public static CADVector RotateInRadian(CADVector v, double rad)
{
double x = v.X * System.Math.Cos(rad) - v.Y * System.Math.Sin(rad);
double y = v.X * System.Math.Sin(rad) + v.Y * System.Math.Cos(rad);
return(new CADVector(x, y));
}
public static CADVector RotateInRadian(CADVector point, CADVector basePoint, double rad)
{
double cos = System.Math.Cos(rad);
double sin = System.Math.Sin(rad);
double x = point.X * cos - point.Y * sin + basePoint.X * (1 - cos) + basePoint.Y * sin;
double y = point.X * sin + point.Y * cos + basePoint.Y * (1 - cos) + basePoint.X * sin;
return(new CADVector(x, y));
}
/// <summary>
/// Returns the signed acute clockwise angle in radians between from and to.
/// The result value range: [-PI, PI]
/// </summary>
public static double SignedAngleInRadian(CADVector from, CADVector to)
{
double rad = AngleInRadian(from, to);
if (Cross(from, to) < 0)
{
rad = -rad;
}
return(rad);
}
/// <summary>
/// Returns the unsigned angle in radians between a and b.
/// The smaller of the two possible angles between the two vectors is used.
/// The result value range: [0, PI]
/// </summary>
public static double AngleInRadian(CADVector a, CADVector b)
{
double num = a.Length * b.Length;
if (num == 0.0)
{
return(0.0);
}
double num2 = Dot(a, b) / num;
return(System.Math.Acos(Utils.Clamp(num2, -1.0, 1.0)));
}
/// <summary>
/// 镜像矩阵
/// </summary>
public static Matrix3 MirrorMatrix(Line2 mirrorLine)
{
CADVector lineDir = mirrorLine.direction;
Matrix3 matPos1 = Matrix3.Translate(-mirrorLine.startPoint);
double rotAngle = CADVector.SignedAngle(lineDir, new CADVector(1, 0));
Matrix3 matRot1 = Matrix3.Rotate(rotAngle);
Matrix3 mirrorMatX = new Matrix3(
1, 0, 0,
0, -1, 0,
0, 0, 1);
Matrix3 matRot2 = Matrix3.Rotate(-rotAngle);
Matrix3 matPos2 = Matrix3.Translate(mirrorLine.startPoint);
return(matPos2 * matRot2 * mirrorMatX * matRot1 * matPos1);
}
/// <summary>
/// 求线段的交点
/// </summary>
/// <param name="line1st">线段1</param>
/// <param name="line2nd">线段2</param>
/// <param name="intersection">交点</param>
/// <returns>
/// true --- 相交
/// false --- 不相交
/// </returns>
public static bool Intersect(Line2 line1st, Line2 line2nd, ref CADPoint intersection,
double tolerance = 1e-10)
{
CADPoint p = line1st.startPoint;
CADVector r = line1st.endPoint - line1st.startPoint;
CADPoint q = line2nd.startPoint;
CADVector s = line2nd.endPoint - line2nd.startPoint;
double rxs = CADVector.Cross(r, s);
if (!Utils.IsEqualZero(rxs, tolerance))
{
double t = CADVector.Cross(q - p, s) / rxs;
double u = CADVector.Cross(q - p, r) / rxs;
if (t >= (0.0 - tolerance) && t <= (1.0 + tolerance) &&
u >= (0.0 - tolerance) && u <= (1.0 + tolerance))
{
intersection = p + t * r;
return(true);
}
}
return(false);
}
public static CADVector Rotate(CADVector point, CADVector basePoint, double angle)
{
return(RotateInRadian(point, basePoint, Utils.DegreeToRadian(angle)));
}
public static CADVector Rotate(CADVector v, double angle)
{
return(RotateInRadian(v, Utils.DegreeToRadian(angle)));
}
public static double Distance(CADVector a, CADVector b)
{
CADVector vector = b - a;
return(vector.Length);
}
/// <summary>
/// Returns the signed acute clockwise angle in degrees between from and to.
/// The result value range: [-180, 180]
/// </summary>
public static double SignedAngle(CADVector from, CADVector to)
{
return(Utils.RadianToDegree(SignedAngleInRadian(from, to)));
}
/// <summary>
/// Returns the unsigned angle in degrees between a and b.
/// The smaller of the two possible angles between the two vectors is used.
/// The result value range: [0, 180]
/// </summary>
public static double Angle(CADVector a, CADVector b)
{
return(Utils.RadianToDegree(AngleInRadian(a, b)));
}
public static double Cross(CADVector a, CADVector b)
{
return((a.X * b.Y) - (a.Y * b.X));
}
public static double Dot(CADVector a, CADVector b)
{
return(a.X * b.X + a.Y * b.Y);
}
/// <summary>
/// NOTE: Rotation will need to be added to this function
/// </summary>
/// <param name="c">Ellipse centre</param>
/// <param name="rx">Ellipse X radius</param>
/// <param name="ry">Ellipse Y radius</param>
/// <param name="a1">Line P1</param>
/// <param name="a2">Line P2</param>
/// <returns></returns>
public static Intersection IntersectEllipseLine(CADPoint c, double rx, double ry, CADPoint a1, CADPoint a2)
{
Intersection result;
var origin = new CADVector(a1.X, a1.Y);
var dir = a2 - a1;
var center = new CADVector(c.X, c.Y);
var diff = origin - center;
var mDir = new CADVector(dir.X / (rx * rx), dir.Y / (ry * ry));
var mDiff = new CADVector(diff.X / (rx * rx), diff.Y / (ry * ry));
var a = CADVector.Dot(dir, mDir);
var b = CADVector.Dot(dir, mDiff);
var cc = CADVector.Dot(diff, mDiff) - 1.0;
var d = b * b - a * cc;
if (d < 0)
{
result = new Intersection(Intersection.IntStatus.Outside);
}
else if (d > 0)
{
var root = Math.Sqrt(d);
var t_a = (-b - root) / a;
var t_b = (-b + root) / a;
if ((t_a < 0 || 1 < t_a) && (t_b < 0 || 1 < t_b))
{
if ((t_a < 0 && t_b < 0) || (t_a > 1 && t_b > 1))
{
result = new Intersection(Intersection.IntStatus.Outside);
}
else
{
result = new Intersection(Intersection.IntStatus.Inside);
}
}
else
{
result = new Intersection(Intersection.IntStatus.Intersection);
if (0 <= t_a && t_a <= 1)
{
result.appendPoint(a1.lerp(a2, t_a));
}
if (0 <= t_b && t_b <= 1)
{
result.appendPoint(a1.lerp(a2, t_b));
}
}
}
else
{
var t = -b / a;
if (0 <= t && t <= 1)
{
result = new Intersection(Intersection.IntStatus.Intersection);
result.appendPoint(a1.lerp(a2, t));
}
else
{
result = new Intersection(Intersection.IntStatus.Outside);
}
}
return(result);
}