[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-134555-en":3,"doc-seo-134555-105":32,"detail-sidebar-cat-0-en-105":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":29,"update_tm":30,"read_time":31},134555,549768072016,"WPS_1786070896","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Op Art rendering with lines and curves","\u003Cp>Non-photorealistic rendering studies artistic expression in digital graphics, yet optical art remains comparatively underexplored. This work focuses on two key Op Art styles—line-based and curve-based—using densely packed lines and curves to reveal a hidden underlying image. It introduces three automated algorithms: an efficient method for artifact-free two-colour inputs, an optimization approach for multi-colour cases to minimize artifacts, and a physical-simulation method for curve-based compositions that avoids intersecting curves while inferring plausible depth from planar region decompositions.\u003C/p>","\u003Cp>Op Art rendering with lines and curves  \u003C/p>\u003Cp>Tiffany C. Inglis (Advisor: Craig S. Kaplan) University of Waterloo [piffany@gmail.com](piffany@gmail.com)  \u003C/p>\u003Cp>(a) (b) (c)  \u003C/p>\u003Cp>Figure 1: (a) Square of Two by Neal (1965) and (b) Gavotte: from Black Series II by Stella (1967) are examples of 2-and 3-colour Op Art respectively, in which each line direction represents a colour in the underlying image. (c) Vasarely's Zbre (1944) is an example of curve-based Op Art.  \u003C/p>\u003Cp>1 Problem and Motivation  \u003C/p>\u003Cp>Non-photorealistic rendering (NPR) is an area of computer graphics that studies artistic expressions for digital art. Unlike traditional computer graphics that emphasizes photorealism, NPR explores a wide variety of artistic styles including painting, sketching, and animated cartoons, and develops algorithms for recreating them. One art form that is largely unexplored in computer graphics is Op Art. Short for Optical Art, Op Art is a style of abstract art associated with optical illusions that gained popularity in 1965 with an exhibition called The Responsive Eye [Seitz 1965] . It explores many fundamental artistic and scientific concepts, from geometric shapes and perspectives to colour theory and the psychology of visual perception. To exaggerate certain visual effects, Op artists often use simple shape primitives such as circles and lines in highly contrasting colours such as black and white. We will focus on two types of Op Art—line-based and curve-based—that make use of densely packed lines and curves to convey a hidden underlying image.  \u003C/p>\u003Cp>In line-based Op Art, line directions are used in place of colours to depict salient regions. Reginald H. Neal's Square of Two (Figure 1a), for example, uses two orthogonal line directions to represent an underlying 2-colour planar map. This particular arrangement of lines creates an optical effect where the different regions seem to scintillate as the eye moves across the image. Moreover, between two regions containing lines of different directions, thereis a series of collinear line bends that creates the illusion of a boundary. A contour that is perceived without a change in luminance from one side to another is called an illusory contour [Petry and Meyer 1987] . In Square of Two, all the concentric squares are outlined with illusory contours. Notice that line breaks and T-junctions (Figure 2) are found on the vertices of these squares. Through experimentation, we found that features other than line bends interfere with the  \u003C/p>\u003Cp>Figure 2: Examples of artifacts in line-based Op Art include: (circled, from left to right) a cross, a line break, and a T-junction.  \u003C/p>\u003Cp>perception of illusory contours and should therefore be avoided.  \u003C/p>\u003Cp>Our goal in this project was to develop an algorithm that converts a coloured planar map into a line-based Op Art composition subject to the following constraints:  \u003C/p>\u003Cp>1. Lines in adjacent regions travel in different directions.  \u003C/p>\u003Cp>2. As much as possible, boundaries between regions appear as illusory contours formed by line bends only. In other words, artifacts such as line breaks, T-junctions and crosses should be minimized, if not completely eliminated.  \u003C/p>\u003Cp>Square of Two is a 2-colour lined-based Op Art composition because it uses two line directions to represent a 2-colour map. However, line-based Op Art can have more than two different line directions, as demonstrated by Frank Stella's Gavotte (Figure 1b), which uses three line directions. To be as general as possible, we want our algorithm to operate on inputs with any number of colours.  \u003C/p>\u003Cp>For curve-based Op Art, the idea is to take a set of parallel lines and curve them in certain regions to create a bas-relief effect. For  \u003C/p>\u003Cp>(a) (b)  \u003C/p>\u003Cp>Figure 3: (a) Current by Riley (1964) and (b) a Lovecraft exhibition poster by Notter and Vigne (2007) .  \u003C/p>\u003Cp>example, Victor Vasarely Ze`bre (see Figure 1c) contains a flat background (depicted by straight lines) and a slightly elevated foreground (depicted by curves) . When developing an algorithm to generate curv\u003C/p>","cbCaieqW5xkD1Gll","https://ap.wps.com/l/cbCaieqW5xkD1Gll","pdf",6969181,3,1,6,"English","en",105,"# Problem and Motivation\n## Line-based Op Art\n## Curve-based Op Art\n# Background and Related Work","[{\"question\":\"What are the two types of Op Art addressed in this paper?\",\"answer\":\"The paper focuses on line-based Op Art and curve-based Op Art, both relying on densely packed lines and curves to convey a hidden underlying image.\"},{\"question\":\"How does the proposed approach generate line-based Op Art from a planar map?\",\"answer\":\"It converts a coloured planar map into a line-based Op Art composition with constraints that adjacent regions use different line directions and that boundaries appear as illusory contours formed by line bends only.\"},{\"question\":\"What does the third algorithm do for curve-based Op Art?\",\"answer\":\"It generates curve-based Op Art using a physical simulation that curves parallel lines toward a target configuration while preventing curve intersections.\"}]","Op Art rendering with lines and curves | PDF","Non-photorealistic rendering studies artistic expression in digital graphics, yet optical art remains comparatively underexplored. This work focuses on two key Op Art styles—line-based and curve-based—using densely packed lines and curves to reveal a hidden underlying image. It introduces three automated algorithms: an efficient method for artifact-free two-colour inputs, an optimization approach for multi-colour cases to minimize artifacts, and a physical-simulation method for curve-based compositions that avoids intersecting curves while inferring plausible depth from planar region decompositions.",1787278050,15,{"code":4,"msg":33,"data":34},"ok",{"site_id":25,"language":24,"slug":35,"title":28,"keywords":36,"description":29,"schema_data":37,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":30},"op-art-rendering-algorithms-generating-line-based-and-curve-based-op-art","",{"@graph":38,"@context":87},[39,55,70],{"@type":40,"itemListElement":41},"BreadcrumbList",[42,46,50,52],{"item":43,"name":44,"@type":45,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":47,"name":48,"@type":45,"position":49},"https://docshare.wps.com/document/","Document",2,{"item":51,"name":12,"@type":45,"position":20},"https://docshare.wps.com/document/research-report/",{"item":53,"name":28,"@type":45,"position":54},"https://docshare.wps.com/document/op-art-rendering-algorithms-generating-line-based-and-curve-based-op-art/134555/",4,{"url":53,"name":28,"@type":56,"author":57,"headline":28,"publisher":59,"fileFormat":62,"inLanguage":24,"description":29,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":43,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-23","2026-08-20",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"What are the two types of Op Art addressed in this paper?","Question",{"text":77,"@type":78},"The paper focuses on line-based Op Art and curve-based Op Art, both relying on densely packed lines and curves to convey a hidden underlying image.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"How does the proposed approach generate line-based Op Art from a planar map?",{"text":82,"@type":78},"It converts a coloured planar map into a line-based Op Art composition with constraints that adjacent regions use different line directions and that boundaries appear as illusory contours formed by line bends only.",{"name":84,"@type":75,"acceptedAnswer":85},"What does the third algorithm do for curve-based Op Art?",{"text":86,"@type":78},"It generates curve-based Op Art using a physical simulation that curves parallel lines toward a target configuration while preventing curve intersections.","https://schema.org",{"og:url":53,"og:type":89,"og:title":28,"og:site_name":60,"og:description":29},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,99,103,107,112,116,121,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":48,"category_name":96,"show_sort_weight":97,"slug":98},"Story & Novel",90,"story-novel",{"id":49,"doc_module":4,"doc_module_name":48,"category_name":100,"show_sort_weight":101,"slug":102},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":48,"category_name":104,"show_sort_weight":105,"slug":106},"Exam",70,"exam",{"id":108,"doc_module":4,"doc_module_name":48,"category_name":109,"show_sort_weight":110,"slug":111},5,"Comic",60,"comic",{"id":22,"doc_module":4,"doc_module_name":48,"category_name":113,"show_sort_weight":114,"slug":115},"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":48,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":48,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":48,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":48,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":48,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":48,"category_name":138,"show_sort_weight":108,"slug":139},19,"General","general"]