{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T18:35:56Z","timestamp":1785436556825,"version":"3.56.0"},"reference-count":22,"publisher":"ASME International","issue":"11","license":[{"start":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T00:00:00Z","timestamp":1754265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.asme.org\/publications-submissions\/publishing-information\/legal-policies"}],"content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This article deals with the computational kinematic geometry of bounded planar objects rather than that of infinitely large moving spaces. In this article, we present a new formulation for kinematic convexity based on an average-distance minimizing motion sweep of a bounded planar object. The resulting single-degree-of-freedom (DOF) motion sweep between two planar poses is represented as a convex combination in the configuration space defined by (x,y,z) where (x,y) is associated with the location of the centroid of the planar object and z=sin\u03b8 with \u03b8 being the angle of rotation. For three poses, a 2DOF motion sweep is developed that not only minimizes the combined average squared distances but also attains a convex combination representation so that existing algorithms for convex hull of points can be readily applied to the construction and analysis of kinematic convex hulls. This results in a new type of convex hull for planar kinematics such that its boundaries are defined by the average-distance minimizing sweeps of the bounded planar object.<\/jats:p>","DOI":"10.1115\/1.4069154","type":"journal-article","created":{"date-parts":[[2025,7,14]],"date-time":"2025-07-14T07:48:47Z","timestamp":1752479327000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":3,"title":["Kinematic Convex Combinations of Multiple Poses of a Bounded Planar Object Based on an Average-Distance Minimizing Motion Sweep"],"prefix":"10.1115","volume":"17","author":[{"given":"Huan","family":"Liu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05qghxh33","id-type":"ROR","asserted-by":"publisher"}],"name":"Stony Brook University Department of Mechanical Engineering, , , \u00a0","place":["Stony Brook, NY, 11794"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiaode","family":"Jeffrey Ge","sequence":"additional","affiliation":[{"name":"Stony Brook University Department of Mechanical Engineering, , , \u00a0","place":["Stony Brook, NY, 11794"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark P.","family":"Langer","sequence":"additional","affiliation":[{"name":"Indiana University Department of Radiation Oncology, , , \u00a0","place":["Indianapolis, IN, 46202"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"33","published-online":{"date-parts":[[2025,8,4]]},"reference":[{"key":"2025080416145378100_CIT0001","first-page":"1305","article-title":"Kinematic Convexity of Planar Displacements Based on an Approximately Bi-Invariant Metric","author":"Ge","year":"2009"},{"key":"2025080416145378100_CIT0002","first-page":"375","article-title":"Kinematic Convexity of Spherical Displacements and Its Application to Collision Prediction","author":"Ge","year":"2008"},{"key":"2025080416145378100_CIT0003","first-page":"715","article-title":"Projective Convexity in Computational Kinematic Geometry","author":"Ge","year":"2002"},{"issue":"3","key":"2025080416145378100_CIT0004","doi-asserted-by":"publisher","first-page":"756","DOI":"10.1115\/1.2919447","article-title":"Computer Aided Geometric Design of Motion Interpolants","volume":"116","author":"Ge","year":"1994","journal-title":"ASME J. 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