public Line2D GetNormalLine(Point2D point)
{
double c = EqB*point.X - EqA*point.Y;
var tempLine = new Line2D(-EqB, EqA, c, Normal, point);
Point2D crossPoint = Geometry.GetCrossing(this, tempLine);
return new Line2D(crossPoint, point);
}
public Frame2D(double x, double y, Angle angle)
{
X = x;
Y = y;
Angle = angle;
Center = new Point2D(x, y);
}
public static bool GetCrossing(Segment2D segment1, Segment2D segment2, out Point2D crossingPoint)
{
var line1 = new Line2D(segment1.Start, segment1.Finish);
var line2 = new Line2D(segment2.Start, segment2.Finish);
crossingPoint = GetCrossing(line1, line2);
var p = (crossingPoint.X - segment1.Finish.X) / (segment1.Start.X - segment1.Finish.X);
return (0 <= p && p <= 1) && (crossingPoint.Y.Equals((p * segment1.Start.Y - (1 - p) * segment1.Finish.Y)));
}
private Line2D(double a, double b, double c, Point2D direction, Point2D start)
{
Begin = start;
End = new Point2D();
Direction = direction;
Normal = new Point2D(-direction.Y, direction.X);
EqA = a;
EqB = b;
EqC = c;
IsEmpty = false;
}
public Line2D(Point2D begin, Point2D end)
{
Begin = begin;
End = end;
Direction = end - begin;
Normal = new Point2D(-Direction.Y, Direction.X);
EqA = Normal.X;
EqB = Normal.Y;
EqC = -EqA*begin.X - EqB*begin.Y;
IsEmpty = Direction.IsEmpty;
}
public void CreateBeachHut(string id, Point2D location, SideColor color)
{
var hut = GameObject.CreatePrimitive(PrimitiveType.Cube);
Point3D size = new Point3D(12, 12, 16);
hut.transform.position = new Vector3((float)location.X, (float)size.Z / 2, (float)location.Y);
hut.transform.localScale = new Vector3((float)size.X, (float)size.Z, (float)size.Y);
hut.GetComponent<Renderer>().material.color = GetDrawingColor(color);
hut.name = id;
}
/// <summary>
/// Формула Герона для вычисления площади треугольника
/// </summary>
/// <param name="A"> Вершина А </param>
/// <param name="B"> Вершина В </param>
/// <param name="C"> Вершина С </param>
/// <returns> </returns>
public static double GetTriangleSquareByGeron(Point2D A, Point2D B, Point2D C)
{
if (!A.IsEmpty && !B.IsEmpty && !C.IsEmpty)
{
double a = Point2D.GetDistance(A, B);
double b = Point2D.GetDistance(B, C);
double c = Point2D.GetDistance(C, A);
double p = (a + b + c)/2;
return Math.Sqrt(p*(p - a)*(p - b)*(p - c));
}
return 0;
}
public Sector(Circle2D circle2D, Point2D start, Point2D finish) : this()
{
if (PointOnCircle(start, circle2D) && PointOnCircle(finish, circle2D))
{
Finish = finish;
Start = start;
Circle = circle2D;
Angle = new Triangle2D(Circle.Center, Start, Finish).AngleA;
if (double.IsNaN(Angle.Radian))
Angle = Angle.Zero;
return;
}
throw new Exception("Не возможно создать сектор");
}
/// <summary>
/// Получить угол дуги окружности, ограниченной точкой (0, 0) и заданной точкой на этой окружности
/// </summary>
/// <param name="point"> Точка </param>
/// <returns> Угол </returns>
public static Angle GetAngleOfArc(Point2D point)
{
return Angle.FromRad(Math.Abs(point.X) <= Double.Epsilon
? Math.PI/2
: 2*Math.Atan2(point.Y, point.X)); //????
}
public static Angle AngleBetweenVectors(Point2D firstVector, Point2D secondVector) {
return AngleBetweenVectors(firstVector.ToPoint3D(), secondVector.ToPoint3D());
}
public void CreateWall(Point2D location, Point2D size)
{
var wall = GameObject.CreatePrimitive(PrimitiveType.Cube);
float sizeZ = floorLevel;
wall.transform.position = new Vector3((float)location.X, sizeZ / 2, (float)location.Y);
wall.transform.localScale = new Vector3((float)size.X, sizeZ, (float)size.Y);
wall.GetComponent<Renderer>().material.color = Color.white;
}
public void CreateRock(Point2D location)
{
var rock = GameObject.CreatePrimitive(PrimitiveType.Cylinder);
rock.transform.position = new Vector3((float)location.X, floorLevel, (float)location.Y);
rock.transform.localScale = new Vector3(60, 4.4f, 60);
rock.GetComponent<CapsuleCollider>().enabled = false;
rock.AddComponent<MeshCollider>();
}
public Seashell(Point2D position, SideColor color)
{
Position = position;
Color = color;
}
private static bool PointOnCircle(Point2D point, Circle2D c)
{
const double epsilon = 0.000001;
double actualyR = point.GetDistanceTo(c.Center);
return (actualyR < c.R + epsilon && actualyR > c.R - epsilon);
}
public double GetDistanceTo(Point2D otherPoint)
{
return GetDistance(this, otherPoint);
//return Math.Sqrt((X-otherPoint.X)*(X-otherPoint.X)+(Y-otherPoint.Y)*(Y-otherPoint.Y));
}
public static double GetDistance(Point2D a, Point2D b)
{
return Math.Sqrt((a.X - b.X) * (a.X - b.X) + (a.Y - b.Y) * (a.Y - b.Y));
}
public bool Equals(Point2D other)
{
return this == other;
}
public Point3D MultiplyVector(Point2D p)
{
return new Point3D(0, 0, X * p.Y - Y * p.X);
}
public static Line2D FromDirection(Point2D begin, Point2D direction)
{
return new Line2D(begin, begin + direction);
}
public static Point2D Orthonorm(Point2D vector, Point2D axis) {
return (vector - Projection(vector, axis)).Normalize();
}
public Segment2D(Point2D start, Point2D finish) : this()
{
Finish = finish;
Start = start;
}
public double MultiplyScalar(Point2D p)
{
return X * p.X + Y * p.Y;
}
public Circle2D(Point2D center, double r) : this()
{
Center = center;
R = r;
}
public Circle2D(Point2D center, double r) : this()
{
Center = center;
R = r;
}
private static Line2D GetBissektor(Point2D startBissector, Point2D leftPoint, Point2D rightPoint)
{
// //Достроим треугольник до равнобедренного
// double alpha = startBissector.GetDistanceTo(leftPoint) / startBissector.GetDistanceTo(rightPoint);
// Point2D newLeftPoint = startBissector + (1 / alpha) * (leftPoint - startBissector);
//
// var expected = startBissector.GetDistanceTo(newLeftPoint) - startBissector.GetDistanceTo(rightPoint);
// Assert.That(expected, Is.LessThan(0.1).And.GreaterThan(-0.1));
//
// //Теорема. В равнобедренном треугольнике медиана == биссектрисе
// //Утверждение: найденная медиана и будет нужной нам прямой
//
// Point2D middle = (newLeftPoint + rightPoint) / 2;
//
// //Но точка middle не лежит на треугольнике... найдем ту что лежит
//
// Line2D line = new Line2D(leftPoint, rightPoint);
// Line2D fakeBissector = new Line2D(startBissector, middle);
//
// Point2D finishBissector = Geometry.GetCrossing(line, fakeBissector);
// return new Line2D(startBissector, finishBissector);
double left = startBissector.GetDistanceTo(leftPoint);
double right = startBissector.GetDistanceTo(rightPoint);
double alpha = left/(left + right);
Point2D finishBissector = leftPoint*(1 - alpha) + rightPoint*alpha;
return new Line2D(startBissector, finishBissector);
}
public void CreateFish(string id, Point2D location, SideColor color)
{
var fish = GameObject.CreatePrimitive(PrimitiveType.Sphere);
fish.transform.position = new Vector3((float)location.X, floorLevel + 5, (float)location.Y);
fish.transform.localScale = new Vector3(5.3f, 5.3f, 9.7f);
fish.GetComponent<Renderer>().material.color = GetDrawingColor(color);
fish.AddComponent<Rigidbody>();
fish.GetComponent<Rigidbody>().drag = fish.GetComponent<Rigidbody>().angularDrag = 4;
fish.GetComponent<Rigidbody>().useGravity = true;
fish.GetComponent<Rigidbody>().mass = 0.3f;
fish.name = id;
}
/// <summary>
/// Возвращает точку пересечения луча и треугольника p0p1p2
/// </summary>
/// <param name="p0">Вершина</param>
/// <param name="p1">Вершина</param>
/// <param name="p2">Вершина</param>
/// <param name="ray">Луч</param>
/// <returns></returns>
public static Point3D? IntersectTriangle(Point3D p0, Point3D p1, Point3D p2, Ray ray)
{
var plane = new ePlane(p0, p1, p2); //Плоскость содержащая треугольник
Point3D? point1 = IntersectPlane(plane, ray);
if (point1 == null)
{
return null;
}
else
{
int i = ProjectPlane(plane); //Определяем куда проецировать треугольник
Point2D point = ProjectPoint(i, point1.Value);
Point2D v0 = ProjectPoint(i, p0);
Point2D v1 = ProjectPoint(i, p1);
Point2D v2 = ProjectPoint(i, p2);
Point2D[] regionPoints = new Point2D[] {v0, v2, v1};
return Geometry.IsFromRegion(point, regionPoints) ? point1 : null;
}
}
public void CreateSeashell(string id, Point2D location, SideColor color)
{
var seashell = GameObject.CreatePrimitive(PrimitiveType.Cylinder);
var locationZ = Math.Abs(location.X) > 120 && location.Y < -70 ? floorLevel + 6 : floorLevel;
seashell.transform.position = new Vector3((float)location.X, locationZ, (float)location.Y);
seashell.transform.localScale = new Vector3(7.62f, 2.5f, 7.62f);
seashell.GetComponent<Renderer>().material.color = GetDrawingColor(color);
seashell.GetComponent<CapsuleCollider>().enabled = false;
seashell.AddComponent<MeshCollider>();
seashell.GetComponent<MeshCollider>().convex = true;
seashell.AddComponent<Rigidbody>();
seashell.GetComponent<Rigidbody>().drag = seashell.GetComponent<Rigidbody>().angularDrag = 4;
seashell.GetComponent<Rigidbody>().useGravity = true;
seashell.GetComponent<Rigidbody>().mass = 0.3f;
seashell.name = id;
}
/// <summary>
/// Получить радиус окружности, касающейся оси Х в (0, 0) и проходящей через заданную точку
/// </summary>
/// <param name="point"> Точка </param>
/// <returns> Радиус </returns>
public static double GetRadiusOfCircle(Point2D point)
{
return Math.Abs(0.5*(point.X*point.X + point.Y*point.Y)/point.Y);
}
public Triangle2D(Point2D vertexA, Point2D vertexB, Point2D vertexC) : this()
{
VertexC = vertexC;
VertexB = vertexB;
VertexA = vertexA;
}
public static bool AreCollinear(Point2D a, Point2D b) {
return Math.Abs(a.MultiplyVector(b).Norm() - 0) < Epsilon;
}