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namespace md {
inline std::ostream& operator<<(std::ostream& os, const AxisType& at)
{
if (at == AxisType::x_type)
os << "x-type";
else
os << "y-type";
return os;
}
inline std::ostream& operator<<(std::ostream& os, const AngleType& at)
{
if (at == AngleType::flat)
os << "flat";
else
os << "steep";
return os;
}
template<class Real>
std::ostream& operator<<(std::ostream& os, const DualPoint<Real>& dp)
{
os << "Line(" << dp.axis_type() << ", ";
os << dp.angle_type() << ", ";
os << dp.lambda() << ", ";
os << dp.mu() << ", equation: ";
if (not dp.is_vertical()) {
os << "y = " << dp.y_slope() << " x + " << dp.y_intercept();
} else {
os << "x = " << dp.x_intercept();
}
os << " )";
return os;
}
template<class Real>
bool DualPoint<Real>::operator<(const DualPoint<Real>& rhs) const
{
return std::tie(axis_type_, angle_type_, lambda_, mu_)
< std::tie(rhs.axis_type_, rhs.angle_type_, rhs.lambda_, rhs.mu_);
}
template<class Real>
DualPoint<Real>::DualPoint(AxisType axis_type, AngleType angle_type, Real lambda, Real mu)
:
axis_type_(axis_type),
angle_type_(angle_type),
lambda_(lambda),
mu_(mu)
{
assert(sanity_check());
}
template<class Real>
bool DualPoint<Real>::sanity_check() const
{
if (lambda_ < 0.0)
throw std::runtime_error("Invalid line, negative lambda");
if (lambda_ > 1.0)
throw std::runtime_error("Invalid line, lambda > 1");
if (mu_ < 0.0)
throw std::runtime_error("Invalid line, negative mu");
return true;
}
template<class Real>
Real DualPoint<Real>::gamma() const
{
if (is_steep())
return atan(Real(1.0) / lambda_);
else
return atan(lambda_);
}
template<class Real>
DualPoint<Real> midpoint(DualPoint<Real> x, DualPoint<Real> y)
{
assert(x.angle_type() == y.angle_type() and x.axis_type() == y.axis_type());
Real lambda_mid = (x.lambda() + y.lambda()) / 2;
Real mu_mid = (x.mu() + y.mu()) / 2;
return DualPoint<Real>(x.axis_type(), x.angle_type(), lambda_mid, mu_mid);
}
// return k in the line equation y = kx + b
template<class Real>
Real DualPoint<Real>::y_slope() const
{
if (is_flat())
return lambda();
else
return Real(1.0) / lambda();
}
// return k in the line equation x = ky + b
template<class Real>
Real DualPoint<Real>::x_slope() const
{
if (is_flat())
return Real(1.0) / lambda();
else
return lambda();
}
// return b in the line equation y = kx + b
template<class Real>
Real DualPoint<Real>::y_intercept() const
{
if (is_y_type()) {
return mu();
} else {
// x = x_slope * y + mu = x_slope * (y + mu / x_slope)
// x-intercept is -mu/x_slope = -mu * y_slope
return -mu() * y_slope();
}
}
// return k in the line equation x = ky + b
template<class Real>
Real DualPoint<Real>::x_intercept() const
{
if (is_x_type()) {
return mu();
} else {
// y = y_slope * x + mu = y_slope (x + mu / y_slope)
// x_intercept is -mu/y_slope = -mu * x_slope
return -mu() * x_slope();
}
}
template<class Real>
Real DualPoint<Real>::x_from_y(Real y) const
{
if (is_horizontal())
throw std::runtime_error("x_from_y called on horizontal line");
else
return x_slope() * y + x_intercept();
}
template<class Real>
Real DualPoint<Real>::y_from_x(Real x) const
{
if (is_vertical())
throw std::runtime_error("x_from_y called on horizontal line");
else
return y_slope() * x + y_intercept();
}
template<class Real>
bool DualPoint<Real>::is_horizontal() const
{
return is_flat() and lambda() == 0;
}
template<class Real>
bool DualPoint<Real>::is_vertical() const
{
return is_steep() and lambda() == 0;
}
template<class Real>
bool DualPoint<Real>::contains(Point<Real> p) const
{
if (is_vertical())
return p.x == x_from_y(p.y);
else
return p.y == y_from_x(p.x);
}
template<class Real>
bool DualPoint<Real>::goes_below(Point<Real> p) const
{
if (is_vertical())
return p.x <= x_from_y(p.y);
else
return p.y >= y_from_x(p.x);
}
template<class Real>
bool DualPoint<Real>::goes_above(Point<Real> p) const
{
if (is_vertical())
return p.x >= x_from_y(p.y);
else
return p.y <= y_from_x(p.x);
}
template<class Real>
Point<Real> DualPoint<Real>::push(Point<Real> p) const
{
Point<Real> result;
// if line is below p, we push horizontally
bool horizontal_push = goes_below(p);
if (is_x_type()) {
if (is_flat()) {
if (horizontal_push) {
result.x = p.y / lambda() + mu();
result.y = p.y;
} else {
// vertical push
result.x = p.x;
result.y = lambda() * (p.x - mu());
}
} else {
// steep
if (horizontal_push) {
result.x = lambda() * p.y + mu();
result.y = p.y;
} else {
// vertical push
result.x = p.x;
result.y = (p.x - mu()) / lambda();
}
}
} else {
// y-type
if (is_flat()) {
if (horizontal_push) {
result.x = (p.y - mu()) / lambda();
result.y = p.y;
} else {
// vertical push
result.x = p.x;
result.y = lambda() * p.x + mu();
}
} else {
// steep
if (horizontal_push) {
result.x = (p.y - mu()) * lambda();
result.y = p.y;
} else {
// vertical push
result.x = p.x;
result.y = p.x / lambda() + mu();
}
}
}
return result;
}
template<class Real>
Real DualPoint<Real>::weighted_push(Point<Real> p) const
{
// if line is below p, we push horizontally
bool horizontal_push = goes_below(p);
if (is_x_type()) {
if (is_flat()) {
if (horizontal_push) {
return p.y;
} else {
// vertical push
return lambda() * (p.x - mu());
}
} else {
// steep
if (horizontal_push) {
return lambda() * p.y;
} else {
// vertical push
return (p.x - mu());
}
}
} else {
// y-type
if (is_flat()) {
if (horizontal_push) {
return p.y - mu();
} else {
// vertical push
return lambda() * p.x;
}
} else {
// steep
if (horizontal_push) {
return lambda() * (p.y - mu());
} else {
// vertical push
return p.x;
}
}
}
}
template<class Real>
bool DualPoint<Real>::operator==(const DualPoint<Real>& other) const
{
return axis_type() == other.axis_type() and
angle_type() == other.angle_type() and
mu() == other.mu() and
lambda() == other.lambda();
}
template<class Real>
Real DualPoint<Real>::weight() const
{
return lambda_ / sqrt(1 + lambda_ * lambda_);
}
} // namespace md
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