arma::vec2
intersectionPoint(const Line2 & l1, const Line2 & l2)
{
const double num1 = l1.b() * l2.c() - l2.b() * l1.c();
const double num2 = l2.a() * l1.c() - l1.a() * l2.c();
const double denom = l1.a() * l2.b() - l2.a() * l1.b();
arma::vec2 pt;
pt << num1 / denom << endr << num2 / denom;
return pt;
}
Solution split(const Line2& line, bool up) const {
Solution result;
result.points = points;
for (const auto& facet: facets) {
if (doIntersect(facet.polygon, line)) {
Facet facet1;
facet1.transformation = facet.transformation;
Facet facet2;
Transformation2 reflection( sqr(line.b()) - sqr(line.a()), -2*line.a()*line.b(), -2*line.a()*line.c(),
-2*line.a()*line.b(), sqr(line.a()) - sqr(line.b()), -2*line.b()*line.c(),
sqr(line.a()) + sqr(line.b()) );
facet2.transformation = reflection*facet.transformation;
auto inverse = facet.transformation.inverse();
bool fail = false;
for (auto edge = facet.polygon.edges_begin(); edge != facet.polygon.edges_end(); ++edge) {
const auto len2 = edge->squared_length();
const auto len2new = edge->transform(facet2.transformation).squared_length();
if (len2 != len2new) {
throw runtime_error("bad transform");
}
if (line.has_on_positive_side(edge->source()) == up) {
facet1.polygon.push_back(edge->source());
} else {
facet2.polygon.push_back(reflection(edge->source()));
}
auto intersect = intersection(*edge, line);
if (intersect) {
Point2* p = boost::get<Point2>(&*intersect);
if (p) {
auto revPoint = inverse(*p);
if (!result.points.count(revPoint)) {
result.points[revPoint] = result.points.size();
}
facet1.polygon.push_back(*p);
facet2.polygon.push_back(*p);
} else {
fail = true;
}
}
}
auto normalize = [&](Facet& f) {
auto area = f.polygon.area();
if (area == 0) {
return;
}
vector<Point2> points(f.polygon.size());
for (size_t i = 0; i < f.polygon.size(); ++i) {
points[i] = f.polygon[i];
}
points.erase(unique(points.begin(), points.end()), points.end());
if (points.empty()) {
return;
}
if (area < 0) {
reverse(points.begin(), points.end());
}
Polygon2 p;
for (const auto& pnt: points) {
p.push_back(pnt);
}
f.polygon = p;
result.facets.push_back(f);
};
if (!fail) {
normalize(facet1);
normalize(facet2);
} else {
result.facets.push_back(facet);
}
} else {
result.facets.push_back(facet);
}
}
for (const auto& f: result.facets) {
result.polygon.join(f.polygon);
}
return result;
}
