void Curve::computeCurvatureAndOrientation ()
{
const_vertex_iterator v = vertices_begin(), vend = vertices_end(), v2, prevV, v0;
Vec2d p0, p1, p2;
Vec3r p;
p = (*v)->point2d();
p0 = Vec2d(p[0], p[1]);
prevV = v;
++v;
p = (*v)->point2d();
p1 = Vec2d(p[0], p[1]);
Vec2d prevDir(p1 - p0);
for (; v! = vend; ++v) {
v2 = v;
++v2;
if (v2 == vend)
break;
Vec3r p2 = (*v2)->point2d();
Vec2d BA = p0 - p1;
Vec2d BC = p2 - p1;
real lba = BA.norm(), lbc = BC.norm();
BA.normalizeSafe();
BC.normalizeSafe();
Vec2d normalCurvature = BA + BC;
Vec2d dir = Vec2d(BC - BA);
Vec2d normal = Vec2d(-dir[1], dir[0]);
normal.normalizeSafe();
real curvature = normalCurvature * normal;
if (lba + lbc > MY_EPSILON)
curvature /= (0.5 * lba + lbc);
if (dir.norm() < MY_EPSILON)
dir = 0.1 * prevDir;
(*v)->setCurvatureFredo(curvature);
(*v)->setDirectionFredo(dir);
prevV = v;
p0 = p1;
p1 = p2;
prevDir = dir;
prevDir.normalize();
}
(*v)->setCurvatureFredo((*prevV)->curvatureFredo());
(*v)->setDirectionFredo((*v)->point2d() - (*prevV)->point2d());
v0 = vertices_begin();
v2 = v0;
++v2;
(*v0)->setCurvatureFredo((*v2)->curvatureFredo());
(*v0)->setDirectionFredo((*v2)->point2d() - (*v0)->point2d());
//closed curve case one day...
//
return;
//numerical degeneracy verification... we'll see later
const_vertex_iterator vLastReliable = vertices_begin();
v = vertices_begin();
p = (*v)->point2d();
p0 = Vec2d(p[0], p[1]);
prevV = v;
++v;
p = (*v)->point2d();
p1 = Vec2d(p[0], p[1]);
bool isReliable = false;
if ((p1 - p0).norm > EPS_CURVA) {
vLastReliable = v;
isReliable = true;
}
for (; v != vend; ++v) {
v2 = v;
++v2;
if (v2 == vend)
break;
Vec3r p2 = (*v2)->point2d();
Vec2d BA = p0 - p1;
Vec2d BC = p2 - p1;
real lba = BA.norm(), lbc = BC.norm();
if ((lba + lbc) < EPS_CURVA) {
isReliable = false;
cerr << "/";
}
else {
if (!isReliable) { //previous points were not reliable
const_vertex_iterator vfix = vLastReliable;
++vfix;
for (; vfix != v; ++vfix) {
(*vfix)->setCurvatureFredo((*v)->curvatureFredo());
(*vfix)->setDirectionFredo((*v)->directionFredo());
}
}
isReliable = true;
vLastReliable = v;
}
prevV = v;
p0 = p1;
p1 = p2;
}
}
static std::vector<Vec2d> make_one_period(double width, double scaleFactor, double z_cos, double z_sin, bool vertical, bool flip)
{
std::vector<Vec2d> points;
double dx = M_PI_4; // very coarse spacing to begin with
double limit = std::min(2*M_PI, width);
for (double x = 0.; x < limit + EPSILON; x += dx) { // so the last point is there too
x = std::min(x, limit);
points.emplace_back(Vec2d(x,f(x, z_sin,z_cos, vertical, flip)));
}
// now we will check all internal points and in case some are too far from the line connecting its neighbours,
// we will add one more point on each side:
const double tolerance = .1;
for (unsigned int i=1;i<points.size()-1;++i) {
auto& lp = points[i-1]; // left point
auto& tp = points[i]; // this point
Vec2d lrv = tp - lp;
auto& rp = points[i+1]; // right point
// calculate distance of the point to the line:
double dist_mm = unscale<double>(scaleFactor) * std::abs(cross2(rp, lp) - cross2(rp - lp, tp)) / lrv.norm();
if (dist_mm > tolerance) { // if the difference from straight line is more than this
double x = 0.5f * (points[i-1](0) + points[i](0));
points.emplace_back(Vec2d(x, f(x, z_sin, z_cos, vertical, flip)));
x = 0.5f * (points[i+1](0) + points[i](0));
points.emplace_back(Vec2d(x, f(x, z_sin, z_cos, vertical, flip)));
// we added the points to the end, but need them all in order
std::sort(points.begin(), points.end(), [](const Vec2d &lhs, const Vec2d &rhs){ return lhs < rhs; });
// decrement i so we also check the first newly added point
--i;
}
}
return points;
}