@inproceedings{39f12eeb8ab346ce9e80f3b307b0505f,
title = "Kinematic convexity of planar displacements based on an approximately bi-invariant metric",
abstract = "This paper explores the concept of kinematic convexity of planar displacements as an extension of the projective convexity in computational geometry to planar kinematics. This is achieved with the help of planar quaternions which converts planar displacements into points in the space of planar quaternions called the image space. In this way, projective convexity of points in the image space is developed and used as a representation of kinematic convexity of planar displacements. To address the issue of distance metric for planar displacements, we explored the connection between planar quaternions and quaternions and formulated the concept of kinematic convexity in the space of quaternions where a bi-invariant metric exists. An example is provided in the end to illustrate the use of kinematic convexity for estimating the {"}closest distance{"} from a fixed body to a moving body undergoing a rational B{\'e}zier motion.",
author = "Ge, \{Q. J.\} and Jun Wu and Anurag Purwar and Feng Gao",
year = "2009",
doi = "10.1115/DETC2009-87812",
language = "English",
isbn = "9780791849040",
series = "Proceedings of the ASME Design Engineering Technical Conference",
number = "PARTS A AND B",
pages = "1305--1313",
booktitle = "ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009",
edition = "PARTS A AND B",
note = "ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009 ; Conference date: 30-08-2009 Through 02-09-2009",
}