lsst::sphgeom::HtmPixelization Class Reference

HtmPixelization provides HTM indexing of points and regions. More...

#include <HtmPixelization.h>

Inheritance diagram for lsst::sphgeom::HtmPixelization:

Public Member Functions
	HtmPixelization (int level)
	This constructor creates an HTM pixelization of the sphere with the given subdivision level. More...
int	getLevel () const
	getLevel returns the subdivision level of this pixelization. More...
RangeSet	universe () const override
	universe returns the set of all pixel indexes for this pixelization. More...
std::unique_ptr< Region >	pixel (uint64_t i) const override
	pixel returns the spherical region corresponding to the pixel with index i. More...
uint64_t	index (UnitVector3d const &) const override
	index computes the index of the pixel for v. More...
std::string	toString (uint64_t i) const override
	toString converts the given pixel index to a human-readable string. More...
RangeSet	envelope (Region const &r, size_t maxRanges=0) const
	envelope returns the indexes of the pixels intersecting the spherical region r. More...
RangeSet	interior (Region const &r, size_t maxRanges=0) const
	interior returns the indexes of the pixels within the spherical region r. More...

Static Public Member Functions
static int	level (uint64_t i)
	level returns the subdivision level of the given HTM index. More...
static ConvexPolygon	triangle (uint64_t i)
	triangle returns the triangle corresponding to the given HTM index. More...
static std::string	asString (uint64_t i)
	asString converts the given HTM index to a human readable string. More...

Static Public Attributes
static constexpr int	MAX_LEVEL = 24
	MAX_LEVEL is the maximum supported HTM subdivision level. More...

Detailed Description

HtmPixelization provides HTM indexing of points and regions.

Instances of this class are immutable and very cheap to copy.

Warning

Setting the maxRanges argument for envelope() or interior() to a non-zero value below 6 can result in very poor region pixelizations regardless of region size. For instance, if maxRanges is 1, a non-empty circle centered on an axis will be approximated by a hemisphere or the entire unit sphere, even as its radius tends to 0.

Definition at line 50 of file HtmPixelization.h.

Constructor & Destructor Documentation

HtmPixelization()

lsst::sphgeom::HtmPixelization::HtmPixelization ( int  level )

explicit

This constructor creates an HTM pixelization of the sphere with the given subdivision level.

If level ∉ [0, MAX_LEVEL], a std::invalid_argument is thrown.

Definition at line 164 of file HtmPixelization.cc.

                                          : _level(level) {
    if (level < 0 || level > MAX_LEVEL) {
        throw std::invalid_argument("Invalid HTM subdivision level");
    }
}

Member Function Documentation

asString()

std::string lsst::sphgeom::HtmPixelization::asString ( uint64_t  i )

static

asString converts the given HTM index to a human readable string.

The first character in the return value is always 'N' or 'S', indicating whether the root triangle containing i is in the northern or southern hemisphere. The second character is the index of the root triangle within that hemisphere (a digit in [0-3]). Each subsequent character is a digit in [0-3] corresponding to a child trixel index, so that reading the string from left to right corresponds to descent of the HTM triangle-tree.

If i is not a valid HTM index, a std::invalid_argument is thrown.

Definition at line 148 of file HtmPixelization.cc.

                                              {
    char s[MAX_LEVEL + 2];
    int l = level(i);
    if (l < 0 || l > MAX_LEVEL) {
        throw std::invalid_argument("Invalid HTM index");
    }
    // Print in base-4, from least to most significant digit.
    char * p = s + (sizeof(s) - 1);
    for (; l >= 0; --l, --p, i >>= 2) {
        *p = '0' + (i & 3);
    }
    // The remaining bit corresponds to the hemisphere.
    *p = (i & 1) == 0 ? 'S' : 'N';
    return std::string(p, sizeof(s) - static_cast<size_t>(p - s));
}

envelope()

RangeSet lsst::sphgeom::Pixelization::envelope ( Region const &  r, size_t  maxRanges = 0  ) const

inlineinherited

envelope returns the indexes of the pixels intersecting the spherical region r.

For hierarchical pixelizations, a good way to implement this is by top down tree traversal. Starting with the root pixels (e.g. Q3C cube faces, or HTM root triangles), a pixel P is tested for intersection with the region r. If P is already at the desired subdivision level and intersects r, its index is added to the output. If r contains P, the indexes of all children of P at the target subdivision level are output. Finally, if P intersects r, then P is subdivided and the algorithm recurses on its child pixels.

Using higher subdivision levels allows a region to be more closely approximated by smaller pixels, but for large input regions the cost of computing and storing their indexes can quickly become prohibitive.

The maxRanges parameter can be used to limit both these costs - setting it to a non-zero value sets a cap on the number of ranges returned by this method. To meet this constraint, implementations are allowed to return pixels that do not intersect r along with those that do. This allows two ranges [a, b) and [c, d), a < b < c < d, to be merged into one range [a, d) (by adding in the pixels [b, c)). Since simplification proceeds by adding pixels, the return value will always be a superset of the intersecting pixels.

In practice, the implementation of this method for a hierarchical pixelization like Q3C or HTM will lower the subdivision level when too many ranges have been found. Each coarse pixel I at level L - n corresponds to pixels [I*4ⁿ, (I + 1)*4ⁿ) at level L.

Definition at line 131 of file Pixelization.h.

                                                                    {
        return _envelope(r, maxRanges);
    }

getLevel()

int lsst::sphgeom::HtmPixelization::getLevel ( ) const

inline

getLevel returns the subdivision level of this pixelization.

Definition at line 84 of file HtmPixelization.h.

{ return _level; }

index()

uint64_t lsst::sphgeom::HtmPixelization::index ( UnitVector3d const &  v ) const

overridevirtual

index computes the index of the pixel for v.

Implements lsst::sphgeom::Pixelization.

Definition at line 170 of file HtmPixelization.cc.

                                                            {
    // Find the root triangle containing v.
    uint64_t r;
    if (v.z() < 0.0) {
        // v is in the southern hemisphere (root triangle 0, 1, 2, or 3).
        if (v.y() > 0.0) {
            r = (v.x() > 0.0) ? 0 : 1;
        } else if (v.y() == 0.0) {
            r = (v.x() >= 0.0) ? 0 : 2;
        } else {
            r = (v.x() < 0.0) ? 2 : 3;
        }
    } else {
        // v is in the northern hemisphere (root triangle 4, 5, 6, or 7).
        if (v.y() > 0.0) {
            r = (v.x() > 0.0) ? 7 : 6;
        } else if (v.y() == 0.0) {
            r = (v.x() >= 0.0) ? 7 : 5;
        } else {
            r = (v.x() < 0.0) ? 5 : 4;
        }
    }
    UnitVector3d v0 = rootVertex(r, 0);
    UnitVector3d v1 = rootVertex(r, 1);
    UnitVector3d v2 = rootVertex(r, 2);
    uint64_t i = r + 8;
    for (int l = 0; l < _level; ++l) {
        UnitVector3d m01 = UnitVector3d(v0 + v1);
        UnitVector3d m20 = UnitVector3d(v2 + v0);
        i <<= 2;
        if (orientation(v, m01, m20) >= 0) {
            v1 = m01; v2 = m20;
            continue;
        }
        UnitVector3d m12 = UnitVector3d(v1 + v2);
        if (orientation(v, m12, m01) >= 0) {
            v0 = v1; v1 = m12; v2 = m01;
            i += 1;
        } else if (orientation(v, m20, m12) >= 0) {
            v0 = v2; v1 = m20; v2 = m12;
            i += 2;
        } else {
            v0 = m12; v1 = m20; v2 = m01;
            i += 3;
        }
    }
    return i;
}

interior()

RangeSet lsst::sphgeom::Pixelization::interior ( Region const &  r, size_t  maxRanges = 0  ) const

inlineinherited

interior returns the indexes of the pixels within the spherical region r.

The maxRanges argument is analogous to the identically named envelope() argument. The only difference is that implementations must remove interior pixels to keep the number of ranges at or below the maximum. The return value is therefore always a subset of the interior pixels.

Definition at line 143 of file Pixelization.h.

                                                                    {
        return _interior(r, maxRanges);
    }

level()

int lsst::sphgeom::HtmPixelization::level ( uint64_t  i )

static

level returns the subdivision level of the given HTM index.

If i is not a valid HTM index, -1 is returned.

Definition at line 110 of file HtmPixelization.cc.

                                     {
    // An HTM index consists of 4 bits encoding the root triangle
    // number (8 - 15), followed by 2l bits, where each of the l bit pairs
    // encodes a child triangle number (0-3), and l is the desired level.
    int j = log2(i);
    // The level l is derivable from the index j of the MSB of i.
    // For i to be valid, j must be an odd integer > 1.
    if ((j & 1) == 0 || (j == 1)) {
        return -1;
    }
    return (j - 3) >> 1;
}

pixel()

std::unique_ptr<Region> lsst::sphgeom::HtmPixelization::pixel ( uint64_t  i ) const

inlineoverridevirtual

pixel returns the spherical region corresponding to the pixel with index i.

This region will contain all unit vectors v with index(v) == i. But it may also contain points with index not equal to i. To see why, consider a point that lies on the edge of a polygonal pixel - it is inside the polygons for both pixels sharing the edge, but must be assigned to exactly one pixel by the pixelization.

If i is not a valid pixel index, a std::invalid_argument is thrown.

Implements lsst::sphgeom::Pixelization.

Definition at line 91 of file HtmPixelization.h.

                                                           {
        return std::unique_ptr<Region>(new ConvexPolygon(triangle(i)));
    }

toString()

std::string lsst::sphgeom::HtmPixelization::toString ( uint64_t  i ) const

inlineoverridevirtual

toString converts the given pixel index to a human-readable string.

Implements lsst::sphgeom::Pixelization.

Definition at line 97 of file HtmPixelization.h.

{ return asString(i); }

triangle()

ConvexPolygon lsst::sphgeom::HtmPixelization::triangle ( uint64_t  i )

static

triangle returns the triangle corresponding to the given HTM index.

If i is not a valid HTM index, a std::invalid_argument is thrown.

Definition at line 123 of file HtmPixelization.cc.

                                                  {
    int l = level(i);
    if (l < 0 || l > MAX_LEVEL) {
        throw std::invalid_argument("Invalid HTM index");
    }
    l *= 2;
    uint64_t r = (i >> l) & 7;
    UnitVector3d v0 = rootVertex(r, 0);
    UnitVector3d v1 = rootVertex(r, 1);
    UnitVector3d v2 = rootVertex(r, 2);
    for (l -= 2; l >= 0; l -= 2) {
        int child = (i >> l) & 3;
        UnitVector3d m12 = UnitVector3d(v1 + v2);
        UnitVector3d m20 = UnitVector3d(v2 + v0);
        UnitVector3d m01 = UnitVector3d(v0 + v1);
        switch (child) {
            case 0: v1 = m01; v2 = m20; break;
            case 1: v0 = v1; v1 = m12; v2 = m01; break;
            case 2: v0 = v2; v1 = m20; v2 = m12; break;
            case 3: v0 = m12; v1 = m20; v2 = m01; break;
        }
    }
    return ConvexPolygon(v0, v1, v2);
}

universe()

RangeSet lsst::sphgeom::HtmPixelization::universe ( ) const

inlineoverridevirtual

universe returns the set of all pixel indexes for this pixelization.

Implements lsst::sphgeom::Pixelization.

Definition at line 86 of file HtmPixelization.h.

                                       {
        return RangeSet(static_cast<uint64_t>(8) << 2 * _level,
                        static_cast<uint64_t>(16) << 2 * _level);
    }

Member Data Documentation

MAX_LEVEL

constexpr int lsst::sphgeom::HtmPixelization::MAX_LEVEL = 24

staticconstexpr

MAX_LEVEL is the maximum supported HTM subdivision level.

Definition at line 53 of file HtmPixelization.h.

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