Streuvektor

Streuvektor, often translated as stroke vector, is a mathematical and computational concept used to describe the orientation and extent of a stroke segment in a line or curve representation. It is typically a vector that encodes the displacement from one point on the stroke to the next, and may be extended to include additional attributes such as pressure, tilt, or width in order to model the appearance of a brushstroke or pen stroke.

In two dimensions, a Streuvektor s is represented as s = (dx, dy). Its length |s| equals the stroke length for that segment, and its direction is the unit vector s/|s|. A sequence of Streuvektorer forms a polyline approximation of a curve, and the curvature can be analyzed by considering successive vectors.

Streuvektorer are used in stroke-based rendering, where a stroke is drawn by placing and orienting samples along a path according to the vectors, producing textures and shading dependent on tangent directions. They also appear in handwriting and gesture recognition as features that capture the dynamics of written input, and in geometric modeling to approximate smooth curves with piecewise-straight segments.

Example: a straight stroke from (0,0) to (3,4) has Streuvektor s = (3,4); its length is 5, and its direction is the unit vector (3/5, 4/5).

Origin and terminology: The term Streuvektor is used primarily in European technical literatures dealing with vector graphics, digital handwriting, and pattern recognition. Different implementations may augment the basic vector with scalar attributes to represent stroke properties such as pressure, speed, or width.