[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-663136-105":59,"doc-detail-663136-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","graph-morphing-via-orthogonal-box-drawings","Graph Morphing via Orthogonal Box Drawings","","Presentation on graph morphing focused on transitioning between graph drawings using orthogonal box representations. Defines graphs, graph drawings, planar and grid-based drawing models, and distinguishes point drawings from non-point drawings via planar straight-line, poly-line, and orthogonal variants. Introduces planar orthogonal box drawings where vertices are axis-aligned rectangles and edges are orthogonal polylines, emphasizing grid drawability. Proposes morphing as continuous deformation between drawings, including linear morphs that linearly interpolate vertex and related locations.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/graph-morphing-via-orthogonal-box-drawings/663136/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/graph-morphing-via-orthogonal-box-drawings/663136.png","ImageObject",300,407,{"name":92,"@type":93},"658056","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-28",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is a graph drawing and what does it mean for a drawing to be planar?","Question",{"text":112,"@type":113},"A graph drawing represents a graph on a plane. A planar graph drawing is one where edges do not intersect.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do planar orthogonal box drawings represent vertices and edges?",{"text":117,"@type":113},"Vertices are axis-aligned rectangles, and edges are orthogonal polylines. The drawing can be constructed on a grid.",{"name":119,"@type":110,"acceptedAnswer":120},"What is graph morphing and what is a linear morph?",{"text":121,"@type":113},"Graph morphing continuously deforms between two drawings. A linear morph linearly interpolates vertex (and other) locations over time.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},663136,1793225307,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":66,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":138,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},658056,"Jack Spalding-Jamieson (Jack S-J) [jacksj@uwaterloo.ca](jacksj@uwaterloo.ca)  \nCheriton School of Computer Science University of Waterloo  \nGraph Morphing via Orthogonal Box Drawings  \nJoint work with my supervisors Therese Biedl and Anna Lubiw  \nPresentation as part of MMath degree, 2023  \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nGraphs, Graph Drawings, Grids  \nGraph: vertex set V , edge set E 􀀚 􀀀 V2􀀁 (no multiedges, no self-loops)  \n1/43  \n Jack S-J ([jacksj@uwaterloo.ca](jacksj@uwaterloo.ca))  Graph Morphing via Orthogonal Box Drawings  University of Waterloo, Computer Science   \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nGraphs, Graph Drawings, Grids  \nGraph: vertex set V , edge set E 􀀚 􀀀 V2􀀁 (no multiedges, no self-loops)  \nGraph drawing: Representation of a graph on a plane  \nPlanar graph drawing: Graph drawing where edges do not intersect  \nVertices: Points  \nEdges: Line segments  \nVertices: Points  \nEdges: Polylines  \nVertices: Points  \nEdges: Orthogonal polylines  \n1/43  \n Jack S-J ([jacksj@uwaterloo.ca](jacksj@uwaterloo.ca))  Graph Morphing via Orthogonal Box Drawings  University of Waterloo, Computer Science   \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nGraphs, Graph Drawings, Grids  \nGraph: vertex set V , edge set E 􀀚 􀀀 V2􀀁 (no multiedges, no self-loops)  \nGraph drawing: Representation of a graph on a plane  \nPlanar graph drawing: Graph drawing where edges do not intersect  \nVertices: Points  \nEdges: Line segments  \nVertices: Points  \nEdges: Polylines  \nOur graphs will always be planar graphs (planar drawing exists) .  \nVertices: Points Edges: Orthogonal polylines  \n1/43  \n Jack S-J ([jacksj@uwaterloo.ca](jacksj@uwaterloo.ca))  Graph Morphing via Orthogonal Box Drawings  University of Waterloo, Computer Science   \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nPoint Drawings  \nPlanar straight-line drawing  \nPlanar poly-line drawing  \nPlanar orthogonal point drawing  \nVertices are points.  \n2/43  \n Jack S-J ([jacksj@uwaterloo.ca](jacksj@uwaterloo.ca))  Graph Morphing via Orthogonal Box Drawings  University of Waterloo, Computer Science   \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nPoint Drawings  \nVertices are points.  \nCan be drawn on a grid.  \n3/43  \n Jack S-J ([jacksj@uwaterloo.ca](jacksj@uwaterloo.ca))  Graph Morphing via Orthogonal Box Drawings  University of Waterloo, Computer Science   \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nNon-Point Drawings  \nPlanar orthogonal box drawing  \nVertices: Axis-aligned rectangles  \nEdges: Orthogonal polylines  \n4/43  \n Jack S-J ([jacksj@uwaterloo.ca](jacksj@uwaterloo.ca))  Graph Morphing via Orthogonal Box Drawings  University of Waterloo, Computer Science   \nIntroduction Methodology Phase I Phase II Phase III Conclusion  \nNon-Point Drawings  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n\nPlanar or","cbCaivrdiTyDQd4l","https://ap.wps.com/l/cbCaivrdiTyDQd4l","pdf",949137,77,"English","# Introduction\n## Graphs, graph drawings, and planar drawing concepts\n# Methodology\n## Point drawings and orthogonal variants\n## Planar orthogonal box drawings (rectangle vertices)\n## Graph morphing and linear morphs\n# Phase I\n## Foundations for morphing between planar orthogonal drawings\n# Phase II\n## Continuous deformation framework\n# Phase III\n## Interpolation of vertex locations\n# Conclusion","[{\"question\":\"What is a graph drawing and what does it mean for a drawing to be planar?\",\"answer\":\"A graph drawing represents a graph on a plane. A planar graph drawing is one where edges do not intersect.\"},{\"question\":\"How do planar orthogonal box drawings represent vertices and edges?\",\"answer\":\"Vertices are axis-aligned rectangles, and edges are orthogonal polylines. The drawing can be constructed on a grid.\"},{\"question\":\"What is graph morphing and what is a linear morph?\",\"answer\":\"Graph morphing continuously deforms between two drawings. A linear morph linearly interpolates vertex (and other) locations over time.\"}]","Graph Morphing via Orthogonal Box Drawings | PDF",194]