paleolimbot commented on code in PR #45459:
URL: https://github.com/apache/arrow/pull/45459#discussion_r2007889283


##########
cpp/src/parquet/types.cc:
##########
@@ -1619,6 +1668,204 @@ class LogicalType::Impl::Float16 final : public 
LogicalType::Impl::Incompatible,
 
 GENERATE_MAKE(Float16)
 
+class LogicalType::Impl::Geometry final : public 
LogicalType::Impl::Incompatible,
+                                          public 
LogicalType::Impl::SimpleApplicable {
+ public:
+  friend class GeometryLogicalType;
+
+  std::string ToString() const override;
+  std::string ToJSON() const override;
+  format::LogicalType ToThrift() const override;
+  bool Equals(const LogicalType& other) const override;
+
+  const std::string& crs() const { return crs_; }
+
+ private:
+  explicit Geometry(std::string crs)
+      : LogicalType::Impl(LogicalType::Type::GEOMETRY, SortOrder::UNKNOWN),
+        LogicalType::Impl::SimpleApplicable(parquet::Type::BYTE_ARRAY),
+        crs_(std::move(crs)) {}
+
+  std::string crs_;
+};
+
+std::string LogicalType::Impl::Geometry::ToString() const {
+  std::stringstream type;
+  type << "Geometry(crs=" << crs_ << ")";
+  return type.str();
+}
+
+std::string LogicalType::Impl::Geometry::ToJSON() const {
+  std::stringstream json;
+  json << R"({"Type": "Geometry")";
+
+  if (!crs_.empty()) {
+    // TODO(paleolimbot): For documented cases the CRS shouldn't contain 
quotes,
+    // but we should probably escape the value of crs_ for backslash and quotes
+    // to be safe.
+    json << R"(, "crs": ")" << crs_ << R"(")";
+  }
+
+  json << "}";
+  return json.str();
+}
+
+format::LogicalType LogicalType::Impl::Geometry::ToThrift() const {
+  format::LogicalType type;
+  format::GeometryType geometry_type;
+
+  // Canonially export crs of "" as an unset CRS
+  if (!crs_.empty()) {
+    geometry_type.__set_crs(crs_);
+  }
+
+  type.__set_GEOMETRY(geometry_type);
+  return type;
+}
+
+bool LogicalType::Impl::Geometry::Equals(const LogicalType& other) const {
+  if (other.is_geometry()) {
+    const auto& other_geometry = checked_cast<const 
GeometryLogicalType&>(other);
+    return crs() == other_geometry.crs();
+  } else {
+    return false;
+  }
+}
+
+const std::string& GeometryLogicalType::crs() const {
+  return (dynamic_cast<const LogicalType::Impl::Geometry&>(*impl_)).crs();

Review Comment:
   I wasn't able to get this to work in mingw (but am open to suggestions if 
I'm missing something obvious!)
   
   ```
   In file included from D:/a/arrow/arrow/cpp/src/parquet/types.cc:25:
   D:/a/arrow/arrow/cpp/src/arrow/util/checked_cast.h:36:10: error: cannot cast 
'const parquet::LogicalType::Impl' to 'const 
parquet::LogicalType::Impl::Geometry &' via virtual base 
'parquet::LogicalType::Impl'
      36 |   return static_cast<OutputType>(value);
         |          ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   D:/a/arrow/arrow/cpp/src/parquet/types.cc:1726:10: note: in instantiation of 
function template specialization 'arrow::internal::checked_cast<const 
parquet::LogicalType::Impl::Geometry &, const parquet::LogicalType::Impl &>' 
requested here
    1726 |   return checked_cast<const 
LogicalType::Impl::Geometry&>(*impl_).crs();
         |          ^
   In file included from D:/a/arrow/arrow/cpp/src/parquet/types.cc:25:
   D:/a/arrow/arrow/cpp/src/arrow/util/checked_cast.h:36:10: error: cannot cast 
'const parquet::LogicalType::Impl' to 'const 
parquet::LogicalType::Impl::Geography &' via virtual base 
'parquet::LogicalType::Impl'
      36 |   return static_cast<OutputType>(value);
         |          ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   D:/a/arrow/arrow/cpp/src/parquet/types.cc:1830:10: note: in instantiation of 
function template specialization 'arrow::internal::checked_cast<const 
parquet::LogicalType::Impl::Geography &, const parquet::LogicalType::Impl &>' 
requested here
    1830 |   return checked_cast<const 
LogicalType::Impl::Geography&>(*impl_).crs();
         |          ^
   2 errors generated.
   ```



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