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+// Copyright 2011 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include "cc/trees/layer_sorter.h"
+
+#include <algorithm>
+#include <deque>
+#include <limits>
+#include <vector>
+
+#include "base/logging.h"
+#include "cc/base/math_util.h"
+#include "cc/layers/render_surface_impl.h"
+#include "ui/gfx/transform.h"
+
+namespace cc {
+
+// This epsilon is used to determine if two layers are too close to each other
+// to be able to tell which is in front of the other. It's a relative epsilon
+// so it is robust to changes in scene scale. This value was chosen by picking
+// a value near machine epsilon and then increasing it until the flickering on
+// the test scene went away.
+const float k_layer_epsilon = 1e-4f;
+
+inline static float PerpProduct(gfx::Vector2dF u, gfx::Vector2dF v) {
+ return u.x() * v.y() - u.y() * v.x();
+}
+
+// Tests if two edges defined by their endpoints (a,b) and (c,d) intersect.
+// Returns true and the point of intersection if they do and false otherwise.
+static bool EdgeEdgeTest(gfx::PointF a,
+ gfx::PointF b,
+ gfx::PointF c,
+ gfx::PointF d,
+ gfx::PointF* r) {
+ gfx::Vector2dF u = b - a;
+ gfx::Vector2dF v = d - c;
+ gfx::Vector2dF w = a - c;
+
+ float denom = PerpProduct(u, v);
+
+ // If denom == 0 then the edges are parallel. While they could be overlapping
+ // we don't bother to check here as the we'll find their intersections from
+ // the corner to quad tests.
+ if (!denom)
+ return false;
+
+ float s = PerpProduct(v, w) / denom;
+ if (s < 0.f || s > 1.f)
+ return false;
+
+ float t = PerpProduct(u, w) / denom;
+ if (t < 0.f || t > 1.f)
+ return false;
+
+ u.Scale(s);
+ *r = a + u;
+ return true;
+}
+
+GraphNode::GraphNode(LayerImpl* layer_impl)
+ : layer(layer_impl),
+ incoming_edge_weight(0.f) {}
+
+GraphNode::~GraphNode() {}
+
+LayerSorter::LayerSorter()
+ : z_range_(0.f) {}
+
+LayerSorter::~LayerSorter() {}
+
+static float CheckFloatingPointNumericAccuracy(float a, float b) {
+ float abs_dif = std::abs(b - a);
+ float abs_max = std::max(std::abs(b), std::abs(a));
+ // Check to see if we've got a result with a reasonable amount of error.
+ return abs_dif / abs_max;
+}
+
+// Checks whether layer "a" draws on top of layer "b". The weight value returned
+// is an indication of the maximum z-depth difference between the layers or zero
+// if the layers are found to be intesecting (some features are in front and
+// some are behind).
+LayerSorter::ABCompareResult LayerSorter::CheckOverlap(LayerShape* a,
+ LayerShape* b,
+ float z_threshold,
+ float* weight) {
+ *weight = 0.f;
+
+ // Early out if the projected bounds don't overlap.
+ if (!a->projected_bounds.Intersects(b->projected_bounds))
+ return None;
+
+ gfx::PointF aPoints[4] = { a->projected_quad.p1(),
+ a->projected_quad.p2(),
+ a->projected_quad.p3(),
+ a->projected_quad.p4() };
+ gfx::PointF bPoints[4] = { b->projected_quad.p1(),
+ b->projected_quad.p2(),
+ b->projected_quad.p3(),
+ b->projected_quad.p4() };
+
+ // Make a list of points that inside both layer quad projections.
+ std::vector<gfx::PointF> overlap_points;
+
+ // Check all four corners of one layer against the other layer's quad.
+ for (int i = 0; i < 4; ++i) {
+ if (a->projected_quad.Contains(bPoints[i]))
+ overlap_points.push_back(bPoints[i]);
+ if (b->projected_quad.Contains(aPoints[i]))
+ overlap_points.push_back(aPoints[i]);
+ }
+
+ // Check all the edges of one layer for intersection with the other layer's
+ // edges.
+ gfx::PointF r;
+ for (int ea = 0; ea < 4; ++ea)
+ for (int eb = 0; eb < 4; ++eb)
+ if (EdgeEdgeTest(aPoints[ea], aPoints[(ea + 1) % 4],
+ bPoints[eb], bPoints[(eb + 1) % 4],
+ &r))
+ overlap_points.push_back(r);
+
+ if (overlap_points.empty())
+ return None;
+
+ // Check the corresponding layer depth value for all overlap points to
+ // determine which layer is in front.
+ float max_positive = 0.f;
+ float max_negative = 0.f;
+
+ // This flag tracks the existance of a numerically accurate seperation
+ // between two layers. If there is no accurate seperation, the layers
+ // cannot be effectively sorted.
+ bool accurate = false;
+
+ for (size_t o = 0; o < overlap_points.size(); o++) {
+ float za = a->LayerZFromProjectedPoint(overlap_points[o]);
+ float zb = b->LayerZFromProjectedPoint(overlap_points[o]);
+
+ // Here we attempt to avoid numeric issues with layers that are too
+ // close together. If we have 2-sided quads that are very close
+ // together then we will draw them in document order to avoid
+ // flickering. The correct solution is for the content maker to turn
+ // on back-face culling or move the quads apart (if they're not two
+ // sides of one object).
+ if (CheckFloatingPointNumericAccuracy(za, zb) > k_layer_epsilon)
+ accurate = true;
+
+ float diff = za - zb;
+ if (diff > max_positive)
+ max_positive = diff;
+ if (diff < max_negative)
+ max_negative = diff;
+ }
+
+ // If we can't tell which should come first, we use document order.
+ if (!accurate)
+ return ABeforeB;
+
+ float max_diff =
+ std::abs(max_positive) > std::abs(max_negative) ?
+ max_positive : max_negative;
+
+ // If the results are inconsistent (and the z difference substantial to rule
+ // out numerical errors) then the layers are intersecting. We will still
+ // return an order based on the maximum depth difference but with an edge
+ // weight of zero these layers will get priority if a graph cycle is present
+ // and needs to be broken.
+ if (max_positive > z_threshold && max_negative < -z_threshold)
+ *weight = 0.f;
+ else
+ *weight = std::abs(max_diff);
+
+ // Maintain relative order if the layers have the same depth at all
+ // intersection points.
+ if (max_diff <= 0.f)
+ return ABeforeB;
+
+ return BBeforeA;
+}
+
+LayerShape::LayerShape() {}
+
+LayerShape::LayerShape(float width,
+ float height,
+ const gfx::Transform& draw_transform) {
+ gfx::QuadF layer_quad(gfx::RectF(0.f, 0.f, width, height));
+
+ // Compute the projection of the layer quad onto the z = 0 plane.
+
+ gfx::PointF clipped_quad[8];
+ int num_vertices_in_clipped_quad;
+ MathUtil::MapClippedQuad(draw_transform,
+ layer_quad,
+ clipped_quad,
+ &num_vertices_in_clipped_quad);
+
+ if (num_vertices_in_clipped_quad < 3) {
+ projected_bounds = gfx::RectF();
+ return;
+ }
+
+ projected_bounds =
+ MathUtil::ComputeEnclosingRectOfVertices(clipped_quad,
+ num_vertices_in_clipped_quad);
+
+ // NOTE: it will require very significant refactoring and overhead to deal
+ // with generalized polygons or multiple quads per layer here. For the sake of
+ // layer sorting it is equally correct to take a subsection of the polygon
+ // that can be made into a quad. This will only be incorrect in the case of
+ // intersecting layers, which are not supported yet anyway.
+ projected_quad.set_p1(clipped_quad[0]);
+ projected_quad.set_p2(clipped_quad[1]);
+ projected_quad.set_p3(clipped_quad[2]);
+ if (num_vertices_in_clipped_quad >= 4) {
+ projected_quad.set_p4(clipped_quad[3]);
+ } else {
+ // This will be a degenerate quad that is actually a triangle.
+ projected_quad.set_p4(clipped_quad[2]);
+ }
+
+ // Compute the normal of the layer's plane.
+ bool clipped = false;
+ gfx::Point3F c1 =
+ MathUtil::MapPoint(draw_transform, gfx::Point3F(0.f, 0.f, 0.f), &clipped);
+ gfx::Point3F c2 =
+ MathUtil::MapPoint(draw_transform, gfx::Point3F(0.f, 1.f, 0.f), &clipped);
+ gfx::Point3F c3 =
+ MathUtil::MapPoint(draw_transform, gfx::Point3F(1.f, 0.f, 0.f), &clipped);
+ // TODO(shawnsingh): Deal with clipping.
+ gfx::Vector3dF c12 = c2 - c1;
+ gfx::Vector3dF c13 = c3 - c1;
+ layer_normal = gfx::CrossProduct(c13, c12);
+
+ transform_origin = c1;
+}
+
+LayerShape::~LayerShape() {}
+
+// Returns the Z coordinate of a point on the layer that projects
+// to point p which lies on the z = 0 plane. It does it by computing the
+// intersection of a line starting from p along the Z axis and the plane
+// of the layer.
+float LayerShape::LayerZFromProjectedPoint(gfx::PointF p) const {
+ gfx::Vector3dF z_axis(0.f, 0.f, 1.f);
+ gfx::Vector3dF w = gfx::Point3F(p) - transform_origin;
+
+ float d = gfx::DotProduct(layer_normal, z_axis);
+ float n = -gfx::DotProduct(layer_normal, w);
+
+ // Check if layer is parallel to the z = 0 axis which will make it
+ // invisible and hence returning zero is fine.
+ if (!d)
+ return 0.f;
+
+ // The intersection point would be given by:
+ // p + (n / d) * u but since we are only interested in the
+ // z coordinate and p's z coord is zero, all we need is the value of n/d.
+ return n / d;
+}
+
+void LayerSorter::CreateGraphNodes(LayerImplList::iterator first,
+ LayerImplList::iterator last) {
+ DVLOG(2) << "Creating graph nodes:";
+ float min_z = FLT_MAX;
+ float max_z = -FLT_MAX;
+ for (LayerImplList::const_iterator it = first; it < last; it++) {
+ nodes_.push_back(GraphNode(*it));
+ GraphNode& node = nodes_.at(nodes_.size() - 1);
+ RenderSurfaceImpl* render_surface = node.layer->render_surface();
+ if (!node.layer->DrawsContent() && !render_surface)
+ continue;
+
+ DVLOG(2) << "Layer " << node.layer->id() <<
+ " (" << node.layer->bounds().width() <<
+ " x " << node.layer->bounds().height() << ")";
+
+ gfx::Transform draw_transform;
+ float layer_width, layer_height;
+ if (render_surface) {
+ draw_transform = render_surface->draw_transform();
+ layer_width = render_surface->content_rect().width();
+ layer_height = render_surface->content_rect().height();
+ } else {
+ draw_transform = node.layer->draw_transform();
+ layer_width = node.layer->content_bounds().width();
+ layer_height = node.layer->content_bounds().height();
+ }
+
+ node.shape = LayerShape(layer_width, layer_height, draw_transform);
+
+ max_z = std::max(max_z, node.shape.transform_origin.z());
+ min_z = std::min(min_z, node.shape.transform_origin.z());
+ }
+
+ z_range_ = std::abs(max_z - min_z);
+}
+
+void LayerSorter::CreateGraphEdges() {
+ DVLOG(2) << "Edges:";
+ // Fraction of the total z_range below which z differences
+ // are not considered reliable.
+ const float z_threshold_factor = 0.01f;
+ float z_threshold = z_range_ * z_threshold_factor;
+
+ for (size_t na = 0; na < nodes_.size(); na++) {
+ GraphNode& node_a = nodes_[na];
+ if (!node_a.layer->DrawsContent() && !node_a.layer->render_surface())
+ continue;
+ for (size_t nb = na + 1; nb < nodes_.size(); nb++) {
+ GraphNode& node_b = nodes_[nb];
+ if (!node_b.layer->DrawsContent() && !node_b.layer->render_surface())
+ continue;
+ float weight = 0.f;
+ ABCompareResult overlap_result = CheckOverlap(&node_a.shape,
+ &node_b.shape,
+ z_threshold,
+ &weight);
+ GraphNode* start_node = NULL;
+ GraphNode* end_node = NULL;
+ if (overlap_result == ABeforeB) {
+ start_node = &node_a;
+ end_node = &node_b;
+ } else if (overlap_result == BBeforeA) {
+ start_node = &node_b;
+ end_node = &node_a;
+ }
+
+ if (start_node) {
+ DVLOG(2) << start_node->layer->id() << " -> " << end_node->layer->id();
+ edges_.push_back(GraphEdge(start_node, end_node, weight));
+ }
+ }
+ }
+
+ for (size_t i = 0; i < edges_.size(); i++) {
+ GraphEdge& edge = edges_[i];
+ active_edges_[&edge] = &edge;
+ edge.from->outgoing.push_back(&edge);
+ edge.to->incoming.push_back(&edge);
+ edge.to->incoming_edge_weight += edge.weight;
+ }
+}
+
+// Finds and removes an edge from the list by doing a swap with the
+// last element of the list.
+void LayerSorter::RemoveEdgeFromList(GraphEdge* edge,
+ std::vector<GraphEdge*>* list) {
+ std::vector<GraphEdge*>::iterator iter =
+ std::find(list->begin(), list->end(), edge);
+ DCHECK(iter != list->end());
+ list->erase(iter);
+}
+
+// Sorts the given list of layers such that they can be painted in a
+// back-to-front order. Sorting produces correct results for non-intersecting
+// layers that don't have cyclical order dependencies. Cycles and intersections
+// are broken (somewhat) aribtrarily. Sorting of layers is done via a
+// topological sort of a directed graph whose nodes are the layers themselves.
+// An edge from node A to node B signifies that layer A needs to be drawn before
+// layer B. If A and B have no dependency between each other, then we preserve
+// the ordering of those layers as they were in the original list.
+//
+// The draw order between two layers is determined by projecting the two
+// triangles making up each layer quad to the Z = 0 plane, finding points of
+// intersection between the triangles and backprojecting those points to the
+// plane of the layer to determine the corresponding Z coordinate. The layer
+// with the lower Z coordinate (farther from the eye) needs to be rendered
+// first.
+//
+// If the layer projections don't intersect, then no edges (dependencies) are
+// created between them in the graph. HOWEVER, in this case we still need to
+// preserve the ordering of the original list of layers, since that list should
+// already have proper z-index ordering of layers.
+//
+void LayerSorter::Sort(LayerImplList::iterator first,
+ LayerImplList::iterator last) {
+ DVLOG(2) << "Sorting start ----";
+ CreateGraphNodes(first, last);
+
+ CreateGraphEdges();
+
+ std::vector<GraphNode*> sorted_list;
+ std::deque<GraphNode*> no_incoming_edge_node_list;
+
+ // Find all the nodes that don't have incoming edges.
+ for (NodeList::iterator la = nodes_.begin(); la < nodes_.end(); la++) {
+ if (!la->incoming.size())
+ no_incoming_edge_node_list.push_back(&(*la));
+ }
+
+ DVLOG(2) << "Sorted list: ";
+ while (active_edges_.size() || no_incoming_edge_node_list.size()) {
+ while (no_incoming_edge_node_list.size()) {
+ // It is necessary to preserve the existing ordering of layers, when there
+ // are no explicit dependencies (because this existing ordering has
+ // correct z-index/layout ordering). To preserve this ordering, we process
+ // Nodes in the same order that they were added to the list.
+ GraphNode* from_node = no_incoming_edge_node_list.front();
+ no_incoming_edge_node_list.pop_front();
+
+ // Add it to the final list.
+ sorted_list.push_back(from_node);
+
+ DVLOG(2) << from_node->layer->id() << ", ";
+
+ // Remove all its outgoing edges from the graph.
+ for (size_t i = 0; i < from_node->outgoing.size(); i++) {
+ GraphEdge* outgoing_edge = from_node->outgoing[i];
+
+ active_edges_.erase(outgoing_edge);
+ RemoveEdgeFromList(outgoing_edge, &outgoing_edge->to->incoming);
+ outgoing_edge->to->incoming_edge_weight -= outgoing_edge->weight;
+
+ if (!outgoing_edge->to->incoming.size())
+ no_incoming_edge_node_list.push_back(outgoing_edge->to);
+ }
+ from_node->outgoing.clear();
+ }
+
+ if (!active_edges_.size())
+ break;
+
+ // If there are still active edges but the list of nodes without incoming
+ // edges is empty then we have run into a cycle. Break the cycle by finding
+ // the node with the smallest overall incoming edge weight and use it. This
+ // will favor nodes that have zero-weight incoming edges i.e. layers that
+ // are being occluded by a layer that intersects them.
+ float min_incoming_edge_weight = FLT_MAX;
+ GraphNode* next_node = NULL;
+ for (size_t i = 0; i < nodes_.size(); i++) {
+ if (nodes_[i].incoming.size() &&
+ nodes_[i].incoming_edge_weight < min_incoming_edge_weight) {
+ min_incoming_edge_weight = nodes_[i].incoming_edge_weight;
+ next_node = &nodes_[i];
+ }
+ }
+ DCHECK(next_node);
+ // Remove all its incoming edges.
+ for (size_t e = 0; e < next_node->incoming.size(); e++) {
+ GraphEdge* incoming_edge = next_node->incoming[e];
+
+ active_edges_.erase(incoming_edge);
+ RemoveEdgeFromList(incoming_edge, &incoming_edge->from->outgoing);
+ }
+ next_node->incoming.clear();
+ next_node->incoming_edge_weight = 0.f;
+ no_incoming_edge_node_list.push_back(next_node);
+ DVLOG(2) << "Breaking cycle by cleaning up incoming edges from " <<
+ next_node->layer->id() <<
+ " (weight = " << min_incoming_edge_weight << ")";
+ }
+
+ // Note: The original elements of the list are in no danger of having their
+ // ref count go to zero here as they are all nodes of the layer hierarchy and
+ // are kept alive by their parent nodes.
+ int count = 0;
+ for (LayerImplList::iterator it = first; it < last; it++)
+ *it = sorted_list[count++]->layer;
+
+ DVLOG(2) << "Sorting end ----";
+
+ nodes_.clear();
+ edges_.clear();
+ active_edges_.clear();
+}
+
+} // namespace cc