page_title: POV-Ray
section_title: Primitives
hierarchical_section_title: POV-Ray / Features / Primitives
caption_attribution_description: The 15 cells of these Venn diagrams (except the surrounding) correspond to the vertices of the tesseracts tetrahedral shadow. This is a 4 shphere Venn diagram, representing a 4-ary Boolean function. The spheres stand for sets or statements A, B, C, D. Examples: A &#x2229; B {\displaystyle A\cap B} &#x2229; {\displaystyle \cap } C &#xA0; {\displaystyle C~} &#160;&#160;&#160;&#160; = &#xA0; {\displaystyle =~} &#160;&#160;&#160;&#160; A &#x2229; B &#x2229; C {\displaystyle A\cap B\cap C} &#x2229; {\displaystyle \cap } &#160;&#160;&#160;&#160; = &#xA0; {\displaystyle =~} &#160;&#160;&#160;&#160; A &#x2229; B &#x2229; C {\displaystyle A\cap B\cap C} &#x2229; {\displaystyle \cap } D &#xA0; {\displaystyle D~} &#160;&#160;&#160;&#160; = &#xA0; {\displaystyle =~} &#160;&#160;&#160;&#160; A &#x2229; B &#x2229; C &#x2229; D {\displaystyle A\cap B\cap C\cap D} &#x2229; {\displaystyle \cap } &#160;&#160;&#160;&#160; = &#xA0; {\displaystyle =~} &#160;&#160;&#160;&#160; { } C &#xA0; {\displaystyle \{\}^{C}~} &#x2216; &#xA0; {\displaystyle \setminus ~} D &#xA0; {\displaystyle D~} &#160;&#160;&#160;&#160; = &#xA0; {\displaystyle =~} &#160;&#160;&#160;&#160; D C &#xA0; {\displaystyle D^{C}~} &#x2216; &#xA0; {\displaystyle \setminus ~} &#160;&#160;&#160;&#160; = &#xA0; {\displaystyle =~} &#160;&#160;&#160;&#160; The POV-Ray source is given for File:Venn 0000 0001 0001 0110.png and File:Venn 1111 1111 0000 0000.png.
context_page_description: The Persistence of Vision Ray Tracer, most commonly acronymed as POV-Ray, is a cross-platform ray-tracing program that generates images from a text-based scene description. It was originally based on DKBTrace, written by David Kirk Buck and Aaron A. Collins for Amiga computers. There are also influences from the earlier Polyray raytracer because of contributions from its author, Alexander Enzmann. POV-Ray is free and open-source software, with the source code available under the AGPLv3.
context_section_description: POV-Ray, in addition to standard 3D geometric shapes like tori, spheres, and heightfields, supports mathematically defined primitives such as the isosurface (a finite approximation of an arbitrary function), the polynomial primitive (an infinite object defined by a 15th order or lower polynomial), the julia fractal (a 3-dimensional slice of a 4-dimensional fractal), the superquadratic ellipsoid (an intermediate between a sphere and a cube), and the parametric primitive (using equations that represent its surface, rather than its interior).
  POV-Ray internally represents objects using their mathematical definitions; all POV-Ray primitive objects can be described by mathematical functions. This is different from many computer programs that include 3D models, which typically use triangle meshes to compose all the objects in a scene.
  This fact provides POV-Ray with several advantages and disadvantages over other rendering and modeling systems; POV-Ray primitives are more accurate than their polygonal counterparts: objects that can be described in terms of spheres, planar surfaces, cylinders, tori, and the like, are perfectly smooth and mathematically accurate in POV-Ray renderings, whereas polygonal artifacts may be visible in mesh-based modeling software. POV-Ray primitives are also simpler to define than most of their polygonal counterparts, e.g., in POV-Ray, a sphere is described simply by its center and radius; in a mesh-based environment, a sphere must be described by a multitude of small connected polygons (usually quads or triangles).
  On the other hand, script-based primitive modeling is not always a practical method to create certain objects, such as realistic characters or complex man-made artifacts like cars. Those objects can and should be created first in mesh-based modeling applications such as Wings 3D and Blender, and then they can be converted to POV-Ray's own mesh format.
caption: Rendering of the Venn diagram of four spheres created with constructive solid geometry, or CSG. The source is on the description page of the image.
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