Subcurves

Subcurves are a concept found in various fields, particularly in mathematics and computer graphics, to describe segments or portions of a larger curve. A subcurve is essentially a subset of points that lie on a given curve, forming a continuous path within that curve. The definition of a subcurve often depends on specifying a start and end point along the original curve, or by defining a range of a parameter used to describe the curve. For instance, if a curve is parameterized by a variable 't' from 0 to 10, a subcurve might be defined by the range of 't' from 2 to 7. The properties of a subcurve, such as its length or curvature, are derived from the properties of the original curve. In computer graphics, subcurves are frequently used for tasks like animation, where specific parts of a path need to be traversed or manipulated. They can also be crucial in geometric modeling for constructing complex shapes by combining or modifying simpler curve segments. The mathematical formalization of subcurves typically involves concepts from topology and differential geometry, ensuring that the subcurve maintains the continuity and smoothness of the parent curve.