Files
OpenSpace/modules/autonavigation/pathcurve.cpp
2021-06-21 13:05:51 +02:00

236 lines
8.9 KiB
C++

/*****************************************************************************************
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#include <modules/autonavigation/pathcurve.h>
#include <modules/autonavigation/helperfunctions.h>
#include <openspace/query/query.h>
#include <openspace/scene/scenegraphnode.h>
#include <ghoul/logging/logmanager.h>
#include <glm/gtx/projection.hpp>
#include <algorithm>
#include <vector>
namespace {
constexpr const char* _loggerCat = "PathCurve";
constexpr const int NrSamplesPerSegment = 100;
} // namespace
namespace openspace::pathnavigation {
PathCurve::~PathCurve() {}
const double PathCurve::length() const {
return _totalLength;
}
glm::dvec3 PathCurve::positionAt(double relativeDistance) {
const double u = curveParameter(relativeDistance * _totalLength);
return interpolate(u);
}
// Compute the curve parameter from an arc length value, using a combination of
// Newton's method and bisection. Source:
// https://www.geometrictools.com/Documentation/MovingAlongCurveSpecifiedSpeed.pdf
// Input s is a length value, in the range [0, _totalLength]
// Returns curve parameter in range [0, 1]
double PathCurve::curveParameter(double s) {
if (s <= 0.0) return 0.0;
if (s >= _totalLength) return 1.0;
unsigned int segmentIndex = 1;
while (s > _lengthSums[segmentIndex]) {
segmentIndex++;
}
const int startIndex = (segmentIndex - 1) * NrSamplesPerSegment;
const int endIndex = segmentIndex * NrSamplesPerSegment + 1;
const double segmentS = s - _lengthSums[segmentIndex - 1];
const double uMin = _curveParameterSteps[segmentIndex - 1];
const double uMax = _curveParameterSteps[segmentIndex];
// Use samples to find an initial guess for Newton's method
// Find first sample with s larger than input s
auto sampleIterator = std::upper_bound(
_parameterSamples.begin() + startIndex,
_parameterSamples.begin() + endIndex,
ParameterPair{ 0.0 , s }, // 0.0 is a dummy value for u
[](ParameterPair lhs, ParameterPair rhs) {
return lhs.s < rhs.s;
}
);
const ParameterPair& sample = *sampleIterator;
const ParameterPair& prevSample = *(sampleIterator - 1);
const double uPrev = prevSample.u;
const double sPrev = prevSample.s;
const double slope = (sample.u - uPrev) / (sample.s - sPrev);
double u = uPrev + slope * (s - sPrev);
constexpr const int maxIterations = 50;
// Initialize root bounding limits for bisection
double lower = uMin;
double upper = uMax;
for (int i = 0; i < maxIterations; ++i) {
double F = arcLength(uMin, u) - segmentS;
// The error we tolerate, in meters. Note that distances are very large
constexpr const double tolerance = 0.005;
if (std::abs(F) <= tolerance) {
return u;
}
// Generate a candidate for Newton's method
double dfdu = approximatedDerivative(u); // > 0
double uCandidate = u - F / dfdu;
// Update root-bounding interval and test candidate
if (F > 0) { // => candidate < u <= upper
upper = u;
u = (uCandidate <= lower) ? (upper + lower) / 2.0 : uCandidate;
}
else { // F < 0 => lower <= u < candidate
lower = u;
u = (uCandidate >= upper) ? (upper + lower) / 2.0 : uCandidate;
}
}
// No root was found based on the number of iterations and tolerance. However, it is
// safe to report the last computed u value, since it is within the segment interval
return u;
}
std::vector<glm::dvec3> PathCurve::points() {
return _points;
}
void PathCurve::initializeParameterData() {
_nSegments = static_cast<int>(_points.size() - 3);
ghoul_assert(_nSegments > 0, "Cannot have a curve with zero segments!");
_curveParameterSteps.clear();
_lengthSums.clear();
_parameterSamples.clear();
// Evenly space out parameter intervals
_curveParameterSteps.reserve(_nSegments + 1);
const double dt = 1.0 / _nSegments;
_curveParameterSteps.push_back(0.0);
for (unsigned int i = 1; i < _nSegments; i++) {
_curveParameterSteps.push_back(dt * i);
}
_curveParameterSteps.push_back(1.0);
// Arc lengths
_lengthSums.reserve(_nSegments + 1);
_lengthSums.push_back(0.0);
for (unsigned int i = 1; i <= _nSegments; i++) {
double u = _curveParameterSteps[i];
double uPrev = _curveParameterSteps[i - 1];
double length = arcLength(uPrev, u);
_lengthSums.push_back(_lengthSums[i - 1] + length);
}
_totalLength = _lengthSums.back();
// Compute a map of arc lengths s and curve parameters u, for reparameterization
_parameterSamples.reserve(NrSamplesPerSegment * _nSegments + 1);
const double uStep = 1.0 / (_nSegments * NrSamplesPerSegment);
for (unsigned int i = 0; i < _nSegments; i++) {
double uStart = _curveParameterSteps[i];
double sStart = _lengthSums[i];
for (int j = 0; j < NrSamplesPerSegment; ++j) {
double u = uStart + j * uStep;
double s = sStart + arcLength(uStart, u);
_parameterSamples.push_back({ u, s });
}
}
_parameterSamples.push_back({ 1.0, _totalLength });
}
double PathCurve::approximatedDerivative(double u, double h) {
if (u <= h) {
return (1.0 / h) * glm::length(interpolate(0.0 + h) - interpolate(0.0));
}
if (u >= 1.0 - h) {
return (1.0 / h) * glm::length(interpolate(1.0) - interpolate(1.0 - h));
}
return (0.5 / h) * glm::length(interpolate(u + h) - interpolate(u - h));
}
double PathCurve::arcLength(double limit) {
return arcLength(0.0, limit);
}
double PathCurve::arcLength(double lowerLimit, double upperLimit) {
return helpers::fivePointGaussianQuadrature(
lowerLimit,
upperLimit,
[this](double u) { return approximatedDerivative(u); }
);
}
glm::dvec3 PathCurve::interpolate(double u) {
ghoul_assert(u >= 0 && u <= 1.0, "Interpolation variable out of range [0, 1]");
if (u < 0.0) {
return _points[1];
}
if (u > 1.0) {
return *(_points.end() - 2);
}
std::vector<double>::iterator segmentEndIt =
std::lower_bound(_curveParameterSteps.begin(), _curveParameterSteps.end(), u);
const int index =
static_cast<int>((segmentEndIt - 1) - _curveParameterSteps.begin());
double segmentStart = _curveParameterSteps[index];
double segmentDuration = (_curveParameterSteps[index + 1] - segmentStart);
double uSegment = (u - segmentStart) / segmentDuration;
return interpolation::catmullRom(
uSegment,
_points[index],
_points[index + 1],
_points[index + 2],
_points[index + 3],
1.0 // chordal version
);
}
LinearCurve::LinearCurve(const Waypoint& start, const Waypoint& end) {
_points.push_back(start.position());
_points.push_back(start.position());
_points.push_back(end.position());
_points.push_back(end.position());
initializeParameterData();
}
} // namespace openspace::pathnavigation