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

 > Analytical Geometry
    with POV-Ray
    - Index -
  - Insert Menu Add-on
    & Download
  - Basics
    Possibilities and Needs

    Points & Lines
    - Points in 3D
    - Line Sections, Straight,
      Vectors, Distance Markers
    - Surfaces & Planes
    - Output of Results,
    - Points of Intersection
    - Circles
    - Tetrahedron
    - Parallelepiped
    - Round Solids
  - Overview by Table
      on ""
  - 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 triangle yz-plane

Analytical Geometry with POV-Ray
Visualizations and Calculations for the Analytical Geometry
in 3d Systems of Coordinates with POV-Ray.

(Uses Javascript for presentation of a higher resolution of most sample images) update: 08-Feb-2014

0. Basics - What's possible and what you need!
An overview on what is possible and what it needs.
Basic sample files and include file ""
1. Points in a 3D System of Coordinates
Methods for unequivocal visualization of points in a 3d system of coordinates.
2. Line Sections, Straight Lines, Vectors, Distance Markers
The representation of line sections, straight lines, vectors, and distance markers.
3. Surfaces and Planes
Triangles, parallelograms,
planes by parameters and plane by normalvector.
4.1 Output of Results and Captions
How to make an output of the calculated results and how to add a caption to objects.
4.2 Calculating Points of Intersection
How to calculate points of intersections between straight lines and planes or other objects and print the results in the image.
5. Circles
Circle, circle inside a triangle, circumcircle - circle around a triangle.
6.1 Solids I - Tetrahedron
Tetrahedron defined by 4 corners,
tetrahedron defined by a starting point and 3 vectors.

6.2 Solids II - Parallelepiped
Parallelepiped defined by the corners,
parallelepiped defined by a starting point and 3 vectors.

6.3 Solids III - Round Solids
Sphere, ellipsoid, cylinder, cone.
7. An Overview by Table
The most important commands of POV-Ray and of my include file "analytical_g.pov" and a list of the colors of my template file for a quick orientation.
8. Vector Analysis with POV-Ray
Table of most important spellings, arithmetic rules and expressions of vector analysis and vector functions in POV-Ray.
9. Righthanded and Lefthanded Systems of Coordinates
and the Cross Product

Basics on the handyness of systems of coordinates
  10. Samples for the Analytical Geometry
10.1 Parallelogram of the Middles of the Edges
The quatrilateral connecting the middles of the edges of a quatrilateral is always a parallelogram.
10.2 Representation of the Trace Points of a Straight Line
The coordinate planes were represented by squared sections of planes.
10.3 Calculations about a Triangle
Calculations of the length of the edges, the normal vector, the area and the angles.
10.4 Area of a Parallelogram and the Cross Product
10.5 Shadow of a Pyramid
Calculation and visualization of the Shadow of a quadratic pyramid.
10.6 Hit a plane || yz-plane
Calculation and visualization of the intersection of a straight line with a plane parallel to the yz-plane.
10.7 Angle, triangle yz-plane
Calculation and visualization of the angles between a triangle surface and the yz-plane.

© Friedrich A. Lohmüller, 2015
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(since May-1999)
Thanks for your visit!