lsst::sphgeom::ConvexPolygon Class Reference

ConvexPolygon is a closed convex polygon on the unit sphere. More...

#include <ConvexPolygon.h>

Inheritance diagram for lsst::sphgeom::ConvexPolygon:

Public Member Functions
	ConvexPolygon (std::vector< UnitVector3d > const &points)
	This constructor creates a convex polygon that is the convex hull of the given set of points. More...
	ConvexPolygon (UnitVector3d const &v0, UnitVector3d const &v1, UnitVector3d const &v2)
	This constructor creates a triangle with the given vertices. More...
	ConvexPolygon (UnitVector3d const &v0, UnitVector3d const &v1, UnitVector3d const &v2, UnitVector3d const &v3)
	This constructor creates a quadrilateral with the given vertices. More...
bool	operator== (ConvexPolygon const &p) const
	Two convex polygons are equal iff they contain the same points. More...
bool	operator!= (ConvexPolygon const &p) const
std::vector< UnitVector3d > const &	getVertices () const
UnitVector3d	getCentroid () const
	The centroid of a polygon is its center of mass projected onto S², assuming a uniform mass distribution over the polygon surface. More...
std::unique_ptr< Region >	clone () const override
	clone returns a deep copy of this region. More...
Box	getBoundingBox () const override
	getBoundingBox returns a bounding-box for this region. More...
Box3d	getBoundingBox3d () const override
	getBoundingBox3d returns a 3-dimensional bounding-box for this region. More...
Circle	getBoundingCircle () const override
	getBoundingCircle returns a bounding-circle for this region. More...
Relationship	relate (Region const &r) const override
Relationship	relate (Box const &) const override
Relationship	relate (Circle const &) const override
Relationship	relate (ConvexPolygon const &) const override
Relationship	relate (Ellipse const &) const override
std::vector< uint8_t >	encode () const override
	encode serializes this region into an opaque byte string. More...
virtual bool	contains (UnitVector3d const &) const=0
	contains tests whether the given unit vector is inside this region. More...
bool	contains (double x, double y, double z) const
	contains tests whether the unit vector defined by the given (not necessarily normalized) coordinates is inside this region. More...
bool	contains (double lon, double lat) const
	contains tests whether the unit vector defined by the given longitude and latitude coordinates (in radians) is inside this region. More...
bool	contains (double x, double y, double z) const
	contains tests whether the unit vector defined by the given (not necessarily normalized) coordinates is inside this region. More...
bool	contains (double lon, double lat) const
	contains tests whether the unit vector defined by the given longitude and latitude coordinates (in radians) is inside this region. More...
bool	contains (UnitVector3d const &v) const override
bool	contains (Region const &r) const
bool	isDisjointFrom (Region const &r) const
bool	intersects (Region const &r) const
bool	isWithin (Region const &r) const

Static Public Member Functions
static ConvexPolygon	convexHull (std::vector< UnitVector3d > const &points)
	convexHull returns the convex hull of the given set of points if it exists and throws an exception otherwise. More...
static std::unique_ptr< ConvexPolygon >	decode (std::vector< uint8_t > const &s)
static std::unique_ptr< ConvexPolygon >	decode (uint8_t const *buffer, size_t n)

Static Public Attributes
static constexpr uint8_t	TYPE_CODE = 'p'

Detailed Description

ConvexPolygon is a closed convex polygon on the unit sphere.

Its edges are great circles (geodesics), and the shorter of the two great circle segments between any two points on the polygon boundary is contained in the polygon.

The vertices of a convex polygon are distinct and have counter-clockwise orientation when viewed from outside the unit sphere. No three consecutive vertices are coplanar and edges do not intersect except at vertices.

Furthermore, if a convex polygon contains a point p of S², then we require that it be disjoint from point -p. This guarantees the existence of a unique shortest great circle segment between any 2 points contained in the polygon, but means e.g. that hemispheres and lunes cannot be represented by convex polygons.

Currently, the only way to construct a convex polygon is to compute the convex hull of a point set.

Definition at line 57 of file ConvexPolygon.h.

Constructor & Destructor Documentation

ConvexPolygon() [1/3]

lsst::sphgeom::ConvexPolygon::ConvexPolygon ( std::vector< UnitVector3d > const &  points )

explicit

This constructor creates a convex polygon that is the convex hull of the given set of points.

Definition at line 255 of file ConvexPolygon.cc.

                                                                   :
    _vertices(points)
{
    computeHull(_vertices);
}

ConvexPolygon() [2/3]

lsst::sphgeom::ConvexPolygon::ConvexPolygon ( UnitVector3d const &  v0, UnitVector3d const &  v1, UnitVector3d const &  v2  )

inline

This constructor creates a triangle with the given vertices.

It is assumed that orientation(v0, v1, v2) = 1. Use with caution - for performance reasons, this is not verified!

Definition at line 77 of file ConvexPolygon.h.

                                           :
        _vertices{v0, v1, v2}
    {}

ConvexPolygon() [3/3]

lsst::sphgeom::ConvexPolygon::ConvexPolygon ( UnitVector3d const &  v0, UnitVector3d const &  v1, UnitVector3d const &  v2, UnitVector3d const &  v3  )

inline

This constructor creates a quadrilateral with the given vertices.

It is assumed that orientation(v0, v1, v2), orientation(v1, v2, v3), orientation(v2, v3, v0), and orientation (v3, v0, v1) are all 1. Use with caution - for performance reasons, this is not verified!

Definition at line 88 of file ConvexPolygon.h.

                                           :
        _vertices{v0, v1, v2, v3}
    {}

Member Function Documentation

clone()

std::unique_ptr<Region> lsst::sphgeom::ConvexPolygon::clone ( ) const

inlineoverridevirtual

clone returns a deep copy of this region.

Implements lsst::sphgeom::Region.

Definition at line 108 of file ConvexPolygon.h.

                                                 {
        return std::unique_ptr<ConvexPolygon>(new ConvexPolygon(*this));
    }

contains() [1/7]

bool lsst::sphgeom::Region::contains

contains tests whether the unit vector defined by the given longitude and latitude coordinates (in radians) is inside this region.

Definition at line 104 of file Region.cc.

                                                  {
    return contains(UnitVector3d(LonLat::fromRadians(lon, lat)));
}

contains() [2/7]

bool lsst::sphgeom::Region::contains ( double  lon, double  lat  ) const

inherited

contains tests whether the unit vector defined by the given longitude and latitude coordinates (in radians) is inside this region.

Definition at line 43 of file Region.cc.

                                                  {
    return contains(UnitVector3d(LonLat::fromRadians(lon, lat)));
}

contains() [3/7]

bool lsst::sphgeom::Region::contains

contains tests whether the unit vector defined by the given (not necessarily normalized) coordinates is inside this region.

Definition at line 100 of file Region.cc.

                                                        {
    return contains(UnitVector3d(x, y, z));
}

contains() [4/7]

bool lsst::sphgeom::Region::contains ( double  x, double  y, double  z  ) const

inherited

contains tests whether the unit vector defined by the given (not necessarily normalized) coordinates is inside this region.

Definition at line 39 of file Region.cc.

                                                        {
    return contains(UnitVector3d(x, y, z));
}

contains() [5/7]

bool lsst::sphgeom::ConvexPolygon::contains

(

Region const &

r

)

const

contains returns true if the intersection of this convex polygon and x is equal to x.

Definition at line 316 of file ConvexPolygon.cc.

                                                   {
    return (relate(r) & CONTAINS) != 0;
}

contains() [6/7]

virtual bool lsst::sphgeom::Region::contains

contains tests whether the given unit vector is inside this region.

contains() [7/7]

bool lsst::sphgeom::ConvexPolygon::contains ( UnitVector3d const &  v ) const

overridevirtual

contains returns true if the intersection of this convex polygon and x is equal to x.

Implements lsst::sphgeom::Region.

Definition at line 312 of file ConvexPolygon.cc.

                                                         {
    return detail::contains(_vertices.begin(), _vertices.end(), v);
}

convexHull()

static ConvexPolygon lsst::sphgeom::ConvexPolygon::convexHull ( std::vector< UnitVector3d > const &  points )

inlinestatic

convexHull returns the convex hull of the given set of points if it exists and throws an exception otherwise.

Though points are supplied in a vector, they really are conceptually a set - the ConvexPolygon returned is invariant under permutation of the input array.

Definition at line 65 of file ConvexPolygon.h.

                                                                            {
        return ConvexPolygon(points);
    }

decode() [1/2]

static std::unique_ptr<ConvexPolygon> lsst::sphgeom::ConvexPolygon::decode ( std::vector< uint8_t > const &  s )

inlinestatic

decode deserializes a ConvexPolygon from a byte string produced by encode.

Definition at line 157 of file ConvexPolygon.h.

                                                                             {
        return decode(s.data(), s.size());
    }

decode() [2/2]

std::unique_ptr< ConvexPolygon > lsst::sphgeom::ConvexPolygon::decode ( uint8_t const *  buffer, size_t  n  )

static

decode deserializes a ConvexPolygon from a byte string produced by encode.

Definition at line 361 of file ConvexPolygon.cc.

{
    if (buffer == nullptr || *buffer != TYPE_CODE ||
        n < 1 + 24*3 || (n - 1) % 24 != 0) {
        throw std::runtime_error("Byte-string is not an encoded ConvexPolygon");
    }
    std::unique_ptr<ConvexPolygon> poly(new ConvexPolygon);
    ++buffer;
    size_t nv = (n - 1) / 24;
    poly->_vertices.reserve(nv);
    for (size_t i = 0; i < nv; ++i, buffer += 24) {
        poly->_vertices.push_back(UnitVector3d::fromNormalized(
            decodeDouble(buffer),
            decodeDouble(buffer + 8),
            decodeDouble(buffer + 16)
        ));
    }
    return poly;
}

encode()

std::vector< uint8_t > lsst::sphgeom::ConvexPolygon::encode ( ) const

overridevirtual

encode serializes this region into an opaque byte string.

Byte strings emitted by encode can be deserialized with decode.

Implements lsst::sphgeom::Region.

Definition at line 348 of file ConvexPolygon.cc.

                                               {
    std::vector<uint8_t> buffer;
    uint8_t tc = TYPE_CODE;
    buffer.reserve(1 + 24 * _vertices.size());
    buffer.push_back(tc);
    for (UnitVector3d const & v: _vertices) {
        encodeDouble(v.x(), buffer);
        encodeDouble(v.y(), buffer);
        encodeDouble(v.z(), buffer);
    }
    return buffer;
}

getBoundingBox()

Box lsst::sphgeom::ConvexPolygon::getBoundingBox ( ) const

overridevirtual

getBoundingBox returns a bounding-box for this region.

Implements lsst::sphgeom::Region.

Definition at line 304 of file ConvexPolygon.cc.

                                        {
    return detail::boundingBox(_vertices.begin(), _vertices.end());
}

getBoundingBox3d()

Box3d lsst::sphgeom::ConvexPolygon::getBoundingBox3d ( ) const

overridevirtual

getBoundingBox3d returns a 3-dimensional bounding-box for this region.

Implements lsst::sphgeom::Region.

Definition at line 308 of file ConvexPolygon.cc.

                                            {
    return detail::boundingBox3d(_vertices.begin(), _vertices.end());
}

getBoundingCircle()

Circle lsst::sphgeom::ConvexPolygon::getBoundingCircle ( ) const

overridevirtual

getBoundingCircle returns a bounding-circle for this region.

Implements lsst::sphgeom::Region.

Definition at line 300 of file ConvexPolygon.cc.

                                              {
    return detail::boundingCircle(_vertices.begin(), _vertices.end());
}

getCentroid()

UnitVector3d lsst::sphgeom::ConvexPolygon::getCentroid

(

)

const

The centroid of a polygon is its center of mass projected onto S², assuming a uniform mass distribution over the polygon surface.

Definition at line 296 of file ConvexPolygon.cc.

                                              {
    return detail::centroid(_vertices.begin(), _vertices.end());
}

getVertices()

std::vector<UnitVector3d> const& lsst::sphgeom::ConvexPolygon::getVertices ( ) const

inline

Definition at line 99 of file ConvexPolygon.h.

                                                        {
        return _vertices;
    }

intersects()

bool lsst::sphgeom::ConvexPolygon::intersects

(

Region const &

r

)

const

intersects returns true if the intersection of this convex polygon and x is non-empty.

Definition at line 324 of file ConvexPolygon.cc.

                                                     {
    return !isDisjointFrom(r);
}

isDisjointFrom()

bool lsst::sphgeom::ConvexPolygon::isDisjointFrom

(

Region const &

r

)

const

isDisjointFrom returns true if the intersection of this convex polygon and x is empty.

Definition at line 320 of file ConvexPolygon.cc.

                                                         {
    return (relate(r) & DISJOINT) != 0;
}

isWithin()

bool lsst::sphgeom::ConvexPolygon::isWithin

(

Region const &

r

)

const

isWithin returns true if the intersection of this convex polygon and x is this convex polygon.

Definition at line 328 of file ConvexPolygon.cc.

                                                   {
    return (relate(r) & WITHIN) != 0;
}

operator!=()

bool lsst::sphgeom::ConvexPolygon::operator!= ( ConvexPolygon const &  p ) const

inline

Definition at line 97 of file ConvexPolygon.h.

{ return !(*this == p); }

operator==()

bool lsst::sphgeom::ConvexPolygon::operator==

(

ConvexPolygon const &

p

)

const

Two convex polygons are equal iff they contain the same points.

Definition at line 261 of file ConvexPolygon.cc.

                                                            {
    if (this == &p) {
        return true;
    }
    if (_vertices.size() != p._vertices.size()) {
        return false;
    }
    VertexIterator i = _vertices.begin();
    VertexIterator f = p._vertices.begin();
    VertexIterator const ep = p._vertices.end();
    // Find vertex f of p equal to the first vertex of this polygon.
    for (; f != ep; ++f) {
        if (*i == *f) {
            break;
        }
    }
    if (f == ep) {
        // No vertex of p is equal to the first vertex of this polygon.
        return false;
    }
    // Now, compare all vertices.
    ++i;
    for (VertexIterator j = f + 1; j != ep; ++i, ++j) {
        if (*i != *j) {
            return false;
        }
    }
    for (VertexIterator j = p._vertices.begin(); j != f; ++i, ++j) {
        if (*i != *j) {
            return false;
        }
    }
    return true;
}

relate() [1/5]

Relationship lsst::sphgeom::ConvexPolygon::relate ( Box const &  ) const

overridevirtual

relate computes the spatial relationships between this region A and another region B. The return value S is a bitset with the following properties:

• Bit S & DISJOINT is set only if A and B do not have any points in common.
• Bit S & CONTAINS is set only if A contains all points in B.
• Bit S & WITHIN is set only if B contains all points in A.

Said another way: if the CONTAINS, WITHIN or DISJOINT bit is set, then the corresponding spatial relationship between the two regions holds conclusively. If it is not set, the relationship may or may not hold.

These semantics allow for conservative relationship computations. In particular, a Region may choose to implement relate by replacing itself and/or the argument with a simplified bounding region.

Implements lsst::sphgeom::Region.

Definition at line 332 of file ConvexPolygon.cc.

                                                      {
    return detail::relate(_vertices.begin(), _vertices.end(), b);
}

relate() [2/5]

Relationship lsst::sphgeom::ConvexPolygon::relate ( Circle const &  ) const

overridevirtual

relate computes the spatial relationships between this region A and another region B. The return value S is a bitset with the following properties:

• Bit S & DISJOINT is set only if A and B do not have any points in common.
• Bit S & CONTAINS is set only if A contains all points in B.
• Bit S & WITHIN is set only if B contains all points in A.

Said another way: if the CONTAINS, WITHIN or DISJOINT bit is set, then the corresponding spatial relationship between the two regions holds conclusively. If it is not set, the relationship may or may not hold.

These semantics allow for conservative relationship computations. In particular, a Region may choose to implement relate by replacing itself and/or the argument with a simplified bounding region.

Implements lsst::sphgeom::Region.

Definition at line 336 of file ConvexPolygon.cc.

                                                         {
    return detail::relate(_vertices.begin(), _vertices.end(), c);
}

relate() [3/5]

Relationship lsst::sphgeom::ConvexPolygon::relate ( ConvexPolygon const &  ) const

overridevirtual

relate computes the spatial relationships between this region A and another region B. The return value S is a bitset with the following properties:

• Bit S & DISJOINT is set only if A and B do not have any points in common.
• Bit S & CONTAINS is set only if A contains all points in B.
• Bit S & WITHIN is set only if B contains all points in A.

Said another way: if the CONTAINS, WITHIN or DISJOINT bit is set, then the corresponding spatial relationship between the two regions holds conclusively. If it is not set, the relationship may or may not hold.

These semantics allow for conservative relationship computations. In particular, a Region may choose to implement relate by replacing itself and/or the argument with a simplified bounding region.

Implements lsst::sphgeom::Region.

Definition at line 340 of file ConvexPolygon.cc.

                                                                {
    return detail::relate(_vertices.begin(), _vertices.end(), p);
}

relate() [4/5]

Relationship lsst::sphgeom::ConvexPolygon::relate ( Ellipse const &  ) const

overridevirtual

relate computes the spatial relationships between this region A and another region B. The return value S is a bitset with the following properties:

• Bit S & DISJOINT is set only if A and B do not have any points in common.
• Bit S & CONTAINS is set only if A contains all points in B.
• Bit S & WITHIN is set only if B contains all points in A.

Said another way: if the CONTAINS, WITHIN or DISJOINT bit is set, then the corresponding spatial relationship between the two regions holds conclusively. If it is not set, the relationship may or may not hold.

These semantics allow for conservative relationship computations. In particular, a Region may choose to implement relate by replacing itself and/or the argument with a simplified bounding region.

Implements lsst::sphgeom::Region.

Definition at line 344 of file ConvexPolygon.cc.

                                                          {
    return detail::relate(_vertices.begin(), _vertices.end(), e);
}

relate() [5/5]

Relationship lsst::sphgeom::ConvexPolygon::relate ( Region const &  ) const

inlineoverridevirtual

relate computes the spatial relationships between this region A and another region B. The return value S is a bitset with the following properties:

• Bit S & DISJOINT is set only if A and B do not have any points in common.
• Bit S & CONTAINS is set only if A contains all points in B.
• Bit S & WITHIN is set only if B contains all points in A.

Said another way: if the CONTAINS, WITHIN or DISJOINT bit is set, then the corresponding spatial relationship between the two regions holds conclusively. If it is not set, the relationship may or may not hold.

These semantics allow for conservative relationship computations. In particular, a Region may choose to implement relate by replacing itself and/or the argument with a simplified bounding region.

Implements lsst::sphgeom::Region.

Definition at line 143 of file ConvexPolygon.h.

                                                         {
        // Dispatch on the type of r.
        return invert(r.relate(*this));
    }

Member Data Documentation

TYPE_CODE

constexpr uint8_t lsst::sphgeom::ConvexPolygon::TYPE_CODE = 'p'

staticconstexpr

Definition at line 59 of file ConvexPolygon.h.

---

The documentation for this class was generated from the following files:

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/sphgeom/22.0.1-6-g1c63a23+7fa3b7d9b6/include/lsst/sphgeom/ConvexPolygon.h
• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/sphgeom/22.0.1-6-g1c63a23+7fa3b7d9b6/src/ConvexPolygon.cc