[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-663413-105":59,"doc-detail-663413-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","drawing-as-transformation-from-primary-geometry-to-secondary-geometry","Drawing as Transformation - From Primary Geometry to Secondary Geometry","","Drawing distinguishes primary geometry—the spatial arrangement of projection lines from a 3-D object onto a projection plane—from secondary geometry—the relationships among points, lines, and shapes of the projected drawing on a 2-D surface. Projection drawing systems, including those classified by British Standard 1192, are treated as definable through primary geometry, while a re-classification via secondary geometry helps first-year drawing students link formal systems to their observational experience. Student drawings support the argument.",{"@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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/drawing-as-transformation-from-primary-geometry-to-secondary-geometry/663413/",{"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/drawing-as-transformation-from-primary-geometry-to-secondary-geometry/663413.png","ImageObject",300,407,{"name":92,"@type":93},"acoobca","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-28",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the difference between primary geometry and secondary geometry?","Question",{"text":112,"@type":113},"Primary geometry refers to the spatial arrangement of projection lines from a 3-D object to a projection plane. Secondary geometry concerns the relationships between points, lines, and shapes of the drawn projection on the 2-D surface.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does British Standard 1192 classify drawing conventions?",{"text":117,"@type":113},"It categorises projection conventions into types such as orthographic, oblique, and perspective (including multi-plane, axonometric, cavalier, cabinet, planometric, and various-point perspective systems).",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the document argue for re-classifying projection systems using secondary geometry?",{"text":121,"@type":113},"It states that re-classifying in terms of secondary geometry enables first-year students of drawing to relate projection systems more easily to their observational experiences, with supporting student drawings.","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},663413,1793227404,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":41},3985747870733,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Drawing as Transformation: From Primary Geometry  \nto Secondary Geometry  \nDr Howard Riley MA(Royal College of Art), PhD  \nSchool of Art & Design, Swansea Institute of Higher Education, Swansea, Wales, UK  \ne-mail: [howard.riley@sihe.ac.uk](howard.riley@sihe.ac.uk)  \nAbstract  \nA distinction is made between primary geometry, the arrangement in space of lines of projection from a 3-D object to a plane of projection, and secondary geometry, the relationships between the points, lines and shapes ofthe drawn projection on a 2-D surface. Drawing projection systems, such as those classified under British Standard 1192, are illustrated, and are shown to be defined in terms of primary geometry.  \nIt is argued that a re-classification of projection systems in terms of secondary geometry enables first-year students of drawing to relate more easily such systems of geometry to their observational experiences. Student drawings illustrate the argument.  \nDrawing Conventions  \nFollowing the criteria of David Marr’s [1] definition of a representation as a “formal system for making explicit certain entities or types of information, together with a specification of how the system does this”, it may be argued that projective geometry is such a means of representation, because it provides a formal systematic procedure for making explicit information about the three-dimensional attributes of objects and spaces upon a twodimensional surface. There are other formal geometric systems which have been devised to represent such information. The various sets of rules which specify how the procedure may operate are termed drawing conventions. British Standard 1192 [2] categorises these conventions:  \nProjection  \nOrthographic  \nOblique  \nPerspective  \nMulti plane  \nAxonometric  \n(single-plane)  \nCavalier  \nCabinet  \nPlanometric Parallel (1 point) Angular (2 point) Three point  \nFirst Angle Third Angle Isometric Dimetric Trimetric  \nFig. 1 B.S. 1192 categories of projection types  \nIn this classification, all orthographic and oblique projections may be specified as parallel projection systems, since their projectors, those lines of projection that link salient features of the object to points on the plane of projection, are parallel. Perspective projections may be classified as convergent since their projectors converge on a point in front of the plane of projection, assumed to be a viewer’s eye.  \nOrthographic projection systems  \n1. Multi-plane orthographic projection  \nThis allows several views of an object to be projected upon several planes, assumed tobe at right angles to each other: Projectors are parallel and are perpendicular to the planes of projection. Each object face is parallel with its plane of projection.  \n2. Axonometric, or single-plane orthographic projection  \nProjectors are parallel and perpendicular to the plane of projection, and all object faces are inclined to the plane of projection. Isometric Projection is a unique case of axonometric in which foreshortening on all three axes is the same. Dimetric  \nprojection is a special case of axonometric in which scales along two axes are equal, the third axis being different. Trimetric projection is the general case of axonometric and occurs when all three axes are randomly orientated and are each of different scales.  \nOblique projection systems  \nOblique projections all have one face of the object parallel to the plane of projection, and the projectors, although parallel to each other, are inclined to the plane of projection in various ways.  \n1. Cavalier oblique projection  \nThe front face of the object is parallel with the plane of projection, while the projectors from the front face are perpendicular to the plane of projection. The projectors from the other two visible faces, although parallel, are inclined to the plane of projection so that the receding edges are represented at the same true scale as the front face.  \n2. Cabinet oblique projection is similar to Cavalier, except recedi","cbCaimkZ3BRPPlxZ","https://ap.wps.com/l/cbCaimkZ3BRPPlxZ","pdf",296917,12,"English","# Abstract\n# Drawing Conventions\n## Projection\n## Orthographic\n## Oblique\n## Perspective\n# Primary geometry and secondary geometry","[{\"question\":\"What is the difference between primary geometry and secondary geometry?\",\"answer\":\"Primary geometry refers to the spatial arrangement of projection lines from a 3-D object to a projection plane. Secondary geometry concerns the relationships between points, lines, and shapes of the drawn projection on the 2-D surface.\"},{\"question\":\"How does British Standard 1192 classify drawing conventions?\",\"answer\":\"It categorises projection conventions into types such as orthographic, oblique, and perspective (including multi-plane, axonometric, cavalier, cabinet, planometric, and various-point perspective systems).\"},{\"question\":\"Why does the document argue for re-classifying projection systems using secondary geometry?\",\"answer\":\"It states that re-classifying in terms of secondary geometry enables first-year students of drawing to relate projection systems more easily to their observational experiences, with supporting student drawings.\"}]","Drawing as Transformation - From Primary Geometry to Secondary Geometry | PDF"]