{"id":225,"date":"2011-06-12T12:36:18","date_gmt":"2011-06-12T10:36:18","guid":{"rendered":"http:\/\/xylem.aegean.gr\/~sofia\/blog\/?page_id=225"},"modified":"2022-01-22T20:44:24","modified_gmt":"2022-01-22T18:44:24","slug":"sketch-realizability","status":"publish","type":"page","link":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/research\/sketch-realizability\/","title":{"rendered":"sketch realizability"},"content":{"rendered":"

Humans have the ability to intuitively realize the 3D geometry from a given 2D sketch. On the contrary, a computer-aided design program encounters sketches as a 2D configuration of lines, without any geometric depth information and requires mathematical criteria to establish if a sketch is realizable, i.e., if it is the projection of a 3D model. Research on the field of “ Sketch realizability” <\/strong> aims at providing geometric, algebraic, or computational criteria\/conditions that determine whether a sketch identifies with the projection of a valid polyhedron.<\/p>\n

\"\"<\/p>\n

My research on this field focuses on the development of an algebraic model of the “cross-section” geometric realizability criterion, which was first introduced by Whiteley in “Weavings, sections and projections of spherical polyhedral<\/em>, Discrete Applied Mathematics, 32(3), 1991, 275-294″.<\/p>\n

The proposed algebraic model describes explicitly the constraints that are involved within the cross-section criterion and forms the basis for an algorithmic implementation of the latter: the developed algorithm constructs a cross-section from a given wireframe sketch in order to evaluate the realizability of it. The realizability evaluation is based on the calculation of a “distance parameter”, which verifies the compatibility of the generated cross-section with the given sketch. The proposed algorithm can also handle inexact sketches, i.e., sketches with noisy vertices.<\/p>\n

The proposed algorithm can be effectively employed within a \u201csketch-to-solid\u201d algorithm in order to (a) facilitate the process of the \u201chidden geometry determination\u201d that is required for natural sketches, (b) correct the geometry of a given wireframe sketch, and (c) generate a compatible cross-section for constructing the trihedral polyhedron from a given sketch.<\/p>\n

Related to this research Publications<\/em><\/strong>:<\/p>\n

Journal Papers:<\/strong><\/em><\/p>\n

    \n
  1. P. Azariadis, S. Kyratzi, N.S. Sapidis, A hybrid-optimization method for assessing the realizability of wireframe sketches, <\/b><\/em>3D Research, 4(1), Article: 3, 2013<\/i>.<\/li>\n
  2. S. Kyratzi, P. Azariadis, N.S. Sapidis, Realizability of a Sketch: An Algorithmic Implementation of the Cross-Section Criterion<\/em>, Computer Aided Design and Applications, 8(5), 665-679, 2011.<\/li>\n
  3. S. Kyratzi, N.S. Sapidis, From Sketch to Solid: An Algebraic Cross-Section Criterion for the Realizability of a Wireframe Sketch<\/em>, Journal of Computing, 86(2-3), 219-234, 2009.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Humans have the ability to intuitively realize the 3D geometry from a given 2D sketch. On the contrary, a computer-aided design program encounters sketches as a 2D configuration of lines, without any geometric depth information and requires mathematical criteria to<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"class_list":["post-225","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/pages\/225"}],"collection":[{"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/comments?post=225"}],"version-history":[{"count":15,"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/pages\/225\/revisions"}],"predecessor-version":[{"id":413,"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/pages\/225\/revisions\/413"}],"up":[{"embeddable":true,"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/xylem.aegean.gr\/~sofia\/blog\/wp-json\/wp\/v2\/media?parent=225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}