Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
    Elementary Geometry for Raytracing
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Home
- POV-Ray Tutorial

  - Geometrical Basics
    for Raytracing

    Right-angled Triangle
    Pythagorean Theorem
    Trigonometry Basics
    Law of cosines
    Equilateral Triangle
    Regular Polygon
    Polyhedron
      Tetrahedron
      Octahedron
      Cube & Cuboid
      Dodecahedron
      Icosahedron
      Cuboctahedron
      Truncated Octahedron
      Rhombicuboctahedron
      Truncated Icosahedron
    Circles
      Tangent circles
      Internal Tangents
      External Tangents
     
     
     
     
     
     
     
     
     
   - Geometric 3D Animations

                                               

Equilateral Triangle
In the following we write for the square root of a number the expression "sqrt(ZAHL)"
conforming to the syntax used in POV-Ray.

Note: To avoid any collision with built-in identifiers and reserved words in POV-Ray,
it's strongly recommanded to use only words beginning with capital letters
for all identifiers of variables declared by the user, i.e. use "Ri" instead of "r" and use "H" instead of "h".

Dimensions
Length of triangle base side: a.
All internal angles: 60°
The height of an equilateral triangle:
h = 1/2 * sqrt(3) * a ; or
h = sin (radians(60)) * a ;

The height of the incenter O or
the incircle radius of an equilateral triangle:

r = 1/6 * sqrt(3) * a ;

The radius of circumcircle of an equilateral triangle:
R = 1/3 * sqrt(3) * a ;
An equilateral triangle
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© Friedrich A. Lohmüller, 2009
http://www.f-lohmueller.de