public bool CheckZoom(Point point, out Ellipse ellipse, out double angle)
{
stroke[curIndex] = point;
if (strokeLength < MAX_CAPACITY) strokeLength++;
angle = 0;
ellipse = new Ellipse();
var curDir = new Point(point.X - stroke[prevIndex].X, point.Y - stroke[prevIndex].Y);
int cnt = 0;
int index = 0;
for (int i = 2; i < strokeLength; i++)
{
var index1 = (curIndex + MAX_CAPACITY - i) % MAX_CAPACITY;
var index2 = (curIndex + MAX_CAPACITY - i + 1) % MAX_CAPACITY;
var x = stroke[index2].X - stroke[index1].X;
var y = stroke[index2].Y - stroke[index1].Y;
if (x * x + y * y < MIN_SQDIR) break;
var dot = x * curDir.X + y * curDir.Y;
if ((cnt % 2 == 0 ? dot : -dot) < 0)
{
cnt++;
if (cnt >= 2)
{
index = index1;
break;
}
}
}
bool ans = false;
if (cnt >= 2)
{
ellipse = GetEllipse(index, curIndex);
// ellise.Eが小さいほどまん丸に近い
if (ellipse.E < 0.9)
{
// ズーム
double x1 = stroke[prevIndex].X - ellipse.X;
double y1 = stroke[prevIndex].Y - ellipse.Y;
double x2 = point.X - ellipse.X;
double y2 = point.Y - ellipse.Y;
double dot = x1 * x2 + y1 * y2;
double d = Math.Sqrt((x1 * x1 + y1 * y1) * (x2 * x2 + y2 * y2));
angle = Math.Acos(dot / d) * (x1 * y2 - x2 * y1 > 0 ? 1 : -1);
ans = true;
}
}
curIndex = (curIndex + 1) % MAX_CAPACITY;
prevIndex = (curIndex + MAX_CAPACITY - 1) % MAX_CAPACITY;
return ans;
}
Ellipse GetEllipse(int start, int end)
{
for (int i = 0; i < m.Length; i++) m[i] = l[i] = u[i] = 0;
for (int i = 0; i < v.Length; i++) v[i] = y[i] = a[i] = 0;
for (int i = start; i != end; i = (i + 1) % MAX_CAPACITY)
{
double px = stroke[i].X;
double py = stroke[i].Y;
double px2 = px * px;
double py2 = py * py;
double px3 = px2 * px;
double py3 = py2 * py;
double py4 = py2 * py2;
m[0] += px2 * py2; m[1] += px * py3; m[2] += px2 * py; m[3] += px * py2; m[4] += px * py;
m[5] += px * py3; m[6] += py4; m[7] += px * py2; m[8] += py3; m[9] += py2;
m[10] += px2 * py; m[11] += px * py2; m[12] += px2; m[13] += px * py; m[14] += px;
m[15] += px * py2; m[16] += py3; m[17] += px * py; m[18] += py2; m[19] += py;
m[20] += px * py; m[21] += py2; m[22] += px; m[23] += py; m[24] += 1;
v[0] -= px3 * py;
v[1] -= px2 * py2;
v[2] -= px3;
v[3] -= px2 * py;
v[4] -= px2;
}
// LU分解
LU(m, l, u);
// Ly = v の y を求める
for (int i = 0; i < 5; i++)
{
double s = 0.0;
for (int j = 0; j < i; j++) s += l[i * N + j] * y[j];
y[i] = (v[i] - s) / l[i * N + i];
}
// Ua = y の a を求める
for (int i = 4; i >= 0; i--)
{
double s = 0.0;
for (int j = 4; j > i; j--) s += u[i * N + j] * a[j];
a[i] = (y[i] - s) / u[i * N + i];
}
double x0 = (a[0] * a[3] - 2 * a[1] * a[2]) / (4 * a[1] - a[0] * a[0]);
double y0 = (a[0] * a[2] - 2 * a[3]) / (4 * a[1] - a[0] * a[0]);
double theta = Math.Atan(a[0] / (1.0 - a[1])) / 2.0;
double sin = Math.Sin(theta), cos = Math.Cos(theta);
double r1 = Math.Sqrt(
(x0 * cos + y0 * sin) * (x0 * cos + y0 * sin) -
a[4] * cos * cos -
((x0 * sin - y0 * cos) * (x0 * sin - y0 * cos) - a[4] * sin * sin) * (sin * sin - a[1] * cos * cos) / (cos * cos - a[1] * sin * sin)
);
double r2 = Math.Sqrt(
(x0 * sin - y0 * cos) * (x0 * sin - y0 * cos) -
a[4] * sin * sin -
((x0 * cos + y0 * sin) * (x0 * cos + y0 * sin) - a[4] * cos * cos) * (cos * cos - a[1] * sin * sin) / (sin * sin - a[1] * cos * cos)
);
double maxR = Math.Max(r1, r2);
double minR = Math.Min(r1, r2);
double e = Math.Sqrt(Math.Abs(maxR * maxR - minR * minR) / (maxR * maxR));
var ellipse = new Ellipse(x0, y0, theta, maxR, minR, e);
return ellipse;
}
