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


Trigonometry Basics
sin, cos, tan - Some useful geometrical facts on sine, cosine and tangens

Note: The trigonometric functions sin(X), cos(X) and tan(X) in POV-Ray
need their arguments X in radians !!!   The symbole π = pi in POV-Ray.

The units for angles: degrees and radians
The angle in degrees: symbol "°"
The angle by arc length: symbol "rad", often in parts of "pi". (360° = 2*pi; 180° = pi)
Conversion of a radiant value RadVal in the according degree value DegVal:
#declare DegVal = degrees(RadVal); or
#declare DegVal = RadVal*(180/pi);

Conversion of a degree value DegVal in the according radiant value RadVal:
#declare RadVal = radians(DegVal); or
#declare RadVal = DegVal*(pi/180);

If we use a value for an angle A in degrees:
#declare SineVal = sin(radians( A ));

The aquivalent is true for the invers functions asin, acos and atan in POV-Ray:
If we want a value for an angle A in degrees:
#declare Angle_in_deg = degrees( asin( 0.50 ));
Otherwise we will get the value in radians:
#declare Angle_in_rad = asin( 0.50 ) ;.

Sine and cosine in a regular triangle
Tangens in a regular triangle

© Friedrich A. Lohmüller, 2011