Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller Elementary Geometry for Raytracing
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- Geometrical Basics
for Raytracing

Right-angled Triangle
Pythagorean Theorem
Trigonometry Basics
Law of cosines
Equilateral Triangle
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Polyhedron
Tetrahedron
Octahedron
Cube & Cuboid
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- 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
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 © Friedrich A. Lohmüller, 2011 http://www.f-lohmueller.de