
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 "analytical_g.inc" 

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 POVRay 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 POVRay
Table of most important spellings, arithmetic rules and expressions of vector analysis
and vector functions in POVRay.


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  yzplane
Calculation and visualization of the intersection of a straight line with a plane parallel to the yzplane.


10.7 
Angle, triangle yzplane
Calculation and visualization of the angles between a triangle surface and the yzplane.
