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Abstract. OpenCASCADE provides the algorithm to search the intersection point between 3 planes. If two of the planes are parallel or identical, will get no result.

Key Words. Plane Intersection

1.Introduction

Ax+By+Cz+D=0

2.Algorithm

void IntAna_Int3Pln::Perform (const gp_Pln& P1, const gp_Pln& P2,
const gp_Pln& P3) {
done=Standard_False;
math_Matrix M(1,3,1,3);
math_Vector V(1,3);
P1.Coefficients(M(1,1),M(1,2),M(1,3),V(1));
P2.Coefficients(M(2,1),M(2,2),M(2,3),V(2));
P3.Coefficients(M(3,1),M(3,2),M(3,3),V(3));
math_Gauss Resol(M,gp::Resolution());
if (!Resol.IsDone()) {
empt=Standard_True;
}
else {
empt=Standard_False;
V=-V;
Resol.Solve(V);
pnt.SetCoord(V(1),V(2),V(3));
}
done=Standard_True;
}

inline void gp_Pln::Coefficients (Standard_Real& A,
Standard_Real& B,
Standard_Real& C,
Standard_Real& D) const
{
const gp_Dir& dir = pos.Direction();
if (pos.Direct()) {
A = dir.X();
B = dir.Y();
C = dir.Z();
}
else {
A = -dir.X();
B = -dir.Y();
C = -dir.Z();
}
const gp_Pnt& P = pos.Location();
D = -(A * P.X() + B * P.Y() + C * P.Z());
}

3. Conclusion