Surfaces and Planes

Triangle and Parallelogram:
If we have 3 points A,B,C.

Triangle ABC:
The area of the triangle we can get by:

triangle { A,B,C pigment{color Green}}

The edges of the triangle we get by:

cylinder{ A,B, Rl/2 pigment{color Green}}
cylinder{ B,C, Rl/2 pigment{color Green}}
cylinder{ C,A, Rl/2 pigment{color Green}}

Parallelogram ABDC:
The 4th point D is calculated with A,B,C as follows:

#declare AB = B-A; // edge vector AB
#declare AC = C-A; // edge vector AC
#declare D = A + AB + AC;

The area of the parallelogram we can show as follows:

triangle { A,B,C pigment{color YellowGreen}}
triangle { B,C,D pigment{color YellowGreen}}

Triangle and Parallelogram
Click here for a complete description
of this scene for POV-Ray:
".txt" file or ".pov" file

Plane by parameters

Given a start point P and two directions by the vectors M₁ und M₂. The representation of a section of the plane we get by a macro from "analytical_g.inc" :

object{ Plane_Dir( P,M1,M2, Start,End)
        pigment{color Green transmit 0.5}}

Here Start = <x_min,y_min,z_min> and End = <x_max,y_max,z_max> mark the borders of the section of the plane.

Plane by parameters (section)
Click here for a complete description
of this scene for POV-Ray:
".txt" file or ".pov" file

Plane by normal vector

We have the normal representation of a plane A*x₁+B*x₂+C*x₃+D=0. With N=<A,B,C> we get a presentation of a section of the plane with a macro from "analytical_g.inc" :

object{ Plane_Nor( N, D, Start, End)
        pigment{color Green transmit 0.5}}

About the borders Start and End see above.

If the normal vector N of a plane and a starting point P is known, we can get a representation of a section of the plane by a macro from "analytical_g.inc" :

object{ Plane_NoP( N, P, Start, End)
        pigment{color Green}}

About the borders Start and End see above.

Plane by normal vector (section)
Klicken Sie hier für die vollständige Beschreibung
dieser Szene für POV-Ray:
".txt"-Datei or ".pov"-Datei