straalvector

Straalvector (English: ray vector) is a mathematical representation used in optics, geometry, and computer graphics to specify the direction of a ray of light or other radiation. In this usage, a ray is defined by an origin point and a direction, and the vector encodes only the directional component.

Mathematically, a ray with origin p and direction d is the set { p + t d | t ≥ 0 }. The direction vector d can be normalized to a unit vector, often denoted û, to focus on direction independent of scale. The magnitude of the ray vector is usually not interpreted as speed; in physical optics, the speed is determined by the medium, while the ray describes the propagation path.

Applications include computer graphics and ray tracing, where straalvector is used to cast rays from a camera into a scene; in geometric optics, it describes the path of light through media, including refraction and reflection at interfaces. In mathematics, it is used in affine geometry to study lines and rays.

Relation to related concepts: straalvector is related to line direction vectors, unit vectors, direction cosines, and to the concept of a ray as a half-line. It is distinct from radiometric quantities like radiance or intensity, which describe the amount of energy, not just direction.

Example: A ray starting at P=(1,2,3) with direction D=(1,0,0) is r(t)= (1,2,3) + t(1,0,0), t≥0.

Origin of term: “straal” is Dutch for ray; “vector” follows the mathematical term.

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