Q3cPixelization.cc

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/*
 * LSST Data Management System
 * Copyright 2016 AURA/LSST.
 *
 * This product includes software developed by the
 * LSST Project (http://www.lsst.org/).
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the LSST License Statement and
 * the GNU General Public License along with this program.  If not,
 * see <https://www.lsstcorp.org/LegalNotices/>.
 */
 
 
#include "lsst/sphgeom/Q3cPixelization.h"
 
#include <stdexcept>
 
#include "lsst/sphgeom/ConvexPolygon.h"
#include "lsst/sphgeom/curve.h"
#include "lsst/sphgeom/UnitVector3d.h"
 
#include "PixelFinder.h"
#include "Q3cPixelizationImpl.h"
 
 
namespace lsst {
namespace sphgeom {
 
namespace {
 
// See commentary in Q3cPixelizationImpl.h for an explanation of
// these lookup tables.
 
constexpr uint8_t UNUSED = 255;
 
alignas(64) uint8_t const FACE_NUM[64] = {
         3,      3,      3,      3, UNUSED,      0, UNUSED, UNUSED,
    UNUSED, UNUSED,      5, UNUSED, UNUSED, UNUSED, UNUSED, UNUSED,
    UNUSED, UNUSED, UNUSED,      2, UNUSED,      0, UNUSED,      2,
    UNUSED, UNUSED,      5,      2, UNUSED, UNUSED, UNUSED,      2,
         4, UNUSED, UNUSED, UNUSED,      4,      0, UNUSED, UNUSED,
         4, UNUSED,      5, UNUSED,      4, UNUSED, UNUSED, UNUSED,
    UNUSED, UNUSED, UNUSED, UNUSED, UNUSED,      0, UNUSED, UNUSED,
    UNUSED, UNUSED,      5, UNUSED,      1,      1,      1,      1
};
 
uint8_t const FACE_COMP[6][4] = {
    {1, 0, 2, UNUSED}, {1, 2, 0, UNUSED}, {0, 2, 1, UNUSED},
    {1, 2, 0, UNUSED}, {0, 2, 1, UNUSED}, {1, 0, 2, UNUSED}
};
 
alignas(16) double const FACE_CONST[6][4] = {
    { 1.0, -1.0,  1.0, 0.0},
    { 1.0,  1.0,  1.0, 0.0},
    {-1.0,  1.0,  1.0, 0.0},
    {-1.0,  1.0, -1.0, 0.0},
    { 1.0,  1.0, -1.0, 0.0},
    { 1.0,  1.0, -1.0, 0.0}
};
 
// The amount by which pixel boundaries are dilated (in u and v) prior to
// being mapped to unit vectors. This dilation ensures that the polygonal
// representation of a pixel contains all unit vectors that map to that
// pixel.
//
// The value is slightly more than the maximum absolute error incurred by
// mapping face coordinates (u,v) to the unit sphere and back.
constexpr double DILATION = 1.0e-15;
 
// `wrapIndex` returns the Q3C index for grid coordinates (face, s, t) at
// the given level. Both s and t may underflow or overflow by 1, i.e. wrap
// to an adjacent face.
uint64_t wrapIndex(int level,
                   int face,
                   uint32_t s,
                   uint32_t t)
{
    uint32_t const stMax = (static_cast<uint32_t>(1) << level) - 1;
    // Wrap until no more underflow or overflow is detected.
    while (true) {
        if (s == static_cast<uint32_t>(-1)) {
            switch (face) {
                case 0: face = 4; s = stMax - t; t = stMax; break;
                case 1: face = 4; s = stMax; break;
                case 2: face = 1; s = stMax; break;
                case 3: face = 2; s = stMax; break;
                case 4: face = 3; s = stMax; break;
                case 5: face = 4; s = t; t = 0; break;
                default: break;
            }
            continue;
        } else if (s > stMax) {
            switch (face) {
                case 0: face = 2; s = t; t = stMax; break;
                case 1: face = 2; s = 0; break;
                case 2: face = 3; s = 0; break;
                case 3: face = 4; s = 0; break;
                case 4: face = 1; s = 0; break;
                case 5: face = 2; s = stMax - t; t = 0; break;
                default: break;
            }
            continue;
        } else if (t == static_cast<uint32_t>(-1)) {
            switch (face) {
                case 0: face = 1; t = stMax; break;
                case 1: face = 5; t = stMax; break;
                case 2: face = 5; t = stMax - s; s = stMax; break;
                case 3: face = 5; t = 0; s = stMax - s; break;
                case 4: face = 5; t = s; s = 0; break;
                case 5: face = 3; t = 0; s = stMax - s; break;
                default: break;
            }
            continue;
        } else if (t > stMax) {
            switch (face) {
                case 0: face = 3; t = stMax; s = stMax - s; break;
                case 1: face = 0; t = 0; break;
                case 2: face = 0; t = s; s = stMax; break;
                case 3: face = 0; t = stMax; s = stMax - s; break;
                case 4: face = 0; t = stMax - s; s = 0; break;
                case 5: face = 1; t = 0; break;
                default: break;
            }
            continue;
        }
        break;
    }
    return (static_cast<uint64_t>(face) << (2 * level)) | mortonIndex(s, t);
}
 
int findNeighborhood(int level, uint64_t i, uint64_t * dst) {
    uint64_t const mask = (static_cast<uint64_t>(1) << (2 * level)) - 1;
    int const face = static_cast<int>(i >> (2 * level));
    uint32_t s, t;
    std::tie(s, t) = mortonIndexInverse(i & mask);
    dst[0] = wrapIndex(level, face, s - 1, t - 1);
    dst[1] = wrapIndex(level, face, s    , t - 1);
    dst[2] = wrapIndex(level, face, s + 1, t - 1);
    dst[3] = wrapIndex(level, face, s - 1, t);
    dst[4] = i;
    dst[5] = wrapIndex(level, face, s + 1, t);
    dst[6] = wrapIndex(level, face, s - 1, t + 1);
    dst[7] = wrapIndex(level, face, s    , t + 1);
    dst[8] = wrapIndex(level, face, s + 1, t + 1);
    std::sort(dst, dst + 9);
    return static_cast<int>(std::unique(dst, dst + 9) - dst);
}
 
#if defined(NO_SIMD) || !defined(__x86_64__)
    void makeQuad(uint64_t i, int level, UnitVector3d * verts) {
        uint64_t const mask = (static_cast<uint64_t>(1) << (2 * level)) - 1;
        int const face = static_cast<int>(i >> (2 * level));
        double const faceScale = FACE_SCALE[level];
        double u0, v0;
        uint32_t s, t;
        std::tie(s, t) = mortonIndexInverse(i & mask);
        std::tie(u0, v0) = gridToFace(
            level, static_cast<int32_t>(s), static_cast<int32_t>(t));
        double u1 = (u0 + faceScale) + DILATION;
        double v1 = (v0 + faceScale) + DILATION;
        u0 -= DILATION;
        v0 -= DILATION;
        verts[0] = faceToSphere(face, u0, v0, FACE_COMP, FACE_CONST);
        verts[1] = faceToSphere(face, u1, v0, FACE_COMP, FACE_CONST);
        verts[2] = faceToSphere(face, u1, v1, FACE_COMP, FACE_CONST);
        verts[3] = faceToSphere(face, u0, v1, FACE_COMP, FACE_CONST);
    }
#else
    void makeQuad(uint64_t i, int level, UnitVector3d * verts) {
        uint64_t const mask = (static_cast<uint64_t>(1) << (2 * level)) - 1;
        int const face = static_cast<int>(i >> (2 * level));
        __m128d faceScale = _mm_set1_pd(FACE_SCALE[level]);
        __m128d dilation = _mm_set1_pd(DILATION);
        __m128d u0v0 = gridToFace(level, mortonIndexInverseSimd(i & mask));
        __m128d u1v1 = _mm_add_pd(u0v0, faceScale);
        u0v0 = _mm_sub_pd(u0v0, dilation);
        u1v1 = _mm_add_pd(u1v1, dilation);
        verts[0] = faceToSphere(face, u0v0, FACE_COMP, FACE_CONST);
        verts[1] = faceToSphere(face, _mm_shuffle_pd(u1v1, u0v0, 2),
                                FACE_COMP, FACE_CONST);
        verts[2] = faceToSphere(face, u1v1, FACE_COMP, FACE_CONST);
        verts[3] = faceToSphere(face, _mm_shuffle_pd(u0v0, u1v1, 2),
                                FACE_COMP, FACE_CONST);
    }
#endif
 
 
// `Q3cPixelFinder` locates Q3C pixels that intersect a region.
//
// For now, we always begin with a loop over the root cube faces. For small
// regions, this could be made significantly faster by computing the Q3C
// index of the region bounding circle center, and looping over that pixel
// and its neighbors.
//
// The subdivision level for the initial index computation would have to be
// chosen such that the 8 or 9 pixel neighborhood of the center pixel is
// guaranteed to contain the bounding circle. The minimum angular pixel width
// could be precomputed per level. Alternatively, the minimum angle (and
// chord length) between two points separated by at least one pixel can be
// shown to be greater than √2/3 * 2^-L at level L. Given the bounding circle
// radius R, the subdivision level L of the initial neighborhood is the binary
// exponent of √2/3/R (and can be extracted by calling std::frexp).
//
// This is left as a future optimization.
template <typename RegionType, bool InteriorOnly>
class Q3cPixelFinder: public detail::PixelFinder<
    Q3cPixelFinder<RegionType, InteriorOnly>, RegionType, InteriorOnly, 4>
{
private:
    using Base = detail::PixelFinder<
        Q3cPixelFinder<RegionType, InteriorOnly>, RegionType, InteriorOnly, 4>;
    using Base::visit;
 
public:
    Q3cPixelFinder(RangeSet & ranges,
                   RegionType const & region,
                   int level,
                   size_t maxRanges):
        Base(ranges, region, level, maxRanges)
    {}
 
    void operator()() {
        UnitVector3d pixel[4];
        // Loop over cube faces
        for (uint64_t f = 0; f < 6; ++f) {
            makeQuad(f, 0, pixel);
            visit(pixel, f, 0);
        }
    }
 
    void subdivide(UnitVector3d const *, uint64_t i, int level) {
        UnitVector3d pixel[4];
        ++level;
        for (uint64_t c = i * 4; c != i * 4 + 4; ++c) {
            makeQuad(c, level, pixel);
            visit(pixel, c, level);
        }
    }
};
 
} // unnamed namespace
 
 
Q3cPixelization::Q3cPixelization(int level) : _level{level} {
    if (level < 0 || level > MAX_LEVEL) {
        throw std::invalid_argument("Q3C subdivision level not in [0, 30]");
    }
}
 
ConvexPolygon Q3cPixelization::quad(uint64_t i) const {
    if (i >= static_cast<uint64_t>(6) << (2 * _level)) {
        throw std::invalid_argument("Invalid Q3C index");
    }
    UnitVector3d verts[4];
    makeQuad(i, _level, verts);
    return ConvexPolygon(verts[0], verts[1], verts[2], verts[3]);
}
 
std::vector<uint64_t> Q3cPixelization::neighborhood(uint64_t i) const {
    if (i >= static_cast<uint64_t>(6) << (2 * _level)) {
        throw std::invalid_argument("Invalid Q3C index");
    }
    uint64_t indexes[9];
    int n = findNeighborhood(_level, i, indexes);
    return std::vector<uint64_t>(indexes, indexes + n);
}
 
std::string Q3cPixelization::toString(uint64_t i) const {
    static char const FACE_NORM[6][2] = {
        {'+', 'Z'}, {'+', 'X'}, {'+', 'Y'},
        {'-', 'X'}, {'-', 'Y'}, {'-', 'Z'},
    };
    char s[MAX_LEVEL + 2];
    if (i >= static_cast<uint64_t>(6) << (2 * _level)) {
        throw std::invalid_argument("Invalid Q3C index");
    }
    // Print in base-4, from least to most significant digit.
    char * p = s + (sizeof(s) - 1);
    for (int l = _level; l > 0; --l, --p, i >>= 2) {
        *p = '0' + (i & 3);
    }
    // The remaining bits correspond to the cube face.
    --p;
    p[0] = FACE_NORM[i][0];
    p[1] = FACE_NORM[i][1];
    return std::string(p, sizeof(s) - static_cast<size_t>(p - s));
}
 
std::unique_ptr<Region> Q3cPixelization::pixel(uint64_t i) const {
    if (i >= static_cast<uint64_t>(6) << (2 * _level)) {
        throw std::invalid_argument("Invalid Q3C index");
    }
    UnitVector3d verts[4];
    makeQuad(i, _level, verts);
    return std::unique_ptr<Region>(
        new ConvexPolygon(verts[0], verts[1], verts[2], verts[3]));
}
 
#if defined(NO_SIMD) || !defined(__x86_64__)
    uint64_t Q3cPixelization::index(UnitVector3d const & p) const {
        int face = faceNumber(p, FACE_NUM);
        double w = std::fabs(p(FACE_COMP[face][2]));
        double u = (p(FACE_COMP[face][0]) / w) * FACE_CONST[face][0];
        double v = (p(FACE_COMP[face][1]) / w) * FACE_CONST[face][1];
        std::tuple<int32_t, int32_t> g = faceToGrid(_level, u, v);
        uint64_t z = mortonIndex(static_cast<uint32_t>(std::get<0>(g)),
                                 static_cast<uint32_t>(std::get<1>(g)));
        return (static_cast<uint64_t>(face) << (2 * _level)) | z;
    }
#else
    uint64_t Q3cPixelization::index(UnitVector3d const & p) const {
        int face = faceNumber(p, FACE_NUM);
        __m128d ww = _mm_set1_pd(p(FACE_COMP[face][2]));
        __m128d uv = _mm_set_pd(p(FACE_COMP[face][1]), p(FACE_COMP[face][0]));
        uv = _mm_mul_pd(
            _mm_div_pd(uv, _mm_andnot_pd(_mm_set_pd(-0.0, -0.0), ww)),
            _mm_set_pd(FACE_CONST[face][1], FACE_CONST[face][0])
        );
        __m128i st = faceToGrid(_level, uv);
        return (static_cast<uint64_t>(face) << (2 * _level)) | mortonIndex(st);
    }
#endif
 
RangeSet Q3cPixelization::_envelope(Region const & r, size_t maxRanges) const {
    return detail::findPixels<Q3cPixelFinder, false>(r, maxRanges, _level);
}
 
RangeSet Q3cPixelization::_interior(Region const & r, size_t maxRanges) const {
    return detail::findPixels<Q3cPixelFinder, true>(r, maxRanges, _level);
}
 
}} // namespace lsst::sphgeom