private bool get_hyperbol()
{
if (string.IsNullOrWhiteSpace(textBox_x.Text) ||
string.IsNullOrWhiteSpace(textBox_y.Text) ||
string.IsNullOrWhiteSpace(textBox_a.Text) ||
string.IsNullOrWhiteSpace(textBox_b.Text))
{
MessageBox.Show("Missing x, y, a, b",
"Error");
return(false);
}
int x, y, a, b;
if (!int.TryParse(textBox_x.Text, out x) ||
!int.TryParse(textBox_y.Text, out y) ||
!int.TryParse(textBox_a.Text, out a) ||
!int.TryParse(textBox_b.Text, out b))
{
MessageBox.Show("Wrong format" + Environment.NewLine +
"x, y, x - a must be non negative integer" + Environment.NewLine +
"a, b must be positive integer" + Environment.NewLine +
"x, x + a must be less than " + bitmap.Width + Environment.NewLine +
"y must be less than " + bitmap.Height + Environment.NewLine +
"Error");
return(false);
}
if (x < 0 || x >= bitmap.Width ||
y < 0 || y >= bitmap.Width ||
a <= 0 || b <= 0 ||
x - a < 0 ||
x + a >= bitmap.Width)
{
MessageBox.Show("Wrong format" + Environment.NewLine +
"x, y, x - a must be non negative integer" + Environment.NewLine +
"a, b must be positive integer" + Environment.NewLine +
"x, x + a must be less than " + bitmap.Width + Environment.NewLine +
"y must be less than " + bitmap.Height + Environment.NewLine +
"Error");
return(false);
}
hyperbol = new Hyperbol(new Point(x, y), a, b);
return(true);
}
public void MidPoint(Hyperbol hyperbol, Color color)
{
// Explain MidPoint algorithm
// F(x, y) = x^2/a^2 - y^2/b^2 - 1
//
// y increase faster than x increase
// F(x + 1/2, y + 1)
// p_i = 4(a^2)(b^2) * F(x + 1/2, y + 1)
//
// p_i = 4b^2 * (x_k + 1/2)^2 - 4a^2 * (y_k + 1)^2 - 4(a^2)(b^2)
// p_(i+1) - p_i = 4b^2 * (x_(k+1)^2 + x_(k+1) - x_k^2 - x_k) - 8a^2 * y_(k+1) - 4a^2
//
// p_i < 0 (outside)
// x_(k+1) = x_k + 1
// p_(i+1) = p_i + 8b^2 * x_(k+1) - 8a^2 * y_(k+1) - 4a^2
// p_i >= 0
// x_(k+1) = x_k
// p_(i+1) = p_i - 8a^2 * y_(k+1) - 4a^2
// start from Point(a, 0)
// p_0 = 4ab^2 + b^2 - 4a
//
// x increase faster than y increase
// F(x + 1, y + 1/2) = (x + 1)^2/a^2 - (y + 1/2)^2/b^2 - 1
// p_i = 4(a^2)(b^2) * F(x + 1, y + 1/2)
//
// p_i = 4b^2 * (x_k + 1)^2 - 4a^2 * (y_k + 1/2)^2 - 4(a^2)(b^2)
// p_(i+1) - p_i = 8b^2 * x_(k+1) + 4b^2 - 4a^2 * (y_(k+1)^2 + y_(k+1) - y_k^2 - y_k)
//
// p_i < 0
// y_(k+1) = y_k
// p_(i+1) = p_i + 8b^2 * x_(k+1) + 4b^2
// p_i >= 0
// y_(k+1) = y_k + 1
// p_(i+1) = p_i + 8b^2 * x_(k+1) + 4b^2 - 8a^2 * y_(k+1)
Point center = hyperbol.center;
int a = hyperbol.a;
int b = hyperbol.b;
// y incre faster than x incre
int x = a;
int y = 0;
int x_incre = 1;
int y_incre = 1;
// p_0 = 4ab^2 + b^2 - 4a
int error_step = 4 * a * b * b + b * b - 4 * a;
while (x * b * b - y * a * a > 0 && x >= 0 && x < bitmap.Width &&
y >= 0 && y < bitmap.Height)
{
if (x < bitmap.Width - center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X + x, center.Y + y, color);
}
if (x < bitmap.Width - center.X && y < center.Y)
{
bitmap.SetPixel(center.X + x, center.Y - y, color);
}
if (x < center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X - x, center.Y + y, color);
}
if (x < center.X && y < center.Y)
{
bitmap.SetPixel(center.X - x, center.Y - y, color);
}
y += y_incre;
if (error_step < 0)
{
x += x_incre;
// p_(i+1) = p_i + 8b^2 * x_(k+1) - 8a^2 * y_(k+1) - 4a^2
error_step += 8 * b * b * x - 8 * a * a * y - 4 * a * a;
}
else
{
// p_(i+1) = p_i - 8a^2 * y_(k+1) - 4a^2
error_step += 0 - 8 * a * a * y - 4 * a * a;
}
}
// x incre faster than y incre
// p_i = 4b^2 * (x_k + 1)^2 - 4a^2 * (y_k + 1/2)^2 - 4(a^2)(b^2)
error_step = 4 * b * b * (x + 1) * (x + 1) - a * a * (2 * y + 1) * (2 * y + 1) - 4 * a * a * b * b;
while (x * b * b - y * a * a <= 0 && x >= 0 && x < bitmap.Width &&
y >= 0 && y < bitmap.Height)
{
if (x < bitmap.Width - center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X + x, center.Y + y, color);
}
if (x < bitmap.Width - center.X && y < center.Y)
{
bitmap.SetPixel(center.X + x, center.Y - y, color);
}
if (x < center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X - x, center.Y + y, color);
}
if (x < center.X && y < center.Y)
{
bitmap.SetPixel(center.X - x, center.Y - y, color);
}
x += x_incre;
if (error_step < 0)
{
// p_(i+1) = p_i + 8b^2 * x_(k+1) + 4b^2
error_step += 8 * b * b * x + 4 * b * b;
}
else
{
y += y_incre;
// p_(i+1) = p_i + 8b^2 * x_(k+1) + 4b^2 - 8a^2 * y_(k+1)
error_step += 8 * b * b * x + 4 * b * b - 8 * a * a * y;
}
}
}
public void DDA(Hyperbol hyperbol, Color color)
{
// F(x, y) = x^2/a^2 - y^2/b^2 - 1
// => 2x/a^2 - 2y/b^2 * dy/dx = 0
// dy/dx = xb^2/ya^2
// y incre faster than x incre <=> dy/dx > 1
// <=> xb^2 - ya^2 > 0
// start from Point(a, 0)
Point center = hyperbol.center;
int a = hyperbol.a;
int b = hyperbol.b;
// y incre faster than x incre
int y = 0;
int x = (int)Math.Round(Math.Sqrt(a * a * (y * y + b * b) / (float)(b * b)));
int x_incre = 1;
int y_incre = 1;
while (x * b * b - y * a * a > 0 && x >= 0 && x < bitmap.Width &&
y >= 0 && y < bitmap.Height)
{
if (x < bitmap.Width - center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X + x, center.Y + y, color);
}
if (x < bitmap.Width - center.X && y < center.Y)
{
bitmap.SetPixel(center.X + x, center.Y - y, color);
}
if (x < center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X - x, center.Y + y, color);
}
if (x < center.X && y < center.Y)
{
bitmap.SetPixel(center.X - x, center.Y - y, color);
}
y += y_incre;
x = (int)Math.Round(Math.Sqrt(a * a * (y * y + b * b) / (float)(b * b)));
}
// x incre faster than y incre
while (x * b * b - y * a * a <= 0 && x >= 0 && x < bitmap.Width &&
y >= 0 && y < bitmap.Height)
{
if (x < bitmap.Width - center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X + x, center.Y + y, color);
}
if (x < bitmap.Width - center.X && y < center.Y)
{
bitmap.SetPixel(center.X + x, center.Y - y, color);
}
if (x < center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X - x, center.Y + y, color);
}
if (x < center.X && y < center.Y)
{
bitmap.SetPixel(center.X - x, center.Y - y, color);
}
x += x_incre;
y = (int)Math.Round(Math.Sqrt(b * b * (x * x - a * a) / (float)(a * a)));
}
}
// Use the idea from paper
// EFFICIENT INTEGER ALGORITHMS FOR THE GENERATION OF CONIC SECTIONS
// http://graphics.di.uoa.gr/Downloads/papers/journals/p7.pdf
public void Bresenham(Hyperbol hyperbol, Color color)
{
// Explain Bresenham algorithm
// F(x, y) = x^2/a^2 - y^2/b^2 - 1
//
// y increase faster than x increase
// F(x, y + 1) or F(x + 1, y + 1)
// d1 = x^2 - x_k^2
// d2 = (x_k + 1)^2 - x^2
// d1 - d2 < -1/2 choose x_k otherwise x_k + 1
//
// p_i = b^2 * (d1 - d2)
// p_i = b^2 * (2x^2 - x_k^2 - (x_k + 1)^2)
// p_i = 2a^2 * (y_k + 1)^2 + 2(a^2)(b^2) - b^2 * (2x_k^2 + 2x_k + 1)
// p_(i+1) - p_i = 4a^2 * y_(k+1) + 2a^2 - 2b^2 * (x_(k+1)^2 + x_(k+1) - x_k^2 - x_k)
//
// p_i < -b^2/2
// x_(k+1) = x_k
// p_(i+1) = p_i + 4a^2 * y_(k+1) + 2a^2
// p_i >= -b^2/2
// x_(k+1) = x_k + 1
// p_(i+1) = p_i + 4a^2 * y_(k+1) + 2a^2 - 4b^2 * x_(k+1)
// start from Point(a, 0)
// p_0 = 2a^2 - 2ab^2 - b^2
//
// x increase faster than y
// F(x + 1, y) or F(x + 1, y + 1)
// d1 = y^2 - y_k^2
// d2 = (y_k + 1)^2 - y^2
// d1 - d2 < -1/2 choose y_k otherwise y_k + 1
//
// p_i = a^2 * (d1 - d2)
// p_i = a^2 *(2y^2 - y_k^2 - (y_k + 1)^2)
// p_i = 2b^2 * (x_k + 1)^2 - 2(a^2)(b^2) - a^2 * (2y_k^2 + 2y_k + 1)
// p_(i+1) - p_i = 4b^2 * x_(k+1) + 2b^2 - 2a^2 * (y_(k+1)^2 + y_(k+1) - y_k^2 - y_k)
//
// p_i < -a^2/2
// y_(k+1) = y_k
// p_(i+1) = p_i + 4b^2 * x_(k+1) + 2b^2
// p_i >= -a^2/2
// y_(k+1) = y_k + 1
// p_(i+1) = p_i + 4b^2 * x_(k+1) + 2b^2 - 4a^2 * y_(k+1)
Point center = hyperbol.center;
int a = hyperbol.a;
int b = hyperbol.b;
// y incre faster than x incre
int x = a;
int y = 0;
int x_incre = 1;
int y_incre = 1;
// p_0 = 2a^2 - 2ab^2 - b^2
int error_step = 2 * a * a - 2 * a * b * b - b * b;
while (x * b * b - y * a * a > 0 && x >= 0 && x < bitmap.Width &&
y >= 0 && y < bitmap.Height)
{
if (x < bitmap.Width - center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X + x, center.Y + y, color);
}
if (x < bitmap.Width - center.X && y < center.Y)
{
bitmap.SetPixel(center.X + x, center.Y - y, color);
}
if (x < center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X - x, center.Y + y, color);
}
if (x < center.X && y < center.Y)
{
bitmap.SetPixel(center.X - x, center.Y - y, color);
}
y += y_incre;
if (error_step * 2 + b * b < 0)
{
// p_(i+1) = p_i + 4a^2 * y_(k+1) + 2a^2
error_step += 4 * a * a * y + 2 * a * a;
}
else
{
x += x_incre;
// p_(i+1) = p_i + 4a^2 * y_(k+1) + 2a^2 - 4b^2 * x_(k+1)
error_step += 4 * a * a * y + 2 * a * a - 4 * b * b * x;
}
}
// x incre faster than y incre
// p_i = 2b^2 * (x_k + 1)^2 - 2(a^2)(b^2) - a^2 * (2y_k^2 + 2y_k + 1)
error_step = 2 * b * b * (x + 1) * (x + 1) - 2 * a * a * b * b - a * a * (2 * y * y + 2 * y + 1);
while (x * b * b - y * a * a <= 0 && x >= 0 && x < bitmap.Width &&
y >= 0 && y < bitmap.Height)
{
if (x < bitmap.Width - center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X + x, center.Y + y, color);
}
if (x < bitmap.Width - center.X && y < center.Y)
{
bitmap.SetPixel(center.X + x, center.Y - y, color);
}
if (x < center.X && y < bitmap.Height - center.Y)
{
bitmap.SetPixel(center.X - x, center.Y + y, color);
}
if (x < center.X && y < center.Y)
{
bitmap.SetPixel(center.X - x, center.Y - y, color);
}
x += x_incre;
if (error_step * 2 + a * a < 0)
{
// p_(i+1) = p_i + 4b^2 * x_(k+1) + 2b^2
error_step += 4 * b * b * x + 2 * b * b;
}
else
{
y += y_incre;
// p_(i+1) = p_i + 4b^2 * x_(k+1) + 2b^2 - 4a^2 * y_(k+1)
error_step += 4 * b * b * x + 2 * b * b - 4 * a * a * y;
}
}
}
