path_component.cc

Go to the documentation of this file.

// Copyright 2013 The Flutter 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 "path_component.h"
 
#include <cmath>
#include <utility>
 
#include "flutter/fml/logging.h"
#include "flutter/impeller/geometry/scalar.h"
#include "flutter/impeller/geometry/wangs_formula.h"
 
namespace impeller {
 
/////////// FanVertexWriter ///////////
 
FanVertexWriter::FanVertexWriter(Point* point_buffer, uint16_t* index_buffer)
    : point_buffer_(point_buffer), index_buffer_(index_buffer) {}
 
FanVertexWriter::~FanVertexWriter() = default;
 
size_t FanVertexWriter::GetIndexCount() const {
  return index_count_;
}
 
void FanVertexWriter::EndContour() {
  if (count_ == 0) {
    return;
  }
  index_buffer_[index_count_++] = 0xFFFF;
}
 
void FanVertexWriter::Write(Point point) {
  index_buffer_[index_count_++] = count_;
  point_buffer_[count_++] = point;
}
 
/////////// StripVertexWriter ///////////
 
StripVertexWriter::StripVertexWriter(Point* point_buffer,
                                     uint16_t* index_buffer)
    : point_buffer_(point_buffer), index_buffer_(index_buffer) {}
 
StripVertexWriter::~StripVertexWriter() = default;
 
size_t StripVertexWriter::GetIndexCount() const {
  return index_count_;
}
 
void StripVertexWriter::EndContour() {
  if (count_ == 0u || contour_start_ == count_ - 1) {
    // Empty or first contour.
    return;
  }
 
  size_t start = contour_start_;
  size_t end = count_ - 1;
 
  index_buffer_[index_count_++] = start;
 
  size_t a = start + 1;
  size_t b = end;
  while (a < b) {
    index_buffer_[index_count_++] = a;
    index_buffer_[index_count_++] = b;
    a++;
    b--;
  }
  if (a == b) {
    index_buffer_[index_count_++] = a;
  }
 
  contour_start_ = count_;
  index_buffer_[index_count_++] = 0xFFFF;
}
 
void StripVertexWriter::Write(Point point) {
  point_buffer_[count_++] = point;
}
 
/////////// LineStripVertexWriter ////////
 
LineStripVertexWriter::LineStripVertexWriter(std::vector<Point>& points)
    : points_(points) {}
 
void LineStripVertexWriter::EndContour() {}
 
void LineStripVertexWriter::Write(Point point) {
  if (offset_ >= points_.size()) {
    overflow_.push_back(point);
  } else {
    points_[offset_++] = point;
  }
}
 
const std::vector<Point>& LineStripVertexWriter::GetOversizedBuffer() const {
  return overflow_;
}
 
std::pair<size_t, size_t> LineStripVertexWriter::GetVertexCount() const {
  return std::make_pair(offset_, overflow_.size());
}
 
/////////// GLESVertexWriter ///////////
 
GLESVertexWriter::GLESVertexWriter(std::vector<Point>& points,
                                   std::vector<uint16_t>& indices)
    : points_(points), indices_(indices) {}
 
void GLESVertexWriter::EndContour() {
  if (points_.size() == 0u || contour_start_ == points_.size() - 1) {
    // Empty or first contour.
    return;
  }
 
  auto start = contour_start_;
  auto end = points_.size() - 1;
  // All filled paths are drawn as if they are closed, but if
  // there is an explicit close then a lineTo to the origin
  // is inserted. This point isn't strictly necesary to
  // correctly render the shape and can be dropped.
  if (points_[end] == points_[start]) {
    end--;
  }
 
  // Triangle strip break for subsequent contours
  if (contour_start_ != 0) {
    auto back = indices_.back();
    indices_.push_back(back);
    indices_.push_back(start);
    indices_.push_back(start);
 
    // If the contour has an odd number of points, insert an extra point when
    // bridging to the next contour to preserve the correct triangle winding
    // order.
    if (previous_contour_odd_points_) {
      indices_.push_back(start);
    }
  } else {
    indices_.push_back(start);
  }
 
  size_t a = start + 1;
  size_t b = end;
  while (a < b) {
    indices_.push_back(a);
    indices_.push_back(b);
    a++;
    b--;
  }
  if (a == b) {
    indices_.push_back(a);
    previous_contour_odd_points_ = false;
  } else {
    previous_contour_odd_points_ = true;
  }
  contour_start_ = points_.size();
}
 
void GLESVertexWriter::Write(Point point) {
  points_.push_back(point);
}
 
/*
 *  Based on: https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Specific_cases
 */
 
static inline Scalar LinearSolve(Scalar t, Scalar p0, Scalar p1) {
  return p0 + t * (p1 - p0);
}
 
static inline Scalar QuadraticSolve(Scalar t, Scalar p0, Scalar p1, Scalar p2) {
  return (1 - t) * (1 - t) * p0 +  //
         2 * (1 - t) * t * p1 +    //
         t * t * p2;
}
 
static inline Scalar QuadraticSolveDerivative(Scalar t,
                                              Scalar p0,
                                              Scalar p1,
                                              Scalar p2) {
  return 2 * (1 - t) * (p1 - p0) +  //
         2 * t * (p2 - p1);
}
 
static inline Scalar ConicSolve(Scalar t,
                                Scalar p0,
                                Scalar p1,
                                Scalar p2,
                                Scalar w) {
  auto u = (1 - t);
  auto coefficient_p0 = u * u;
  auto coefficient_p1 = 2 * t * u * w;
  auto coefficient_p2 = t * t;
 
  return ((p0 * coefficient_p0 + p1 * coefficient_p1 + p2 * coefficient_p2) /
          (coefficient_p0 + coefficient_p1 + coefficient_p2));
}
 
static inline Scalar CubicSolve(Scalar t,
                                Scalar p0,
                                Scalar p1,
                                Scalar p2,
                                Scalar p3) {
  return (1 - t) * (1 - t) * (1 - t) * p0 +  //
         3 * (1 - t) * (1 - t) * t * p1 +    //
         3 * (1 - t) * t * t * p2 +          //
         t * t * t * p3;
}
 
static inline Scalar CubicSolveDerivative(Scalar t,
                                          Scalar p0,
                                          Scalar p1,
                                          Scalar p2,
                                          Scalar p3) {
  return -3 * p0 * (1 - t) * (1 - t) +  //
         p1 * (3 * (1 - t) * (1 - t) - 6 * (1 - t) * t) +
         p2 * (6 * (1 - t) * t - 3 * t * t) +  //
         3 * p3 * t * t;
}
 
Point LinearPathComponent::Solve(Scalar time) const {
  return {
      LinearSolve(time, p1.x, p2.x),  // x
      LinearSolve(time, p1.y, p2.y),  // y
  };
}
 
void LinearPathComponent::AppendPolylinePoints(
    std::vector<Point>& points) const {
  if (points.size() == 0 || points.back() != p2) {
    points.push_back(p2);
  }
}
 
std::vector<Point> LinearPathComponent::Extrema() const {
  return {p1, p2};
}
 
std::optional<Vector2> LinearPathComponent::GetStartDirection() const {
  if (p1 == p2) {
    return std::nullopt;
  }
  return (p1 - p2).Normalize();
}
 
std::optional<Vector2> LinearPathComponent::GetEndDirection() const {
  if (p1 == p2) {
    return std::nullopt;
  }
  return (p2 - p1).Normalize();
}
 
Point QuadraticPathComponent::Solve(Scalar time) const {
  return {
      QuadraticSolve(time, p1.x, cp.x, p2.x),  // x
      QuadraticSolve(time, p1.y, cp.y, p2.y),  // y
  };
}
 
Point QuadraticPathComponent::SolveDerivative(Scalar time) const {
  return {
      QuadraticSolveDerivative(time, p1.x, cp.x, p2.x),  // x
      QuadraticSolveDerivative(time, p1.y, cp.y, p2.y),  // y
  };
}
 
void QuadraticPathComponent::ToLinearPathComponents(
    Scalar scale,
    VertexWriter& writer) const {
  Scalar line_count = std::ceilf(ComputeQuadradicSubdivisions(scale, *this));
  for (size_t i = 1; i < line_count; i += 1) {
    writer.Write(Solve(i / line_count));
  }
  writer.Write(p2);
}
 
void QuadraticPathComponent::AppendPolylinePoints(
    Scalar scale_factor,
    std::vector<Point>& points) const {
  ToLinearPathComponents(scale_factor, [&points](const Point& point) {
    points.emplace_back(point);
  });
}
 
void QuadraticPathComponent::ToLinearPathComponents(
    Scalar scale_factor,
    const PointProc& proc) const {
  Scalar line_count =
      std::ceilf(ComputeQuadradicSubdivisions(scale_factor, *this));
  for (size_t i = 1; i < line_count; i += 1) {
    proc(Solve(i / line_count));
  }
  proc(p2);
}
 
size_t QuadraticPathComponent::CountLinearPathComponents(Scalar scale) const {
  return std::ceilf(ComputeQuadradicSubdivisions(scale, *this)) + 2;
}
 
std::vector<Point> QuadraticPathComponent::Extrema() const {
  CubicPathComponent elevated(*this);
  return elevated.Extrema();
}
 
std::optional<Vector2> QuadraticPathComponent::GetStartDirection() const {
  if (p1 != cp) {
    return (p1 - cp).Normalize();
  }
  if (p1 != p2) {
    return (p1 - p2).Normalize();
  }
  return std::nullopt;
}
 
std::optional<Vector2> QuadraticPathComponent::GetEndDirection() const {
  if (p2 != cp) {
    return (p2 - cp).Normalize();
  }
  if (p2 != p1) {
    return (p2 - p1).Normalize();
  }
  return std::nullopt;
}
 
Point ConicPathComponent::Solve(Scalar time) const {
  return {
      ConicSolve(time, p1.x, cp.x, p2.x, weight.x),  // x
      ConicSolve(time, p1.y, cp.y, p2.y, weight.y),  // y
  };
}
 
void ConicPathComponent::ToLinearPathComponents(Scalar scale_factor,
                                                const PointProc& proc) const {
  Scalar line_count = std::ceilf(ComputeConicSubdivisions(scale_factor, *this));
  for (size_t i = 1; i < line_count; i += 1) {
    proc(Solve(i / line_count));
  }
  proc(p2);
}
 
void ConicPathComponent::AppendPolylinePoints(
    Scalar scale_factor,
    std::vector<Point>& points) const {
  ToLinearPathComponents(scale_factor, [&points](const Point& point) {
    if (point != points.back()) {
      points.emplace_back(point);
    }
  });
}
 
void ConicPathComponent::ToLinearPathComponents(Scalar scale,
                                                VertexWriter& writer) const {
  Scalar line_count = std::ceilf(ComputeConicSubdivisions(scale, *this));
  for (size_t i = 1; i < line_count; i += 1) {
    writer.Write(Solve(i / line_count));
  }
  writer.Write(p2);
}
 
size_t ConicPathComponent::CountLinearPathComponents(Scalar scale) const {
  return std::ceilf(ComputeConicSubdivisions(scale, *this)) + 2;
}
 
std::vector<Point> ConicPathComponent::Extrema() const {
  std::vector<Point> points;
  for (auto quad : ToQuadraticPathComponents()) {
    auto quad_extrema = quad.Extrema();
    points.insert(points.end(), quad_extrema.begin(), quad_extrema.end());
  }
  return points;
}
 
std::optional<Vector2> ConicPathComponent::GetStartDirection() const {
  if (p1 != cp) {
    return (p1 - cp).Normalize();
  }
  if (p1 != p2) {
    return (p1 - p2).Normalize();
  }
  return std::nullopt;
}
 
std::optional<Vector2> ConicPathComponent::GetEndDirection() const {
  if (p2 != cp) {
    return (p2 - cp).Normalize();
  }
  if (p2 != p1) {
    return (p2 - p1).Normalize();
  }
  return std::nullopt;
}
 
void ConicPathComponent::SubdivideToQuadraticPoints(
    std::array<Point, 5>& points) const {
  FML_DCHECK(weight.IsFinite() && weight.x > 0 && weight.y > 0);
 
  // Observe that scale will always be smaller than 1 because weight > 0.
  const Scalar scale = 1.0f / (1.0f + weight.x);
 
  // The subdivided control points below are the sums of the following three
  // terms. Because the terms are multiplied by something <1, and the resulting
  // control points lie within the control points of the original then the
  // terms and the sums below will not overflow. Note that weight * scale
  // approaches 1 as weight becomes very large.
  Point tp1 = p1 * scale;
  Point tcp = cp * (weight.x * scale);
  Point tp2 = p2 * scale;
 
  // Calculate the subdivided control points
  Point sub_cp1 = tp1 + tcp;
  Point sub_cp2 = tcp + tp2;
 
  // The middle point shared by the 2 sub-divisions, the interpolation of
  // the original curve at its halfway point.
  Point sub_mid = (tp1 + tcp + tcp + tp2) * 0.5f;
 
  FML_DCHECK(sub_cp1.IsFinite() && sub_mid.IsFinite() && sub_cp2.IsFinite());
 
  points[0] = p1;
  points[1] = sub_cp1;
  points[2] = sub_mid;
  points[3] = sub_cp2;
  points[4] = p2;
 
  // Update w.
  // Currently this method only subdivides a single time directly to 2
  // quadratics, but if we eventually want to keep the weights for further
  // subdivision, this was the code that did it in Skia:
  // sub_w1 = sub_w2 = SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf)
}
 
std::array<QuadraticPathComponent, 2>
ConicPathComponent::ToQuadraticPathComponents() const {
  std::array<Point, 5> points;
  SubdivideToQuadraticPoints(points);
 
  return {
      QuadraticPathComponent(points[0], points[1], points[2]),
      QuadraticPathComponent(points[2], points[3], points[4]),
  };
}
 
Point CubicPathComponent::Solve(Scalar time) const {
  return {
      CubicSolve(time, p1.x, cp1.x, cp2.x, p2.x),  // x
      CubicSolve(time, p1.y, cp1.y, cp2.y, p2.y),  // y
  };
}
 
Point CubicPathComponent::SolveDerivative(Scalar time) const {
  return {
      CubicSolveDerivative(time, p1.x, cp1.x, cp2.x, p2.x),  // x
      CubicSolveDerivative(time, p1.y, cp1.y, cp2.y, p2.y),  // y
  };
}
 
void CubicPathComponent::AppendPolylinePoints(
    Scalar scale,
    std::vector<Point>& points) const {
  ToLinearPathComponents(
      scale, [&points](const Point& point) { points.emplace_back(point); });
}
 
void CubicPathComponent::ToLinearPathComponents(Scalar scale,
                                                VertexWriter& writer) const {
  Scalar line_count = std::ceilf(ComputeCubicSubdivisions(scale, *this));
  for (size_t i = 1; i < line_count; i++) {
    writer.Write(Solve(i / line_count));
  }
  writer.Write(p2);
}
 
size_t CubicPathComponent::CountLinearPathComponents(Scalar scale) const {
  return std::ceilf(ComputeCubicSubdivisions(scale, *this)) + 2;
}
 
inline QuadraticPathComponent CubicPathComponent::Lower() const {
  return QuadraticPathComponent(3.0 * (cp1 - p1), 3.0 * (cp2 - cp1),
                                3.0 * (p2 - cp2));
}
 
CubicPathComponent CubicPathComponent::Subsegment(Scalar t0, Scalar t1) const {
  auto p0 = Solve(t0);
  auto p3 = Solve(t1);
  auto d = Lower();
  auto scale = (t1 - t0) * (1.0 / 3.0);
  auto p1 = p0 + scale * d.Solve(t0);
  auto p2 = p3 - scale * d.Solve(t1);
  return CubicPathComponent(p0, p1, p2, p3);
}
 
void CubicPathComponent::ToLinearPathComponents(Scalar scale,
                                                const PointProc& proc) const {
  Scalar line_count = std::ceilf(ComputeCubicSubdivisions(scale, *this));
  for (size_t i = 1; i < line_count; i++) {
    proc(Solve(i / line_count));
  }
  proc(p2);
}
 
static inline bool NearEqual(Scalar a, Scalar b, Scalar epsilon) {
  return (a > (b - epsilon)) && (a < (b + epsilon));
}
 
static inline bool NearZero(Scalar a) {
  return NearEqual(a, 0.0, 1e-12);
}
 
static void CubicPathBoundingPopulateValues(std::vector<Scalar>& values,
                                            Scalar p1,
                                            Scalar p2,
                                            Scalar p3,
                                            Scalar p4) {
  const Scalar a = 3.0 * (-p1 + 3.0 * p2 - 3.0 * p3 + p4);
  const Scalar b = 6.0 * (p1 - 2.0 * p2 + p3);
  const Scalar c = 3.0 * (p2 - p1);
 
  /*
   *  Boundary conditions.
   */
  if (NearZero(a)) {
    if (NearZero(b)) {
      return;
    }
 
    Scalar t = -c / b;
    if (t >= 0.0 && t <= 1.0) {
      values.emplace_back(t);
    }
    return;
  }
 
  Scalar b2Minus4AC = (b * b) - (4.0 * a * c);
 
  if (b2Minus4AC < 0.0) {
    return;
  }
 
  Scalar rootB2Minus4AC = ::sqrt(b2Minus4AC);
 
  /* From Numerical Recipes in C.
   *
   * q = -1/2 (b + sign(b) sqrt[b^2 - 4ac])
   * x1 = q / a
   * x2 = c / q
   */
  Scalar q = (b < 0) ? -(b - rootB2Minus4AC) / 2 : -(b + rootB2Minus4AC) / 2;
 
  {
    Scalar t = q / a;
    if (t >= 0.0 && t <= 1.0) {
      values.emplace_back(t);
    }
  }
 
  {
    Scalar t = c / q;
    if (t >= 0.0 && t <= 1.0) {
      values.emplace_back(t);
    }
  }
}
 
std::vector<Point> CubicPathComponent::Extrema() const {
  /*
   *  As described in: https://pomax.github.io/bezierinfo/#extremities
   */
  std::vector<Scalar> values;
 
  CubicPathBoundingPopulateValues(values, p1.x, cp1.x, cp2.x, p2.x);
  CubicPathBoundingPopulateValues(values, p1.y, cp1.y, cp2.y, p2.y);
 
  std::vector<Point> points = {p1, p2};
 
  for (const auto& value : values) {
    points.emplace_back(Solve(value));
  }
 
  return points;
}
 
std::optional<Vector2> CubicPathComponent::GetStartDirection() const {
  if (p1 != cp1) {
    return (p1 - cp1).Normalize();
  }
  if (p1 != cp2) {
    return (p1 - cp2).Normalize();
  }
  if (p1 != p2) {
    return (p1 - p2).Normalize();
  }
  return std::nullopt;
}
 
std::optional<Vector2> CubicPathComponent::GetEndDirection() const {
  if (p2 != cp2) {
    return (p2 - cp2).Normalize();
  }
  if (p2 != cp1) {
    return (p2 - cp1).Normalize();
  }
  if (p2 != p1) {
    return (p2 - p1).Normalize();
  }
  return std::nullopt;
}
 
}  // namespace impeller