root/cc/trees/layer_sorter.cc

DEFINITIONS

1. PerpProduct
2. EdgeEdgeTest
3. incoming_edge_weight
4. CheckFloatingPointNumericAccuracy
5. CheckOverlap
6. LayerZFromProjectedPoint
7. CreateGraphNodes
8. CreateGraphEdges
9. RemoveEdgeFromList

// 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(const gfx::Vector2dF& u,
                                const 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(const gfx::PointF& a,
                         const gfx::PointF& b,
                         const gfx::PointF& c,
                         const 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(const 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