/// <summary>
/// Constructs a new instance of the <see cref="PolarPointsGenerator"/> class.
/// </summary>
/// <param name="center">The central point around which this class will generate other points.</param>
/// <param name="xBase">Basis vector that serves as the X axis</param>
/// <param name="yBase">Basis vector that serves as the Y axis</param>
/// <remarks><paramref name="xBase"/> and <paramref name="yBase"/> vectors must be orthogonal</remarks>
public PolarPointsGenerator(Point3D center, Vector3D xBase, Vector3D yBase)
{
Contract.Requires(xBase.LengthSquared > 0);
Contract.Requires(yBase.LengthSquared > 0);
Contract.Requires(MathUtils3D.AreOrthogonal(xBase, yBase));
this.center = center;
xBase.Normalize();
yBase.Normalize();
this.xBase = xBase;
this.yBase = yBase;
}
public SketchPlane(string name, Point3D center, Vector3D xAxis, Vector3D yAxis, Vector3D normal, double width, double height)
{
Contract.Requires(!string.IsNullOrEmpty(name));
Contract.Requires(width > 0);
Contract.Requires(height > 0);
Contract.Requires(MathUtils3D.AreOrthogonal(xAxis, yAxis));
Contract.Requires(MathUtils3D.AreOrthogonal(xAxis, normal));
Contract.Requires(MathUtils3D.AreOrthogonal(yAxis, normal));
xAxis.Normalize();
yAxis.Normalize();
normal.Normalize();
Name = name;
Center = center;
XAxis = xAxis;
YAxis = yAxis;
Normal = normal;
Width = width;
Height = height;
}
/// <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);
}