Bézier motions with end-constraints on speed

Abstract

• Finding a motion for given precision poses and speeds is discussed • Additive combinations of control poses are used within a geometric algebra • Analogies with the case of curve-fitting are shown

C1 and G1 continuous rational motions using a conformal geometric algebra

“…In order to be able to join motion segments together smoothly, it is necessary to know the derivative of a motion at the ends of its segment. This is straightforward and well-known for an additive Bézier segment as in (18).…”

“…Recent research has shown that free-form motions can be constructed through additive combinations of even-grade elements [17] and end-conditions for such additive motions have been investigated geometrically [18]. Many of the existing techniques from curve design, such as interpolation, naturally move over into motion design.…”