Hermite interpolation of discrete data --- points, tangents, curvatures, etc.

--- is a common approach to the construction of planar and spatial curves. The

imposition of global (integral) constraints is more difficult, and therefore

less commonly considered. We consider two types of global constraints that can

be exactly achieved by using Pythagorean--hodograph curves. The first is the

imposition of an exact arc length for the interpolant, and it is shown that

this can be achieved for both for planar and spatial $G^1$ end--point data by

use of quintic Pythagorean--hodograph curves \cite{farouki16,farouki19}. The

second constraint involves the construction of a rational adapted orthonormal

frame (comprising the curve tangent and two unit vectors spanning the curve

normal plane) that satisfies prescribed initial/final orientations. Since the

well--known rotation--minimizing frames are solutions of an initial--value

problem, they are incompatible with this constraint. Consequently, the \emph

{minimal--twist frame} is introduced --- an orthonormal frame with prescribed

initial and final instances, with the least possible value for the integral

of the tangent component of its angular velocity. The construction of rational

minimal twist frames on both open and smooth closed--loop Pythagorean--hodograph

curves is demonstrated \cite{farouki18,farouki20}.