bool checkPointBelongLine(Point4D M, Point4D N, Point4D A, double eps)
{
if (M.Equals(A) || N.Equals(A))
{
return(true);
}
double t = Math.Abs(calculateCosVectors(N.X - M.X,
N.Y - M.Y,
N.Z - M.Z,
N.W - M.W,
A.X - M.X,
A.Y - M.Y,
A.Z - M.Z,
A.W - M.W));
return(1 - eps < t && t < 1 + eps);
}
//проверка параллельности двух прямых
int checkParallelLines(Point4D M, Point4D N, Point4D A, Point4D B, double eps)
{
/*
* Point4D Q1 = new Point4D(M.X + B.X - A.X,
* M.Y + B.Y - A.Y,
* M.Z + B.Z - A.Z, 1);
* if (checkPointBelongLine(M, N, Q1, eps))
* return 1;
*
* Point4D Q2 = new Point4D(A.X + N.X - M.X,
* A.Y + N.Y - M.Y,
* A.Z + N.Z - M.Z, 1);
* if (checkPointBelongLine(A, B, Q2, eps))
* return 1;
*/
if (checkСrossLines(M, N, A, B) == 0)
{
double ValueA = calculateCosVectors(N.X - M.X,
N.Y - M.Y,
N.Z - M.Z,
N.W - M.W,
N.X - A.X,
N.Y - A.Y,
N.Z - A.Z,
N.W - A.W);
double ValueB = calculateCosVectors(A.X - B.X,
A.Y - B.Y,
A.Z - B.Z,
A.W - B.W,
A.X - N.X,
A.Y - N.Y,
A.Z - N.Z,
A.W - N.W);
if (ValueA != 0 && ValueB != 0)
{
if (Math.Abs(ValueA) == Math.Abs(ValueB))
{
return(1);
}
}
}
return(0);
}
//MN - прямая, ABC - прямая
//пересечение двух прямых
Point4D intersectionLines(Point4D M, Point4D N, Point4D A, Point4D B, double eps)
{
if (checkСrossLines(M, N, A, B) == 0 &&
checkSameLines(M, N, A, B, eps) == 0 &&
checkParallelLines(M, N, A, B, eps) == 0 && !A.Equals(B))
{
Point4D Vector = calculateCompositionVectors(B.X - A.X,
B.Y - A.Y,
B.Z - A.Z,
N.X - M.X,
N.Y - M.Y,
N.Z - M.Z);
Point4D Z = new Point4D(Vector.X + A.X, Vector.Y + A.Y, Vector.Z + A.Z, 1);
Point4D T = intersectionFlatLine(M, N, A, B, Z, eps);
return(T);
}
return(null);
}
//MN - прямая, ABC - плоскость
//пересечение прямой с плоскостью
Point4D intersectionFlatLine(Point4D M, Point4D N, Point4D A, Point4D B, Point4D C, double eps)
{
double[] coefficient = methodNewell(A, B, C);
double a = coefficient[0],
b = coefficient[1],
c = coefficient[2],
d = coefficient[3];
double t = (-1) * ((M.X * a + M.Y * b + M.Z * c + d) /
((N.X - M.X) * a + (N.Y - M.Y) * b + (N.Z - M.Z) * c));
if ((-1) * eps <= t && t <= eps + 1)
{
Point4D T = new Point4D(0, 0, 0, 1);
T.X = (M.X + (N.X - M.X) * t);
T.Y = (M.Y + (N.Y - M.Y) * t);
T.Z = (M.Z + (N.Z - M.Z) * t);
return(T);
}
return(null); //должно вернуть 0
}
//проверка совпадения двух прямых
int checkSameLines(Point4D M, Point4D N, Point4D A, Point4D B, double eps)
{
if (checkPointBelongLine(M, N, A, eps))
{
if (checkPointBelongLine(M, N, B, eps))
{
return(1);
}
}
if (checkPointBelongLine(A, B, M, eps))
{
if (checkPointBelongLine(A, B, N, eps))
{
return(1);
}
}
return(0);
}
/////////////////////////////////////////////////////////////////////////////////////////////////////
//метод Ньюэла
double[] methodNewell(Point4D p1, Point4D p2, Point4D p3)
{
double[] coefficient = new double[4];
coefficient[0] = (p1.Y - p2.Y) * (p1.Z + p2.Z) +
(p2.Y - p3.Y) * (p2.Z + p3.Z) +
(p3.Y - p1.Y) * (p3.Z + p1.Z);
coefficient[1] = (p1.Z - p2.Z) * (p1.X + p2.X) +
(p2.Z - p3.Z) * (p2.X + p3.X) +
(p3.Z - p1.Z) * (p3.X + p1.X);
coefficient[2] = (p1.X - p2.X) * (p1.Y + p2.Y) +
(p2.X - p3.X) * (p2.Y + p3.Y) +
(p3.X - p1.X) * (p3.Y + p1.Y);
coefficient[3] = -(coefficient[0] * p1.X +
coefficient[1] * p1.Y +
coefficient[2] * p1.Z);
return(coefficient);
}
//проверка параллельности прямой и плоскости
int checkLineParallelFlat(Point4D M, Point4D N, Point4D A, Point4D B, Point4D C, double eps)
{
if (checkLineBelongFlat(M, N, A, B, C) == 0)
{
double[] coefficient = methodNewell(A, B, C);
double a = coefficient[0],
b = coefficient[1],
c = coefficient[2],
d = coefficient[3];
if (a * (M.X - N.X) + b * (M.Y - N.Y) + c * (M.Z - N.Z) == 0)
{
return(1);
}
}
//if (intersectionFlatLine(M, N, A, B, C, eps) == null && checkLineBelongFlat(M, N, A, B, C) == 0)
// return 1;
return(0);
}
public void VisibleMN(Point4D M, Point4D N, Point4D A, Point4D B, Point4D C, Point4D L, Point4D T, double eps, ref bool isVisMN, ref bool isVisM, ref bool isVisN, ref bool isNoVis)
{
isVisMN = false; isVisM = false; isVisN = false; isNoVis = false;
Section4D VisibleSection = sectionVisibleLine(M, N, A, B, C, L, T, eps);
Section4D compare1 = new Section4D(M, N);
Section4D compare2 = new Section4D(M, T);
Section4D compare3 = new Section4D(T, N);
if (VisibleSection == null)
{
return;
}
if (!compare1.CheckNull())
{
if (VisibleSection.Equals(compare1))
{
isVisMN = true;
return;
}
}
if (!compare2.CheckNull())
{
if (VisibleSection.Equals(compare2))
{
isVisM = true;
return;
}
}
if (!compare3.CheckNull())
{
if (VisibleSection.Equals(compare3))
{
isVisN = true;
return;
}
}
isNoVis = true;
}
public Axonomertry(Point4D[] p4d, Point4D p4dT, Section4D section4d, int lengthAxis, int indent, double eps, bool changeL)
{
red = new Pen(Color.Red);
green = new Pen(Color.Green);
blue = new Pen(Color.Blue);
black = new Pen(Color.Black);
aqua = new Pen(Color.Aqua, 2);
darkOrange = new Pen(Color.DarkOrange, 2);
this.changeL = changeL;
this.p4d = p4d;
p4dTrans = new Point4D[p4d.Length];
p2d = new Point2D[p4d.Length];
this.p4dT = p4dT;
this.section4d = section4d;
sectionTrans = new Section4D();
section2d = new Section2D();
transformMatrix = new MatrixTransform();
operations = new Operations3D();
Rz = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
Rx = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
Mx = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
Pz = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
T = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
Ao = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
Cz = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
Ac = new Matrix(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
this.Lx = p4d[5].X;
this.Ly = p4d[5].Y;
this.Lz = p4d[5].Z;
this.eps = eps;
this.lengthAxis = lengthAxis;
this.indent = indent;
}
public Section4D pointsTIntersection(Point4D M, Point4D N, Point4D A, Point4D B, Point4D C, double eps)
{
if (checkDegenLine(M, N) == 0 && checkDegenFlat(A, B, C) == 0)
{
if (checkLineBelongFlat(M, N, A, B, C) == 1)
{
statusMessage = "Прямая лежит на плоскости";
return(new Section4D(M, N));
}
}
//if (checkDegenLine(M, N) == 0 && checkDegenFlat(A, B, C) == 1)
// if (checkSameLines(M, N, A, B, eps) == 1 || checkSameLines(M, N, A, C, eps) == 1 || checkSameLines(M, N, B, C, eps) == 1)
// {
// statusMessage = "Прямая лежит на прямой";
// return new Section4D(M, N);
// }
if (checkDegenLine(M, N) == 0 && checkDegenFlat(A, B, C) == 1)
{
if (checkSameLines(M, N, A, B, eps) == 1 && !A.Equals(B))
{
statusMessage = "Прямая лежит на прямой";
return(new Section4D(M, N));
}
if (checkSameLines(M, N, A, C, eps) == 1 && !A.Equals(C))
{
statusMessage = "Прямая лежит на прямой";
return(new Section4D(M, N));
}
if (checkSameLines(M, N, B, C, eps) == 1 && !B.Equals(C))
{
statusMessage = "Прямая лежит на прямой";
return(new Section4D(M, N));
}
}
return(null);
}
void transformTforCentral()
{
if (p4dT != null)
{
p4dT = p4dT * Ac;
p4dT = new Point4D
(
p4dT.X / p4dT.W,
p4dT.Y / p4dT.W,
p4dT.Z / p4dT.W,
p4dT.W / p4dT.W
);
p2dT = transformPoint(p4dT);
}
else if (section4d != null)
{
sectionTrans.Start = section4d.Start * Ac;
sectionTrans.End = section4d.End * Ac;
sectionTrans.Start = new Point4D
(
sectionTrans.Start.X / sectionTrans.Start.W,
sectionTrans.Start.Y / sectionTrans.Start.W,
sectionTrans.Start.Z / sectionTrans.Start.W,
sectionTrans.Start.W / sectionTrans.Start.W
);
sectionTrans.End = new Point4D
(
sectionTrans.End.X / sectionTrans.End.W,
sectionTrans.End.Y / sectionTrans.End.W,
sectionTrans.End.Z / sectionTrans.End.W,
sectionTrans.End.W / sectionTrans.End.W
);
section2d.Start = transformPoint(sectionTrans.Start);
section2d.End = transformPoint(sectionTrans.End);
}
}
void transformPointsForCentral()
{
for (int i = 0; i < p4d.Length; i++)
{
if (p4d[i].name == "X" || p4d[i].name == "Y" || p4d[i].name == "Z")
{
p4dTrans[i] = p4d[i] * Ao;
}
else
{
p4dTrans[i] = p4d[i] * Ac;
p4dTrans[i] = new Point4D
(
p4dTrans[i].X / p4dTrans[i].W,
p4dTrans[i].Y / p4dTrans[i].W,
p4dTrans[i].Z / p4dTrans[i].W,
p4dTrans[i].W / p4dTrans[i].W,
p4dTrans[i].name, p4dTrans[i].color
);
}
p2d[i] = transformPoint(p4dTrans[i]);
}
}
//вырожденность плоскости в точку (проверка)
bool checkFlatAtPoint(Point4D A, Point4D B, Point4D C)
{
return(A.Equals(B) && B.Equals(C));
}
Point2D transformPoint(Point4D p4d)
{
return(new Point2D(p4d.X, p4d.Y, p4d.name, p4d.color));
}
public Section4D(double x1, double y1, double z1, double x2, double y2, double z2)
{
Start = new Point4D(x1, y1, z1, 1);
End = new Point4D(x2, y2, z2, 1);
}
public Section4D(Point4D Start, Point4D End)
{
this.Start = Start;
this.End = End;
}
public Section4D()
{
Start = new Point4D(0, 0, 0, 1);
End = new Point4D(0, 0, 0, 1);
}
public bool Equals(Point4D point)
{
return(X == point.X && Y == point.Y && Z == point.Z);
}
public static Point4D MatrixToPoint(Matrix A, Point4D point)
{
//
return(new Point4D(A.matrix[0][0], A.matrix[0][1], A.matrix[0][2], A.matrix[0][3], point.name, point.color));
}
public Matrix PointToMatrix(Point4D point)
{
//
return(new Matrix(point.X, point.Y, point.Z, point.W));
}
Section4D sectionVisibleLine(Point4D M, Point4D N, Point4D A, Point4D B, Point4D C, Point4D L, Point4D T, double eps)
{
double[] coefficient = methodNewell(A, B, C);
double a = coefficient[0],
b = coefficient[1],
c = coefficient[2],
d = coefficient[3];
if (checkDegenFlat(A, B, C) > 0)
{
return(new Section4D(M, N));
}
if (checkLookAtObserved(a, b, c, d, L, eps) == 0)
{
a = -1 * a;
b = -1 * b;
c = -1 * c;
d = -1 * d;
}
if (checkPositionFlat(a, b, c, d, L, eps) == 0)
{
return(new Section4D(M, N));
}
if (calculateCosVectors(a, b, c, d, M.X, M.Y, M.Z, N.W) >= 0)
{
if (calculateCosVectors(a, b, c, d, N.X, N.Y, N.Z, N.W) >= 0)
{
return(new Section4D(M, N));
}
else
{
return(new Section4D(M, T));
}
}
else
{
if (calculateCosVectors(a, b, c, d, N.X, N.Y, N.Z, N.W) > 0)
{
return(new Section4D(T, N));
}
else
{
return(null);
}
}
}
/////////////////////////////////////////////////////////////////////////////////////////////////////
public Point4D pointTIntersection(Point4D M, Point4D N, Point4D A, Point4D B, Point4D C, double eps, ref Label mesABC, ref Label mesMN)
{
Point4D T = null;
if (checkDegenLine(M, N) == 0 && checkDegenFlat(A, B, C) == 0)
{
mesABC.Text = "Плоскость ABC"; mesMN.Text = "Прямая MN";
T = intersectionFlatLine(M, N, A, B, C, eps);
if (T != null)
{
statusMessage = "Пересечение прямой с плоскостью";
}
else
{
if (checkLineParallelFlat(M, N, A, B, C, eps) == 1)
{
statusMessage = "Прямая и плоскость параллельны";
}
else
{
statusMessage = "Прямая и плоскость не пересекаются";
}
}
return(T);
}
if (checkDegenLine(M, N) == 0 && checkDegenFlat(A, B, C) == 1)
{
if (A.Equals(B))
{
mesABC.Text = "Прямая AC(BC)";
}
if (A.Equals(C))
{
mesABC.Text = "Прямая AB(BC)";
}
if (B.Equals(C))
{
mesABC.Text = "Прямая AB(AC)";
}
mesMN.Text = "Прямая MN";
if (intersectionLines(M, N, A, B, eps) != null)
{
statusMessage = "Прямые MN и AB пересекаютcя";
return(intersectionLines(M, N, A, B, eps));
}
else
{
statusMessage = "Прямые MN и AB не пересекаются";
}
if (intersectionLines(M, N, B, C, eps) != null)
{
statusMessage = "Прямые MN и BC пересекаютcя";
return(intersectionLines(M, N, B, C, eps));
}
else
{
statusMessage = "Прямые MN и BC не пересекаются";
}
if (intersectionLines(M, N, A, C, eps) != null)
{
statusMessage = "Прямые MN и AC пересекаютcя";
return(intersectionLines(M, N, A, C, eps));
}
else
{
statusMessage = "Прямые MN и AC не пересекаются";
}
if (checkParallelLines(M, N, A, B, eps) == 1 && !A.Equals(B))
{
statusMessage = "Прямые MN и AB параллельны";
}
if (checkParallelLines(M, N, A, C, eps) == 1 && !A.Equals(C))
{
statusMessage = "Прямые MN и AC параллельны";
}
if (checkParallelLines(M, N, B, C, eps) == 1 && !B.Equals(C))
{
statusMessage = "Прямые MN и BC параллельны";
}
if (checkСrossLines(M, N, A, B) == 1)
{
statusMessage = "Прямые MN и AB скрещиваются";
}
if (checkСrossLines(M, N, A, C) == 1)
{
statusMessage = "Прямые MN и AC скрещиваются";
}
if (checkСrossLines(M, N, B, C) == 1)
{
statusMessage = "Прямые MN и BC скрещиваются";
}
}
if (checkDegenLine(M, N) == 0 && checkDegenFlat(A, B, C) == 2)
{
mesABC.Text = "Точка A(B, C)"; mesMN.Text = "Прямая MN";
T = intersectionPointLine2(M, N, A, eps);
if (T != null)
{
statusMessage = "Пересечение прямой с точкой";
}
else
{
statusMessage = "Прямая и точка не пересекаются";
}
return(T);
}
if (checkDegenLine(M, N) == 1 && checkDegenFlat(A, B, C) == 0)
{
mesABC.Text = "Плоскость ABC"; mesMN.Text = "Точка M(N)";
T = intersectionPointFlat(M, A, B, C);
if (T != null)
{
statusMessage = "Пересечение точки с плоскостью";
}
else
{
statusMessage = "Точка и плоскость не пересекаются";
}
return(T);
}
if (checkDegenLine(M, N) == 1 && checkDegenFlat(A, B, C) == 1)
{
if (A.Equals(B))
{
mesABC.Text = "Прямая AC(BC)";
}
if (A.Equals(C))
{
mesABC.Text = "Прямая AB(BC)";
}
if (B.Equals(C))
{
mesABC.Text = "Прямая AB(AC)";
}
mesMN.Text = "Точка M(N)";
if (intersectionPointLine(A, B, M, eps) != null)
{
T = intersectionPointLine(A, B, M, eps);
}
if (intersectionPointLine(B, C, M, eps) != null)
{
T = intersectionPointLine(B, C, M, eps);
}
if (intersectionPointLine(A, C, N, eps) != null)
{
T = intersectionPointLine(A, C, N, eps);
}
if (T != null)
{
statusMessage = "Пересечение прямой с точкой";
}
else
{
statusMessage = "Прямая и точка не пересекаются";
}
return(T);
}
if (checkDegenLine(M, N) == 1 && checkDegenFlat(A, B, C) == 2)
{
mesABC.Text = "Точка A(B, C)"; mesMN.Text = "Точка M(N)";
T = intersectionPoints(M, A);
if (T != null)
{
statusMessage = "Пересечение двух точек";
}
else
{
statusMessage = "Две точки не пересекаются";
}
return(T);
}
//statusMessage = "";
return(null);
}