A, eWarpInterpCubic); //all pixels are black
return croppedImage;
}
void
BeamContact2Dp::ComputeB(void)
// this function computes the finite element equation vectors Bn and Bs
{
double Ka1n;
double Kb1n;
double Ka1g;
double Kb1g;
Vector a1(BC2D_NUM_DIM);
Vector b1(BC2D_NUM_DIM);
// initialize Bn and Bs
mBn.Zero();
mBs.Zero();
// get tangent vectors
a1 = Geta1();
b1 = Getb1();
// compute terms for vector Bn
Ka1n = (mEyeS*a1)^mNormal;
Kb1n = (mEyeS*b1)^mNormal;
mBn(0) = -mShape(0)*mNormal(0);
mBn(1) = -mShape(0)*mNormal(1);
mBn(2) = -mShape(1)*mLength*Ka1n;
mBn(3) = -mShape(2)*mNormal(0);
mBn(4) = -mShape(2)*mNormal(1);
mBn(5) = -mShape(3)*mLength*Kb1n;
mBn(6) = mNormal(0);
mBn(7) = mNormal(1);
// compute terms for vector Bs
Ka1g = (mEyeS*a1)^mg_xi;
Kb1g = (mEyeS*b1)^mg_xi;
mBs(0) = -mg_xi(0)*(mShape(0) + mRadius*mDshape(0));
mBs(1) = -mg_xi(1)*(mShape(0) + mRadius*mDshape(0));
mBs(2) = -Ka1g*mLength*(mShape(1) + mRadius*mDshape(1));
mBs(3) = -mg_xi(0)*(mShape(2) + mRadius*mDshape(2));
mBs(4) = -mg_xi(1)*(mShape(2) + mRadius*mDshape(2));
mBs(5) = -Kb1g*mLength*(mShape(3) + mRadius*mDshape(3));
mBs(6) = mg_xi(0);
mBs(7) = mg_xi(1);
return;
}
double
BeamContact2Dp::Project(double xi)
// this function computes the centerline projection for the current step
{
double xi_p;
double H1;
double H2;
double H3;
double H4;
double dH1;
double dH2;
double dH3;
double dH4;
double R;
double DR;
double dxi;
Vector a1(BC2D_NUM_DIM);
Vector b1(BC2D_NUM_DIM);
Vector x_c_p(BC2D_NUM_DIM);
Vector t_c(BC2D_NUM_DIM);
Vector ddx_c(BC2D_NUM_DIM);
// initialize to previous projection location
xi_p = xi;
// update end point tangents
UpdateEndFrames();
// set tangent vectors
a1 = Geta1();
b1 = Getb1();
// Hermitian basis functions and first derivatives
H1 = 1.0 - 3.0*xi_p*xi_p + 2.0*xi_p*xi_p*xi_p;
H2 = xi_p - 2.0*xi_p*xi_p + xi_p*xi_p*xi_p;
H3 = 3.0*xi_p*xi_p - 2*xi_p*xi_p*xi_p;
H4 = -xi_p*xi_p + xi_p*xi_p*xi_p;
dH1 = -6.0*xi_p + 6.0*xi_p*xi_p;
dH2 = 1.0 - 4.0*xi_p + 3.0*xi_p*xi_p;
dH3 = 6.0*xi_p - 6.0*xi_p*xi_p;
dH4 = -2.0*xi_p + 3.0*xi_p*xi_p;
// compute current projection coordinate and tangent
x_c_p = mDcrd_a*H1 + a1*mLength*H2 + mDcrd_b*H3 + b1*mLength*H4;
t_c = mDcrd_a*dH1 + a1*mLength*dH2 + mDcrd_b*dH3 + b1*mLength*dH4;
// compute initial value of residual
R = (mDcrd_s - x_c_p)^t_c;
// iterate to determine new value of xi
int Gapcount = 0;
while (fabs(R/mLength) > 1.0e-10 && Gapcount < 50) {
// compute current curvature vector
ddx_c = Get_dxc_xixi(xi_p);
// increment projection location
DR = ((mDcrd_s - x_c_p)^ddx_c) - (t_c^t_c);
dxi = -R/DR;
xi_p = xi_p + dxi;
// Hermitian basis functions and first derivatives
H1 = 1.0 - 3.0*xi_p*xi_p + 2.0*xi_p*xi_p*xi_p;
H2 = xi_p - 2.0*xi_p*xi_p + xi_p*xi_p*xi_p;
H3 = 3.0*xi_p*xi_p - 2*xi_p*xi_p*xi_p;
H4 = -xi_p*xi_p + xi_p*xi_p*xi_p;
dH1 = -6.0*xi_p + 6.0*xi_p*xi_p;
dH2 = 1.0 - 4.0*xi_p + 3.0*xi_p*xi_p;
dH3 = 6.0*xi_p - 6.0*xi_p*xi_p;
dH4 = -2.0*xi_p + 3.0*xi_p*xi_p;
// update projection coordinate and tangent
x_c_p = mDcrd_a*H1 + a1*mLength*H2 + mDcrd_b*H3 + b1*mLength*H4;
t_c = mDcrd_a*dH1 + a1*mLength*dH2 + mDcrd_b*dH3 + b1*mLength*dH4;
// compute residual
R = (mDcrd_s - x_c_p)^t_c;
Gapcount += 1;
}
// update normal vector for current projection
mNormal = (mDcrd_s - x_c_p)/((mDcrd_s - x_c_p).Norm());
// update Hermitian basis functions and derivatives
mShape(0) = H1;
mShape(1) = H2;
mShape(2) = H3;
mShape(3) = H4;
mDshape(0) = dH1;
mDshape(1) = dH2;
mDshape(2) = dH3;
mDshape(3) = dH4;
return xi_p;
}
int
BeamContact2Dp::update(void)
// this function updates variables for an incremental step n to n+1
{
double tensileStrength;
Vector a1(BC2D_NUM_DIM);
Vector b1(BC2D_NUM_DIM);
Vector a1_n(BC2D_NUM_DIM);
Vector b1_n(BC2D_NUM_DIM);
Vector disp_a(3);
Vector disp_b(3);
Vector disp_L(BC2D_NUM_DIM);
double rot_a;
double rot_b;
Vector x_c(BC2D_NUM_DIM);
// update slave node coordinates
mDcrd_s = mIcrd_s + theNodes[2]->getTrialDisp();
// update nodal coordinates
disp_a = theNodes[0]->getTrialDisp();
disp_b = theNodes[1]->getTrialDisp();
for (int i = 0; i < 2; i++) {
mDcrd_a(i) = mIcrd_a(i) + disp_a(i);
mDcrd_b(i) = mIcrd_b(i) + disp_b(i);
}
// compute incremental rotation from step n to step n+1
rot_a = disp_a(2) - mDisp_a_n(2);
rot_b = disp_b(2) - mDisp_b_n(2);
// get tangent vectors from last converged step
a1_n = Geta1();
b1_n = Getb1();
// linear update of tangent vectors
a1 = a1_n + rot_a*mEyeS*a1_n;
b1 = b1_n + rot_b*mEyeS*b1_n;
// update centerline projection coordinate
x_c = mDcrd_a*mShape(0) + a1*mLength*mShape(1) + mDcrd_b*mShape(2) + b1*mLength*mShape(3);
// update penetration function
mGap = (mNormal^(mDcrd_s - x_c)) - mRadius;
if (mGap < 0.0 && in_bounds) {
inContact = true;
} else {
mGap = 0.0;
inContact = false;
}
// update normal contact force
if (was_inContact) {
mLambda = mPenalty*mGap;
} else {
mLambda = 0.0;
}
// get tensile strength from contact material
tensileStrength = theMaterial->getTensileStrength();
// determine trial strain vector based on contact state
if (inContact) {
Vector strain(3);
double slip;
Vector c1n1(2);
Vector c2n1(2);
// tangent at the centerline projection in step n+1
c1n1 = mDshape(0)*mDcrd_a + mDshape(1)*mLength*ma_1 + mDshape(2)*mDcrd_b + mDshape(3)*mLength*mb_1;
// update vector c2 for step n+1
c2n1 = (mDcrd_s - x_c)/((mDcrd_s - x_c).Norm());
// update vector c2 for step n+1
c2n1(0) = -c1n1(1);
c2n1(1) = c1n1(0);
// compute the slip
slip = mg_xi^(mDcrd_s - x_c - mrho*c2n1);
// set the strain vector
strain(0) = mGap;
strain(1) = slip;
strain(2) = -mLambda;
theMaterial->setTrialStrain(strain);
} else {
Vector strain(3);
// set the strain vector
strain(0) = mGap;
strain(1) = 0.0;
strain(2) = -mLambda;
theMaterial->setTrialStrain(strain);
}
return 0;
}
void
BeamContact2Dp::setDomain(Domain *theDomain)
{
Vector x_c(BC2D_NUM_DIM);
mEye1.Zero();
mEye1(0,0) = 1.0;
mEye1(1,1) = 1.0;
mEyeS.Zero();
mEyeS(0,1) = -1.0;
mEyeS(1,0) = 1.0;
theNodes[0] = theDomain->getNode(mExternalNodes(0));
theNodes[1] = theDomain->getNode(mExternalNodes(1));
theNodes[2] = theDomain->getNode(mExternalNodes(2));
for (int i = 0; i < 3; i++) {
if (theNodes[i] == 0)
return; // don't go any further - otherwise segmentation fault
}
// initialize coordinate vectors
mIcrd_a = theNodes[0]->getCrds();
mIcrd_b = theNodes[1]->getCrds();
mIcrd_s = theNodes[2]->getCrds();
mDcrd_a = mIcrd_a;
mDcrd_b = mIcrd_b;
mDcrd_s = mIcrd_s;
mDisp_a_n.Zero();
mDisp_b_n.Zero();
// length of beam element
mLength = (mDcrd_b - mDcrd_a).Norm();
// initialize tangent vectors at beam nodes
ma_1 = (mDcrd_b - mDcrd_a)/mLength;
mb_1 = ma_1;
// perform projection of slave node to beam centerline
mXi = ((mDcrd_b - mDcrd_s)^(mDcrd_b - mDcrd_a))/mLength; // initial assumption
mXi = Project(mXi); // actual location
// update contact state based on projection
in_bounds = ((mXi > 0.000) && (mXi < 1.000));
inContact = (was_inContact && in_bounds);
// centerline projection coordinate
x_c = mDcrd_a*mShape(0) + ma_1*mLength*mShape(1) + mDcrd_b*mShape(2) + mb_1*mLength*mShape(3);
// update surface tangent vector, g_xi
UpdateBase(mXi);
// adjust cohesion force
theMaterial->ScaleCohesion(mLength);
theMaterial->ScaleTensileStrength(mLength);
// compute vectors Bn and Bs
ComputeB();
// call the base class method
this->DomainComponent::setDomain(theDomain);
}
/******************* TO DO 5 *********************
* BlendImages:
* INPUT:
* ipv: list of input images and their relative positions in the mosaic
* blendWidth: width of the blending function
* OUTPUT:
* create & return final mosaic by blending all images
* and correcting for any vertical drift
*/
CByteImage BlendImages(CImagePositionV& ipv, float blendWidth)
{
// Assume all the images are of the same shape (for now)
CByteImage& img0 = ipv[0].img;
CShape sh = img0.Shape();
int width = sh.width;
int height = sh.height;
int nBands = sh.nBands;
// int dim[2] = {width, height};
int n = ipv.size();
if (n == 0) return CByteImage(0,0,1);
bool is360 = false;
// Hack to detect if this is a 360 panorama
if (ipv[0].imgName == ipv[n-1].imgName)
is360 = true;
// Compute the bounding box for the mosaic
float min_x = FLT_MAX, min_y = FLT_MAX;
float max_x = 0, max_y = 0;
int i;
for (i = 0; i < n; i++)
{
CTransform3x3 &T = ipv[i].position;
// BEGIN TODO
// add some code here to update min_x, ..., max_y
printf("TODO: %s:%d\n", __FILE__, __LINE__);
// END TODO
}
// Create a floating point accumulation image
CShape mShape((int)(ceil(max_x) - floor(min_x)),
(int)(ceil(max_y) - floor(min_y)), nBands + 1);
CFloatImage accumulator(mShape);
accumulator.ClearPixels();
double x_init, x_final;
double y_init, y_final;
// Add in all of the images
for (i = 0; i < n; i++) {
// Compute the sub-image involved
CTransform3x3 &M = ipv[i].position;
CTransform3x3 M_t = CTransform3x3::Translation(-min_x, -min_y) * M;
CByteImage& img = ipv[i].img;
// Perform the accumulation
AccumulateBlend(img, accumulator, M_t, blendWidth);
if (i == 0) {
CVector3 p;
p[0] = 0.5 * width;
p[1] = 0.0;
p[2] = 1.0;
p = M_t * p;
x_init = p[0];
y_init = p[1];
} else if (i == n - 1) {
CVector3 p;
p[0] = 0.5 * width;
p[1] = 0.0;
p[2] = 1.0;
p = M_t * p;
x_final = p[0];
y_final = p[1];
}
}
// Normalize the results
mShape = CShape((int)(ceil(max_x) - floor(min_x)),
(int)(ceil(max_y) - floor(min_y)), nBands);
CByteImage compImage(mShape);
NormalizeBlend(accumulator, compImage);
bool debug_comp = false;
if (debug_comp)
WriteFile(compImage, "tmp_comp.tga");
// Allocate the final image shape
int outputWidth = 0;
if (is360) {
outputWidth = mShape.width - width;
} else {
outputWidth = mShape.width;
}
CShape cShape(outputWidth, mShape.height, nBands);
CByteImage croppedImage(cShape);
// Compute the affine transformation
CTransform3x3 A = CTransform3x3(); // identify transform to initialize
// BEGIN TODO
// fill in appropriate entries in A to trim the left edge and
// to take out the vertical drift if this is a 360 panorama
// (i.e. is360 is true)
printf("TODO: %s:%d\n", __FILE__, __LINE__);
// END TODO
// Warp and crop the composite
WarpGlobal(compImage, croppedImage, A, eWarpInterpLinear);
return croppedImage;
}