std::deque<Vector> FlowMath::computeStreamlineEuler(const Flow& flow,
const Vector& r0,
const float length,
const float stepwidth,
int* const startIndex,
const tgt::vec2& thresholds)
{
// N: number of partitions
//
const float h = fabsf(stepwidth);
float fn = ceilf(fabsf(length) / h);
const unsigned int N = (length != 0.0f) ? static_cast<unsigned int>(fn) : 0;
Vector r(r0), r_(r0);
std::deque<Vector> points;
points.push_back(r0);
int indexR0 = 0;
bool lookupPos = true; // integrate along the streamline in positive direction?
bool lookupNeg = true; // integrate along the streamline in negative direction?
bool useThresholds = (thresholds != tgt::vec2::zero);
for (unsigned int i = 0; ((N == 0) || (i < N)) ; ++i) {
if (lookupPos == true) {
const Vector& v = flow.lookupFlow(r);
if (useThresholds == true) {
float magnitude = tgt::length(v);
if ((magnitude < thresholds.x) || (magnitude > thresholds.y)) {
lookupPos = false;
break;
}
}
if (v != Vector::zero) {
r += normalize(v) * h;
lookupPos = flow.isInsideBoundings(r);
if (r == points.back()) // in case of no progress on streamline in this direction...
lookupPos = false;
else if (lookupPos == true)
points.push_back(r);
} else
lookupPos = false;
}
if (lookupNeg == true) {
const Vector& v = flow.lookupFlow(r_);
if (useThresholds == true) {
float magnitude = tgt::length(v);
if ((magnitude < thresholds.x) || (magnitude > thresholds.y)) {
lookupNeg = false;
break;
}
}
if (v != Vector::zero) {
r_ -= normalize(v) * h;
lookupNeg = flow.isInsideBoundings(r_);
if (r_ == points.front()) // in case of no progress on streamline in this direction...
lookupNeg = false;
else if (lookupNeg == true) {
points.push_front(r_);
++indexR0;
}
} else
lookupNeg = false;
}
if ((lookupPos == false) && (lookupNeg == false))
break;
} // for ( ; ; ++i)
if (startIndex != 0)
*startIndex = indexR0;
return points;
}
std::deque<Vector> FlowMath::computeStreamlineRungeKutta(const Flow& flow,
const Vector& r0,
const float length,
const float stepwidth,
int* const startIndex,
const tgt::vec2& thresholds)
{
// N: number of partitions
//
const float h = fabsf(stepwidth);
float fn = ceilf(fabsf(length) / h);
const unsigned int N = (length != 0.0f) ? static_cast<unsigned int>(fn) : 0;
Vector r(r0), r_(r0);
Vector k1(0.0f), k2(0.0f), k3(0.0f), k4(0.0f);
Vector k1_(0.0f), k2_(0.0f), k3_(0.0f), k4_(0.0f);
std::deque<Vector> points; // points on streamline in positive direction
points.push_back(r0); // avoid that one of the deque is empty
int indexR0 = 0; // position of r0 within deque
bool lookupPos = true; // integrate along the streamline in positive direction?
bool lookupNeg = true; // integrate along the streamline in negative direction?
bool useThresholds = (thresholds != tgt::vec2::zero);
for (unsigned int i = 0; ((N == 0) || (i < N)); ++i) {
if (lookupPos == true) {
const Vector& v = flow.lookupFlow(r);
if (useThresholds == true) {
float magnitude = tgt::length(v);
if ((magnitude < thresholds.x) || (magnitude > thresholds.y)) {
lookupPos = false;
break;
}
}
if (v != Vector::zero) {
k1 = normalize(v) * h;
k2 = normalize( flow.lookupFlow(r + (k1 / 2.0f)) ) * h;
k3 = normalize( flow.lookupFlow(r + (k2 / 2.0f)) ) * h;
k4 = normalize( flow.lookupFlow(r + k3) ) * h;
r += ((k1 / 6.0f) + (k2 / 3.0f) + (k3 / 3.0f) + (k4 / 6.0f));
lookupPos = flow.isInsideBoundings(r);
if (r == points.back()) // in case of no progress on streamline in this direction...
lookupPos = false;
else if (lookupPos == true)
points.push_back(r);
} else
lookupPos = false;
}
if (lookupNeg == true) {
const Vector& v = flow.lookupFlow(r_);
if (useThresholds == true) {
float magnitude = tgt::length(v);
if ((magnitude < thresholds.x) || (magnitude > thresholds.y)) {
lookupNeg = false;
break;
}
}
if (v != Vector::zero) {
k1_ = normalize(v) * h;
k2_ = normalize( flow.lookupFlow(r_ - (k1_ / 2.0f)) ) * h;
k3_ = normalize( flow.lookupFlow(r_ - (k2_ / 2.0f)) ) * h;
k4_ = normalize( flow.lookupFlow(r_ - k3_) ) * h;
r_ -= ((k1_ / 6.0f) + (k2_ / 3.0f) + (k3_ / 3.0f) + (k4_ / 6.0f));
lookupNeg = flow.isInsideBoundings(r_);
if (r_ == points.front()) // in case of no progress on streamline in this direction...
lookupNeg = false;
else if (lookupNeg == true) {
points.push_front(r_);
++indexR0;
}
} else
lookupNeg = false;
}
if ((lookupPos == false) && (lookupNeg == false))
break;
} // for (; ; ++i)
if (startIndex != 0)
*startIndex = indexR0;
return points;
}