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OpenSpace/modules/autonavigation/pathcurves.cpp

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/*****************************************************************************************
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* OpenSpace *
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* Copyright (c) 2014-2019 *
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, *
* INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A *
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#include <modules/autonavigation/pathcurves.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>
namespace {
constexpr const char* _loggerCat = "PathCurve";
const double Epsilon = 1E-7;
} // namespace
namespace openspace::autonavigation {
PathCurve::~PathCurve() {}
const double PathCurve::length() const {
return _totalLength;
}
glm::dvec3 PathCurve::positionAt(double relativeLength) {
double u = curveParameter(relativeLength * _totalLength); // TODO: only use relative length?
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, _length]
// Returns curve parameter in range [0, 1]
double PathCurve::curveParameter(double s) {
if (s <= Epsilon) return 0.0;
if (s >= _totalLength) return 1.0;
unsigned int segmentIndex;
for (segmentIndex = 1; segmentIndex < _nrSegments; ++segmentIndex) {
if (s <= _lengthSums[segmentIndex])
break;
}
// initial guess for Newton's method
double segmentS = s - _lengthSums[segmentIndex - 1];
double segmentLength = _lengths[segmentIndex];
const double uMin = _parameterIntervals[segmentIndex - 1];
const double uMax = _parameterIntervals[segmentIndex];
double u = uMin + (uMax - uMin) * (segmentS / segmentLength);
const int nrIterations = 40;
// initialize root bounding limits for bisection
double lower = uMin;
double upper = uMax;
for (int i = 0; i < nrIterations; ++i) {
double F = arcLength(uMin, u) - segmentS;
const double tolerance = 0.1; // meters. Note that distances are very large
if (std::abs(F) <= tolerance) {
return u;
}
// generate a candidate for Newton's method
double dfdu = approximatedDerivative(u, Epsilon); // > 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;
}
// TODO: remove when not needed
// Created for debugging
std::vector<glm::dvec3> PathCurve::getPoints() {
return _points;
}
void PathCurve::initParameterIntervals() {
ghoul_assert(_nrSegments > 0, "Cannot have a curve with zero segments!");
_parameterIntervals.clear();
_parameterIntervals.reserve(_nrSegments + 1);
// compute initial values, to be able to compute lengths
double dt = 1.0 / _nrSegments;
_parameterIntervals.push_back(0.0);
for (unsigned int i = 1; i < _nrSegments; i++) {
_parameterIntervals.push_back(dt * i);
}
_parameterIntervals.push_back(1.0);
// lengths
_lengths.clear();
_lengths.reserve(_nrSegments + 1);
_lengthSums.clear();
_lengthSums.reserve(_nrSegments + 1);
_lengths.push_back(0.0);
_lengthSums.push_back(0.0);
for (unsigned int i = 1; i <= _nrSegments; i++) {
double u = _parameterIntervals[i];
double uPrev = _parameterIntervals[i - 1];
_lengths.push_back(arcLength(uPrev, u)); // OBS! Is this length computed well enough?
_lengthSums.push_back(_lengthSums[i - 1] + _lengths[i]);
}
_totalLength = _lengthSums.back();
// scale parameterIntervals to better match arc lengths
for (unsigned int i = 1; i <= _nrSegments; i++) {
_parameterIntervals[i] = _lengthSums[i] / _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);
}
// Approximate the arc length using 5-point Gaussian quadrature
// https://en.wikipedia.org/wiki/Gaussian_quadrature
double PathCurve::arcLength(double lowerLimit, double upperLimit) {
double a = lowerLimit;
double b = upperLimit;
struct GaussLengendreCoefficient {
double abscissa; // xi
double weight; // wi
};
static constexpr GaussLengendreCoefficient coefficients[] =
{
{ 0.0, 0.5688889 },
{ -0.5384693, 0.47862867 },
{ 0.5384693, 0.47862867 },
{ -0.90617985, 0.23692688 },
{ 0.90617985, 0.23692688 }
};
double length = 0.0;
for (auto coefficient : coefficients) {
double const t = 0.5 * ((b - a)*coefficient.abscissa + (b + a)); // change of interval to [a, b] from [-1, 1] (also 0.5 * (b - a) below)
length += approximatedDerivative(t) * coefficient.weight;
}
return 0.5 * (b - a) * length;
}
Bezier3Curve::Bezier3Curve(const Waypoint& start, const Waypoint& end) {
glm::dvec3 startNodePos = start.node()->worldPosition();
glm::dvec3 endNodePos = end.node()->worldPosition();
double startNodeRadius = start.nodeDetails.validBoundingSphere;
double endNodeRadius = end.nodeDetails.validBoundingSphere;
glm::dvec3 startNodeToStartPos = start.position() - startNodePos;
glm::dvec3 endNodeToEndPos = end.position() - endNodePos;
double startTangentLength = 2.0 * startNodeRadius;
double endTangentLength = 2.0 * endNodeRadius;
glm::dvec3 startTangentDirection = normalize(startNodeToStartPos);
glm::dvec3 endTangentDirection = normalize(endNodeToEndPos);
// Start by going outwards
_points.push_back(start.position());
_points.push_back(start.position() + startTangentLength * startTangentDirection);
const std::string& startNode = start.nodeDetails.identifier;
const std::string& endNode = end.nodeDetails.identifier;
if (startNode != endNode) {
glm::dvec3 startNodeToEndNode = endNodePos - startNodePos;
glm::dvec3 startToEndDirection = normalize(end.position() - start.position());
// Assuming we move straigh out to point to a distance proportional to radius, angle is enough to check collision risk
double cosStartAngle = glm::dot(startTangentDirection, startToEndDirection);
double cosEndAngle = glm::dot(endTangentDirection, startToEndDirection);
//TODO: investigate suitable values, could be risky close to surface..
bool TARGET_BEHIND_STARTNODE = cosStartAngle < -0.8;
bool TARGET_BEHIND_ENDNODE = cosEndAngle > 0.8;
bool TARGET_IN_OPPOSITE_DIRECTION = cosStartAngle > 0.7;
// Avoid collision with startnode by adding control points on the side of it
if (TARGET_BEHIND_STARTNODE) {
glm::dvec3 parallell = glm::proj(startNodeToStartPos, startNodeToEndNode);
glm::dvec3 orthogonal = normalize(startNodeToStartPos - parallell);
double dist = 5.0 * startNodeRadius;
glm::dvec3 extraKnot = startNodePos + dist * orthogonal;
_points.push_back(extraKnot + parallell);
_points.push_back(extraKnot);
_points.push_back(extraKnot - parallell);
}
// Zoom out, to get a better understanding in a 180 degree turn situation
if (TARGET_IN_OPPOSITE_DIRECTION) {
glm::dvec3 parallell = glm::proj(startNodeToStartPos, startNodeToEndNode);
glm::dvec3 orthogonal = normalize(startNodeToStartPos - parallell);
double dist = 0.5 * glm::length(startNodeToEndNode);
// Distant middle point
glm::dvec3 extraKnot = startNodePos + dist * normalize(parallell) + 3.0 * dist * orthogonal;
_points.push_back(extraKnot - 0.3 * dist * normalize(parallell));
_points.push_back(extraKnot);
_points.push_back(extraKnot + 0.3 * dist * normalize(parallell));
}
// Avoid collision with endnode by adding control points on the side of it
if (TARGET_BEHIND_ENDNODE) {
glm::dvec3 parallell = glm::proj(endNodeToEndPos, startNodeToEndNode);
glm::dvec3 orthogonal = normalize(endNodeToEndPos - parallell);
double dist = 5.0 * endNodeRadius;
glm::dvec3 extraKnot = endNodePos + dist * orthogonal;
_points.push_back(extraKnot - parallell);
_points.push_back(extraKnot);
_points.push_back(extraKnot + parallell);
}
}
_points.push_back(end.position() + endTangentLength * endTangentDirection);
_points.push_back(end.position());
_nrSegments = (unsigned int)std::floor((_points.size() - 1) / 3.0);
initParameterIntervals();
}
// Interpolate a list of control points and knot times
glm::dvec3 Bezier3Curve::interpolate(double u) {
ghoul_assert(u >= 0 && u <= 1.0, "Interpolation variable out of range [0, 1]");
ghoul_assert(_points.size() > 4, "Minimum of four control points needed for interpolation!");
ghoul_assert((_points.size() - 1) % 3 == 0, "A vector containing 3n + 1 control points must be provided!");
ghoul_assert(_nrSegments == (_parameterIntervals.size() - 1), "Number of interval times must match number of intervals");
if (u <= Epsilon)
return _points.front();
if (u >= 1.0 - Epsilon)
return _points.back();
// compute current segment, by first finding iterator to the first value that is larger than s
std::vector<double>::iterator segmentEndIt =
std::lower_bound(_parameterIntervals.begin(), _parameterIntervals.end(), u);
unsigned int segmentIdx = (unsigned int)((segmentEndIt - 1) - _parameterIntervals.begin());
double segmentStart = _parameterIntervals[segmentIdx];
double segmentDuration = (_parameterIntervals[segmentIdx + 1] - segmentStart);
double uScaled = (u - segmentStart) / segmentDuration;
unsigned int idx = segmentIdx * 3;
// Interpolate using De Casteljau's algorithm
return interpolation::cubicBezier(uScaled, _points[idx], _points[idx + 1],
_points[idx + 2], _points[idx + 3]);
}
LinearCurve::LinearCurve(const Waypoint& start, const Waypoint& end) {
_points.push_back(start.position());
_points.push_back(end.position());
_nrSegments = 1;
initParameterIntervals();
}
glm::dvec3 LinearCurve::interpolate(double u) {
ghoul_assert(u >= 0 && u <= 1.0, "Interpolation variable out of range [0, 1]");
return interpolation::linear(u, _points[0], _points[1]);
}
} // namespace openspace::autonavigation