OrcaSlicer/src/libnest2d/include/libnest2d/geometry_traits.hpp

1270 lines
34 KiB
C++

#ifndef GEOMETRY_TRAITS_HPP
#define GEOMETRY_TRAITS_HPP
#include <string>
#include <type_traits>
#include <algorithm>
#include <array>
#include <vector>
#include <numeric>
#include <iterator>
#include <cmath>
#include <cstdint>
#include <libnest2d/common.hpp>
namespace libnest2d {
// Meta tags for different geometry concepts.
struct PointTag {};
struct PolygonTag {};
struct PathTag {};
struct MultiPolygonTag {};
struct BoxTag {};
struct CircleTag {};
/// Meta-function to derive the tag of a shape type.
template<class Shape> struct ShapeTag { using Type = typename Shape::Tag; };
/// Tag<S> will be used instead of `typename ShapeTag<S>::Type`
template<class S> using Tag = typename ShapeTag<remove_cvref_t<S>>::Type;
/// Meta function to derive the contour type for a polygon which could be itself
template<class S> struct ContourType { using Type = S; };
/// TContour<S> instead of `typename ContourType<S>::type`
template<class S>
using TContour = typename ContourType<remove_cvref_t<S>>::Type;
/// Getting the type of point structure used by a shape.
template<class Sh> struct PointType {
using Type = typename PointType<TContour<Sh>>::Type;
};
/// TPoint<ShapeClass> as shorthand for `typename PointType<ShapeClass>::Type`.
template<class Shape>
using TPoint = typename PointType<remove_cvref_t<Shape>>::Type;
/// Getting the coordinate data type for a geometry class.
template<class GeomClass> struct CoordType {
using Type = typename CoordType<TPoint<GeomClass>>::Type;
};
/// TCoord<GeomType> as shorthand for typename `CoordType<GeomType>::Type`.
template<class GeomType>
using TCoord = typename CoordType<remove_cvref_t<GeomType>>::Type;
/// Getting the computation type for a certain geometry type.
/// It is the coordinate type by default but it is advised that a type with
/// larger precision and (or) range is specified.
template<class T, bool = std::is_arithmetic<T>::value> struct ComputeType {};
/// A compute type is introduced to hold the results of computations on
/// coordinates and points. It should be larger in range than the coordinate
/// type or the range of coordinates should be limited to not loose precision.
template<class GeomClass> struct ComputeType<GeomClass, false> {
using Type = typename ComputeType<TCoord<GeomClass>>::Type;
};
/// libnest2d will choose a default compute type for various coordinate types
/// if the backend has not specified anything.
template<class T> struct DoublePrecision { using Type = T; };
template<> struct DoublePrecision<int8_t> { using Type = int16_t; };
template<> struct DoublePrecision<int16_t> { using Type = int32_t; };
template<> struct DoublePrecision<int32_t> { using Type = int64_t; };
template<> struct DoublePrecision<float> { using Type = double; };
template<> struct DoublePrecision<double> { using Type = long double; };
template<class I> struct ComputeType<I, true> {
using Type = typename DoublePrecision<I>::Type;
};
/// TCompute<T> shorthand for `typename ComputeType<T>::Type`
template<class T> using TCompute = typename ComputeType<remove_cvref_t<T>>::Type;
/// A meta function to derive a container type for holes in a polygon
template<class S>
struct HolesContainer { using Type = std::vector<TContour<S>>; };
/// Shorthand for `typename HolesContainer<S>::Type`
template<class S>
using THolesContainer = typename HolesContainer<remove_cvref_t<S>>::Type;
/*
* TContour, TPoint, TCoord and TCompute should be usable for any type for which
* it makes sense. For example, the point type could be derived from the contour,
* the polygon and (or) the multishape as well. The coordinate type also and
* including the point type. TCoord<Polygon>, TCoord<Path>, TCoord<Point> are
* all valid types and derives the coordinate type of template argument Polygon,
* Path and Point. This is also true for TCompute, but it can also take the
* coordinate type as argument.
*/
/*
* A Multi shape concept is also introduced. A multi shape is something that
* can contain the result of an operation where the input is one polygon and
* the result could be many polygons or path -> paths. The MultiShape should be
* a container type. If the backend does not specialize the MultiShape template,
* a default multi shape container will be used.
*/
/// The default multi shape container.
template<class S> struct DefaultMultiShape: public std::vector<S> {
using Tag = MultiPolygonTag;
template<class...Args> DefaultMultiShape(Args&&...args):
std::vector<S>(std::forward<Args>(args)...) {}
};
/// The MultiShape Type trait which gets the container type for a geometry type.
template<class S> struct MultiShape { using Type = DefaultMultiShape<S>; };
/// use TMultiShape<S> instead of `typename MultiShape<S>::Type`
template<class S>
using TMultiShape = typename MultiShape<remove_cvref_t<S>>::Type;
// A specialization of ContourType to work with the default multishape type
template<class S> struct ContourType<DefaultMultiShape<S>> {
using Type = typename ContourType<S>::Type;
};
enum class Orientation {
CLOCKWISE,
COUNTER_CLOCKWISE
};
template<class S>
struct OrientationType {
// Default Polygon orientation that the library expects
static const Orientation Value = Orientation::CLOCKWISE;
};
template<class T> inline /*constexpr*/ bool is_clockwise() {
return OrientationType<TContour<T>>::Value == Orientation::CLOCKWISE;
}
/**
* \brief A point pair base class for other point pairs (segment, box, ...).
* \tparam P The actual point type to use.
*/
template<class P>
struct PointPair {
P p1;
P p2;
};
/**
* \brief An abstraction of a box;
*/
template<class P>
class _Box: PointPair<P> {
using PointPair<P>::p1;
using PointPair<P>::p2;
public:
using Tag = BoxTag;
using PointType = P;
inline _Box(const P& center = {TCoord<P>(0), TCoord<P>(0)}):
_Box(TCoord<P>(0), TCoord<P>(0), center) {}
inline _Box(const P& p, const P& pp):
PointPair<P>({p, pp}) {}
inline _Box(TCoord<P> width, TCoord<P> height,
const P& p = {TCoord<P>(0), TCoord<P>(0)});/*:
_Box(p, P{width, height}) {}*/
inline const P& minCorner() const BP2D_NOEXCEPT { return p1; }
inline const P& maxCorner() const BP2D_NOEXCEPT { return p2; }
inline P& minCorner() BP2D_NOEXCEPT { return p1; }
inline P& maxCorner() BP2D_NOEXCEPT { return p2; }
inline TCoord<P> width() const BP2D_NOEXCEPT;
inline TCoord<P> height() const BP2D_NOEXCEPT;
inline P center() const BP2D_NOEXCEPT;
template<class Unit = TCompute<P>>
inline Unit area() const BP2D_NOEXCEPT {
return Unit(width())*height();
}
static inline _Box infinite(const P &center = {TCoord<P>(0), TCoord<P>(0)});
};
template<class S> struct PointType<_Box<S>> {
using Type = typename _Box<S>::PointType;
};
template<class P>
class _Circle {
P center_;
double radius_ = 0;
public:
using Tag = CircleTag;
using PointType = P;
_Circle() = default;
_Circle(const P& center, double r): center_(center), radius_(r) {}
inline const P& center() const BP2D_NOEXCEPT { return center_; }
inline void center(const P& c) { center_ = c; }
inline double radius() const BP2D_NOEXCEPT { return radius_; }
inline void radius(double r) { radius_ = r; }
inline double area() const BP2D_NOEXCEPT {
return Pi_2 * radius_ * radius_;
}
};
template<class S> struct PointType<_Circle<S>> {
using Type = typename _Circle<S>::PointType;
};
/**
* \brief An abstraction of a directed line segment with two points.
*/
template<class P>
class _Segment: PointPair<P> {
using PointPair<P>::p1;
using PointPair<P>::p2;
mutable Radians angletox_ = std::nan("");
public:
using PointType = P;
inline _Segment() = default;
inline _Segment(const P& p, const P& pp):
PointPair<P>({p, pp}) {}
/**
* @brief Get the first point.
* @return Returns the starting point.
*/
inline const P& first() const BP2D_NOEXCEPT { return p1; }
/**
* @brief The end point.
* @return Returns the end point of the segment.
*/
inline const P& second() const BP2D_NOEXCEPT { return p2; }
inline void first(const P& p) BP2D_NOEXCEPT
{
angletox_ = std::nan(""); p1 = p;
}
inline void second(const P& p) BP2D_NOEXCEPT {
angletox_ = std::nan(""); p2 = p;
}
/// Returns the angle measured to the X (horizontal) axis.
inline Radians angleToXaxis() const;
/// The length of the segment in the measure of the coordinate system.
template<class Unit = TCompute<P>> inline Unit sqlength() const;
};
template<class S> struct PointType<_Segment<S>> {
using Type = typename _Circle<S>::PointType;
};
// This struct serves almost as a namespace. The only difference is that is can
// used in friend declarations.
namespace pointlike {
template<class P>
inline TCoord<P> x(const P& p)
{
return p.x();
}
template<class P>
inline TCoord<P> y(const P& p)
{
return p.y();
}
template<class P>
inline TCoord<P>& x(P& p)
{
return p.x();
}
template<class P>
inline TCoord<P>& y(P& p)
{
return p.y();
}
template<class P, class Unit = TCompute<P>>
inline Unit squaredDistance(const P& p1, const P& p2)
{
auto x1 = Unit(x(p1)), y1 = Unit(y(p1)), x2 = Unit(x(p2)), y2 = Unit(y(p2));
Unit a = (x2 - x1), b = (y2 - y1);
return a * a + b * b;
}
template<class P>
inline double distance(const P& p1, const P& p2)
{
return std::sqrt(squaredDistance<P, double>(p1, p2));
}
// create perpendicular vector
template<class Pt> inline Pt perp(const Pt& p)
{
return Pt(y(p), -x(p));
}
template<class Pt, class Unit = TCompute<Pt>>
inline Unit dotperp(const Pt& a, const Pt& b)
{
return Unit(x(a)) * Unit(y(b)) - Unit(y(a)) * Unit(x(b));
}
// dot product
template<class Pt, class Unit = TCompute<Pt>>
inline Unit dot(const Pt& a, const Pt& b)
{
return Unit(x(a)) * x(b) + Unit(y(a)) * y(b);
}
// squared vector magnitude
template<class Pt, class Unit = TCompute<Pt>>
inline Unit magnsq(const Pt& p)
{
return Unit(x(p)) * x(p) + Unit(y(p)) * y(p);
}
template<class P, class Unit = TCompute<P>>
inline std::pair<Unit, bool> horizontalDistance(
const P& p, const _Segment<P>& s)
{
namespace pl = pointlike;
auto x = Unit(pl::x(p)), y = Unit(pl::y(p));
auto x1 = Unit(pl::x(s.first())), y1 = Unit(pl::y(s.first()));
auto x2 = Unit(pl::x(s.second())), y2 = Unit(pl::y(s.second()));
Unit ret;
if( (y < y1 && y < y2) || (y > y1 && y > y2) )
return {0, false};
if ((y == y1 && y == y2) && (x > x1 && x > x2))
ret = std::min( x-x1, x -x2);
else if( (y == y1 && y == y2) && (x < x1 && x < x2))
ret = -std::min(x1 - x, x2 - x);
else if(y == y1 && y == y2)
ret = 0;
else
ret = x - x1 + (x1 - x2)*(y1 - y)/(y1 - y2);
return {ret, true};
}
template<class P, class Unit = TCompute<P>>
inline std::pair<Unit, bool> verticalDistance(
const P& p, const _Segment<P>& s)
{
namespace pl = pointlike;
auto x = Unit(pl::x(p)), y = Unit(pl::y(p));
auto x1 = Unit(pl::x(s.first())), y1 = Unit(pl::y(s.first()));
auto x2 = Unit(pl::x(s.second())), y2 = Unit(pl::y(s.second()));
Unit ret;
if( (x < x1 && x < x2) || (x > x1 && x > x2) )
return {0, false};
if ((x == x1 && x == x2) && (y > y1 && y > y2))
ret = std::min( y-y1, y -y2);
else if( (x == x1 && x == x2) && (y < y1 && y < y2))
ret = -std::min(y1 - y, y2 - y);
else if(x == x1 && x == x2)
ret = 0;
else
ret = y - y1 + (y1 - y2)*(x1 - x)/(x1 - x2);
return {ret, true};
}
}
template<class P>
TCoord<P> _Box<P>::width() const BP2D_NOEXCEPT
{
return pointlike::x(maxCorner()) - pointlike::x(minCorner());
}
template<class P>
TCoord<P> _Box<P>::height() const BP2D_NOEXCEPT
{
return pointlike::y(maxCorner()) - pointlike::y(minCorner());
}
template<class P>
TCoord<P> getX(const P& p) { return pointlike::x<P>(p); }
template<class P>
TCoord<P> getY(const P& p) { return pointlike::y<P>(p); }
template<class P>
void setX(P& p, const TCoord<P>& val)
{
pointlike::x<P>(p) = val;
}
template<class P>
void setY(P& p, const TCoord<P>& val)
{
pointlike::y<P>(p) = val;
}
template<class P>
inline Radians _Segment<P>::angleToXaxis() const
{
if(std::isnan(static_cast<double>(angletox_))) {
TCoord<P> dx = getX(second()) - getX(first());
TCoord<P> dy = getY(second()) - getY(first());
double a = std::atan2(dy, dx);
auto s = std::signbit(a);
if(s) a += Pi_2;
angletox_ = a;
}
return angletox_;
}
template<class P>
template<class Unit>
inline Unit _Segment<P>::sqlength() const
{
return pointlike::squaredDistance<P, Unit>(first(), second());
}
template<class T>
enable_if_t<std::is_floating_point<T>::value, T> modulo(const T &v, const T &m)
{
return 0;
}
template<class T>
enable_if_t<std::is_integral<T>::value, T> modulo(const T &v, const T &m)
{
return v % m;
}
template<class P>
inline _Box<P>::_Box(TCoord<P> width, TCoord<P> height, const P & center) :
PointPair<P>({center - P{width / 2, height / 2},
center + P{width / 2, height / 2} +
P{modulo(width, TCoord<P>(2)),
modulo(height, TCoord<P>(2))}}) {}
template<class P>
inline _Box<P> _Box<P>::infinite(const P& center) {
using C = TCoord<P>;
_Box<P> ret;
// It is important for Mx and My to be strictly less than half of the
// range of type C. width(), height() and area() will not overflow this way.
C Mx = C((std::numeric_limits<C>::lowest() + 2 * getX(center)) / 2.01);
C My = C((std::numeric_limits<C>::lowest() + 2 * getY(center)) / 2.01);
ret.maxCorner() = center - P{Mx, My};
ret.minCorner() = center + P{Mx, My};
return ret;
}
template<class P>
inline P _Box<P>::center() const BP2D_NOEXCEPT {
auto& minc = minCorner();
auto& maxc = maxCorner();
using Coord = TCoord<P>;
P ret = { // No rounding here, we dont know if these are int coords
Coord( (getX(minc) + getX(maxc)) / Coord(2) ),
Coord( (getY(minc) + getY(maxc)) / Coord(2) )
};
return ret;
}
enum class Formats {
WKT,
SVG
};
// This struct serves as a namespace. The only difference is that it can be
// used in friend declarations and can be aliased at class scope.
namespace shapelike {
template<class S>
inline S create(const TContour<S>& contour, const THolesContainer<S>& holes)
{
return S(contour, holes);
}
template<class S>
inline S create(TContour<S>&& contour, THolesContainer<S>&& holes)
{
return S(contour, holes);
}
template<class S>
inline S create(const TContour<S>& contour)
{
return create<S>(contour, {});
}
template<class S>
inline S create(TContour<S>&& contour)
{
return create<S>(contour, {});
}
template<class S>
inline THolesContainer<S>& holes(S& /*sh*/)
{
static THolesContainer<S> empty;
return empty;
}
template<class S>
inline const THolesContainer<S>& holes(const S& /*sh*/)
{
static THolesContainer<S> empty;
return empty;
}
template<class S>
inline TContour<S>& hole(S& sh, unsigned long idx)
{
return holes(sh)[idx];
}
template<class S>
inline const TContour<S>& hole(const S& sh, unsigned long idx)
{
return holes(sh)[idx];
}
template<class S>
inline size_t holeCount(const S& sh)
{
return holes(sh).size();
}
template<class S>
inline TContour<S>& contour(S& sh)
{
static_assert(always_false<S>::value,
"shapelike::contour() unimplemented!");
return sh;
}
template<class S>
inline const TContour<S>& contour(const S& sh)
{
static_assert(always_false<S>::value,
"shapelike::contour() unimplemented!");
return sh;
}
// Optional, does nothing by default
template<class RawPath>
inline void reserve(RawPath& p, size_t vertex_capacity, const PathTag&)
{
p.reserve(vertex_capacity);
}
template<class S, class...Args>
inline void addVertex(S& sh, const PathTag&, Args...args)
{
sh.emplace_back(std::forward<Args>(args)...);
}
template<class S, class Fn>
inline void foreachVertex(S& sh, Fn fn, const PathTag&) {
std::for_each(sh.begin(), sh.end(), fn);
}
template<class S>
inline typename S::iterator begin(S& sh, const PathTag&)
{
return sh.begin();
}
template<class S>
inline typename S::iterator end(S& sh, const PathTag&)
{
return sh.end();
}
template<class S>
inline typename S::const_iterator
cbegin(const S& sh, const PathTag&)
{
return sh.cbegin();
}
template<class S>
inline typename S::const_iterator
cend(const S& sh, const PathTag&)
{
return sh.cend();
}
template<class S>
inline std::string toString(const S& /*sh*/)
{
return "";
}
template<Formats, class S>
inline std::string serialize(const S& /*sh*/, double /*scale*/=1)
{
static_assert(always_false<S>::value,
"shapelike::serialize() unimplemented!");
return "";
}
template<Formats, class S>
inline void unserialize(S& /*sh*/, const std::string& /*str*/)
{
static_assert(always_false<S>::value,
"shapelike::unserialize() unimplemented!");
}
template<class Cntr, class Unit = double>
inline Unit area(const Cntr& poly, const PathTag& );
template<class S>
inline bool intersects(const S& /*sh*/, const S& /*sh*/)
{
static_assert(always_false<S>::value,
"shapelike::intersects() unimplemented!");
return false;
}
template<class TGuest, class THost>
inline bool isInside(const TGuest&, const THost&,
const PointTag&, const PolygonTag&) {
static_assert(always_false<THost>::value,
"shapelike::isInside(point, path) unimplemented!");
return false;
}
template<class TGuest, class THost>
inline bool isInside(const TGuest&, const THost&,
const PolygonTag&, const PolygonTag&) {
static_assert(always_false<THost>::value,
"shapelike::isInside(shape, shape) unimplemented!");
return false;
}
template<class S>
inline bool touches( const S& /*shape*/,
const S& /*shape*/)
{
static_assert(always_false<S>::value,
"shapelike::touches(shape, shape) unimplemented!");
return false;
}
template<class S>
inline bool touches( const TPoint<S>& /*point*/,
const S& /*shape*/)
{
static_assert(always_false<S>::value,
"shapelike::touches(point, shape) unimplemented!");
return false;
}
template<class S>
inline _Box<TPoint<S>> boundingBox(const S& /*sh*/,
const PathTag&)
{
static_assert(always_false<S>::value,
"shapelike::boundingBox(shape) unimplemented!");
}
template<class RawShapes>
inline _Box<TPoint<RawShapes>>
boundingBox(const RawShapes& /*sh*/, const MultiPolygonTag&)
{
static_assert(always_false<RawShapes>::value,
"shapelike::boundingBox(shapes) unimplemented!");
}
template<class S>
inline S convexHull(const S& sh, const PathTag&);
template<class RawShapes, class S = typename RawShapes::value_type>
inline S convexHull(const RawShapes& sh, const MultiPolygonTag&);
template<class S>
inline void rotate(S& /*sh*/, const Radians& /*rads*/)
{
static_assert(always_false<S>::value,
"shapelike::rotate() unimplemented!");
}
template<class S, class P>
inline void translate(S& /*sh*/, const P& /*offs*/)
{
static_assert(always_false<S>::value,
"shapelike::translate() unimplemented!");
}
template<class S>
inline void offset(S& /*sh*/, TCoord<S> /*distance*/, const PathTag&)
{
dout() << "The current geometry backend does not support offsetting!\n";
}
template<class S>
inline void offset(S& sh, TCoord<S> distance, const PolygonTag&)
{
offset(contour(sh), distance);
for(auto &h : holes(sh)) offset(h, -distance);
}
template<class S>
inline std::pair<bool, std::string> isValid(const S& /*sh*/)
{
return {false, "shapelike::isValid() unimplemented!"};
}
template<class RawPath> inline bool isConvex(const RawPath& sh, const PathTag&)
{
using Vertex = TPoint<RawPath>;
auto first = begin(sh);
auto middle = std::next(first);
auto last = std::next(middle);
using CVrRef = const Vertex&;
auto zcrossproduct = [](CVrRef k, CVrRef k1, CVrRef k2) {
auto dx1 = getX(k1) - getX(k);
auto dy1 = getY(k1) - getY(k);
auto dx2 = getX(k2) - getX(k1);
auto dy2 = getY(k2) - getY(k1);
return dx1*dy2 - dy1*dx2;
};
auto firstprod = zcrossproduct( *(std::prev(std::prev(end(sh)))),
*first,
*middle );
bool ret = true;
bool frsign = firstprod > 0;
while(last != end(sh)) {
auto &k = *first, &k1 = *middle, &k2 = *last;
auto zc = zcrossproduct(k, k1, k2);
ret &= frsign == (zc > 0);
++first; ++middle; ++last;
}
return ret;
}
// *****************************************************************************
// No need to implement these
// *****************************************************************************
template<class S>
inline typename TContour<S>::iterator
begin(S& sh, const PolygonTag&)
{
return begin(contour(sh), PathTag());
}
template<class S> // Tag dispatcher
inline auto begin(S& sh) -> decltype(begin(sh, Tag<S>()))
{
return begin(sh, Tag<S>());
}
template<class S>
inline typename TContour<S>::const_iterator
cbegin(const S& sh, const PolygonTag&)
{
return cbegin(contour(sh), PathTag());
}
template<class S> // Tag dispatcher
inline auto cbegin(const S& sh) -> decltype(cbegin(sh, Tag<S>()))
{
return cbegin(sh, Tag<S>());
}
template<class S>
inline typename TContour<S>::iterator
end(S& sh, const PolygonTag&)
{
return end(contour(sh), PathTag());
}
template<class S> // Tag dispatcher
inline auto end(S& sh) -> decltype(begin(sh, Tag<S>()))
{
return end(sh, Tag<S>());
}
template<class S>
inline typename TContour<S>::const_iterator
cend(const S& sh, const PolygonTag&)
{
return cend(contour(sh), PathTag());
}
template<class S> // Tag dispatcher
inline auto cend(const S& sh) -> decltype(cend(sh, Tag<S>()))
{
return cend(sh, Tag<S>());
}
template<class It> std::reverse_iterator<It> _backward(It iter) {
return std::reverse_iterator<It>(iter);
}
template<class P> auto rbegin(P& p) -> decltype(_backward(end(p)))
{
return _backward(end(p));
}
template<class P> auto rcbegin(const P& p) -> decltype(_backward(end(p)))
{
return _backward(end(p));
}
template<class P> auto rend(P& p) -> decltype(_backward(begin(p)))
{
return _backward(begin(p));
}
template<class P> auto rcend(const P& p) -> decltype(_backward(cbegin(p)))
{
return _backward(cbegin(p));
}
template<class P> TPoint<P> front(const P& p) { return *shapelike::cbegin(p); }
template<class P> TPoint<P> back (const P& p) {
return *backward(shapelike::cend(p));
}
// Optional, does nothing by default
template<class S>
inline void reserve(S& sh, size_t vertex_capacity, const PolygonTag&)
{
reserve(contour(sh), vertex_capacity, PathTag());
}
template<class T> // Tag dispatcher
inline void reserve(T& sh, size_t vertex_capacity) {
reserve(sh, vertex_capacity, Tag<T>());
}
template<class S, class...Args>
inline void addVertex(S& sh, const PolygonTag&, Args...args)
{
addVertex(contour(sh), PathTag(), std::forward<Args>(args)...);
}
template<class S, class...Args> // Tag dispatcher
inline void addVertex(S& sh, Args...args)
{
addVertex(sh, Tag<S>(), std::forward<Args>(args)...);
}
template<class S>
inline _Box<TPoint<S>> boundingBox(const S& poly, const PolygonTag&)
{
return boundingBox(contour(poly), PathTag());
}
template<class Box>
inline Box boundingBox(const Box& box, const BoxTag& )
{
return box;
}
template<class Circle>
inline _Box<typename Circle::PointType> boundingBox(
const Circle& circ, const CircleTag&)
{
using Point = typename Circle::PointType;
using Coord = TCoord<Point>;
Point pmin = {
static_cast<Coord>(getX(circ.center()) - circ.radius()),
static_cast<Coord>(getY(circ.center()) - circ.radius()) };
Point pmax = {
static_cast<Coord>(getX(circ.center()) + circ.radius()),
static_cast<Coord>(getY(circ.center()) + circ.radius()) };
return {pmin, pmax};
}
template<class S> // Dispatch function
inline _Box<TPoint<S>> boundingBox(const S& sh)
{
return boundingBox(sh, Tag<S>() );
}
template<class P> _Box<P> boundingBox(const _Box<P>& bb1, const _Box<P>& bb2 )
{
auto& pminc = bb1.minCorner();
auto& pmaxc = bb1.maxCorner();
auto& iminc = bb2.minCorner();
auto& imaxc = bb2.maxCorner();
P minc, maxc;
setX(minc, std::min(getX(pminc), getX(iminc)));
setY(minc, std::min(getY(pminc), getY(iminc)));
setX(maxc, std::max(getX(pmaxc), getX(imaxc)));
setY(maxc, std::max(getY(pmaxc), getY(imaxc)));
return _Box<P>(minc, maxc);
}
template<class S1, class S2>
_Box<TPoint<S1>> boundingBox(const S1 &s1, const S2 &s2)
{
return boundingBox(boundingBox(s1), boundingBox(s2));
}
template<class Box>
inline double area(const Box& box, const BoxTag& )
{
return box.template area<double>();
}
template<class Circle>
inline double area(const Circle& circ, const CircleTag& )
{
return circ.area();
}
template<class Cntr, class Unit>
inline Unit area(const Cntr& poly, const PathTag& )
{
namespace sl = shapelike;
if (sl::cend(poly) - sl::cbegin(poly) < 3) return 0.0;
Unit a = 0;
for (auto i = sl::cbegin(poly), j = std::prev(sl::cend(poly));
i < sl::cend(poly); ++i)
{
auto xj = Unit(getX(*j)), yj = Unit(getY(*j));
auto xi = Unit(getX(*i)), yi = Unit(getY(*i));
a += (xj + xi) * (yj - yi);
j = i;
}
a /= 2;
return is_clockwise<Cntr>() ? a : -a;
}
template<class S> inline double area(const S& poly, const PolygonTag& )
{
auto hls = holes(poly);
return std::accumulate(hls.begin(), hls.end(),
area(contour(poly), PathTag()),
[](double a, const TContour<S> &h){
return a + area(h, PathTag());
});
}
template<class S> // Dispatching function
inline double area(const S& sh)
{
return area(sh, Tag<S>());
}
template<class RawShapes>
inline double area(const RawShapes& shapes, const MultiPolygonTag&)
{
using S = typename RawShapes::value_type;
return std::accumulate(shapes.begin(), shapes.end(), 0.0,
[](double a, const S& b) {
return a += area(b);
});
}
template<class S>
inline S convexHull(const S& sh, const PolygonTag&)
{
return create<S>(convexHull(contour(sh), PathTag()));
}
template<class S>
inline auto convexHull(const S& sh)
-> decltype(convexHull(sh, Tag<S>())) // TODO: C++14 could deduce
{
return convexHull(sh, Tag<S>());
}
template<class S>
inline S convexHull(const S& sh, const PathTag&)
{
using Unit = TCompute<S>;
using Point = TPoint<S>;
namespace sl = shapelike;
size_t edges = sl::cend(sh) - sl::cbegin(sh);
if(edges <= 3) return {};
bool closed = false;
std::vector<Point> U, L;
U.reserve(1 + edges / 2); L.reserve(1 + edges / 2);
std::vector<Point> pts; pts.reserve(edges);
std::copy(sl::cbegin(sh), sl::cend(sh), std::back_inserter(pts));
auto fpt = pts.front(), lpt = pts.back();
if(getX(fpt) == getX(lpt) && getY(fpt) == getY(lpt)) {
closed = true; pts.pop_back();
}
std::sort(pts.begin(), pts.end(),
[](const Point& v1, const Point& v2)
{
Unit x1 = getX(v1), x2 = getX(v2), y1 = getY(v1), y2 = getY(v2);
return x1 == x2 ? y1 < y2 : x1 < x2;
});
auto dir = [](const Point& p, const Point& q, const Point& r) {
return (Unit(getY(q)) - getY(p)) * (Unit(getX(r)) - getX(p)) -
(Unit(getX(q)) - getX(p)) * (Unit(getY(r)) - getY(p));
};
auto ik = pts.begin();
while(ik != pts.end()) {
while(U.size() > 1 && dir(U[U.size() - 2], U.back(), *ik) <= 0)
U.pop_back();
while(L.size() > 1 && dir(L[L.size() - 2], L.back(), *ik) >= 0)
L.pop_back();
U.emplace_back(*ik);
L.emplace_back(*ik);
++ik;
}
S ret; reserve(ret, U.size() + L.size());
if(is_clockwise<S>()) {
for(auto it = U.begin(); it != std::prev(U.end()); ++it)
addVertex(ret, *it);
for(auto it = L.rbegin(); it != std::prev(L.rend()); ++it)
addVertex(ret, *it);
if(closed) addVertex(ret, *std::prev(L.rend()));
} else {
for(auto it = L.begin(); it != std::prev(L.end()); ++it)
addVertex(ret, *it);
for(auto it = U.rbegin(); it != std::prev(U.rend()); ++it)
addVertex(ret, *it);
if(closed) addVertex(ret, *std::prev(U.rend()));
}
return ret;
}
template<class RawShapes, class S>
inline S convexHull(const RawShapes& sh, const MultiPolygonTag&)
{
namespace sl = shapelike;
S cntr;
for(auto& poly : sh)
for(auto it = sl::cbegin(poly); it != sl::cend(poly); ++it)
addVertex(cntr, *it);
return convexHull(cntr, Tag<S>());
}
template<class TP, class TC>
inline bool isInside(const TP& point, const TC& circ,
const PointTag&, const CircleTag&)
{
auto r = circ.radius();
return pointlike::squaredDistance(point, circ.center()) < r * r;
}
template<class TP, class TB>
inline bool isInside(const TP& point, const TB& box,
const PointTag&, const BoxTag&)
{
auto px = getX(point);
auto py = getY(point);
auto minx = getX(box.minCorner());
auto miny = getY(box.minCorner());
auto maxx = getX(box.maxCorner());
auto maxy = getY(box.maxCorner());
return px > minx && px < maxx && py > miny && py < maxy;
}
template<class S, class TC>
inline bool isInside(const S& sh, const TC& circ,
const PolygonTag&, const CircleTag&)
{
return std::all_of(cbegin(sh), cend(sh), [&circ](const TPoint<S>& p)
{
return isInside(p, circ, PointTag(), CircleTag());
});
}
template<class TB, class TC>
inline bool isInside(const TB& box, const TC& circ,
const BoxTag&, const CircleTag&)
{
return isInside(box.minCorner(), circ, PointTag(), CircleTag()) &&
isInside(box.maxCorner(), circ, PointTag(), CircleTag());
}
template<class TBGuest, class TBHost>
inline bool isInside(const TBGuest& ibb, const TBHost& box,
const BoxTag&, const BoxTag&)
{
auto iminX = getX(ibb.minCorner());
auto imaxX = getX(ibb.maxCorner());
auto iminY = getY(ibb.minCorner());
auto imaxY = getY(ibb.maxCorner());
auto minX = getX(box.minCorner());
auto maxX = getX(box.maxCorner());
auto minY = getY(box.minCorner());
auto maxY = getY(box.maxCorner());
return iminX >= minX && imaxX <= maxX && iminY >= minY && imaxY <= maxY;
}
template<class S, class TB>
inline bool isInside(const S& poly, const TB& box,
const PolygonTag&, const BoxTag&)
{
return isInside(boundingBox(poly), box, BoxTag(), BoxTag());
}
template<class TGuest, class THost>
inline bool isInside(const TGuest& guest, const THost& host) {
return isInside(guest, host, Tag<TGuest>(), Tag<THost>());
}
template<class S> // Potential O(1) implementation may exist
inline TPoint<S>& vertex(S& sh, unsigned long idx,
const PolygonTag&)
{
return *(shapelike::begin(contour(sh)) + idx);
}
template<class S> // Potential O(1) implementation may exist
inline TPoint<S>& vertex(S& sh, unsigned long idx,
const PathTag&)
{
return *(shapelike::begin(sh) + idx);
}
template<class S> // Potential O(1) implementation may exist
inline TPoint<S>& vertex(S& sh, unsigned long idx)
{
return vertex(sh, idx, Tag<S>());
}
template<class S> // Potential O(1) implementation may exist
inline const TPoint<S>& vertex(const S& sh,
unsigned long idx,
const PolygonTag&)
{
return *(shapelike::cbegin(contour(sh)) + idx);
}
template<class S> // Potential O(1) implementation may exist
inline const TPoint<S>& vertex(const S& sh,
unsigned long idx,
const PathTag&)
{
return *(shapelike::cbegin(sh) + idx);
}
template<class S> // Potential O(1) implementation may exist
inline const TPoint<S>& vertex(const S& sh,
unsigned long idx)
{
return vertex(sh, idx, Tag<S>());
}
template<class S>
inline size_t contourVertexCount(const S& sh)
{
return shapelike::cend(sh) - shapelike::cbegin(sh);
}
template<class S, class Fn>
inline void foreachVertex(S& sh, Fn fn, const PolygonTag&) {
foreachVertex(contour(sh), fn, PathTag());
for(auto& h : holes(sh)) foreachVertex(h, fn, PathTag());
}
template<class S, class Fn>
inline void foreachVertex(S& sh, Fn fn) {
foreachVertex(sh, fn, Tag<S>());
}
template<class Poly> inline bool isConvex(const Poly& sh, const PolygonTag&)
{
bool convex = true;
convex &= isConvex(contour(sh), PathTag());
convex &= holeCount(sh) == 0;
return convex;
}
template<class S> inline bool isConvex(const S& sh) // dispatch
{
return isConvex(sh, Tag<S>());
}
template<class Box> inline void offset(Box& bb, TCoord<Box> d, const BoxTag&)
{
TPoint<Box> md{d, d};
bb.minCorner() -= md;
bb.maxCorner() += md;
}
template<class C> inline void offset(C& circ, TCoord<C> d, const CircleTag&)
{
circ.radius(circ.radius() + double(d));
}
// Dispatch function
template<class S> inline void offset(S& sh, TCoord<S> d) {
offset(sh, d, Tag<S>());
}
}
#define DECLARE_MAIN_TYPES(T) \
using Polygon = T; \
using Point = TPoint<T>; \
using Coord = TCoord<Point>; \
using Contour = TContour<T>; \
using Box = _Box<Point>; \
using Circle = _Circle<Point>; \
using Segment = _Segment<Point>; \
using Polygons = TMultiShape<T>
namespace sl = shapelike;
namespace pl = pointlike;
}
#endif // GEOMETRY_TRAITS_HPP