Mega Code Archive
Determine if 3 points are collinear in 3D
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Title: Determine if 3 points are collinear in 3D?
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 := IsEqual(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 *)
// vérifier si 3 points appartiennent à une même droite tridimensionnelle
// c.a.d s'ils sont alignés.
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