Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmueller
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- POV-Ray Tutorials

  - Analytical Geometry
    with POV-Ray
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  - Basics
    Possibilities and Needs

    Points & Lines
    - Points in 3D
    - Line Sections, Straight,
      Vectors, Distance Markers
   > Surfaces & Planes
    - Output of Results,
      Captions
    - Points of Intersection
    - Circles
    Solids
    - Tetrahedron
    - Parallelepiped
    - Round Solids
    -
  - Overview by Table
      on "analytical_g.inc"
  - Vector Analysis
      with POV-Ray
  - Righthanded & Lefthanded
    Systems of Coordinates
    and the Cross Product

  - Samples from
    Analytical Geometry
    - Parallelogram of the
        Middles of the Edges
    - Trace Points of a Straight Line
    - Calculations about a Triangle
    - Area of a Parallelogram
        and Cross Product
    - Shadow of a Pyramid
    - Hit a plane || yz-plane
    - Angle of triangle & yz-plane
                                       

Analytical Geometry with POV-Ray

 
Surfaces and Planes

Triangle and Parallelogram,
Plane by Parameters and Plane by Normal Vector


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}}
Click me!
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 = <xmin,ymin,zmin> and End = <xmax,ymax,zmax> 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
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© Friedrich A. Lohmüller, 2007
www.f-lohmueller.de