Real DistancePointEllipse (const Real e[2], const Real y[2], Real x[2])
{
// Determine reflections for y to the first quadrant.
bool reflect[2];
int i, j;
for (i = 0; i < 2; ++i)
{
reflect[i] = (y[i] < (Real)0);
}
// Determine the axis order for decreasing extents.
int permute[2];
if (e[0] < e[1])
{
permute[0] = 1;
permute[1] = 0;
}
else
{
permute[0] = 0;
permute[1] = 1;
}
int invpermute[2];
for (i = 0; i < 2; ++i)
{
invpermute[permute[i]] = i;
}
Real locE[2], locY[2];
for (i = 0; i < 2; ++i)
{
j = permute[i];
locE[i] = e[j];
locY[i] = y[j];
if (reflect[j])
{
locY[i] = -locY[i];
}
}
Real locX[2];
Real distance = DistancePointEllipseSpecial(locE, locY, locX);
// Restore the axis order and reflections.
for (i = 0; i < 2; ++i)
{
j = invpermute[i];
if (reflect[i])
{
locX[j] = -locX[j];
}
x[i] = locX[j];
}
return distance;
}
/* from www.geometrictools.com (by David Eberly) */
double
Ellipse_Point_Distance(double dU, double dV, /* test point (u,v) */
double dA, double dB, /* ellipse (x/a)^2 + (y/b)^2 = 1 */
double *rdX, double *rdY)
{
double dEpsilon = 1e-5; /* zero tolerance for Newton's method */
int iMax = 100; /* maximum iterations in Newton's method */
//int riIFinal;
double tmp_rdX, tmp_rdY;
if (rdX == NULL) {
rdX = &tmp_rdX;
}
if (rdY == NULL) {
rdY = &tmp_rdY;
}
// special case of circle
if (fabs(dA-dB) < dEpsilon) {
double dLength = sqrt(dU*dU+dV*dV);
*rdX = dA / dLength * dU;
*rdY = dA / dLength * dV;
return fabs(dLength - dA);
}
// reflect U = -U if necessary, clamp to zero if necessary
BOOL bXReflect;
if (dU > dEpsilon) {
bXReflect = FALSE;
} else if (dU < -dEpsilon) {
bXReflect = TRUE;
dU = -dU;
} else {
bXReflect = FALSE;
dU = 0.0;
}
// reflect V = -V if necessary, clamp to zero if necessary
BOOL bYReflect;
if (dV > dEpsilon) {
bYReflect = FALSE;
} else if (dV < -dEpsilon) {
bYReflect = TRUE;
dV = -dV;
} else {
bYReflect = FALSE;
dV = 0.0;
}
// transpose if necessary
double dSave;
BOOL bTranspose;
if (dA >= dB) {
bTranspose = FALSE;
} else {
bTranspose = TRUE;
dSave = dA;
dA = dB;
dB = dSave;
dSave = dU;
dU = dV;
dV = dSave;
}
double dDistance;
if (dU != 0.0) {
if (dV != 0.0) {
dDistance = DistancePointEllipseSpecial(dU,dV,dA,dB,dEpsilon,iMax,
/*riIFinal,*/rdX,rdY);
} else {
double dBSqr = dB*dB;
if (dU < dA - dBSqr/dA) {
double dASqr = dA*dA;
*rdX = dASqr*dU/(dASqr-dBSqr);
double dXDivA = *rdX/dA;
*rdY = dB*sqrt(fabs(1.0-dXDivA*dXDivA));
double dXDelta = *rdX - dU;
dDistance = sqrt(dXDelta*dXDelta+(*rdY) * (*rdY));
//riIFinal = 0;
} else {
dDistance = fabs(dU - dA);
*rdX = dA;
*rdY = 0.0;
//riIFinal = 0;
}
}
} else {
dDistance = fabs(dV - dB);
*rdX = 0.0;
*rdY = dB;
//riIFinal = 0;
}
if (bTranspose) {
dSave = *rdX;
*rdX = *rdY;
*rdY = dSave;
}
if (bYReflect) {
*rdY = -(*rdY);
}
if (bXReflect) {
*rdX = -(*rdX);
}
return dDistance;
}
