/// <summary>
/// Generates an approximation of a circle given its center, a normal vector for the plane, and its radius.
/// </summary>
/// <param name="center">The circle's center</param>
/// <param name="normal">Normal vector to the circle's plane</param>
/// <param name="radius">Circle's radius.</param>
/// <param name="count">Number of points that approximate the circle</param>
/// <returns>An array of points that form the circle's approximation</returns>
public static Point3D[] GenerateCircle(Point3D center, Vector3D normal, double radius, int count)
{
Contract.Requires(radius > 0);
Contract.Requires(count >= 3);
Contract.Ensures(Contract.Result <Point3D[]>() != null);
Contract.Ensures(Contract.Result <Point3D[]>().Length == count);
Contract.Ensures(Contract.ForAll(
Contract.Result <Point3D[]>(),
pnt => NumericUtils.AlmostEqual(radius * radius, (pnt - center).LengthSquared, 100)));
var xAxis = MathUtils3D.NormalVector(normal).Normalized();
var yAxis = Vector3D.CrossProduct(normal, xAxis).Normalized();
return(GenerateCircle(center, xAxis, yAxis, radius, count));
}
/// <summary>
/// Generates an approximation of a circle given its center, two orthonormal basis vectors for the plane, and its radius.
/// </summary>
/// <param name="center">The circle's center</param>
/// <param name="u">First basis vector. This is the "X" axis.</param>
/// <param name="v">Second basis vector. This is the "Y" axis.</param>
/// <param name="radius">Circle's radius.</param>
/// <param name="count">Number of points that approximate the circle</param>
/// <returns>An array of points that form the circle's approximation</returns>
public static Point3D[] GenerateCircle(Point3D center, Vector3D u, Vector3D v, double radius, int count)
{
Contract.Requires(MathUtils3D.AreOrthogonal(u, v));
Contract.Requires(NumericUtils.AlmostEqual(u.LengthSquared, 1, 10));
Contract.Requires(NumericUtils.AlmostEqual(v.LengthSquared, 1, 10));
Contract.Requires(radius > 0);
Contract.Requires(count >= 3);
Contract.Ensures(Contract.Result <Point3D[]>() != null);
Contract.Ensures(Contract.Result <Point3D[]>().Length == count);
// we cannot really ensure that (?)
//Contract.Ensures(Contract.ForAll(
// Contract.Result<Point3D[]>(),
// pnt => NumericUtils.AlmostEqual((pnt - center).LengthSquared, radius * radius, 100)));
var result = new Point3D[count];
for (int i = 0; i < count; ++i)
{
var fraction = i / (double)count;
var angle = 2 * Math.PI * fraction;
result[i] = center + radius * (Math.Cos(angle) * u + Math.Sin(angle) * v);
}
return(result);
}