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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" |
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1. |
Points in a 3D System of Coordinates
Methods for unequivocal visualization of points in a 3d system of coordinates.
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2. |
Line Sections, Straight Lines, Vectors, Distance Markers
The representation of line sections, straight lines, vectors, and distance markers.
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3. |
Surfaces and Planes
Triangles, parallelograms, planes by parameters and plane by normalvector. |
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4.1 |
Output of Results and Captions
How to make an output of the calculated results and how to add a caption to objects.
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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.
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5. |
Circles
Circle, circle inside a triangle, circumcircle - circle around a triangle.
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6.1 |
Solids I - Tetrahedron
Tetrahedron defined by 4 corners,
tetrahedron defined by a starting point and 3 vectors.
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6.2 |
Solids II - Parallelepiped
Parallelepiped defined by the corners,
parallelepiped defined by a starting point and 3 vectors.
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6.3 |
Solids III - Round Solids
Sphere, ellipsoid, cylinder, cone.
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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.
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8. |
Vector Analysis with POV-Ray
Table of most important spellings, arithmetic rules and expressions of vector analysis
and vector functions in POV-Ray.
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9. |
Righthanded and Lefthanded Systems of Coordinates and the Cross Product
Basics on the handyness of systems of coordinates |
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10. |
Samples for the Analytical Geometry |
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10.1 |
Parallelogram of the Middles of the Edges
The quatrilateral connecting the middles of the edges of a quatrilateral is always a parallelogram.
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10.2 |
Representation of the Trace Points of a Straight Line
The coordinate planes were represented by squared sections of planes.
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10.3 |
Calculations about a Triangle
Calculations of the length of the edges, the normal vector, the area and the angles.
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10.4 |
Area of a Parallelogram and the Cross Product
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10.5 |
Shadow of a Pyramid
Calculation and visualization of the Shadow of a quadratic pyramid.
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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.
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10.7 |
Angle, triangle yz-plane
Calculation and visualization of the angles between a triangle surface and the yz-plane.
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