Throughpoint

Throughpoint is a term used in several disciplines to denote a point that a curve, path, or geometric object is required to pass through. In mathematics and data fitting, throughpoints are the data points that a function or curve must interpolate; for example, in polynomial interpolation a polynomial is constructed to pass through a set of throughpoints.

In geometry and computer graphics, throughpoints are used to constrain curves such as splines or Bezier curves. Depending on the curve model, the curve may be designed to pass exactly through the given throughpoints or to approximate them while preserving continuity with adjacent segments. Throughpoint constraints are common in CAD and vector graphics editing, where designers specify exact locations that a routed or drawn curve must meet.

In navigation, robotics, and route planning, throughpoints (often called waypoints) serve as mandatory checkpoints that a planned path must visit in a given order. Algorithms may optimize the route around these throughpoints, subject to constraints such as distance, obstacles, or motion limits.

Overall, throughpoint serves as a transferable concept indicating a required intersection with a path or curve. The exact interpretation—interpolating a curve, visiting a sequence of coordinates, or passing through specific design points—varies by field, with related terms including waypoint, interpolation point, and control point.

See also: waypoint, interpolation, spline, Bezier, control point, data point.