github-actions[bot] commented on code in PR #69032:
URL: https://github.com/apache/doris/pull/69032#discussion_r4434477659
##########
be/src/exprs/function/geo/wkb_parse.cpp:
##########
@@ -31,6 +39,315 @@
namespace doris {
+namespace {
+
+constexpr const char* wkb_names[] = {
+ "", "POINT", "LINESTRING", "POLYGON",
+ "MULTIPOINT", "MULTILINESTRING", "MULTIPOLYGON", "GEOMETRYCOLLECTION"};
+
+GeoParseStatus read_wkb_type(WkbParseContext& ctx, uint32_t* type, uint32_t*
dimensions = nullptr) {
+ if (ctx.dis.size() < 5) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ const auto order = ctx.dis.readByte();
+ if (order > 1) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ ctx.dis.setOrder(order == static_cast<unsigned char>(byteOrder::wkbNDR)
+ ? ByteOrderValues::EndianType::ENDIAN_LITTLE
+ : ByteOrderValues::EndianType::ENDIAN_BIG);
+ auto encoded = ctx.dis.readUnsigned();
+ constexpr uint32_t ewkb_metadata_flags = 0x80000000 | 0x40000000 |
WKB_SRID_FLAG;
+ // CRS belongs to the typed schema; PostGIS EWKB flags/SRID remain
legacy-only.
+ // Historical STRING constructors retain their EWKB XY interpretation.
+ if (!ctx.allow_ewkb_srid && (encoded & ewkb_metadata_flags) != 0) {
+ return GeoParseStatus::GEO_PARSE_WKB_UNSUPPORTED_METADATA;
+ }
+ if ((encoded & WKB_SRID_FLAG) != 0) {
+ if (!ctx.allow_ewkb_srid || ctx.dis.size() < sizeof(uint32_t)) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ ctx.srid = static_cast<int>(ctx.dis.readUnsigned());
+ encoded &= ~WKB_SRID_FLAG;
+ }
+ if (ctx.allow_ewkb_srid) {
+ // Preserve the legacy parser: ignore EWKB dimension flags and read XY
coordinates.
+ // Typed constructors keep rejecting these EWKB flags above.
+ encoded &= 0xFF;
+ }
+ const uint32_t dimension = encoded / 1000;
+ // Raw access preserves ISO XYZ/XYM/XYZM. The S2 parser does not request
dimensions,
+ // so POINT Z (1 2 3) is rejected before it can be read as an XY
calculation point.
+ if (dimension != 0 && dimensions == nullptr && !ctx.allow_ewkb_srid) {
+ return GeoParseStatus::GEO_PARSE_WKB_UNSUPPORTED_METADATA;
+ }
+ if (dimensions != nullptr) {
+ *dimensions = dimension;
+ }
+ encoded %= 1000;
+ // ISO adds 1000/2000/3000 to the base type; higher dimensional codes are
not defined.
+ if (dimension > 3) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ if (encoded < static_cast<uint32_t>(wkbType::wkbPoint) ||
+ encoded > static_cast<uint32_t>(wkbType::wkbGeometryCollection)) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ *type = encoded;
+ return GeoParseStatus::GEO_PARSE_OK;
+}
+
+// One cursor walks both validation and WKT output. Collection frames are
bounded
+// by the input size, rather than by the C++ call stack. Coordinates remain
raw.
+class RawWkbReader {
+public:
+ RawWkbReader(WkbParseContext& context, bool geographic, std::ostream*
output = nullptr,
+ GeoCoordinateListList* sequences = nullptr)
+ : _ctx(context), _geographic(geographic), _output(output),
_sequences(sequences) {}
+
+ GeoParseStatus read() {
+ do {
+ uint32_t type;
+ const auto status = read_wkb_type(_ctx, &type, &_dimensions);
+ if (status != GeoParseStatus::GEO_PARSE_OK) {
+ return status;
+ }
+ if (!matches_parent(type)) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ if (_frames.empty()) {
+ _root_type = type;
+ }
+ if (_frames.empty() ||
+ _frames.back().type ==
static_cast<uint32_t>(wkbType::wkbGeometryCollection)) {
+ emit(wkb_names[type]);
+ emit(" ");
+ constexpr std::string_view dimension_names[] = {"", "Z ", "M
", "ZM "};
+ emit(dimension_names[_dimensions]);
+ }
+ if (type <= static_cast<uint32_t>(wkbType::wkbPolygon)) {
+ if (!read_primitive(type)) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ } else {
+ uint32_t count;
+ if (!read_count(&count) || count > _ctx.dis.size() / 5) {
+ return GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+ if (count != 0) {
+ emit("(");
+ _frames.push_back({type, count, _dimensions});
+ continue;
+ }
+ emit("EMPTY");
+ }
+ finish_member();
+ } while (!_frames.empty());
+ return _ctx.dis.size() == 0 ? GeoParseStatus::GEO_PARSE_OK
+ :
GeoParseStatus::GEO_PARSE_WKB_SYNTAX_ERROR;
+ }
+
+ uint32_t root_type() const { return _root_type; }
+
+private:
+ struct Frame {
+ uint32_t type;
Review Comment:
[P1] Reject ISO dimensional metadata on typed spatial operations.
RawWkbReader::read() always passes &_dimensions, so read_wkb_type() skips its
nonzero-dimension rejection and validate_spatial_wkb() accepts ISO XYZ/XYM/XYZM
bytes. SpatialWkbGeoFunction then lets ST_AsText and other typed operations
consume values that the new function_geo_st_astext_rejects_spatial_wkb_with_z
test requires to fail with the unsupported-metadata error. Keep ISO dimensions
available for raw typed storage, but use a strict operation validator before
calculation/accessor functions.
##########
fe/fe-connector/fe-connector-iceberg/src/main/java/org/apache/doris/connector/iceberg/IcebergSpatialSchemaValidator.java:
##########
@@ -0,0 +1,157 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements. See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership. The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License. You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied. See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+package org.apache.doris.connector.iceberg;
+
+import org.apache.doris.connector.spi.DorisConnectorException;
+
+import org.apache.iceberg.BaseTable;
+import org.apache.iceberg.Schema;
+import org.apache.iceberg.StaticTableOperations;
+import org.apache.iceberg.Table;
+import org.apache.iceberg.TableMetadata;
+import org.apache.iceberg.TableOperations;
+import org.apache.iceberg.TableProperties;
+import org.apache.iceberg.encryption.EncryptionManager;
+import org.apache.iceberg.io.FileIO;
+import org.apache.iceberg.io.LocationProvider;
+import org.apache.iceberg.types.Type;
+import org.apache.iceberg.types.Types;
+
+import java.util.Map;
+
+/** Constraints of the Doris spatial Parquet writer, checked before DDL
commits and data writes. */
+final class IcebergSpatialSchemaValidator {
+ private IcebergSpatialSchemaValidator() {
+ }
+
+ /** Returns whether any leaf is spatial so V3/Parquet checks also apply to
nested columns. */
+ static boolean containsSpatial(Type type) {
+ if (type.typeId() == Type.TypeID.GEOMETRY || type.typeId() ==
Type.TypeID.GEOGRAPHY) {
+ return true;
+ }
+ boolean spatial = false;
+ if (type.isNestedType()) {
+ for (Types.NestedField field : type.asNestedType().fields()) {
+ spatial |= containsSpatial(field.type());
+ }
+ }
+ return spatial;
+ }
+
+ static boolean containsSpatial(Schema schema) {
+ return schema.columns().stream().anyMatch(field ->
containsSpatial(field.type()));
+ }
+
+ static void validateTable(int formatVersion, String fileFormat) {
Review Comment:
[P2] Reject unsupported projjson: CRS tables before Iceberg write planning.
validateTable() admits any v3 Parquet spatial schema, while the BE writer
returns NotImplemented for every referenced projjson: CRS in
validate_spatial_crs_for_write(). This lets CREATE/ALTER and plan construction
succeed, then fails when the data-file schema is built. Either reject this CRS
during DDL and every data-file write-plan validation or carry its definition
into Parquet metadata, and add a custom-CRS write regression.
##########
be/src/exprs/function/geo/geography_calculation.cpp:
##########
@@ -0,0 +1,1779 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements. See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership. The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License. You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied. See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+#include "exprs/function/geo/geography_calculation.h"
+
+#include <glog/logging.h>
+#include <s2/mutable_s2shape_index.h>
+#include <s2/s2boolean_operation.h>
+#include <s2/s2closest_edge_query.h>
+#include <s2/s2closest_point_query.h>
+#include <s2/s2contains_point_query.h>
+#include <s2/s2earth.h>
+#include <s2/s2edge_distances.h>
+#include <s2/s2lax_polygon_shape.h>
+#include <s2/s2loop.h>
+#include <s2/s2loop_measures.h>
+#include <s2/s2point.h>
+#include <s2/s2point_index.h>
+#include <s2/s2point_vector_shape.h>
+#include <s2/s2pointutil.h>
+#include <s2/s2polygon.h>
+#include <s2/s2polyline.h>
+#include <s2/s2predicates.h>
+#include <s2/s2shape_measures.h>
+
+#include <algorithm>
+#include <array>
+#include <bit>
+#include <boost/iterator/iterator_facade.hpp>
+// Integer proofs and software-wide arithmetic need no quadmath wrappers.
Boost's float128
+// numeric_limits specialization conflicts with libstdc++ 15 in the GCC
performance build.
+#if defined(__GNUC__) && !defined(__clang__) && __GNUC__ >= 15
+#define BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT
+#endif
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/multiprecision/cpp_int.hpp>
+#if defined(__GNUC__) && !defined(__clang__) && __GNUC__ >= 15
+#undef BOOST_CSTDFLOAT_NO_LIBQUADMATH_SUPPORT
+#endif
+#include <cmath>
+#include <cstdint>
+#include <limits>
+#include <map>
+#include <numbers>
+#include <optional>
+#include <set>
+#include <type_traits>
+#include <utility>
+
+#include "core/assert_cast.h"
+#include "core/custom_allocator.h"
+#include "exprs/function/geo/geo_types.h"
+#include "exprs/function/geo/wkb_parse.h"
+
+namespace doris {
+
+// Apple ARM64 long double has binary64 precision/range. Keep native wide
arithmetic
+// where available; software quad preserves the tiny residual products on
narrower ABIs.
+using GeographyFloat =
+ std::conditional_t<std::numeric_limits<long double>::digits >= 64 &&
+ std::numeric_limits<long
double>::min_exponent <= -4096,
+ long double,
boost::multiprecision::cpp_bin_float_quad>;
+static_assert(std::numeric_limits<GeographyFloat>::digits >= 64 &&
+ std::numeric_limits<GeographyFloat>::min_exponent <= -4096);
+
+template <typename Float>
+static Float geography_pi() {
+ if constexpr (std::is_same_v<Float, long double>) {
+ return std::numbers::pi_v<long double>;
+ } else {
+ // Public software acos avoids float128 constant
conversions/libquadmath on GCC.
+ static const Float pi = boost::multiprecision::acos(Float(-1));
+ return pi;
+ }
+}
+
+// Error-free TwoSum preserves tiny differences from a half-turn (e.g. -1e-15
+ 180).
+static std::pair<double, double> geography_degree_sum(double a, double b) {
+ const double high = a + b;
+ const double offset = high - a;
+ return {high, (a - (high - offset)) + (b - offset)};
+}
+
+// Reduce the exact degree sum before converting to radians. In particular,
+// 180 + (-1e-300) must retain its small sine instead of becoming sin(pi).
+template <typename Float = GeographyFloat>
+static std::pair<Float, Float> geography_degree_sincos(double a, double b = 0,
bool half = false) {
+ const auto [high, low] = geography_degree_sum(a, b);
+ int quadrant;
+ const Float reduced = [&] {
+ if constexpr (std::is_same_v<Float, long double>) {
+ return std::remquo(static_cast<Float>(high), half ? 180.0L :
90.0L, &quadrant) +
+ static_cast<Float>(low);
+ } else {
+ // high is binary64 and the periods are exact integers: its
reduced remainder
+ // is representable in binary64. Add TwoSum's low residual only
after widening.
+ return Float(std::remquo(high, half ? 180.0 : 90.0, &quadrant)) +
Float(low);
+ }
+ }();
+ const Float radians = reduced * (geography_pi<Float>() / 180) / (half ? 2
: 1);
+ using std::cos;
+ using std::sin;
+ const Float sine = sin(radians);
+ const Float cosine = cos(radians);
+ switch ((quadrant % 4 + 4) % 4) {
+ case 0:
+ return {sine, cosine};
+ case 1:
+ return {cosine, -sine};
+ case 2:
+ return {-sine, -cosine};
+ default:
+ return {-cosine, sine};
+ }
+}
+
+// Unlike cross(ToPoint(a), ToPoint(b)), these product identities do not
subtract
+// rounded nearly opposite vectors. Longitude-midpoint coordinates give
+// (-sin(dLon/2)*sin(latA+latB), cos(dLon/2)*sin(latA-latB),
+// cos(latA)*cos(latB)*sin(dLon)) for the oriented normal.
+template <typename Float = GeographyFloat>
+struct GeographyRawArc {
+ S2Point normal;
+ S2Point midpoint;
+
+ GeographyRawArc(const GeoCoordinate& a, const GeoCoordinate& b) {
+ const auto [sd, cd] = geography_degree_sincos<Float>(b.x, -a.x, true);
+ const auto [sm, cm] = geography_degree_sincos<Float>(a.x, b.x, true);
+ const auto rotate_unit = [&](Float x, Float y, Float z) {
+ using std::sqrt;
+ const Float norm = sqrt(x * x + y * y + z * z);
+ DCHECK_GT(norm, 0);
+ return S2Point(static_cast<double>((cm * x - sm * y) / norm),
+ static_cast<double>((sm * x + cm * y) / norm),
+ static_cast<double>(z / norm));
+ };
+ normal = rotate_unit(-sd * geography_degree_sincos<Float>(a.y,
b.y).first,
+ cd * geography_degree_sincos<Float>(a.y,
-b.y).first,
+ geography_degree_sincos<Float>(a.y).second *
+
geography_degree_sincos<Float>(b.y).second *
+ geography_degree_sincos<Float>(b.x,
-a.x).first);
+ const auto [sl, cl] = geography_degree_sincos<Float>(a.y, b.y, true);
+ const auto [st, ct] = geography_degree_sincos<Float>(b.y, -a.y, true);
+ midpoint = rotate_unit(cd * cl * ct, -sd * sl * st, sl * ct);
+ }
+};
+
+// Raw identity must survive ToPoint rounding: 58 and 58.00000000000001 degrees
+// produce the same S2Point, but only one is an endpoint of the original edge.
+struct GeographyVertex {
+ GeoCoordinate coordinate;
+ S2Point point;
+
+ GeographyVertex() : GeographyVertex({.x = 0, .y = 0}) {}
+ explicit GeographyVertex(GeoCoordinate value) : coordinate(value) {
+ if (std::abs(coordinate.y) == 90) {
+ coordinate.x = 0;
+ point = {0, 0, coordinate.y > 0 ? 1.0 : -1.0};
+ } else {
+ if (coordinate.x == 180) {
+ coordinate.x = -180;
+ }
+ point = S2LatLng::FromDegrees(coordinate.y,
coordinate.x).ToPoint();
+ }
+ }
+ bool operator==(const GeographyVertex& other) const {
+ return coordinate.x == other.coordinate.x && coordinate.y ==
other.coordinate.y;
+ }
+ bool operator<(const GeographyVertex& other) const {
+ return std::pair {coordinate.x, coordinate.y} <
+ std::pair {other.coordinate.x, other.coordinate.y};
+ }
+};
+
+static bool geography_antipodal(const GeographyVertex& a, const
GeographyVertex& b) {
+ return a.coordinate.y == -b.coordinate.y &&
+ (std::abs(a.coordinate.y) == 90 ||
+ geography_degree_sum(std::max(a.coordinate.x, b.coordinate.x),
+ -std::min(a.coordinate.x, b.coordinate.x)) ==
+ std::pair {180.0, 0.0});
+}
+
+struct GeographyCoordinates {
+ GeoShapeType type = GeoShapeType::GEO_SHAPE_ANY;
+ DorisVector<DorisVector<GeographyVertex>> sequences;
+ GeoParseStatus status;
+
+ explicit GeographyCoordinates(StringRef wkb) {
+ GeoCoordinateListList raw;
+ status = WkbParse::calculation_coordinates(wkb.data, wkb.size, &raw,
&type);
+ if (status != GeoParseStatus::GEO_PARSE_OK) {
+ return;
+ }
+ for (const auto& sequence : raw.list) {
+ auto& vertices = sequences.emplace_back();
+ for (const auto& coordinate : sequence->list) {
+ vertices.emplace_back(coordinate);
+ }
+ }
+ }
+};
+
+static bool geography_stable_points(const DorisVector<GeographyVertex>&
sequence,
+ std::vector<S2Point>* points) {
+ for (size_t i = 0; i + 1 < sequence.size(); ++i) {
+ const auto& a = sequence[i];
+ const auto& b = sequence[i + 1];
+ // (0,0)->(180,0) has no unique arc and would normalize a zero raw
normal.
+ if (geography_antipodal(a, b)) {
+ return false;
+ }
+ points->push_back(a.point);
+ // Stabilize before S2 admission: rounded (30,58)->(-150,-58-e) can be
+ // exactly antipodal despite its unique raw arc passing through the
south pole.
+ if (a.point.DotProd(b.point) < 0) {
+ points->push_back(GeographyRawArc(a.coordinate,
b.coordinate).midpoint);
+ }
+ }
+ // A line's final vertex is real, including its closing edge; only rings
remove it.
+ points->push_back(sequence.back().point);
+ points->erase(std::ranges::unique(*points).begin(), points->end());
+ return true;
+}
+
+static std::unique_ptr<GeoShape> decode_geography_line(const
GeographyCoordinates& raw,
+ StringRef value) {
+ std::vector<S2Point> points;
+ if (!geography_stable_points(raw.sequences.front(), &points)) {
+ return nullptr;
+ }
+ if (points.size() < 2) {
+ // Canonical pole aliases such as (0,90),(90,90) collapse to one
calculation
+ // point. Preserve their prior admission; the old parser still rejects
a
+ // truly duplicate-only line such as (1,1),(1,1).
+ GeoParseStatus status;
+ return GeoShape::from_wkb_bytes(value.data, value.size, status);
+ }
+ auto polyline = std::make_unique<S2Polyline>(points, S2Debug::DISABLE);
+ if (!polyline->IsValid()) {
+ return nullptr;
+ }
+ return GeoLine::create_unique(std::move(polyline));
+}
+
+std::unique_ptr<GeoShape> decode_geography_calculation_shape(StringRef value) {
+ GeographyCoordinates raw(value);
+ if (raw.status != GeoParseStatus::GEO_PARSE_OK) {
+ return nullptr;
+ }
+ if (raw.type == GeoShapeType::GEO_SHAPE_POINT) {
+ GeoParseStatus status;
+ return GeoShape::from_wkb_bytes(value.data, value.size, status);
+ }
+ if (raw.type == GeoShapeType::GEO_SHAPE_LINE_STRING) {
+ return decode_geography_line(raw, value);
+ }
+ std::vector<std::unique_ptr<S2Loop>> loops;
+ std::vector<const S2Loop*> input_loops;
+ for (const auto& ring : raw.sequences) {
+ std::vector<S2Point> points;
+ // Validate holes against stable raw arcs, as with typed line
admission.
+ if (!geography_stable_points(ring, &points)) {
+ return nullptr;
+ }
+ // Validated WKB rings are closed; only polygon admission removes that
endpoint.
+ DCHECK(points.front() == points.back());
+ points.pop_back();
+ if (points.size() < 3) {
+ return nullptr;
+ }
+ auto loop = std::make_unique<S2Loop>(points, S2Debug::DISABLE);
+ if (!loop->IsValid()) {
+ return nullptr;
+ }
+ loop->Normalize();
+ if (!loops.empty() && !loops.front()->Contains(*loop)) {
+ return nullptr;
+ }
+ input_loops.push_back(loop.get());
+ loops.push_back(std::move(loop));
+ }
+ auto polygon = std::make_unique<S2Polygon>(std::move(loops),
S2Debug::DISABLE);
+ if (!polygon->IsValid()) {
+ return nullptr;
+ }
+ std::vector<int> depths;
+ for (const auto* loop : input_loops) {
+ depths.push_back(loop->depth());
+ }
+ return GeoPolygon::create_unique(std::move(polygon), std::move(depths));
+}
+
+#ifdef BE_TEST
+static thread_local size_t geography_exact_proofs = 0;
+static thread_local size_t geography_candidate_visits = 0;
+#endif
+
+// Test coplanarity of the original degree ordinates, not independently
rounded S2 vectors.
+// For example (45,-45), (90,0), (135,45) share an arc although ToPoint's
determinant is nonzero.
+// Keep this exact cancellation proof together during the behavior-preserving
module extraction.
+// NOLINTNEXTLINE(readability-function-size)
+static bool geography_common_great_circle(const GeoCoordinate& a, const
GeoCoordinate& b,
+ const GeoCoordinate& c) {
+#ifdef BE_TEST
+ ++geography_exact_proofs;
+#endif
+ using boost::multiprecision::cpp_int;
+ const std::array<double, 6> ordinates {a.y, a.x, b.y, b.x, c.y, c.x};
+ std::array<uint64_t, 6> significands;
+ std::array<int, 6> exponents;
+ int denominator_bits = 0;
+ for (size_t i = 0; i < ordinates.size(); ++i) {
+ const auto bits = std::bit_cast<uint64_t>(ordinates[i]);
+ const int biased = (bits >> 52) & 0x7ff;
+ uint64_t significand = bits & ((uint64_t {1} << 52) - 1);
+ int exponent = biased ? biased - 1075 : -1074;
+ if (biased) {
+ significand |= uint64_t {1} << 52;
+ }
+ if (significand != 0) {
+ const int zeros = std::countr_zero(significand);
+ significand >>= zeros;
+ exponent += zeros;
+ denominator_bits = std::max(denominator_bits, -exponent);
+ } else {
+ exponent = 0;
+ }
+ significands[i] = significand;
+ exponents[i] = exponent;
+ }
+ std::array<cpp_int, 6> angles;
+ for (size_t i = 0; i < angles.size(); ++i) {
+ angles[i] = cpp_int(significands[i]) << (denominator_bits +
exponents[i]);
+ if (std::signbit(ordinates[i])) {
+ angles[i] = -angles[i];
+ }
+ }
+ // Binary-rational degrees have denominator 2^q. Exp(i*angle) is a power
of a
+ // root of unity of order 360*2^q. Its minimal polynomial is Phi_90(t),
with
+ // t = z^(2^(q+2)), and Phi_90(t) = t^24+t^21-t^15-t^12-t^9+t^3+1.
+ // Expand cos(lat_i)cos(lat_j)sin(lat_k)sin(lon_j-lon_i), cyclically, into
+ // 48 integer-coefficient powers. Equal residues modulo 2^(q+2) share one
+ // polynomial; reduction by Phi_90 proves zero exactly, including tiny
nonzero controls.
+ const int shift = denominator_bits + 2;
+ const cpp_int basis = cpp_int(1) << shift;
+ const cpp_int period = 90 * basis;
+ std::map<cpp_int, std::array<int, 90>> polynomials;
+ for (int i = 0; i < 3; ++i) {
+ const int j = (i + 1) % 3;
+ const int k = (i + 2) % 3;
+ for (int mask = 0; mask < 16; ++mask) {
+ std::array<int, 4> signs;
+ for (int bit = 0; bit < 4; ++bit) {
+ signs[bit] = (mask & (1 << bit)) ? 1 : -1;
+ }
+ cpp_int power = signs[0] * angles[2 * i] + signs[1] * angles[2 *
j] +
+ signs[2] * angles[2 * k] +
+ signs[3] * (angles[2 * j + 1] - angles[2 * i + 1]);
+ power %= period;
+ if (power < 0) {
+ power += period;
+ }
+ const int quotient = (power >> shift).convert_to<int>();
+ const cpp_int residue = power - (cpp_int(quotient) << shift);
+ polynomials[residue][quotient] += signs[2] * signs[3];
+ }
+ }
+ for (auto& [residue, coefficients] : polynomials) {
+ for (int i = 89; i >= 24; --i) {
+ const int coefficient = coefficients[i];
+ coefficients[i] = 0;
+ coefficients[i - 3] -= coefficient;
+ coefficients[i - 9] += coefficient;
+ coefficients[i - 12] += coefficient;
+ coefficients[i - 15] += coefficient;
+ coefficients[i - 21] -= coefficient;
+ coefficients[i - 24] -= coefficient;
+ }
+ if (std::ranges::any_of(coefficients, [](int value) { return value !=
0; })) {
+ return false;
+ }
+ }
+ return true;
+}
+
+// Keep each atomic segment in its own shape. Pinned S2 ProcessEdge1 uses a
chain's
+// global start as a local offset in one endpoint path, so multiple chains per
line
+// shape are unsafe. Closed AA shapes restore internal vertices in the OPEN
model.
+class GeographyLineShape final : public S2Shape {
+public:
+ GeographyLineShape(const S2Point& a, const S2Point& b) {
_edge.emplace_back(a, b); }
+ int num_edges() const override { return 1; }
+ Edge edge(int i) const override {
+ DCHECK_EQ(i, 0);
+ return _edge.front();
+ }
+ int dimension() const override { return 1; }
+ ReferencePoint GetReferencePoint() const override { return
ReferencePoint::Contained(false); }
+ int num_chains() const override { return 1; }
+ Chain chain(int i) const override {
+ DCHECK_EQ(i, 0);
+ return {0, 1};
+ }
+ Edge chain_edge(int i, int j) const override {
+ DCHECK_EQ(i, 0);
+ return edge(j);
+ }
+ ChainPosition chain_position(int i) const override {
+ DCHECK_EQ(i, 0);
+ return {0, 0};
+ }
+
+private:
+ // Owning storage is checked/accounted by the current query's allocator.
+ DorisVector<Edge> _edge;
+};
+
+class GeographyEdgeNodes {
+public:
+ using LineEdge = std::pair<GeographyVertex, GeographyVertex>;
+ using LineEdges = std::set<LineEdge, std::less<>,
CustomStdAllocator<LineEdge>>;
+ using PolygonEdges = std::array<LineEdges, 2>;
+
+ struct RawEdges {
+ LineEdges line;
+ PolygonEdges polygon;
+
+ auto vertices(const GeographyCoordinates& raw) const {
+ std::set<GeographyVertex, std::less<>,
CustomStdAllocator<GeographyVertex>> result;
+ // A pole-alias line can have no edges but still denotes one
canonical position.
+ result.insert(raw.sequences.front().front());
+ const auto append = [&](const LineEdges& edges) {
+ for (const auto& [a, b] : edges) {
+ result.insert(a);
+ result.insert(b);
+ }
+ };
+ append(line);
+ for (const auto& ring_edges : polygon) {
+ append(ring_edges);
+ }
+ return result;
+ }
+ };
+
+ GeographyCoordinates left;
+ GeographyCoordinates right;
+
+ GeographyEdgeNodes(StringRef left_wkb, StringRef right_wkb) :
left(left_wkb), right(right_wkb) {
+ DCHECK_EQ(left.status, GeoParseStatus::GEO_PARSE_OK);
+ DCHECK_EQ(right.status, GeoParseStatus::GEO_PARSE_OK);
+ DorisMap<double, DorisVector<GeographyVertex>> longitude_vertices;
+ std::set<GeographyVertex, std::less<>,
CustomStdAllocator<GeographyVertex>> coordinates;
+ for (const auto* shape : {&left, &right}) {
+ for (const auto& sequence : shape->sequences) {
+ for (const auto& point : sequence) {
+ if (!coordinates.insert(point).second) {
+ continue;
+ }
+ const auto& coordinate = point.coordinate;
+ longitude_vertices[coordinate.x].push_back(point);
+ if (std::abs(coordinate.y) != 90) {
+ _meridians[meridian(coordinate.x)][coordinate.x <
0].push_back(
+ {coordinate.y, point});
+ }
+ }
+ }
+ }
+ // Polygon rings retain directed edges, unlike the merged line
intervals. Raw
+ // coordinate bands avoid recalling a whole tiny zigzag ring for every
edge.
+ if (left.type == GeoShapeType::GEO_SHAPE_POLYGON ||
+ right.type == GeoShapeType::GEO_SHAPE_POLYGON) {
+ _longitude_order.assign(coordinates.begin(), coordinates.end());
+ _latitude_order = _longitude_order;
+ std::ranges::sort(_latitude_order, {},
+ [](const auto& vertex) { return
vertex.coordinate.y; });
+ }
+ // Keep dense longitude groups separately so a circle can skip its
known
+ // endpoint longitudes before enumerating nearby points. At sqrt(N)
points
+ // per group there are at most sqrt(N) extra indexes, even with
unrelated
+ // vertices padding a near-antipodal spoke input.
+ const auto dense_size =
+ std::max(size_t {2},
static_cast<size_t>(std::ceil(std::sqrt(coordinates.size()))));
+ for (const auto& [longitude, points] : longitude_vertices) {
+ auto& index =
+ points.size() >= dense_size ? _dense_longitudes[longitude]
: _vertex_index;
+ for (const auto& point : points) {
+ index.Add(point.point, point);
+ }
+ }
+ for (auto& entry : _meridians) {
+ for (auto& side : entry.second) {
+ side.push_back({-90, GeographyVertex({.x = 0, .y = -90})});
+ side.push_back({90, GeographyVertex({.x = 0, .y = 90})});
+ std::ranges::sort(side, {}, &Vertex::latitude);
+ }
+ }
+ }
+
+ bool contains_point(const GeographyVertex& start, const GeographyVertex&
end,
+ const GeographyVertex& point) const {
+ // Preserve exact endpoints, including date-line and pole aliases.
+ if (point == start || point == end) {
+ return true;
+ }
+ if (start == end) {
+ return false;
+ }
+ const auto& a = start.coordinate;
+ const auto& b = end.coordinate;
+ const auto& c = point.coordinate;
+ const auto key = meridian(std::abs(a.y) == 90 ? b.x : a.x);
+ bool member = false;
+ if (meridian_edge(start, end, [&](const auto& vertices, double from,
double to) {
+ // Opposite-longitude edges can pass through a pole; the pole
belongs
+ // to both legs, whereas other positions must be on the
selected side.
+ const bool same_side =
+ std::abs(c.y) == 90 ||
+ (meridian(c.x) == key && &_meridians.at(key)[c.x < 0]
== &vertices);
+ member |= same_side && c.y >= std::min(from, to) && c.y <=
std::max(from, to);
+ })) {
+ return member;
+ }
+ const bool wraps = geography_degree_sum(std::max(a.x, b.x),
-std::min(a.x, b.x)) >
+ std::pair {180.0, 0.0};
+ const bool within = wraps ? (c.x < std::min(a.x, b.x) || c.x >
std::max(a.x, b.x))
+ : (c.x > std::min(a.x, b.x) && c.x <
std::max(a.x, b.x));
+ // Near-antipodal endpoint conversion can rotate the S2 plane
substantially.
+ // POINT(45 0) is on (-44.99999999999997 -45,134.99999999999997 45);
+ // decide from raw degrees rather than accepting a larger distance
tolerance.
+ return within && geography_common_great_circle(a, b, c);
+ }
+
+ bool line_contains_point(const GeographyCoordinates& shape,
+ const GeographyVertex& point) const {
+ const auto& line = shape.sequences.front();
+ for (size_t i = 0; i + 1 < line.size(); ++i) {
+ if (contains_point(line[i], line[i + 1], point)) {
+ return true;
+ }
+ }
+ return false;
+ }
+
+ bool line_boundary_touches(const GeographyCoordinates& line,
+ const GeographyCoordinates& other) const {
+ const auto& vertices = line.sequences.front();
+ // Closed lines have no boundary. An open endpoint must belong to the
other raw line:
+ // a rounded coincidence across the gap 58 -> 58+ulp is not a contact.
+ return vertices.front() != vertices.back() &&
+ (line_contains_point(other, vertices.front()) ||
+ line_contains_point(other, vertices.back()));
+ }
+
+ void append_edge(const GeographyVertex& start, const GeographyVertex& end,
+ DorisVector<GeographyVertex>* output) const {
+ output->push_back(start);
+ if (start == end) {
+ return;
+ }
+ if (meridian_edge(start, end, [&](const auto& vertices, double from,
double to) {
+ append_range(vertices, from, to, output);
+ if (std::abs(to) == 90) {
+ const GeographyVertex pole({.x = 0, .y = to});
+ if (end != pole) {
+ output->push_back(pole);
+ }
+ }
+ })) {
+ return;
+ }
+ const auto& a = start.coordinate;
+ const auto& b = end.coordinate;
+ const bool wraps = geography_degree_sum(std::max(a.x, b.x),
-std::min(a.x, b.x)) >
+ std::pair {180.0, 0.0};
+ const bool east = (a.x < b.x) != wraps;
+ DorisVector<GeographyVertex> on_edge;
+ const auto append = [&](const GeographyVertex& point) {
+ const auto& c = point.coordinate;
+ // Longitude is strictly monotone along every non-meridian minor
arc.
+ // Retain the raw interval and exact proof for both candidate
strategies.
+ const bool within = wraps ? (c.x < std::min(a.x, b.x) || c.x >
std::max(a.x, b.x))
+ : (c.x > std::min(a.x, b.x) && c.x <
std::max(a.x, b.x));
+ if (within && geography_common_great_circle(a, b, c)) {
+ on_edge.push_back(point);
+ }
+ };
+ if (!visit_small_raw_candidates(start, end, wraps, append)) {
+ // Near-antipodal conversion can miss raw nodes. Preserve the
existing
+ // stable half-arc recall whenever a small raw band is unavailable.
+ const auto midpoint = GeographyRawArc(a, b).midpoint;
+ for (const auto& endpoint : {start, end}) {
+ visit_edge_candidates(
+ endpoint.point, midpoint, [](double) { return false;
}, append);
+ }
+ }
+ std::ranges::sort(on_edge, [&](const GeographyVertex& x, const
GeographyVertex& y) {
+ const double x_lon = x.coordinate.x;
+ const double y_lon = y.coordinate.x;
+ if ((x_lon < a.x) != (y_lon < a.x)) {
+ return east ? x_lon >= a.x : x_lon < a.x;
+ }
+ return east ? x_lon < y_lon : x_lon > y_lon;
+ });
+ on_edge.erase(std::ranges::unique(on_edge).begin(), on_edge.end());
+ output->insert(output->end(), on_edge.begin(), on_edge.end());
+ }
+
+ // Calculation-only points never enter the raw-degree identity/noding map.
+ std::optional<S2Point> arc_midpoint(const GeographyVertex& a, const
GeographyVertex& b) const {
+ if (a.point.DotProd(b.point) < 0) {
+ return GeographyRawArc(a.coordinate, b.coordinate).midpoint;
+ }
+ return std::nullopt;
+ }
+
+ void add_line(const GeographyCoordinates& shape, MutableS2ShapeIndex*
index,
+ LineEdges* raw_line_edges = nullptr) const {
+ using Interval = std::pair<double, double>;
+ DorisMap<const DorisVector<Vertex>*, DorisVector<Interval>> intervals;
+ LineEdges raw_edges;
+ const auto& line = shape.sequences.front();
+ for (size_t i = 0; i + 1 < line.size(); ++i) {
+ const auto& a = line[i];
+ const auto& b = line[i + 1];
+ if (a == b) {
+ continue;
+ }
+ if (!meridian_edge(a, b, [&](const auto& vertices, double from,
double to) {
+ intervals[&vertices].emplace_back(std::min(from, to),
std::max(from, to));
+ })) {
+ raw_edges.emplace(std::min(a, b), std::max(a, b));
+ }
+ }
+ LineEdges edges;
+ auto add_edge = [&](const GeographyVertex& a, const GeographyVertex&
b) {
+ // Equality must distinguish (0,58)->(0,59) from
(0,58+ulp)->(0,59),
+ // even when conversion collapses the raw 58->58+ulp subedge to
one S2Point.
+ if (raw_line_edges != nullptr) {
+ raw_line_edges->emplace(std::min(a, b), std::max(a, b));
+ }
+ // Rounded adjacent vertices can share one S2Point while remaining
distinct raw
+ // WKB vertices, for example 58 and 58.00000000000001 degrees. The
raw edge is
+ // retained for identity, but its zero-length S2 representation
must not become
+ // an OPEN/AA boundary marker at the original line endpoint.
+ if (a.point == b.point) {
+ return;
+ }
+ edges.emplace(std::min(a, b), std::max(a, b));
+ };
+ // Merge latitude coverage before splitting: N repeated or overlapping
edges
+ // and M collinear vertices produce O(N+M) scratch, never an N*M
vertex walk.
+ for (auto& [vertices, ranges] : intervals) {
+ std::ranges::sort(ranges);
+ auto emit = [&](double from, double to) {
+ auto begin = std::ranges::lower_bound(*vertices, from, {},
&Vertex::latitude);
+ const auto end = std::ranges::upper_bound(*vertices, to, {},
&Vertex::latitude);
+ for (auto next = begin + 1; next != end; ++begin, ++next) {
+ add_edge(begin->point, next->point);
+ }
+ };
+ double from = ranges.front().first;
+ double to = ranges.front().second;
+ for (const auto& range : ranges) {
+ if (range.first > to) {
+ emit(from, to);
+ from = range.first;
+ }
+ to = std::max(to, range.second);
+ }
+ emit(from, to);
+ }
+ add_circle_edges(raw_edges, add_edge);
+ add_line_shapes(line, edges, index);
+ }
+
+private:
+ template <typename Visit>
+ bool visit_small_raw_candidates(const GeographyVertex& start, const
GeographyVertex& end,
+ bool wraps, Visit&& visit) const {
+ // The S2 recall radius can cover an entire 1e-14-degree ring. Ordinary
+ // edges keep the spatial query; this threshold only selects an index.
+ constexpr double recall_radius = 64 *
std::numeric_limits<double>::epsilon();
+ if ((start.point - end.point).Norm2() > recall_radius * recall_radius)
{
+ return false;
+ }
+ const auto& a = start.coordinate;
+ const auto& b = end.coordinate;
+ const auto longitude = [](const auto& vertex) { return
vertex.coordinate.x; };
+ const auto lo =
+ std::ranges::upper_bound(_longitude_order, std::min(a.x, b.x),
{}, longitude);
+ const auto hi =
+ std::ranges::lower_bound(_longitude_order, std::max(a.x, b.x),
{}, longitude);
+ auto first = wraps ? _longitude_order.begin() : lo;
+ auto last = hi;
+ auto second = wraps ? lo : _longitude_order.end();
+ if (wraps) {
+ // At the date-line cut the strict longitude interval has two
pieces.
+ last = std::ranges::lower_bound(_longitude_order, std::min(a.x,
b.x), {}, longitude);
+ second = std::ranges::upper_bound(_longitude_order, std::max(a.x,
b.x), {}, longitude);
+ }
+ size_t count = (last - first) + (_longitude_order.end() - second);
+ const double dx = std::nextafter(std::abs(b.x - a.x), INFINITY);
+ const double dy = std::nextafter(std::abs(b.y - a.y), 0.0);
+ // For |A|,|B|<=45 and |dLon|<=90, endpoint latitude tangents have
signs of
+ // sin(B-A) plus sin(A)cos(B)*(1-cos(dLon)), or minus
sin(B)cos(A)*(1-cos(dLon)).
+ // In degrees, |sin(dLat)|
+ // >= |dLat|/90 and 1-cos(dLon) < dLon^2/5000. Thus dy>dx^2 proves
+ // monotonicity, with outward rounding below. A (0,45)->(90,45) arc
+ // fails this certificate: its latitude bows above both endpoints.
+ if (std::abs(a.y) <= 45 && std::abs(b.y) <= 45 && dx <= 90 &&
+ dy > std::nextafter(dx * dx, INFINITY)) {
+ const auto latitude = [](const auto& vertex) { return
vertex.coordinate.y; };
+ const auto from =
+ std::ranges::lower_bound(_latitude_order, std::min(a.y,
b.y), {}, latitude);
+ const auto to =
+ std::ranges::upper_bound(_latitude_order, std::max(a.y,
b.y), {}, latitude);
+ if (static_cast<size_t>(to - from) < count) {
+ first = from;
+ last = to;
+ second = _longitude_order.end();
+ count = to - from;
+ }
+ }
+ // Eight is only a strategy crossover, never a result cap. Larger or
+ // unproven bands use the complete existing S2 recall without
truncation.
+ if (count > 8) {
+ return false;
+ }
+ for (const auto& range :
+ {std::pair {first, last}, std::pair {second,
_longitude_order.end()}}) {
+ for (auto point = range.first; point != range.second; ++point) {
+#ifdef BE_TEST
+ ++geography_candidate_visits;
+#endif
+ visit(*point);
+ }
+ }
+ return true;
+ }
+
+ void add_line_shapes(const DorisVector<GeographyVertex>& line, const
LineEdges& edges,
+ MutableS2ShapeIndex* index) const {
+ const auto& first = line.front();
+ const auto& last = line.back();
+ auto add = [&](const S2Point& a, const S2Point& b) {
+ index->Add(std::make_unique<GeographyLineShape>(a, b));
+ };
+ if (edges.empty()) {
+ // A raw pole-alias line may collapse to one canonical calculation
position.
+ add(first.point, first.point);
+ }
+ std::set<S2Point, std::less<>, CustomStdAllocator<S2Point>>
interior_vertices;
+ for (const auto& [a, b] : edges) {
+ const auto midpoint = arc_midpoint(a, b);
+ if (midpoint) {
+ add(a.point, *midpoint);
+ add(*midpoint, b.point);
+ // The synthetic split is interior, not a new OPEN line
boundary:
+ // a crossing at this point must not become ST_Touches=true.
+ interior_vertices.insert(*midpoint);
+ } else {
+ add(a.point, b.point);
+ }
+ interior_vertices.insert(a.point);
+ interior_vertices.insert(b.point);
+ }
+ for (const auto& point : interior_vertices) {
+ if (first == last || (point != first.point && point !=
last.point)) {
+ add(point, point);
+ }
+ }
+ }
+
+ struct Vertex {
+ double latitude;
+ GeographyVertex point;
+ };
+ struct Circle {
+ GeographyVertex a;
+ GeographyVertex b;
+ S2Point normal;
+ DorisVector<std::pair<double, double>> ranges;
+ DorisMap<double, GeographyVertex> vertices;
+ };
+
+ template <typename Edges, typename AddEdge>
+ void add_circle_edges(const Edges& edges, AddEdge&& add_edge) const {
+ DorisVector<Circle> circles;
+ S2PointIndex<size_t> normal_index;
+ const double rounding = 64 * std::numeric_limits<double>::epsilon();
+ for (const auto& [a, b] : edges) {
+ const auto normal = GeographyRawArc(a.coordinate,
b.coordinate).normal;
+ size_t group = circles.size();
+ S2ClosestPointQuery<size_t> query(&normal_index);
+ // Raw trigonometric products avoid the epsilon/sin(length) error
+ // amplification. Normals only recall candidates; exact proof
decides.
+
query.mutable_options()->set_conservative_max_distance(S1Angle::Radians(rounding));
+ S2ClosestPointQuery<size_t>::PointTarget target(normal);
+ for (const auto& candidate : query.FindClosestPoints(&target)) {
+#ifdef BE_TEST
+ ++geography_candidate_visits;
+#endif
+ const auto& circle = circles[candidate.data()];
+ const auto& x = circle.a.coordinate;
+ const auto& y = circle.b.coordinate;
+ const auto on_circle = [&](const GeographyVertex& point) {
+ return point == circle.a || point == circle.b ||
+ geography_common_great_circle(x, y,
point.coordinate);
+ };
+ if (on_circle(a) && on_circle(b)) {
+ group = candidate.data();
+ break;
+ }
+ }
+ if (group == circles.size()) {
+ normal_index.Add(normal, group);
+ // The pinned S2 unary transform repeatedly moves a stateless
lambda.
+ // Component negation is identical and avoids that analyzer
false positive.
+ normal_index.Add(S2Point(-normal.x(), -normal.y(),
-normal.z()), group);
+ circles.push_back({a, b, normal, {}, {}});
+ }
+ auto& circle = circles[group];
+ const double lo = std::min(a.coordinate.x, b.coordinate.x);
+ const double hi = std::max(a.coordinate.x, b.coordinate.x);
+ // Longitude cut points are interval sentinels, not fabricated
spatial
+ // vertices. For 170->-170 the real wrap edge is emitted below.
+ if (geography_degree_sum(hi, -lo) > std::pair {180.0, 0.0}) {
+ circle.ranges.emplace_back(-180, lo);
+ circle.ranges.emplace_back(hi, 180);
+ } else {
+ circle.ranges.emplace_back(lo, hi);
+ }
+ // Keep every raw endpoint, especially original open-line endpoints
+ // inside a larger merged interval: OPEN must still exclude those
points.
+ circle.vertices.emplace(a.coordinate.x, a);
+ circle.vertices.emplace(b.coordinate.x, b);
+ }
+ for (auto& circle : circles) {
+ collect_circle_vertices(circle);
+ emit_circle_edges(circle, add_edge);
+ }
+ }
+
+ template <typename SkipLongitude, typename Visit>
+ void visit_edge_candidates(const S2Point& a, const S2Point& b,
SkipLongitude&& skip_longitude,
+ Visit&& visit) const {
+ const auto query_index = [&](const S2PointIndex<GeographyVertex>&
index) {
+ S2ClosestPointQuery<GeographyVertex> query(&index);
+ query.mutable_options()->set_conservative_max_distance(
+ S1Angle::Radians(64 *
std::numeric_limits<double>::epsilon()));
+ S2ClosestPointQuery<GeographyVertex>::EdgeTarget target(a, b);
+ for (const auto& candidate : query.FindClosestPoints(&target)) {
+#ifdef BE_TEST
+ ++geography_candidate_visits;
+#endif
+ visit(candidate.data());
+ }
+ };
+ query_index(_vertex_index);
+ for (const auto& [longitude, index] : _dense_longitudes) {
+#ifdef BE_TEST
+ ++geography_candidate_visits;
+#endif
+ // A non-meridian circle has only one nonpolar point at each
longitude.
+ // Dense endpoint groups must be skipped before the S2 query,
including
+ // when unrelated vertices make them a minority of the complete
input.
+ if (!skip_longitude(longitude)) {
+ query_index(index);
+ }
+ }
+ }
+
+ void collect_circle_vertices(Circle& circle) const {
+ // Query a whole circle once, using four non-antipodal quarter arcs.
+ const auto u = S2::Ortho(circle.normal);
+ const auto v = circle.normal.CrossProd(u).Normalize();
+ // Explicit component negation avoids the pinned S2 transform's
repeated moves of
+ // a stateless lambda (clang-analyzer-cplusplus.Move), preserving
signed zero too.
+ const std::array<S2Point, 4> quarter {
+ u, v, {-u.x(), -u.y(), -u.z()}, {-v.x(), -v.y(), -v.z()}};
+ std::set<GeographyVertex, std::less<>,
CustomStdAllocator<GeographyVertex>> seen;
+ for (size_t i = 0; i < quarter.size(); ++i) {
+ visit_edge_candidates(
+ quarter[i], quarter[(i + 1) % 4],
+ [&](double longitude) { return
circle.vertices.contains(longitude); },
+ [&](const GeographyVertex& point) {
+ const auto& coordinate = point.coordinate;
+ if (seen.insert(point).second &&
!circle.vertices.contains(coordinate.x) &&
+ geography_common_great_circle(circle.a.coordinate,
circle.b.coordinate,
+ coordinate)) {
+ circle.vertices.emplace(coordinate.x, point);
+ }
+ });
+ }
+ }
+
+ template <typename AddEdge>
+ static void emit_circle_edges(Circle& circle, AddEdge&& add_edge) {
+ std::ranges::sort(circle.ranges);
+ DorisVector<std::pair<double, double>> merged;
+ for (const auto& range : circle.ranges) {
+ if (merged.empty() || range.first > merged.back().second) {
+ merged.push_back(range);
+ } else {
+ merged.back().second = std::max(merged.back().second,
range.second);
+ }
+ }
+ for (const auto& [lo, hi] : merged) {
+ const auto begin = circle.vertices.lower_bound(lo);
+ const auto end = circle.vertices.upper_bound(hi);
+ // Each original interval retains an endpoint, including either
side
+ // of the date-line cut. Merging and node collection never remove
it.
+ DCHECK(begin != end);
+ auto previous = begin;
+ for (auto next = std::next(begin); next != end; ++previous,
++next) {
+ add_edge(previous->second, next->second);
+ }
+ }
+ if (merged.front().first == -180 && merged.back().second == 180) {
+ add_edge(circle.vertices.rbegin()->second,
circle.vertices.begin()->second);
+ }
+ }
+
+ static std::pair<double, double> meridian(double longitude) {
+ return longitude >= 0 ? std::pair {longitude, 0.0} :
geography_degree_sum(longitude, 180);
+ }
+ template <typename Append>
+ bool meridian_edge(const GeographyVertex& start, const GeographyVertex&
end,
+ Append&& append) const {
+ const auto& a = start.coordinate;
+ const auto& b = end.coordinate;
+ const bool a_pole = std::abs(a.y) == 90;
+ const bool b_pole = std::abs(b.y) == 90;
+ const auto key = meridian(a_pole ? b.x : a.x);
+ if (!a_pole && !b_pole && key != meridian(b.x)) {
+ return false;
+ }
+ // Exact opposite endpoints (e.g. (0,10),(180,-10)) have no unique
minor arc.
+ if (a.y == -b.y && ((a_pole && b_pole) || (a.x < 0) != (b.x < 0))) {
+ throw Exception(ErrorCode::NOT_IMPLEMENTED_ERROR,
+ "Geography calculations do not support antipodal
edges");
+ }
+ const bool a_side = (a_pole ? b.x : a.x) < 0;
+ const bool b_side = (b_pole ? a.x : b.x) < 0;
+ const auto& group = _meridians.at(key);
+ if (a_side == b_side) {
+ append(group[a_side], a.y, b.y);
+ } else {
+ // (10,80)->(-170,80) goes via the north pole; retain raw latitude
on each side.
+ const double latitude = a.y > -b.y ? 90 : -90;
+ append(group[a_side], a.y, latitude);
+ append(group[b_side], latitude, b.y);
+ }
+ return true;
+ }
+ static void append_range(const DorisVector<Vertex>& vertices, double from,
double to,
+ DorisVector<GeographyVertex>* output) {
+ const auto first =
+ std::ranges::upper_bound(vertices, std::min(from, to), {},
&Vertex::latitude);
+ const auto last =
+ std::ranges::lower_bound(vertices, std::max(from, to), {},
&Vertex::latitude);
+ if (from < to) {
+ for (auto it = first; it != last; ++it) {
+ output->push_back(it->point);
+ }
+ } else {
+ auto current = last;
+ while (current != first) {
+ output->push_back((--current)->point);
+ }
+ }
+ }
+ DorisMap<double, S2PointIndex<GeographyVertex>> _dense_longitudes;
+ S2PointIndex<GeographyVertex> _vertex_index;
+ DorisMap<std::pair<double, double>, std::array<DorisVector<Vertex>, 2>>
_meridians;
+ DorisVector<GeographyVertex> _longitude_order;
+ DorisVector<GeographyVertex> _latitude_order;
+};
+
+static void geography_shape_index(const GeoShape& shape, const
GeographyCoordinates& raw,
+ const GeographyEdgeNodes& nodes,
MutableS2ShapeIndex* index,
+ GeographyEdgeNodes::RawEdges* raw_edges =
nullptr) {
+ switch (shape.type()) {
+ case GeoShapeType::GEO_SHAPE_POINT:
+ index->Add(std::make_unique<S2PointVectorShape>(
+ std::vector<S2Point> {raw.sequences.front().front().point}));
+ break;
+ case GeoShapeType::GEO_SHAPE_LINE_STRING:
+ nodes.add_line(raw, index, raw_edges == nullptr ? nullptr :
&raw_edges->line);
+ break;
+ case GeoShapeType::GEO_SHAPE_POLYGON: {
+ const auto& depths = assert_cast<const
GeoPolygon&>(shape).calculation_ring_depths();
+ DCHECK_EQ(depths.size(), raw.sequences.size());
+ std::vector<S2LaxPolygonShape::Loop> loops;
+ for (size_t i = 0; i < raw.sequences.size(); ++i) {
+ auto& vertices = loops.emplace_back();
+ const auto& ring = raw.sequences[i];
+ DorisVector<GeographyVertex> edge;
+ for (size_t j = 0; j + 1 < ring.size(); ++j) {
+ edge.clear();
+ nodes.append_edge(ring[j], ring[j + 1], &edge);
+ edge.push_back(ring[j + 1]);
+ for (size_t k = 0; k + 1 < edge.size(); ++k) {
+ // Keep raw apex 58 distinct from 58+ulp before S2
conversion. Depth parity
+ // preserves shell/hole roles; duplicate aliases and
synthetic points add no edge.
+ if (raw_edges != nullptr && edge[k] != edge[k + 1]) {
+ raw_edges->polygon[depths[i] %
2].emplace(std::min(edge[k], edge[k + 1]),
+
std::max(edge[k], edge[k + 1]));
+ }
+ vertices.push_back(edge[k].point);
+ // Use the same stable long arcs for interiors and
distances.
+ // The raw (-45+e,-45)->(135-e,45) edge otherwise changes
sides
+ // around POINT(45 0.000001) when its midpoint is inserted.
+ if (const auto midpoint = nodes.arc_midpoint(edge[k],
edge[k + 1])) {
+ vertices.push_back(*midpoint);
+ }
+ }
+ }
+ // Noding (0,58)->(0,59) at raw 58+ulp can repeat its rounded
endpoint,
+ // including across the ring seam. Lax zero-length edges change
OPEN boundary
+ // ownership; retain the raw edges above but compact this
calculation-only ring.
+ vertices.erase(std::ranges::unique(vertices).begin(),
vertices.end());
+ if (vertices.front() == vertices.back()) {
+ vertices.pop_back();
+ }
+ DCHECK_GE(vertices.size(), 3);
+ // A thin near-antipodal ring may have been reversed by
normalization
+ // of the rounded edge. Restore the smaller-region shell
orientation
+ // after stabilization while preserving the admitted hole depths.
+ // Span normalization also retains canonical pole-alias
degeneracies.
+ if (S2::IsNormalized(vertices) == (depths[i] % 2 != 0)) {
+ std::ranges::reverse(vertices);
+ }
+ }
+ index->Add(std::make_unique<S2LaxPolygonShape>(loops));
+ break;
+ }
+ default:
+ throw Exception(ErrorCode::INTERNAL_ERROR, "Unexpected Geography
calculation shape");
+ }
+}
+
+#ifdef BE_TEST
+size_t geography_calculation_edges_for_test(const std::string& left, const
std::string& right,
+ size_t* exact_proofs, size_t*
candidate_visits) {
+ geography_exact_proofs = 0;
+ geography_candidate_visits = 0;
+ const auto a = decode_geography_calculation_shape(StringRef(left));
+ const auto b = decode_geography_calculation_shape(StringRef(right));
+ const GeographyEdgeNodes nodes {StringRef(left), StringRef(right)};
+ MutableS2ShapeIndex a_index;
+ MutableS2ShapeIndex b_index;
+ geography_shape_index(*a, nodes.left, nodes, &a_index);
+ geography_shape_index(*b, nodes.right, nodes, &b_index);
+ size_t edges = 0;
+ for (const auto* shape : a_index) {
+ edges += shape->num_edges();
+ }
+ for (const auto* shape : b_index) {
+ edges += shape->num_edges();
+ }
+ if (exact_proofs != nullptr) {
+ *exact_proofs = geography_exact_proofs;
+ }
+ if (candidate_visits != nullptr) {
+ *candidate_visits = geography_candidate_visits;
+ }
+ return edges;
+}
+#endif
+
+static S1ChordAngle geography_conversion_error() {
+ // S2LatLng::ToPoint and degrees-to-radians rounding can separate
positions on
+ // the same meridian. This is about 1e-8 metres, not a user snap radius.
+ return S1ChordAngle(S1Angle::Radians(8 *
std::numeric_limits<double>::epsilon()));
+}
+
+// Compare only nonshared raw edges with the already built rounded polygon
boundary.
+// Open segments omit isolated endpoint contacts; call this only after polygon
interiors
+// were found disjoint, so a real transverse crossing cannot masquerade as
boundary overlap.
+static bool geography_rounded_boundary_contact(const
GeographyEdgeNodes::RawEdges& source,
+ const
GeographyEdgeNodes::RawEdges& polygon,
+ const S2ShapeIndex&
polygon_index,
+ const GeographyEdgeNodes&
nodes) {
+ if (polygon.polygon[0].empty() && polygon.polygon[1].empty()) {
+ return false;
+ }
+ MutableS2ShapeIndex boundary;
+ MutableS2ShapeIndex distinct;
+ for (const auto* shape : polygon_index) {
+ for (int i = 0; i < shape->num_edges(); ++i) {
+ const auto edge = shape->edge(i);
+ boundary.Add(std::make_unique<GeographyLineShape>(edge.v0,
edge.v1));
+ }
+ }
+ for (const auto* edges : {&source.line, source.polygon.data(),
source.polygon.data() + 1}) {
+ for (const auto& edge : *edges) {
+ if (polygon.polygon[0].contains(edge) ||
polygon.polygon[1].contains(edge)) {
+ continue;
+ }
+ if (const auto midpoint = nodes.arc_midpoint(edge.first,
edge.second)) {
+
distinct.Add(std::make_unique<GeographyLineShape>(edge.first.point, *midpoint));
+ distinct.Add(std::make_unique<GeographyLineShape>(*midpoint,
edge.second.point));
+ } else {
+ distinct.Add(
+ std::make_unique<GeographyLineShape>(edge.first.point,
edge.second.point));
+ }
+ }
+ }
+ S2BooleanOperation::Options options;
+ options.set_polyline_model(S2BooleanOperation::PolylineModel::OPEN);
+ options.set_polyline_loops_have_boundaries(true);
+ return S2BooleanOperation::Intersects(distinct, boundary, options);
+}
+
+static bool geography_rounded_vertex_collision(const
GeographyEdgeNodes::RawEdges& left_edges,
+ const GeographyCoordinates&
left_raw,
+ const
GeographyEdgeNodes::RawEdges& right_edges,
+ const GeographyCoordinates&
right_raw) {
+ const auto a = left_edges.vertices(left_raw);
+ const auto b = right_edges.vertices(right_raw);
+ const auto collision = [](const auto& source, const auto& other) {
+ std::set<S2Point, std::less<>, CustomStdAllocator<S2Point>> distinct;
+ for (const auto& vertex : source) {
+ if (!other.contains(vertex)) {
+ distinct.insert(vertex.point);
+ }
+ }
+ return std::ranges::any_of(
+ other, [&](const auto& vertex) { return
distinct.contains(vertex.point); });
+ };
+ return collision(a, b) || collision(b, a);
+}
+
+static Status geography_check_polygon_interiors(std::string_view name, const
S2ShapeIndex& left,
+ const S2ShapeIndex& right,
+ const GeographyEdgeNodes&
nodes,
+ const
GeographyEdgeNodes::RawEdges& left_edges,
+ const
GeographyEdgeNodes::RawEdges& right_edges,
+ bool interior) {
+ // Raw longitude 58+ulp can become meridian 58 in S2, losing a line or
polygon interior.
+ // Check batched boundary contacts, including partial arcs, instead of
guessing the raw region.
+ if (!interior && (geography_rounded_boundary_contact(left_edges,
right_edges, right, nodes) ||
+ geography_rounded_boundary_contact(right_edges,
left_edges, left, nodes))) {
+ return Status::NotSupported(
+ "{} does not support ambiguous spherical Polygon boundary
interiors", name);
+ }
+ return Status::OK();
+}
+
+static S1ChordAngle geography_conversion_error();
+
+// Return the side of a raw spherical edge using the original degree values.
The
+// calculation index uses binary64 S2 points, so a point one ULP outside an
edge
+// can move to the other side after conversion. Keep this check local to points
+// already within the conversion error of a polygon edge; distant points cannot
+// be affected by the bounded coordinate conversion.
+static int geography_raw_side(const GeoCoordinate& a, const GeoCoordinate& b,
+ const GeoCoordinate& point) {
+ using RawSideFloat = boost::multiprecision::cpp_bin_float_quad;
+ const auto vector = [](const GeoCoordinate& coordinate) {
+ const auto [sin_lon, cos_lon] =
geography_degree_sincos<RawSideFloat>(coordinate.x);
+ const auto [sin_lat, cos_lat] =
geography_degree_sincos<RawSideFloat>(coordinate.y);
+ return std::array<RawSideFloat, 3> {cos_lat * cos_lon, cos_lat *
sin_lon, sin_lat};
+ };
+ const auto first = vector(a);
+ const auto second = vector(b);
+ const auto query = vector(point);
+ const RawSideFloat determinant = (first[1] * second[2] - first[2] *
second[1]) * query[0] +
+ (first[2] * second[0] - first[0] *
second[2]) * query[1] +
+ (first[0] * second[1] - first[1] *
second[0]) * query[2];
+ return (determinant > 0) - (determinant < 0);
+}
+
+static bool geography_raw_rounded_side_mismatch(const GeographyCoordinates&
polygon,
+ const GeographyVertex& point) {
+ const S1Angle conversion_error = geography_conversion_error().ToAngle();
+ for (const auto& ring : polygon.sequences) {
+ for (size_t i = 0; i + 1 < ring.size(); ++i) {
+ const auto& start = ring[i];
+ const auto& end = ring[i + 1];
+ if (start == end || point == start || point == end ||
+ S2::GetDistance(point.point, start.point, end.point) >
conversion_error) {
+ continue;
+ }
+ const int raw_side =
+ geography_raw_side(start.coordinate, end.coordinate,
point.coordinate);
+ const int rounded_side =
+ s2pred::ExpensiveSign(start.point, end.point, point.point,
false);
+ if (raw_side != 0 && rounded_side != 0 && raw_side !=
rounded_side) {
+ return true;
+ }
+ }
+ }
+ return false;
+}
+
+static bool geography_polygon_boundary_contains_point(const
GeographyCoordinates& polygon,
+ const
GeographyEdgeNodes& nodes,
+ const GeographyVertex&
point) {
+ for (const auto& ring : polygon.sequences) {
+ for (size_t i = 0; i + 1 < ring.size(); ++i) {
+ if (nodes.contains_point(ring[i], ring[i + 1], point)) {
+ return true;
+ }
+ }
+ }
+ return false;
+}
+
+enum class GeographyPolygonInterior { OUTSIDE, INSIDE, ROUNDED_BOUNDARY,
ROUNDED_SIDE };
+
+// The caller has already excluded exact raw boundary contact. Reuse this
admission for both
+// point relations and independent interior witnesses in a pair with a rounded
vertex collision.
+static GeographyPolygonInterior geography_polygon_point_interior(
+ const GeographyCoordinates& polygon, const S2ShapeIndex& index,
+ const GeographyVertex& point) {
+ MutableS2ShapeIndex point_index;
+ point_index.Add(std::make_unique<S2PointVectorShape>(std::vector<S2Point>
{point.point}));
+ S2BooleanOperation::Options options;
+ options.set_polygon_model(S2BooleanOperation::PolygonModel::CLOSED);
+ const bool closed = S2BooleanOperation::Contains(index, point_index,
options);
+ options.set_polygon_model(S2BooleanOperation::PolygonModel::OPEN);
+ const bool interior = S2BooleanOperation::Contains(index, point_index,
options);
+ // A raw vertex can round onto a different boundary vertex without owning
its interior.
+ if (closed && !interior) {
+ return GeographyPolygonInterior::ROUNDED_BOUNDARY;
+ }
+ if (geography_raw_rounded_side_mismatch(polygon, point)) {
+ return GeographyPolygonInterior::ROUNDED_SIDE;
+ }
+ return interior ? GeographyPolygonInterior::INSIDE :
GeographyPolygonInterior::OUTSIDE;
+}
+
+static bool geography_polygon_has_rounded_side_mismatch(const
GeographyCoordinates& polygon,
+ const S2ShapeIndex&
polygon_index,
+ const
GeographyCoordinates& other,
+ const
GeographyEdgeNodes& nodes) {
+ for (const auto& sequence : other.sequences) {
+ for (const auto& point : sequence) {
+ // A raw boundary vertex is an actual contact, even if S2 rounds
it onto a
+ // neighboring edge. The existing raw edge checks own that case.
+ if (geography_polygon_boundary_contains_point(polygon, nodes,
point)) {
+ continue;
+ }
+ const auto location = geography_polygon_point_interior(polygon,
polygon_index, point);
+ if (location == GeographyPolygonInterior::ROUNDED_BOUNDARY ||
+ location == GeographyPolygonInterior::ROUNDED_SIDE) {
+ return true;
+ }
+ }
+ }
+ return false;
+}
+
+static bool geography_has_polygon_intersection_witness(const
GeographyCoordinates& polygon,
+ const S2ShapeIndex&
index,
+ const
GeographyCoordinates& other,
+ const
GeographyEdgeNodes& nodes) {
+ for (const auto& sequence : other.sequences) {
+ for (const auto& point : sequence) {
+ if (geography_polygon_boundary_contains_point(polygon, nodes,
point) ||
+ geography_polygon_point_interior(polygon, index, point) ==
+ GeographyPolygonInterior::INSIDE) {
+ return true;
+ }
+ // An uncertain vertex proves nothing about the rest of the shape.
In particular,
+ // a later endpoint can lie strictly inside even if the first
rounds onto the boundary.
+ }
+ }
+ return false;
+}
+
+static Status geography_point_relation(std::string_view name, const GeoShape&
lhs,
+ const GeoShape& rhs, const
GeographyEdgeNodes& nodes,
+ bool* result) {
+ const auto& other = lhs.type() == GeoShapeType::GEO_SHAPE_POINT ? rhs :
lhs;
+ const auto& point_raw = lhs.type() == GeoShapeType::GEO_SHAPE_POINT ?
nodes.left : nodes.right;
+ const auto& other_raw = lhs.type() == GeoShapeType::GEO_SHAPE_POINT ?
nodes.right : nodes.left;
+ const auto& point = point_raw.sequences.front().front();
+ bool interior = false;
+ bool boundary = false;
+ if (other.type() == GeoShapeType::GEO_SHAPE_POINT) {
+ interior = point == other_raw.sequences.front().front();
+ } else if (other.type() == GeoShapeType::GEO_SHAPE_LINE_STRING) {
+ const auto& line = other_raw.sequences.front();
+ const bool member = nodes.line_contains_point(other_raw, point);
+ const auto& first = line.front();
+ const auto& last = line.back();
+ boundary = first != last && (point == first || point == last);
+ interior = member && !boundary;
+ } else {
+ DCHECK(other.type() == GeoShapeType::GEO_SHAPE_POLYGON);
+ boundary = geography_polygon_boundary_contains_point(other_raw, nodes,
point);
+ if (!boundary && name != "st_touches") {
+ MutableS2ShapeIndex index;
+ geography_shape_index(other, other_raw, nodes, &index);
+ const auto location = geography_polygon_point_interior(other_raw,
index, point);
+ if (location == GeographyPolygonInterior::ROUNDED_BOUNDARY) {
+ return Status::NotSupported(
+ "{} does not support ambiguous spherical Polygon
boundary ownership", name);
+ }
+ if (location == GeographyPolygonInterior::ROUNDED_SIDE) {
+ return Status::NotSupported(
+ "{} does not support ambiguous spherical Polygon
boundary side conversion",
+ name);
+ }
+ interior = location == GeographyPolygonInterior::INSIDE;
+ }
+ }
+ if (name == "st_intersects") {
+ *result = interior || boundary;
+ } else if (name == "st_disjoint") {
+ *result = !interior && !boundary;
+ } else if (name == "st_touches") {
+ *result = boundary;
+ } else {
+ *result = interior;
+ }
+ return Status::OK();
+}
+
+static Status geography_relation_impl(std::string_view name, const GeoShape&
lhs,
+ const GeoShape& rhs, const
GeographyEdgeNodes& nodes,
+ bool* result);
+
+Status geography_relation(std::string_view name, const GeoShape& lhs, const
GeoShape& rhs,
+ StringRef left_wkb, StringRef right_wkb, bool*
result) {
+ const auto& container = name == "st_within" ? rhs : lhs;
+ const auto& value = name == "st_within" ? lhs : rhs;
+ const bool containment = name == "st_contains" || name == "st_within";
+ // A point cannot contain a line or polygon; this is a defined false
result.
+ if (containment && container.type() == GeoShapeType::GEO_SHAPE_POINT &&
+ value.type() != GeoShapeType::GEO_SHAPE_POINT) {
+ *result = false;
+ return Status::OK();
+ }
+ if (name == "st_equals" && lhs.type() != rhs.type()) {
+ *result = false;
+ return Status::OK();
+ }
+ if (name == "st_overlaps" &&
+ (lhs.type() != rhs.type() || lhs.type() ==
GeoShapeType::GEO_SHAPE_POINT)) {
+ *result = false;
+ return Status::OK();
+ }
+ const GeographyEdgeNodes nodes(left_wkb, right_wkb);
+ return geography_relation_impl(name, lhs, rhs, nodes, result);
+}
+
+// Keep operation-specific raw/S2 admission together so uncertain rounded
boundaries are checked
+// before accepting a Boolean, while independent raw contact or interior
witnesses stay valid.
+//
NOLINTNEXTLINE(readability-function-size,readability-function-cognitive-complexity)
+static Status geography_relation_impl(std::string_view name, const GeoShape&
lhs,
+ const GeoShape& rhs, const
GeographyEdgeNodes& nodes,
+ bool* result) {
+ const auto& container = name == "st_within" ? rhs : lhs;
+ const auto& value = name == "st_within" ? lhs : rhs;
+ const bool containment = name == "st_contains" || name == "st_within";
+ if (lhs.type() == GeoShapeType::GEO_SHAPE_POINT ||
+ rhs.type() == GeoShapeType::GEO_SHAPE_POINT) {
+ // Point equality has the same canonical position test as point
containment.
+ return geography_point_relation(name, lhs, rhs, nodes, result);
+ }
+ MutableS2ShapeIndex left;
+ MutableS2ShapeIndex right;
+ GeographyEdgeNodes::RawEdges left_edges;
+ GeographyEdgeNodes::RawEdges right_edges;
+ const bool raw_polygon_coverage = lhs.type() ==
GeoShapeType::GEO_SHAPE_POLYGON &&
+ rhs.type() ==
GeoShapeType::GEO_SHAPE_POLYGON &&
+ (containment || name == "st_equals" ||
name == "st_overlaps");
+ // (0,58)->(0,59) covers a longer raw interval than (0,58+ulp)->(0,59),
+ // even when their S2 endpoints collide. Reuse the shared noding for these
relations.
+ const bool raw_line_coverage =
+ container.type() == GeoShapeType::GEO_SHAPE_LINE_STRING &&
+ value.type() == GeoShapeType::GEO_SHAPE_LINE_STRING &&
+ (containment || name == "st_equals" || name == "st_overlaps" ||
name == "st_touches");
+ const bool raw_coverage = raw_line_coverage || raw_polygon_coverage ||
containment ||
+ name == "st_touches" || name == "st_overlaps" ||
+ name == "st_intersects" || name == "st_disjoint";
+ geography_shape_index(container, name == "st_within" ? nodes.right :
nodes.left, nodes, &left,
+ raw_coverage ? &left_edges : nullptr);
+ geography_shape_index(value, name == "st_within" ? nodes.left :
nodes.right, nodes, &right,
+ raw_coverage ? &right_edges : nullptr);
+ const auto check_polygon_admission =
+ [&](const GeographyCoordinates& polygon_raw, const S2ShapeIndex&
polygon_index,
+ const GeoShape& other, const GeographyCoordinates& other_raw) {
+ if (other.type() != GeoShapeType::GEO_SHAPE_LINE_STRING) {
+ return false;
+ }
+ if ((name == "st_intersects" || name == "st_disjoint") &&
+ geography_has_polygon_intersection_witness(polygon_raw,
polygon_index,
+ other_raw,
nodes)) {
+ return false;
+ }
+ return
geography_polygon_has_rounded_side_mismatch(polygon_raw, polygon_index,
+ other_raw,
nodes);
+ };
+ const auto& lhs_index = name == "st_within" ? right : left;
+ const auto& rhs_index = name == "st_within" ? left : right;
+ const bool inverse_dimensional_containment =
+ containment && container.type() ==
GeoShapeType::GEO_SHAPE_LINE_STRING &&
+ value.type() == GeoShapeType::GEO_SHAPE_POLYGON;
+ if (name != "st_touches" && !inverse_dimensional_containment &&
+ ((lhs.type() == GeoShapeType::GEO_SHAPE_POLYGON &&
+ check_polygon_admission(nodes.left, lhs_index, rhs, nodes.right)) ||
+ (rhs.type() == GeoShapeType::GEO_SHAPE_POLYGON &&
+ check_polygon_admission(nodes.right, rhs_index, lhs, nodes.left)))) {
+ return Status::NotSupported(
+ "{} does not support ambiguous spherical Polygon boundary
interiors", name);
+ }
+ S2BooleanOperation::Options options;
+ options.set_polygon_model(S2BooleanOperation::PolygonModel::CLOSED);
+ options.set_polyline_model(S2BooleanOperation::PolylineModel::CLOSED);
+ options.set_polyline_loops_have_boundaries(false);
+ const auto shares_raw_line_edge = [&] {
+ return std::ranges::any_of(
+ left_edges.line, [&](const auto& edge) { return
right_edges.line.contains(edge); });
+ };
+ const auto shares_raw_vertex = [&] {
+ const auto left_vertices = left_edges.vertices(nodes.left);
+ const auto right_vertices = right_edges.vertices(nodes.right);
+ return std::ranges::any_of(
+ left_vertices, [&](const auto& vertex) { return
right_vertices.contains(vertex); });
+ };
+ const auto has_rounded_only_endpoint = [&] {
+ if (lhs.type() != GeoShapeType::GEO_SHAPE_LINE_STRING ||
+ rhs.type() != GeoShapeType::GEO_SHAPE_LINE_STRING) {
+ return false;
+ }
+ const auto endpoint = [](const GeographyCoordinates& shape, size_t
index) {
+ const auto& line = shape.sequences.front();
+ return line[index == 0 ? 0 : line.size() - 1];
+ };
+ for (size_t left_index : {size_t {0}, size_t {1}}) {
+ for (size_t right_index : {size_t {0}, size_t {1}}) {
+ const auto left = endpoint(nodes.left, left_index);
+ const auto right = endpoint(nodes.right, right_index);
+ if (left != right && left.point == right.point) {
+ return true;
+ }
+ }
+ }
+ return false;
+ };
+ if (name == "st_equals") {
+ *result = left_edges.line == right_edges.line &&
+ left_edges.polygon == right_edges.polygon &&
+ S2BooleanOperation::Equals(left, right, options);
+ return Status::OK();
+ }
+ // Different raw triangle apexes can produce the same S2 region. Boundary
identity decides
+ // equality, but cannot decide which raw region contains the other; do not
accept a false bool.
+ if (raw_polygon_coverage && left_edges.polygon != right_edges.polygon &&
+ S2BooleanOperation::Equals(left, right, options)) {
+ return Status::NotSupported(
+ "{} does not support distinct raw Polygon boundaries with the
same spherical "
+ "representation",
+ name);
+ }
+ // An exterior raw apex or line endpoint at 58+ulp can round onto 58 while
+ // the remaining vertices lie inside. Check before coverage accepts either
shape.
+ const bool polygon_line_coverage = containment &&
+ container.type() ==
GeoShapeType::GEO_SHAPE_POLYGON &&
+ value.type() ==
GeoShapeType::GEO_SHAPE_LINE_STRING;
+ if ((raw_polygon_coverage || polygon_line_coverage) &&
+ geography_rounded_vertex_collision(
+ left_edges, name == "st_within" ? nodes.right : nodes.left,
right_edges,
+ name == "st_within" ? nodes.left : nodes.right)) {
+ return Status::NotSupported(
+ "{} does not support ambiguous spherical Polygon boundary
interiors", name);
+ }
+ if (containment && container.type() == GeoShapeType::GEO_SHAPE_LINE_STRING
&&
+ value.type() == GeoShapeType::GEO_SHAPE_POLYGON) {
+ *result = false;
+ return Status::OK();
+ }
+ const auto covers = [&](bool reverse) {
+ const auto& a = reverse ? right_edges.line : left_edges.line;
+ const auto& b = reverse ? left_edges.line : right_edges.line;
+ return (!raw_line_coverage || std::ranges::includes(a, b)) &&
+ S2BooleanOperation::Contains(reverse ? right : left, reverse ?
left : right,
+ options);
+ };
+ // Rounded indexes alone would let the shorter raw line contain the longer
one.
+ if (containment && !covers(false)) {
+ *result = false;
+ return Status::OK();
+ }
+ auto interior_options = options;
+ interior_options.set_polygon_model(S2BooleanOperation::PolygonModel::OPEN);
+
interior_options.set_polyline_model(S2BooleanOperation::PolylineModel::OPEN);
+ if (containment) {
+ // CLOSED Contains is covers: a polygon must not contain a line solely
on its boundary.
+ *result = S2BooleanOperation::Intersects(left, right,
interior_options);
+ return geography_check_polygon_interiors(name, left, right, nodes,
left_edges, right_edges,
+ *result);
+ }
+ if (name == "st_overlaps") {
+ // Neither equality nor containment is a partial overlap.
+ if (covers(false) || covers(true)) {
+ *result = false;
+ return Status::OK();
+ }
+ if (lhs.type() == GeoShapeType::GEO_SHAPE_POLYGON) {
+ *result = S2BooleanOperation::Intersects(left, right,
interior_options);
+ return geography_check_polygon_interiors(name, left, right, nodes,
left_edges,
+ right_edges, *result);
+ }
+ // A crossing point has no shared raw edge. Conversely, a positive raw
overlap
+ // such as (0,58)->(0,58+ulp) must survive even when S2 rounds it to
one point.
+ *result = shares_raw_line_edge();
+ return Status::OK();
+ }
+ bool intersects = S2BooleanOperation::Intersects(left, right, options);
+ if ((name == "st_intersects" || name == "st_disjoint") &&
has_rounded_only_endpoint()) {
+ return Status::NotSupported(
+ "{} does not support ambiguous spherical Polygon boundary line
endpoint contact",
+ name);
+ }
+ if (intersects && (name == "st_intersects" || name == "st_disjoint") &&
+ (lhs.type() == GeoShapeType::GEO_SHAPE_POLYGON ||
+ rhs.type() == GeoShapeType::GEO_SHAPE_POLYGON) &&
+ geography_rounded_vertex_collision(left_edges, nodes.left,
right_edges, nodes.right) &&
Review Comment:
[P2] Do not reject certified raw polygon crossings because of an unrelated
rounded vertex collision. With Intersects already true, this guard treats any
rounded-only collision without a raw vertex or vertex/interior witness as
ambiguous; a proper edge crossing whose endpoints are all outside the other
polygon has no such witness and returns NotSupported. Add a raw edge-crossing
witness (and test both operand orders), rejecting only when the rounded
collision is the sole possible contact.
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