Allow external Eigen3 (RobotLocomotion#16700)

Add logic (only when using the CMake wrapper) to allow the user to
select and use an external version of Eigen3.

CMakeLists.txt

@@ -396,6 +396,20 @@ endmacro()
 
 set(BAZEL_OVERRIDE_REPOS)
 
+option(WITH_USER_EIGEN "Use user-provided Eigen3" OFF)
+
+if(WITH_USER_EIGEN)
+  find_package(Eigen3 CONFIG REQUIRED)
+
+  symlink_external_repository_includes(eigen Eigen3::Eigen)
+  generate_external_repository_file(eigen/WORKSPACE)
+  generate_external_repository_file(
+    eigen/BUILD.bazel
+    eigen/BUILD.bazel.in)
+
+  override_repository(eigen)
+endif()
+
 option(WITH_USER_FMT "Use user-provided fmt" OFF)
 
 if(WITH_USER_FMT)

cmake/external/workspace/eigen/BUILD.bazel.in

@@ -0,0 +1,24 @@
+# -*- python -*-
+
+load("@drake//tools/install:install.bzl", "install")
+load("@drake//tools/workspace:cmake_util.bzl", "split_cmake_list")
+
+EIGEN_DEFINES = split_cmake_list(
+    "$<TARGET_PROPERTY:Eigen3::Eigen,INTERFACE_COMPILE_DEFINITIONS>",
+)
+
+cc_library(
+    name = "eigen",
+    hdrs = glob(
+        ["include/**"],
+        allow_empty = False,
+    ),
+    defines = EIGEN_DEFINES,
+    includes = ["include"],
+    visibility = ["//visibility:public"],
+)
+
+install(
+    name = "install",
+    visibility = ["//visibility:public"],
+)