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

  - Geometrical Basics
    for Raytracing

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


Right-angled Triangle (rectangled triangle)

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 and Names
The longest side is the side opposite to the right angle γ at Point C
is called hypotenuse c,
the other two sides are called legs or catheti (singular: cathetus) a and b.
The angle α is at A and ϐ is the angle at B.    
α + ϐ = 90 degrees.
The radius of the circumcircle:
R = 1/2 * c = 1/2* d(A,B);

The median theorem:
A rule for all right triangles:
If MAB is the midpoint of the hypotenuse c, then CMAB = ½ c.
One can also say that point C is located on the circle with diameter [AB].
Conversely, if C is any point of the circle with diameter [AB], then angle at C in the triangle ABC is a right angle.
A right-angled triangle
A right-angled triangle, the median theorem
Thales' theorem:
If AB is a diameter, then the angle at C is a right angle.

© Friedrich A. Lohmüller, 2009