internal void ReadCache(ref SimplexCache cache, ref DistanceProxy proxyA, ref Transform transformA, ref DistanceProxy proxyB, ref Transform transformB)
        {
            Debug.Assert(cache.Count <= 3);

            // Copy data from cache.
            Count = cache.Count;
            for (int i = 0; i < Count; ++i)
            {
                SimplexVertex v = V[i];
                v.IndexA = cache.IndexA[i];
                v.IndexB = cache.IndexB[i];
                Vector2 wALocal = proxyA.Vertices[v.IndexA];
                Vector2 wBLocal = proxyB.Vertices[v.IndexB];
                v.WA = Transform.Multiply(ref wALocal, ref transformA);
                v.WB = Transform.Multiply(ref wBLocal, ref transformB);
                v.W  = v.WB - v.WA;
                v.A  = 0.0f;
                V[i] = v;
            }

            // Compute the new simplex metric, if it is substantially different than
            // old metric then flush the simplex.
            if (Count > 1)
            {
                float metric1 = cache.Metric;
                float metric2 = GetMetric();
                if (metric2 < 0.5f * metric1 || 2.0f * metric1 < metric2 || metric2 < Settings.Epsilon)
                {
                    // Reset the simplex.
                    Count = 0;
                }
            }

            // If the cache is empty or invalid ...
            if (Count == 0)
            {
                SimplexVertex v = V[0];
                v.IndexA = 0;
                v.IndexB = 0;
                Vector2 wALocal = proxyA.Vertices[0];
                Vector2 wBLocal = proxyB.Vertices[0];
                v.WA  = Transform.Multiply(ref wALocal, ref transformA);
                v.WB  = Transform.Multiply(ref wBLocal, ref transformB);
                v.W   = v.WB - v.WA;
                v.A   = 1.0f;
                V[0]  = v;
                Count = 1;
            }
        }
        public static void Set(ref SimplexCache cache, ref DistanceProxy proxyA, ref Sweep sweepA, ref DistanceProxy proxyB, ref Sweep sweepB, float t1)
        {
            _localPoint = Vector2.Zero;
            _proxyA     = proxyA;
            _proxyB     = proxyB;
            int count = cache.Count;

            Debug.Assert(0 < count && count < 3);

            _sweepA = sweepA;
            _sweepB = sweepB;

            Transform xfA, xfB;

            _sweepA.GetTransform(out xfA, t1);
            _sweepB.GetTransform(out xfB, t1);

            if (count == 1)
            {
                _type = SeparationFunctionType.Points;
                Vector2 localPointA = _proxyA.Vertices[cache.IndexA[0]];
                Vector2 localPointB = _proxyB.Vertices[cache.IndexB[0]];
                Vector2 pointA      = Transform.Multiply(ref localPointA, ref xfA);
                Vector2 pointB      = Transform.Multiply(ref localPointB, ref xfB);
                _axis = pointB - pointA;
                _axis.Normalize();
            }
            else if (cache.IndexA[0] == cache.IndexA[1])
            {
                // Two points on B and one on A.
                _type = SeparationFunctionType.FaceB;
                Vector2 localPointB1 = proxyB.Vertices[cache.IndexB[0]];
                Vector2 localPointB2 = proxyB.Vertices[cache.IndexB[1]];

                Vector2 a = localPointB2 - localPointB1;
                _axis = new Vector2(a.Y, -a.X);
                _axis.Normalize();
                Vector2 normal = Complex.Multiply(ref _axis, ref xfB.q);

                _localPoint = 0.5f * (localPointB1 + localPointB2);
                Vector2 pointB = Transform.Multiply(ref _localPoint, ref xfB);

                Vector2 localPointA = proxyA.Vertices[cache.IndexA[0]];
                Vector2 pointA      = Transform.Multiply(ref localPointA, ref xfA);

                float s = Vector2.Dot(pointA - pointB, normal);
                if (s < 0.0f)
                {
                    _axis = -_axis;
                }
            }
            else
            {
                // Two points on A and one or two points on B.
                _type = SeparationFunctionType.FaceA;
                Vector2 localPointA1 = _proxyA.Vertices[cache.IndexA[0]];
                Vector2 localPointA2 = _proxyA.Vertices[cache.IndexA[1]];

                Vector2 a = localPointA2 - localPointA1;
                _axis = new Vector2(a.Y, -a.X);
                _axis.Normalize();
                Vector2 normal = Complex.Multiply(ref _axis, ref xfA.q);

                _localPoint = 0.5f * (localPointA1 + localPointA2);
                Vector2 pointA = Transform.Multiply(ref _localPoint, ref xfA);

                Vector2 localPointB = _proxyB.Vertices[cache.IndexB[0]];
                Vector2 pointB      = Transform.Multiply(ref localPointB, ref xfB);

                float s = Vector2.Dot(pointB - pointA, normal);
                if (s < 0.0f)
                {
                    _axis = -_axis;
                }
            }
        }