Fixeddistance

Fixeddistance is a geometric or computational constraint that enforces a constant distance d between two specified points, P and Q, across their motion. The constraint is fundamental in modeling rigid connections and in scenarios where the separation must remain unchanged.

In mathematics and physics, fixeddistance constraints reduce the degrees of freedom in a system and are a core component of linkage design and rigid body kinematics. The constraint is typically expressed as |P - Q| = d, or equivalently (P - Q)·(P - Q) = d^2.

In computer graphics, robotics, and molecular dynamics, fixeddistance constraints help simulate rods, bonds, or joints. A classic example is a two-bar linkage or a dumbbell-like molecule, where two endpoints must stay separated by a fixed length.

Numerical methods to enforce fixeddistance include constraint-based solvers using Lagrange multipliers, penalty methods, or velocity constraints in integration schemes. These methods ensure the constraint is satisfied while advancing the system in time.

Variants may impose fixed distances among more than two points, producing rigid bodies or frameworks. The term fixeddistance is sometimes used in software libraries as a constraint type, such as fixeddistance constraints in physics engines or animation systems.

Related topics include rigid body dynamics, distance geometry, inverse kinematics, and constraint satisfaction problems.