protected override void updatePointsPosition()
{
this.b = -2 * this.a * this.systemCenter.X;
this.c = this.a * this.a * this.systemCenter.X + this.systemCenter.Y;
this.COS = directVector.deltaX / directVector.Length;
this.SIN = directVector.deltaY / directVector.Length;
float yFocus = 1 / Math.Abs(4 * a);
this.parabolaFocus = new GlPointR2(-yFocus * SIN + systemCenter.X, yFocus * COS + systemCenter.Y);
this.parabolaDirectriss = new GlLineR2(new GlPointR2(yFocus * SIN + systemCenter.X, -yFocus * COS + systemCenter.Y), new GlVectorR2(1, 0).getRotatedVector(-SIN, COS));
for (int i = 0; i < 180; i++)
{
float SIN_A = (float)Math.Sin(i * Math.PI / 180);
float COS_A = (float)Math.Cos(i * Math.PI / 180);
float SINH_A = (float)Math.Sin(i * Math.PI / 360);
float AbsedA = (float)Math.Abs(a);
float PartRes = (float)(Math.Sqrt(2 * AbsedA) * Math.Sqrt(2 * a * SIN_A * SIN_A - 8 * a * SINH_A * SINH_A + 8 * SINH_A * SINH_A * AbsedA));
float fDevider = 8 * AbsedA * AbsedA - 4 * a * AbsedA + 4 * a * AbsedA * COS_A;
float x1 = PartRes / fDevider;
float x2 = PartRes / -fDevider;
float y1 = a * x1 * x1;
float y2 = a * x2 * x2;
this.curvePoints[180 + i] = new GlPointR2(x1 * COS - y1 * SIN + systemCenter.X, x1 * SIN + y1 * COS + systemCenter.Y);
this.curvePoints[179 - i] = new GlPointR2(x2 * COS - y2 * SIN + systemCenter.X, x2 * SIN + y2 * COS + systemCenter.Y);
}
}
//////////////TRANSFORM_METHODS////////////////
///////////////////////////////////////////////
/////////////INTERSECTION_METHODS//////////////
public override GlPointR2[] getIntersection(GlLineR2 L)
{
if (L == null || this.isNullParabola() || L.isNullLine())
{
return new GlPointR2[] { }
}
;
GlParabola PC = new GlParabola(this.A, new GlPointR2(0, 0), new GlVectorR2(1, 0));
GlPointR2 LP0 = L.PointOfLine.getPointTranslatedToRotatedSystem(this.SIN, this.COS, this.Vertex);
GlPointR2 LP1 = L.DirectVector.getRotatedVector(this.SIN, this.COS).fromPointToPoint(LP0);
float fPartRes = LP0.Y - LP1.Y;
float sPartRes = (float)Math.Sqrt(4 * PC.A * (LP0.X - LP1.X) * (LP0.X * LP1.Y - LP1.X * LP0.Y + PC.C * (LP1.X - LP0.X)) + (float)Math.Pow(PC.B * (LP0.X - LP1.X) - LP0.Y + LP1.Y, 2.0));
float tPartRes = PC.B * (LP1.X - LP0.X);
float devider = 2 * PC.A * (LP0.X - LP1.X);
float x1 = (fPartRes + sPartRes + tPartRes) / devider;
float x2 = (fPartRes - sPartRes + tPartRes) / devider;
float y1 = PC.A * x1 * x1 + PC.B * x1 + PC.C;
float y2 = PC.A * x2 * x2 + PC.B * x2 + PC.C;
return(new GlPointR2[] {
new GlPointR2(x1, y1).getTranslatedBackPoint(this.SIN, this.COS, this.Vertex),
new GlPointR2(x2, y2).getTranslatedBackPoint(this.SIN, this.COS, this.Vertex)
});
}
public override GlPointR2[] getIntersection(GlPolygon POLY)
{
List <GlPointR2> Intersections = new List <GlPointR2>();
GlLineR2 fCurLine = new GlLineR2(this[this.CountOfPoints - 1], new GlVectorR2(this[0].X - this[this.CountOfPoints - 1].X, this[0].Y - this[this.CountOfPoints - 1].Y));
GlPointR2[] faultInter = fCurLine.getIntersection(POLY);
foreach (GlPointR2 j in faultInter)
{
if (new GlLineSegment(this[this.CountOfPoints - 1], this[0]).isPointBelongs(j))
{
Intersections.Add(j);
}
}
for (int i = 0; i < this.CountOfPoints - 1; i++)
{
fCurLine = new GlLineR2(this[i], new GlVectorR2(this[i + 1].X - this[i].X, this[i + 1].Y - this[i].Y));
faultInter = fCurLine.getIntersection(POLY);
foreach (GlPointR2 j in faultInter)
{
if (new GlLineSegment(this[i], this[i + 1]).isPointBelongs(j))
{
Intersections.Add(j);
}
}
}
return(Intersections.ToArray());
}
public override GlPointR2[] getIntersection(GlPolygon POLY)
{
if (POLY == null || POLY.CountOfPoints == 0)
{
return new GlPointR2[] { }
}
;
GlPointR2[] Intersections = new GlPointR2[POLY.CountOfPoints];
int countOfIntersections = 0;
GlPointR2[] faultInter = new GlLineR2(POLY[POLY.CountOfPoints - 1], new GlVectorR2(POLY[0].X - POLY[POLY.CountOfPoints - 1].X, POLY[0].Y - POLY[POLY.CountOfPoints - 1].Y)).getIntersection(this);
if (faultInter.Length == 1 && new GlLineSegment(POLY[0], POLY[POLY.CountOfPoints - 1]).isPointBelongs(faultInter[0]))
{
Intersections[countOfIntersections++] = faultInter[0];
}
for (int i = 0; i < POLY.CountOfPoints - 1; i++)
{
faultInter = new GlLineR2(POLY[i], new GlVectorR2(POLY[i + 1].X - POLY[i].X, POLY[i + 1].Y - POLY[i].Y)).getIntersection(this);
if (faultInter.Length == 1 && new GlLineSegment(POLY[i + 1], POLY[i]).isPointBelongs(faultInter[0]))
{
Intersections[countOfIntersections++] = faultInter[0];
}
}
GlPointR2[] result = new GlPointR2[countOfIntersections];
Array.Copy(Intersections, result, countOfIntersections);
return(result);
}
//////////////TRANSFORM_METHODS////////////////
///////////////////////////////////////////////
/////////////INTERSECTION_METHODS//////////////
public override GlPointR2[] getIntersection(GlLineR2 L)
{
if (!this.isIntersects(L))
{
return new GlPointR2[] { }
}
;
GlPointR2[] Intersections = new GlPointR2[2];
GlPointR2 LineMovedPoint = L.PointOfLine.getPointTranslatedToRotatedSystem(this.SIN, this.COS, new GlPointR2(this.CenterX, this.CenterY));
GlLineR2 IL = new GlLineR2(LineMovedPoint, L.DirectVector.getRotatedVector(this.SIN, this.COS));
float Devider = (float)(Math.Pow(this.RadA * IL.DirectVector.deltaY, 2.0) + Math.Pow(this.RadB * IL.DirectVector.deltaX, 2.0));
float PartRes = (float)Math.Sqrt(Math.Pow(this.RadA * IL.DirectVector.deltaY, 2.0) + Math.Pow(this.RadB * IL.DirectVector.deltaX, 2.0) - Math.Pow(IL.PointOfLine.X * IL.DirectVector.deltaY, 2.0) + (double)(2 * IL.PointOfLine.X * IL.PointOfLine.Y * IL.DirectVector.deltaX * IL.DirectVector.deltaY) - Math.Pow(IL.DirectVector.deltaX * IL.PointOfLine.Y, 2.0));
float xPart = this.RadA * IL.PointOfLine.X * (float)Math.Pow(IL.DirectVector.deltaY, 2.0) - this.RadA * IL.DirectVector.deltaX * IL.DirectVector.deltaY * IL.PointOfLine.Y;
float yPart = this.RadB * IL.PointOfLine.Y * (float)Math.Pow(IL.DirectVector.deltaX, 2.0) - this.RadB * IL.DirectVector.deltaX * IL.DirectVector.deltaY * IL.PointOfLine.X;
float xC1 = this.RadA * (this.RadB * IL.DirectVector.deltaX * PartRes + xPart) / Devider;
float yC1 = this.RadB * (this.RadA * IL.DirectVector.deltaY * PartRes + yPart) / Devider;
float xC2 = -this.RadA * (this.RadB * IL.DirectVector.deltaX * PartRes - xPart) / Devider;
float yC2 = -this.RadB * (this.RadA * IL.DirectVector.deltaY * PartRes - yPart) / Devider;
Intersections[0] = new GlPointR2(xC1, yC1).getTranslatedBackPoint(this.SIN, this.COS, new GlPointR2(this.CenterX, this.CenterY));
Intersections[1] = new GlPointR2(xC2, yC2).getTranslatedBackPoint(this.SIN, this.COS, new GlPointR2(this.CenterX, this.CenterY));
return(Intersections);
}
/// <returns>If the line intersects the oval</returns>
public bool isIntersects(GlLineR2 L)
{
if (L == null || L.isNullLine())
{
return(false);
}
GlVectorR2 LV = L.DirectVector.getRotatedVector(this.SIN, this.COS);
return(Math.Pow(this.RadA * LV.deltaY, 2.0) + Math.Pow(this.RadB * LV.deltaX, 2.0) != 0);
}
/////////////INTERSECTION_METHODS//////////////
///////////////////////////////////////////////
////////////////TANGENT_METHODS////////////////
public override GlLineR2 getTangentFromBelongs(GlPointR2 P)
{
if (P == null || !this.isPointBelongs(P))
{
return(new GlLineR2(new GlPointR2(null), new GlVectorR2(null)));
}
GlPointR2 TP = P.getPointTranslatedToRotatedSystem(this.SIN, this.COS, this.Center);
float k = (TP.Y >= 0 ? 1 : -1) * AdditionalHalfAixis * TP.X / (RealHalfAixis * (float)Math.Sqrt(TP.X * TP.X - Math.Pow(RealHalfAixis, 2.0)));
GlLineR2 tangent = new GlLineR2(P, new GlVectorR2(1, 0).getRotatedVector((float)Math.Atan(k)));
tangent.Rotate(this.SIN, this.COS);
return(tangent);
}
/////////////INTERSECTION_METHODS//////////////
///////////////////////////////////////////////
////////////////TANGENT_METHODS////////////////
public override GlLineR2 getTangentFromBelongs(GlPointR2 P)
{
if (P == null || P.isNullPoint())
{
return(new GlLineR2(new GlPointR2(null), new GlVectorR2(null)));
}
GlParabola TPB = new GlParabola(this.A, new GlPointR2(0, 0), new GlVectorR2(1, 0));
GlPointR2 TP = P.getPointTranslatedToRotatedSystem(this.SIN, this.COS, this.Vertex);
float k = 2 * TPB.A * TP.X + TPB.B;
GlLineR2 tangent = new GlLineR2(P, new GlVectorR2(1, 0).getRotatedVector((float)Math.Atan(k)));
tangent.Rotate(this.SIN, this.COS);
return(tangent);
}
public override GlLineR2 getTangentFromBelongs(GlPointR2 P)
{
if (P == null || P.isNullPoint() || !this.isPointBelongs(P) || this.RadA == 0.0f)
{
return(new GlLineR2(new GlPointR2(null), new GlVectorR2(null)));
}
GlOval IO = new GlOval(this.RadA, this.RadB, new GlVectorR2(this.RadA, 0.0f), new GlPointR2(0.0f, 0.0f));
GlPointR2 MovedPoint = P.getPointTranslatedToRotatedSystem(this.SIN, this.COS, new GlPointR2(this.CenterX, this.CenterY));
GlLineR2 tangent = new GlLineR2(MovedPoint, new GlVectorR2(-(float)Math.Pow(this.RadA, 2.0) * MovedPoint.Y, (float)Math.Pow(this.RadB, 2.0) * MovedPoint.X));
tangent.Rotate(this.SIN, this.COS);
tangent.moveTo(P);
return(tangent);
}
//////////////TRANSFORM_METHODS////////////////
///////////////////////////////////////////////
/////////////INTERSECTION_METHODS//////////////
public override GlPointR2[] getIntersection(GlLineR2 L)
{
GlVectorR2 translatedVector = new GlVectorR2(L.DirectVector).getRotatedVector(this.SIN, this.COS);
GlPointR2 FP = L.PointOfLine.getPointTranslatedToRotatedSystem(this.SIN, this.COS, this.Center);
GlPointR2 SP = translatedVector.fromPointToPoint(FP);
float fPartRes = (float)Math.Pow(AdditionalHalfAixis * (FP.X - SP.X), 2.0);
float sPartRes = (float)Math.Pow(RealHalfAixis * (FP.Y - SP.Y), 2.0);
float tPartRes = FP.X * SP.Y - SP.X * FP.Y;
float sqrtPart = RealHalfAixis * AdditionalHalfAixis * (FP.X - SP.X) * (float)Math.Sqrt(fPartRes - sPartRes + Math.Pow(tPartRes, 2.0));
float x1 = (-(float)Math.Pow(RealHalfAixis, 2.0) * (FP.Y - SP.Y) * tPartRes + sqrtPart) / (sPartRes - fPartRes);
float x2 = (-(float)Math.Pow(RealHalfAixis, 2.0) * (FP.Y - SP.Y) * tPartRes - sqrtPart) / (sPartRes - fPartRes);
float y1 = AdditionalHalfAixis * (float)Math.Sqrt(x1 * x1 - Math.Pow(RealHalfAixis, 2.0)) / RealHalfAixis;
float y2 = -AdditionalHalfAixis * (float)Math.Sqrt(x2 * x2 - Math.Pow(RealHalfAixis, 2.0)) / RealHalfAixis;
float y3 = -AdditionalHalfAixis * (float)Math.Sqrt(x1 * x1 - Math.Pow(RealHalfAixis, 2.0)) / RealHalfAixis;
float y4 = AdditionalHalfAixis * (float)Math.Sqrt(x2 * x2 - Math.Pow(RealHalfAixis, 2.0)) / RealHalfAixis;
GlPointR2[] RP =
{
new GlPointR2(x1, y1).getTranslatedBackPoint(this.SIN, this.COS, this.Center),
new GlPointR2(x2, y2).getTranslatedBackPoint(this.SIN, this.COS, this.Center),
new GlPointR2(x1, y3).getTranslatedBackPoint(this.SIN, this.COS, this.Center),
new GlPointR2(x2, y4).getTranslatedBackPoint(this.SIN, this.COS, this.Center)
};
List <GlPointR2> res = new List <GlPointR2>();
for (int i = 0; i < RP.Length; i++)
{
bool a = this.isPointBelongs(RP[i]);
bool b = L.isPointBelongs(RP[i]);
if (a && b)
{
res.Add(RP[i]);
}
}
return(res.ToArray());
}
//////////////TRANSFORM_METHODS////////////////
///////////////////////////////////////////////
/////////////INTERSECTION_METHODS//////////////
/// <summary>
/// Determines the intersection of a point and a line
/// </summary>
/// <returns>An array containing a copy of given point if it belongs to the line</returns>
public override GlPointR2[] getIntersection(GlLineR2 L)
{
return(L == null ? new GlPointR2[] { } : L.getIntersection(this));
}
/// <summary> /// Determines an anmount of points, created by intersection of a figure and a line /// </summary> /// <returns>An array of intersections</returns> public abstract GlPointR2[] getIntersection(GlLineR2 L);
private void DrawPoints(GlRectangle Border, int GlDrawMode)
{
if (Border == null || !ActivateDrawStart())
{
return;
}
ActivateDrawing();
bool isInside = Border.isPointInside(this[0]);
GlPolygon ToDraw = new GlPolygon(this.Center);
if (Border.isPointInside(this[this.CountOfPoints - 1]) != isInside)
{
if (!isInside)
{
ToDraw.AddVertex(this[this.CountOfPoints - 1]);
}
GlPointR2[] I = new GlLineR2(this[0], new GlVectorR2(this[0].X - this[this.CountOfPoints - 1].X,
this[0].Y - this[this.CountOfPoints - 1].Y)).getIntersection(Border);
if (I.Length == 2)
{
ToDraw.AddVertex(new GlLineSegment(this[this.CountOfPoints - 1], this[0]).isPointBelongs(I[0]) ? I[0] : I[1]);
}
else if (I.Length == 1 && new GlLineSegment(this[this.CountOfPoints - 1], this[0]).isPointBelongs(I[0]))
{
ToDraw.AddVertex(I[0]);
}
}
for (int i = 0; i < this.CountOfPoints - 1; i++)
{
if (isInside)
{
ToDraw.AddVertex(this[i]);
}
if (Border.isPointInside(this[i + 1]) != isInside)
{
GlPointR2[] I = new GlLineR2(this[i], new GlVectorR2(this[i + 1].X - this[i].X,
this[i + 1].Y - this[i].Y)).getIntersection(Border);
if (I.Length == 2)
{
ToDraw.AddVertex(new GlLineSegment(this[i], this[i + 1]).isPointBelongs(I[0]) ? I[0] : I[1]);
}
else if (I.Length == 1 && new GlLineSegment(this[i], this[i + 1]).isPointBelongs(I[0]))
{
ToDraw.AddVertex(I[0]);
}
isInside = !isInside;
}
}
Gl.glBegin(GlDrawMode);
for (int i = 0; i < ToDraw.CountOfPoints; i++)
{
if (ToDraw[i] != null)
{
Gl.glVertex2f(ToDraw[i].X, ToDraw[i].Y);
}
}
Gl.glEnd();
ActivateDrawed();
}
public static bool Equals(GlLineR2 L1, GlLineR2 L2)
{
return((L1 == null || L2 == null || L1.isNullLine() || L2.isNullLine()) ? false : GlVectorR2.isParallel(L1.DirectVector, L2.DirectVector) && GlVectorR2.isParallel(L1.DirectVector, new GlVectorR2(L2.pointOfLine.X - L1.pointOfLine.X, L2.pointOfLine.Y - L1.pointOfLine.Y)));
}
public GlLineR2(GlLineR2 copyLine) :
this(copyLine == null ? new GlPointR2(float.NaN, float.NaN) : copyLine.PointOfLine,
copyLine == null ? new GlVectorR2(0, 0) : copyLine.DirectVector)
{
}
//////////////TRANSFORM_METHODS////////////////
///////////////////////////////////////////////
/////////////INTERSECTION_METHODS//////////////
public override GlPointR2[] getIntersection(GlLineR2 L)
{
if (L == null || L.pointOfLine.isNullPoint())
{
return new GlPointR2[] { }
}
;
if (GlPointR2.Equals(this.pointOfLine, L.pointOfLine))//already have a result
{
return new GlPointR2[] { new GlPointR2(L.pointOfLine) }
}
;
bool isL1Point = this.DirectVector.isNullVector();
bool isL2Point = L.DirectVector.isNullVector();
if (isL1Point && isL2Point)//same points were catched in previous step
{
return new GlPointR2[] { }
}
;
if (this.DirectVector.isNullVector() && L.isPointBelongs(this.pointOfLine))//line and a point
{
return new GlPointR2[] { new GlPointR2(this.pointOfLine) }
}
;
if (L.DirectVector.isNullVector() && this.isPointBelongs(L.pointOfLine))//line and a point
{
return new GlPointR2[] { new GlPointR2(L.pointOfLine) }
}
;
if (GlLineR2.Equals(this, L))//lines are identical
{
return new GlPointR2[] { new GlPointR2(this.pointOfLine), new GlPointR2(L.PointOfLine) }
}
;
if (GlVectorR2.isParallel(this.DirectVector, L.DirectVector))//lines are parallel
{
return new GlPointR2[] { }
}
;
if (L.DirectVector.deltaX == 0)//L2 is parallel to Y axis
{
return new GlPointR2[] { new GlPointR2(L.pointOfLine.X, this.DirectVector.deltaY * (L.pointOfLine.X - this.pointOfLine.X) / this.DirectVector.deltaX + this.pointOfLine.Y) }
}
;
if (this.DirectVector.deltaY == 0)//L1 is parallel to X axis
{
return new GlPointR2[] { new GlPointR2(L.DirectVector.deltaX * (this.pointOfLine.Y - L.pointOfLine.Y) / L.DirectVector.deltaY + L.pointOfLine.X, this.pointOfLine.Y) }
}
;
float v2RatYX = L.DirectVector.deltaY / L.DirectVector.deltaX;
float v1RatXY = this.DirectVector.deltaX / this.DirectVector.deltaY;
float yInter = (v1RatXY * v2RatYX * this.pointOfLine.Y - v2RatYX * this.pointOfLine.X + v2RatYX * L.pointOfLine.X - L.pointOfLine.Y) / (v1RatXY * v2RatYX - 1);
float xInter = v1RatXY * (yInter - this.pointOfLine.Y) + this.pointOfLine.X;
return(new GlPointR2[] { new GlPointR2(xInter, yInter) });//common situation
}
