diff options
Diffstat (limited to 'game')
| -rw-r--r-- | game/geoData.cpp | 427 | ||||
| -rw-r--r-- | game/geoData.h | 106 |
2 files changed, 177 insertions, 356 deletions
diff --git a/game/geoData.cpp b/game/geoData.cpp index 1a1e530..a5fc4ef 100644 --- a/game/geoData.cpp +++ b/game/geoData.cpp @@ -66,7 +66,7 @@ GeoData::loadFromAsciiGrid(const std::filesystem::path & input) }); } } - mesh.update_vertex_normals_only(); + mesh.updateAllVertexNormals(); return mesh; }; @@ -105,7 +105,7 @@ GeoData::createFlat(GlobalPosition2D lower, GlobalPosition2D upper, GlobalDistan } } - mesh.update_vertex_normals_only(); + mesh.updateAllVertexNormals(); return mesh; } @@ -361,7 +361,7 @@ GeoData::findBoundaryStart() const [[nodiscard]] RelativePosition3D GeoData::difference(const HalfedgeHandle heh) const { - return point(to_vertex_handle(heh)) - point(from_vertex_handle(heh)); + return ::difference(point(to_vertex_handle(heh)), point(from_vertex_handle(heh))); } [[nodiscard]] RelativeDistance @@ -377,23 +377,28 @@ GeoData::centre(const HalfedgeHandle heh) const } void -GeoData::update_vertex_normals_only() +GeoData::updateAllVertexNormals() { - update_vertex_normals_only(vertices_sbegin()); + updateAllVertexNormals(vertices()); } +template<std::ranges::range R> void -GeoData::update_vertex_normals_only(VertexIter start) +GeoData::updateAllVertexNormals(const R & range) { - std::for_each(start, vertices_end(), [this](const auto vh) { - if (normal(vh) == Normal3D {}) { - Normal3D n; - calc_vertex_normal_correct(vh, n); - this->set_normal(vh, glm::normalize(n)); - } + std::ranges::for_each(range, [this](const auto vertex) { + updateVertexNormal(vertex); }); } +void +GeoData::updateVertexNormal(VertexHandle vertex) +{ + Normal3D n; + calc_vertex_normal_correct(vertex, n); + set_normal(vertex, glm::normalize(n)); +} + bool GeoData::triangleOverlapsTriangle(const Triangle<2> & a, const Triangle<2> & b) { @@ -411,281 +416,161 @@ GeoData::triangleContainsTriangle(const Triangle<2> & a, const Triangle<2> & b) } void -GeoData::split(FaceHandle _fh) +GeoData::setHeights(const std::span<const GlobalPosition3D> triangleStrip, const SetHeightsOpts & opts) { - // Collect halfedges of face - const HalfedgeHandle he0 = halfedge_handle(_fh); - const HalfedgeHandle he1 = next_halfedge_handle(he0); - const HalfedgeHandle he2 = next_halfedge_handle(he1); - - const EdgeHandle eh0 = edge_handle(he0); - const EdgeHandle eh1 = edge_handle(he1); - const EdgeHandle eh2 = edge_handle(he2); - - // Collect points of face - const VertexHandle p0 = to_vertex_handle(he0); - const VertexHandle p1 = to_vertex_handle(he1); - const VertexHandle p2 = to_vertex_handle(he2); - - // Calculate midpoint coordinates - const Point new0 = centre(he0); - const Point new1 = centre(he1); - const Point new2 = centre(he2); - - // Add vertices at midpoint coordinates - const VertexHandle v0 = add_vertex(new0); - const VertexHandle v1 = add_vertex(new1); - const VertexHandle v2 = add_vertex(new2); - - const bool split0 = !is_boundary(eh0); - const bool split1 = !is_boundary(eh1); - const bool split2 = !is_boundary(eh2); - - // delete original face - delete_face(_fh, false); - - // split boundary edges of deleted face ( if not boundary ) - if (split0) { - split(eh0, v0); - } - - if (split1) { - split(eh1, v1); - } - - if (split2) { - split(eh2, v2); - } - - // Retriangulate - add_face(v0, p0, v1); - add_face(p2, v0, v2); - add_face(v2, v1, p1); - add_face(v2, v0, v1); -} - -void -GeoData::setHeights(const std::span<const GlobalPosition3D> triangleStrip, const Surface & newFaceSurface) -{ - static const RelativeDistance MAX_SLOPE = 1.5F; - static const RelativeDistance MIN_ARC = 0.01F; - if (triangleStrip.size() < 3) { return; } + const auto stripMinMax = std::ranges::minmax(triangleStrip, {}, &GlobalPosition3D::z); + lowerExtent.z = std::min(upperExtent.z, stripMinMax.min.z); + upperExtent.z = std::max(upperExtent.z, stripMinMax.max.z); - const auto initialVertexCount = static_cast<unsigned int>(n_vertices()); + const auto vertexDistFrom = [this](GlobalPosition2D p) { + return [p, this](const VertexHandle v) { + return std::make_pair(v, glm::length(::difference(p, this->point(v).xy()))); + }; + }; - // Create new vertices + std::set<VertexHandle> newOrChangedVerts; + auto addVertexForNormalUpdate = [this, &newOrChangedVerts](const VertexHandle vertex) { + newOrChangedVerts.emplace(vertex); + std::ranges::copy(vv_range(vertex), std::inserter(newOrChangedVerts, newOrChangedVerts.end())); + }; + + // New vertices for each vertex in triangleStrip std::vector<VertexHandle> newVerts; newVerts.reserve(newVerts.size()); - std::transform(triangleStrip.begin(), triangleStrip.end(), std::back_inserter(newVerts), [this](const auto tsVert) { - return add_vertex(tsVert); - }); - // Create new faces - const auto initialFaceCount = static_cast<int>(n_faces()); - std::for_each(strip_begin(newVerts), strip_end(newVerts), [this](const auto & newVert) { - const auto [a, b, c] = newVert; - add_face(a, b, c); - }); - for (auto fhi = FaceIter {*this, FaceHandle {initialFaceCount}, true}; fhi != faces_end(); fhi++) { - static constexpr auto MAX_FACE_AREA = 100'000'000.F; - const auto fh = *fhi; - if (triangle<3>(fh).area() > MAX_FACE_AREA) { - split(fh); - } - } - std::vector<FaceHandle> newFaces; - std::copy_if(FaceIter {*this, FaceHandle {initialFaceCount}, true}, faces_end(), std::back_inserter(newFaces), - [this](FaceHandle fh) { - return !this->status(fh).deleted(); + std::transform(triangleStrip.begin(), triangleStrip.end(), std::back_inserter(newVerts), + [this, &newVerts, &vertexDistFrom, &opts](const auto tsPoint) { + const auto face = findPoint(tsPoint); + if (const auto nearest = std::ranges::min(std::views::iota(fv_begin(face), fv_end(face)) + | std::views::transform(vertexDistFrom(tsPoint)), + {}, &std::pair<VertexHandle, float>::second); + nearest.second < opts.nearNodeTolerance && !std::ranges::contains(newVerts, nearest.first)) { + point(nearest.first) = tsPoint; + return nearest.first; + } + return split(face, tsPoint); }); - - // Extrude corners - struct Extrusion { - VertexHandle boundaryVertex, extrusionVertex; - Direction3D lowerLimit, upperLimit; + std::ranges::for_each(newVerts, addVertexForNormalUpdate); + + // Create temporary triangles from triangleStrip + std::vector<Triangle<3>> strip; + std::transform( + strip_begin(triangleStrip), strip_end(triangleStrip), std::back_inserter(strip), [](const auto & newVert) { + const auto [a, b, c] = newVert; + return Triangle<3> {a, b, c}; + }); + auto getTriangle = [&strip](const auto point) -> const Triangle<3> * { + if (const auto t = std::ranges::find_if(strip, + [point](const auto & triangle) { + return triangleContainsPoint(point, triangle); + }); + t != strip.end()) { + return &*t; + } + return nullptr; }; - std::vector<Extrusion> extrusionExtents; - boundaryWalk( - [this, &extrusionExtents](const auto boundaryHeh) { - const auto prevBoundaryHeh = prev_halfedge_handle(boundaryHeh); - const auto prevBoundaryVertex = from_vertex_handle(prevBoundaryHeh); - const auto boundaryVertex = from_vertex_handle(boundaryHeh); - const auto nextBoundaryVertex = to_vertex_handle(boundaryHeh); - const auto p0 = point(prevBoundaryVertex); - const auto p1 = point(boundaryVertex); - const auto p2 = point(nextBoundaryVertex); - const auto e0 = glm::normalize(vector_normal(RelativePosition2D(p1 - p0))); - const auto e1 = glm::normalize(vector_normal(RelativePosition2D(p2 - p1))); - - const auto addExtrusionFor = [this, &extrusionExtents, boundaryVertex, p1](Direction2D direction) { - const auto doExtrusion = [this](VertexHandle & extrusionVertex, Direction2D direction, - GlobalPosition3D boundaryVertex, RelativeDistance vert) { - const auto extrusionDir = glm::normalize(direction || vert); - const auto intersectAsNeeded = [this, &extrusionVertex](FaceHandle face, GlobalPosition3D pos) { - if (const auto closeVertex = std::find_if(fv_begin(face), fv_end(face), - [this, pos](const auto & vertex) { - return glm::length(::difference(pos, this->point(vertex))) < 10.F; - }); - closeVertex != fv_end(face)) { - extrusionVertex = *closeVertex; - return; - } - extrusionVertex = split(face, pos); - }; - - if (!extrusionVertex.is_valid()) { - if (const auto intersect = intersectRay({boundaryVertex, extrusionDir})) { - intersectAsNeeded(intersect->second, intersect->first); - } - else if (const auto intersect - = intersectRay({boundaryVertex + GlobalPosition3D {1, 1, 0}, extrusionDir})) { - intersectAsNeeded(intersect->second, intersect->first); - } - else if (const auto intersect - = intersectRay({boundaryVertex + GlobalPosition3D {1, 0, 0}, extrusionDir})) { - intersectAsNeeded(intersect->second, intersect->first); - } - } - - return extrusionDir; - }; - - VertexHandle extrusionVertex; - extrusionExtents.emplace_back(boundaryVertex, extrusionVertex, - doExtrusion(extrusionVertex, direction, p1, -MAX_SLOPE), - doExtrusion(extrusionVertex, direction, p1, MAX_SLOPE)); - assert(extrusionVertex.is_valid()); - if (extrusionExtents.size() >= 2) { - const auto & last = *extrusionExtents.rbegin(); - const auto & prev = *++extrusionExtents.rbegin(); - if (last.boundaryVertex == prev.boundaryVertex - && last.extrusionVertex == prev.extrusionVertex) { - extrusionExtents.pop_back(); - } - } - }; - if (const Arc arc {e0, e1}; arc.length() < MIN_ARC) { - addExtrusionFor(normalize(e0 + e1) / cosf(arc.length() / 2.F)); - } - else if (arc.length() < pi) { - // Previous half edge end to current half end start arc tangents - const auto limit = std::ceil(arc.length() * 5.F / pi); - const auto inc = arc.length() / limit; - for (float step = 0; step <= limit; step += 1.F) { - addExtrusionFor(sincos(arc.first + (step * inc))); - } - } - else { - // Single tangent bisecting the difference - addExtrusionFor(normalize(e0 + e1) / sinf((arc.length() - pi) / 2.F)); - } - }, - *voh_begin(newVerts.front())); - - // Cut existing terrain - extrusionExtents.emplace_back(extrusionExtents.front()); // Circular next - std::vector<std::vector<VertexHandle>> boundaryFaces; - for (const auto & [first, second] : extrusionExtents | std::views::adjacent<2>) { - const auto p0 = point(first.boundaryVertex); - const auto p1 = point(second.boundaryVertex); - const auto bdir = RelativePosition3D(p1 - p0); - const auto make_plane = [p0](auto y, auto z) { - return GeometricPlaneT<GlobalPosition3D> {p0, crossProduct(y, z)}; - }; - const auto planes = ((first.boundaryVertex == second.boundaryVertex) - ? std::array {make_plane(second.lowerLimit, first.lowerLimit), - make_plane(second.upperLimit, first.upperLimit), - } - : std::array { - make_plane(bdir, second.lowerLimit), - make_plane(bdir, second.upperLimit), - }); - assert(planes.front().normal.z > 0.F); - assert(planes.back().normal.z > 0.F); - - auto & out = boundaryFaces.emplace_back(); - out.emplace_back(first.boundaryVertex); - out.emplace_back(first.extrusionVertex); - for (auto currentVertex = first.extrusionVertex; - !find_halfedge(currentVertex, second.extrusionVertex).is_valid();) { - [[maybe_unused]] const auto n - = std::any_of(voh_begin(currentVertex), voh_end(currentVertex), [&](const auto currentVertexOut) { - const auto next = next_halfedge_handle(currentVertexOut); - const auto nextVertex = to_vertex_handle(next); - const auto startVertex = from_vertex_handle(next); - if (nextVertex == *++out.rbegin()) { - // This half edge goes back to the previous vertex - return false; - } - const auto edge = edge_handle(next); - const auto ep0 = point(startVertex); - const auto ep1 = point(nextVertex); - if (planes.front().getRelation(ep1) == GeometricPlane::PlaneRelation::Below - || planes.back().getRelation(ep1) == GeometricPlane::PlaneRelation::Above) { - return false; - } - const auto diff = RelativePosition3D(ep1 - ep0); - const auto length = glm::length(diff); - const auto dir = diff / length; - const Ray r {ep1, -dir}; - const auto dists = planes * [r](const auto & plane) { - RelativeDistance dist {}; - if (r.intersectPlane(plane.origin, plane.normal, dist)) { - return dist; - } - return INFINITY; - }; - const auto dist = *std::min_element(dists.begin(), dists.end()); - const auto splitPos = ep1 - (dir * dist); - if (dist <= length) { - currentVertex = split(edge, splitPos); - out.emplace_back(currentVertex); - return true; - } - return false; - }); - assert(n); + // Cut along each edge of triangleStrip AB, AC, BC, BD, CD, CE etc + std::map<VertexHandle, const Triangle<3> *> boundaryTriangles; + auto doBoundaryPart = [this, &boundaryTriangles, &newVerts, &vertexDistFrom, &opts, &addVertexForNormalUpdate]( + VertexHandle start, VertexHandle end, const Triangle<3> & triangle) { + boundaryTriangles.emplace(start, &triangle); + const auto endPoint = point(end); + while (!std::ranges::contains(vv_range(start), end) + && std::ranges::any_of(voh_range(start), [&](const auto & outHalf) { + const auto next = next_halfedge_handle(outHalf); + const auto startPoint = point(start); + const auto nexts = std::array {from_vertex_handle(next), to_vertex_handle(next)}; + const auto nextPoints = nexts | std::views::transform([this](const auto v) { + return std::make_pair(v, this->point(v)); + }); + if (linesCross(startPoint, endPoint, nextPoints.front().second, nextPoints.back().second)) { + if (const auto intersection = linesIntersectAt(startPoint.xy(), endPoint.xy(), + nextPoints.front().second.xy(), nextPoints.back().second.xy())) { + if (const auto nextDist + = std::ranges::min(nexts | std::views::transform(vertexDistFrom(*intersection)), + {}, &std::pair<VertexHandle, float>::second); + nextDist.second < opts.nearNodeTolerance + && !boundaryTriangles.contains(nextDist.first) + && !std::ranges::contains(newVerts, nextDist.first)) { + start = nextDist.first; + point(start) = positionOnTriangle(*intersection, triangle); + } + else { + start = split(edge_handle(next), positionOnTriangle(*intersection, triangle)); + } + addVertexForNormalUpdate(start); + boundaryTriangles.emplace(start, &triangle); + return true; + } + } + return false; + })) { } + }; + auto doBoundary = [&doBoundaryPart, triangle = strip.begin()](const auto & verts) mutable { + const auto & [a, b, c] = verts; + doBoundaryPart(a, b, *triangle); + doBoundaryPart(a, c, *triangle); + triangle++; + }; + std::ranges::for_each(newVerts | std::views::adjacent<3>, doBoundary); + doBoundaryPart(*++newVerts.rbegin(), newVerts.back(), *strip.rbegin()); + + std::set<HalfedgeHandle> done; + std::set<HalfedgeHandle> todo; + auto todoOutHalfEdges = [&todo, &done, this](const VertexHandle v) { + std::copy_if(voh_begin(v), voh_end(v), std::inserter(todo, todo.end()), [&done](const auto & h) { + return !done.contains(h); + }); + }; + std::ranges::for_each(newVerts, todoOutHalfEdges); + while (!todo.empty()) { + const auto heh = todo.extract(todo.begin()).value(); + const auto fromVertex = from_vertex_handle(heh); + const auto toVertex = to_vertex_handle(heh); + const auto & fromPoint = point(fromVertex); + auto & toPoint = point(toVertex); + auto toTriangle = getTriangle(toPoint); + if (!toTriangle) { + if (const auto boundaryVertex = boundaryTriangles.find(toVertex); + boundaryVertex != boundaryTriangles.end()) { + toTriangle = boundaryVertex->second; + } } - out.emplace_back(second.extrusionVertex); - if (first.boundaryVertex != second.boundaryVertex) { - out.emplace_back(second.boundaryVertex); + if (toTriangle) { // point within the new strip, adjust vertically by triangle + toPoint.z = positionOnTriangle(toPoint, *toTriangle).z; + addVertexForNormalUpdate(toVertex); + todoOutHalfEdges(toVertex); } + else if (!toTriangle) { // point without the new strip, adjust vertically by limit + const auto maxOffset = static_cast<GlobalDistance>(opts.maxSlope * glm::length(difference(heh).xy())); + const auto newHeight = std::clamp(toPoint.z, fromPoint.z - maxOffset, fromPoint.z + maxOffset); + if (newHeight != toPoint.z) { + toPoint.z = newHeight; + addVertexForNormalUpdate(toVertex); + std::copy_if(voh_begin(toVertex), voh_end(toVertex), std::inserter(todo, todo.end()), + [this, &boundaryTriangles](const auto & heh) { + return !boundaryTriangles.contains(to_vertex_handle(heh)); + }); + } + } + done.insert(heh); } - // Remove old faces - std::set<FaceHandle> visited; - auto removeOld = [&](auto & self, const auto face) -> void { - if (visited.insert(face).second) { - std::for_each(fh_begin(face), fh_end(face), [&](const auto fh) { - const auto b1 = to_vertex_handle(fh); - const auto b2 = from_vertex_handle(fh); - if (opposite_face_handle(fh).is_valid() - && std::none_of(boundaryFaces.begin(), boundaryFaces.end(), [b2, b1](const auto & bf) { - return std::adjacent_find(bf.begin(), bf.end(), [b2, b1](const auto v1, const auto v2) { - return b1 == v1 && b2 == v2; - }) != bf.end(); - })) { - self(self, opposite_face_handle(fh)); - } - }); - - delete_face(face, false); + auto surfaceStripWalk = [this, &getTriangle, &opts](const auto & surfaceStripWalk, const auto & face) -> void { + if (!property(surface, face)) { + property(surface, face) = &opts.surface; + std::ranges::for_each( + ff_range(face), [this, &getTriangle, &surfaceStripWalk](const auto & adjacentFaceHandle) { + if (getTriangle(this->triangle<2>(adjacentFaceHandle).centroid())) { + surfaceStripWalk(surfaceStripWalk, adjacentFaceHandle); + } + }); } }; - removeOld(removeOld, findPoint(triangleStrip.front())); - - std::for_each(boundaryFaces.begin(), boundaryFaces.end(), [&](auto & boundaryFace) { - std::reverse(boundaryFace.begin(), boundaryFace.end()); - add_face(boundaryFace); - }); - - // Tidy up - update_vertex_normals_only(VertexIter {*this, vertex_handle(initialVertexCount), true}); + surfaceStripWalk(surfaceStripWalk, findPoint(strip.front().centroid())); - std::for_each(newFaces.begin(), newFaces.end(), [&newFaceSurface, this](const auto fh) { - property(surface, fh) = &newFaceSurface; - }); + updateAllVertexNormals(newOrChangedVerts); } diff --git a/game/geoData.h b/game/geoData.h index ed1734c..79924d3 100644 --- a/game/geoData.h +++ b/game/geoData.h @@ -4,6 +4,7 @@ #include "config/types.h" #include "ray.h" #include "surface.h" +#include "triangle.h" #include <OpenMesh/Core/Mesh/TriMesh_ArrayKernelT.hh> #include <filesystem> #include <glm/vec2.hpp> @@ -52,76 +53,7 @@ public: mutable FaceHandle _face {}; }; - template<glm::length_t Dim> struct Triangle : public glm::vec<3, glm::vec<Dim, GlobalDistance>> { - using base = glm::vec<3, glm::vec<Dim, GlobalDistance>>; - using base::base; - - template<IterableCollection Range> Triangle(const GeoData * m, Range range) - { - assert(std::distance(range.begin(), range.end()) == 3); - std::transform(range.begin(), range.end(), &base::operator[](0), [m](auto vh) { - return m->point(vh); - }); - } - - [[nodiscard]] glm::vec<Dim, GlobalDistance> - operator*(BaryPosition bari) const - { - return p(0) + (difference(p(0), p(1)) * bari.x) + (difference(p(0), p(2)) * bari.y); - } - - [[nodiscard]] auto - area() const - requires(Dim == 3) - { - return glm::length(crossProduct(difference(p(0), p(1)), difference(p(0), p(2)))) / 2.F; - } - - [[nodiscard]] Normal3D - normal() const - requires(Dim == 3) - { - return crossProduct(difference(p(0), p(1)), difference(p(0), p(2))); - } - - [[nodiscard]] Normal3D - nnormal() const - requires(Dim == 3) - { - return glm::normalize(normal()); - } - - [[nodiscard]] auto - angle(glm::length_t c) const - { - return Arc {P(c), P(c + 2), P(c + 1)}.length(); - } - - template<glm::length_t D = Dim> - [[nodiscard]] auto - angleAt(const GlobalPosition<D> pos) const - requires(D <= Dim) - { - for (glm::length_t i {}; i < 3; ++i) { - if (GlobalPosition<D> {p(i)} == pos) { - return angle(i); - } - } - return 0.F; - } - - [[nodiscard]] inline auto - p(const glm::length_t i) const - { - return base::operator[](i); - } - - [[nodiscard]] inline auto - P(const glm::length_t i) const - { - return base::operator[](i % 3); - } - }; + template<glm::length_t Dim> using Triangle = ::Triangle<Dim, GlobalDistance>; [[nodiscard]] FaceHandle findPoint(GlobalPosition2D) const; [[nodiscard]] FaceHandle findPoint(GlobalPosition2D, FaceHandle start) const; @@ -142,7 +74,16 @@ public: [[nodiscard]] HalfedgeHandle findEntry(const GlobalPosition2D from, const GlobalPosition2D to) const; - void setHeights(const std::span<const GlobalPosition3D> triangleStrip, const Surface &); + struct SetHeightsOpts { + static constexpr auto DEFAULT_NEAR_NODE_TOLERANACE = 500.F; + static constexpr auto DEFAULT_MAX_SLOPE = 0.5F; + + const Surface & surface; + RelativeDistance nearNodeTolerance = DEFAULT_NEAR_NODE_TOLERANACE; + RelativeDistance maxSlope = DEFAULT_MAX_SLOPE; + }; + + void setHeights(std::span<const GlobalPosition3D> triangleStrip, const SetHeightsOpts &); [[nodiscard]] auto getExtents() const @@ -160,9 +101,13 @@ public: protected: template<glm::length_t Dim> [[nodiscard]] Triangle<Dim> - triangle(FaceHandle f) const + triangle(FaceHandle face) const { - return {this, fv_range(f)}; + Triangle<Dim> triangle; + std::ranges::transform(fv_range(face), triangle.begin(), [this](auto vertex) { + return point(vertex); + }); + return triangle; } [[nodiscard]] static bool triangleContainsPoint(const GlobalPosition2D, const Triangle<2> &); @@ -172,21 +117,12 @@ protected: [[nodiscard]] HalfedgeHandle findBoundaryStart() const; [[nodiscard]] RelativePosition3D difference(const HalfedgeHandle) const; - template<glm::length_t D> - [[nodiscard]] static RelativePosition<D> - difference(const GlobalPosition<D> a, const GlobalPosition<D> b) - { - return b - a; - } - [[nodiscard]] RelativeDistance length(const HalfedgeHandle) const; [[nodiscard]] GlobalPosition3D centre(const HalfedgeHandle) const; - void update_vertex_normals_only(); - void update_vertex_normals_only(VertexIter start); - - using OpenMesh::TriMesh_ArrayKernelT<GeoDataTraits>::split; - void split(FaceHandle); + void updateAllVertexNormals(); + template<std::ranges::range R> void updateAllVertexNormals(const R &); + void updateVertexNormal(VertexHandle); private: GlobalPosition3D lowerExtent {}, upperExtent {}; |