In this paper trans nite interpolation/approximation is discussed. This is a powerful approach to generation of curves, surfaces and solids (and even higher dimensional manifolds) by blending lower dimensional geometric objects. Trans nite blending, e.g. used in Gordon-Coons patches, is well known to mathematicians and CAD people. It is presented here in a very simple conceptual and computation...

New analytical formulations of bounded blending for functionally defined set-theoretic operations are proposed. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional bounding solid. The proposed blending using a b...

This paper focuses on the blending of a plane with surfaces of revolution relying on Dupin cyclides, which are algebraic surfaces of degree 4 discovered by the French mathematician Pierre-Charles Dupin early in the 19th century. A general algorithm is presented for the construction of two kinds of blends: pillar and recipient. This algorithm uses Rational Quadric Bézier Curves (RQBCs) to model ...

PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G0 continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and blend the corresponding Bézier triangles using a univariate blending function formulated in terms of barycentric coordinates. This produces G2 continu...

The literature on conceptual blending and metaphor-making has illustrations galore of how these mechanisms may support the creation and grounding of new concepts (or whole domains) in terms of a complex, integrated network of older ones. In spite of this, as of yet there is no general computational account of blending and metaphor-making that has proven powerful enough as to cover all the examp...

Issues of representation arise in natural language processing, user interface design, art, and indeed, communication with any medium. This paper addresses such issues using algebraic semiotics, which draws on algebraic specification to give (among other things) an algebraic theory of representation, and a generalization of blending in the sense of cognitive linguistics. New ideas in this paper ...

Assistive Teleoperation as Policy Blending In assistive teleoperation, the robot attempts to predict the user’s intent and augments his or her input based on this prediction, in order to simplify the task. Our recent work on policy blending (Dragan and Srinivasa 2012) formalizes assistance as an arbitration of the user’s input and the robot’s prediction. At any instant, the robot combines the i...

Lexical blending is a highly productive and frequent process by which new words enter a language. A blend is formed when two or more source words are combined, with at least one them shortened, as in brunch (breakfast+lunch). We use linguistic and cognitive aspects of this process to motivate a computational treatment of neologisms formed by blending. We propose statistical features that can in...