template <typename T>
struct CubicBezier {
  CubicBezier(T const &_p0, T const &_p1, T const &_p2, T const &_p3) : p0(_p1), p1(_p1), p2(_p2), p3(_p3) {}
  CubicBezier() {}
  T p0, p1, p2, p3;
};

template <typename T>
CubicBezier<T> operator*(double const &a, CubicBezier<T> const &b)
{
  return CubicBezier<T>(a * b.p0, a * b.p1, a * b.p2, a * b.p3);
}

template <typename T>
double linearMetric(CubicBezier<T> const &a, CubicBezier<T> const &b)
{
  return linearMetric(a.p0, b.p0) + linearMetric(a.p1, b.p1) + linearMetric(a.p2, b.p2) + linearMetric(a.p3, b.p3);
}

template <typename T>
CubicBezier<T> linearComb(double aCoeff, CubicBezier<T> const &a, double bCoeff, CubicBezier<T> const &b)
{
  return CubicBezier<T>(
      linearComb(aCoeff, a.p0, bCoeff, b.p0),
      linearComb(aCoeff, a.p1, bCoeff, b.p1),
      linearComb(aCoeff, a.p2, bCoeff, b.p2),
      linearComb(aCoeff, a.p3, bCoeff, b.p3));
}

template <typename T>
bool hasNaN(CubicBezier<T> const &a)
{
  return hasNaN(a.p0) || hasNaN(a.p1) || hasNaN(a.p2) || hasNaN(a.p3);
}

template <typename T>
T bezier(CubicBezier<T> const &a, double t)
{
  return (1.0 - t) * (1.0 - t) * (1.0 - t) * a.p0 + 3 * (1.0 - t) * (1.0 - t) * t * a.p1 + 3 * (1.0 - t) * t * t * a.p2
         + t * t * t * a.p3;
}

/*
  CubicBezier<T>
*/
template <typename POINT>
void wrJsonSize(WrJsonContext &ctx, CubicBezier<POINT> const &it)
{
  ctx.size += 100;
  wrJsonSize(ctx, it.p0);
  wrJsonSize(ctx, it.p1);
  wrJsonSize(ctx, it.p2);
  wrJsonSize(ctx, it.p3);
}
template <typename POINT>
void wrJson(WrJsonContext &ctx, CubicBezier<POINT> const &it)
{
  ctx.emit("{\"__type\":\"CubicBezier\",\"p0\":");
  wrJson(ctx, it.p0);
  ctx.emit(",\"p1\":");
  wrJson(ctx, it.p1);
  ctx.emit(",\"p2\":");
  wrJson(ctx, it.p2);
  ctx.emit(",\"p3\":");
  wrJson(ctx, it.p3);
  *ctx.s++ = '}';
}
template <typename POINT>
bool rdJson(RdJsonContext &ctx, CubicBezier<POINT> &it)
{
  bool typeOk = false;
  ctx.skipSpace();
  if (*ctx.s != '{') return ctx.fail(typeid(it), "expected {");
  ctx.s++;

  while (true) {
    ctx.skipSpace();
    if (*ctx.s == '}') {
      ctx.s++;
      break;
    }
    if (ctx.matchKey("p0")) {
      if (!rdJson(ctx, it.p0)) return ctx.fail(typeid(it), "rdJson(it.p0)");
      if (*ctx.s == ',') {
        ctx.s++;
        continue;
      }
      if (*ctx.s == '}') {
        ctx.s++;
        break;
      }
    }
    else if (ctx.matchKey("p1")) {
      if (!rdJson(ctx, it.p1)) return ctx.fail(typeid(it), "rdJson(it.p1)");
      if (*ctx.s == ',') {
        ctx.s++;
        continue;
      }
      if (*ctx.s == '}') {
        ctx.s++;
        break;
      }
    }
    else if (ctx.matchKey("p2")) {
      if (!rdJson(ctx, it.p2)) return ctx.fail(typeid(it), "rdJson(it.p2)");
      if (*ctx.s == ',') {
        ctx.s++;
        continue;
      }
      if (*ctx.s == '}') {
        ctx.s++;
        break;
      }
    }
    else if (ctx.matchKey("p3")) {
      if (!rdJson(ctx, it.p3)) return ctx.fail(typeid(it), "rdJson(it.p3)");
      if (*ctx.s == ',') {
        ctx.s++;
        continue;
      }
      if (*ctx.s == '}') {
        ctx.s++;
        break;
      }
    }
    else if (ctx.match("\"__type\" : \"CubicBezier\"")) {
      typeOk = true;
      if (*ctx.s == ',') {
        ctx.s++;
        continue;
      }
      if (*ctx.s == '}') {
        ctx.s++;
        break;
      }
    }
  }
  return typeOk;
}