Mega Code Archive
Determine if three 3D Points are collinear to each other
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Title: Determine if three 3D Points are collinear to each other
Function Collinear(x1,y1,z1,x2,y2,z2,x3,y3,z3:Double):Boolean;
Var Dx1,Dx2 : Double;
Dy1,Dy2 : Double;
Dz1,Dz2 : Double;
Cx,Cy,Cz : Double;
//Var AB,AC,BC:Double;
Begin
{find the difference between the 2 points P2 and P3 to P1 }
Dx1 := x2 - x1;
Dy1 := y2 - y1;
Dz1 := z2 - z1;
Dx2 := x3 - x1;
Dy2 := y3 - y1;
Dz2 := z3 - z1;
{perform a 3d cross product}
Cx := Dy1*Dz2- Dy2*Dz1;
Cy := Dx2*Dz1- Dx1*Dz2;
Cz := Dx1*Dy2- Dx2*Dy1;
Result := ((Cx*Cx + Cy*Cy + Cz*Cz)=0.0);
{
Note:
The method below is very stable and logical, however at the same time
it is "VERY" inefficient, it requires 3 SQRTs which is not acceptable...
Result:=False;
AB:=Distance(x1,y1,z1,x2,y2,z2);
AC:=Distance(x1,y1,z1,x3,y3,z3);
BC:=Distance(x2,y2,z2,x3,y3,z3);
If (AB+AC) = BC Then Result:=True
Else
If (AB+BC) = AC Then Result:=True
Else
If (AC+BC) = AB Then Result:=True;
}
End;
(* End Of Collinear *)
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