{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:13:07Z","timestamp":1760177587272,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,16]],"date-time":"2020-07-16T00:00:00Z","timestamp":1594857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article presents evidence of the convenience of implementing the geometric places of the plane into commercial computer-aided design (CAD) software as auxiliary tools in the computer-aided sketching process. Additionally, the research considers the possibility of adding several intuitive spatial geometric places to improve the efficiency of the three-dimensional geometric design. For demonstrative purposes, four examples are presented. A two-dimensional figure positioned on the flat face of an object shows the significant improvement over tools currently available in commercial CAD software, both vector and parametric: it is more intuitive and does not require the designer to execute as many operations. Two more complex three-dimensional examples are presented to show how the use of spatial geometric places, implemented as CAD software functions, would be an effective and highly intuitive tool. Using these functions produces auxiliary curved surfaces with points whose notable features are a significant innovation. A final example provided solves a geometric place problem using own software designed for this purpose. The proposal to incorporate geometric places into CAD software would lead to a significant improvement in the field of computational geometry. Consequently, the incorporation of geometric places into CAD software could increase technical-design productivity by eliminating some intermediate operations, such as symmetry, among others, and improving the geometry training of less skilled users.<\/jats:p>","DOI":"10.3390\/sym12071181","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T05:10:30Z","timestamp":1595394630000},"page":"1181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Computer-Aided Sketching: Incorporating the Locus to Improve the Three-Dimensional Geometric Design"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9001-1050","authenticated-orcid":false,"given":"Jos\u00e9 Ignacio","family":"Rojas-Sola","sequence":"first","affiliation":[{"name":"Department of Engineering Graphics, Design and Projects, University of Ja\u00e9n, 23071 Ja\u00e9n, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2928-6631","authenticated-orcid":false,"given":"David","family":"Hern\u00e1ndez-D\u00edaz","sequence":"additional","affiliation":[{"name":"Department of Engineering Graphics and Design, Serra Hunter Programme, Polytechnic University of Catalonia, Terrassa, 08222 Barcelona, Spain"}]},{"given":"Ricardo","family":"Villar-Ribera","sequence":"additional","affiliation":[{"name":"Department of Engineering Graphics and Design, Polytechnic University of Catalonia, Terrassa, 08222 Barcelona, Spain"}]},{"given":"Vicente","family":"Hern\u00e1ndez-Abad","sequence":"additional","affiliation":[{"name":"Department of Engineering Graphics and Design, Polytechnic University of Catalonia, Terrassa, 08222 Barcelona, Spain"}]},{"given":"Francisco","family":"Hern\u00e1ndez-Abad","sequence":"additional","affiliation":[{"name":"Department of Engineering Graphics and Design, Polytechnic University of Catalonia, Terrassa, 08222 Barcelona, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hu, G., Bo, C.C., Wu, J.L., Wei, G., and Hu, F. (2018). Modeling of free-form complex curves using SG-Bezier curves with constraints of geometric continuities. Symmetry, 10.","DOI":"10.3390\/sym10110545"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Rojas-Sola, J.I., and De la Morena-de la Fuente, E. (2019). The Hay inclined plane in Coalbrookdale (Shropshire, England): Geometric modeling and virtual reconstruction. Symmetry, 11.","DOI":"10.3390\/sym11040589"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rojas-Sola, J.I., Gal\u00e1n-Moral, B., and De la Morena-de la Fuente, E. (2018). Agust\u00edn de Betancourt\u2019s double-acting steam engine: Geometric modeling and virtual reconstruction. Symmetry, 10.","DOI":"10.3390\/sym10080351"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.destud.2013.10.003","article-title":"Creative Segment: A descriptive theory applied to computer-aided sketching","volume":"35","author":"Sun","year":"2014","journal-title":"Des. Stud."},{"key":"ref_5","first-page":"181","article-title":"Comparative Study of CAD Software, Web3D Technologies and Existing Solutions to Support Distance-Learning Students of Engineering Profile","volume":"9","author":"Kostic","year":"2012","journal-title":"Int. J. Comput. Sci. Issues"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0010-4485(03)00056-3","article-title":"Solving spatial basic geometric constraint configurations with locus intersection","volume":"36","author":"Gao","year":"2004","journal-title":"Comput. Aided Des."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.compind.2015.05.004","article-title":"Computer-aided design-while-engineering technology in top-down modeling of mechanical product","volume":"75","author":"Pan","year":"2016","journal-title":"Comput. Ind."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/j.jclepro.2018.03.213","article-title":"An innovative eco-design approach based on integration of LCA, CAD\/CAE and optimization tools, and its implementation perspectives","volume":"187","author":"Tao","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.jclepro.2013.10.003","article-title":"Study on the technical feasibility of replacing glass fibers by old newspaper recycled fibers as polypropylene reinforcement","volume":"65","author":"Serrano","year":"2014","journal-title":"J. Clean. Prod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.jclepro.2019.04.047","article-title":"Research on the use of lignocellulosic fibers reinforced bio-polyamide 11 with composites for automotive parts: Car door handle case study","volume":"226","author":"Julian","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Le\u00f3n-Rovira, N. (2007). Trends in Computer Aided Innovation: Second IFIP Working Conference on Computer Aided Innovation, 8\u20139 October 2007, Michigan, USA, Springer Science & Business Media. IFIP Advances in Information and Communication Technology.","DOI":"10.1007\/978-0-387-75456-7"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/j.compind.2009.05.014","article-title":"Integrated Computer-Aided Innovation: The PROSIT approach","volume":"60","author":"Cugini","year":"2009","journal-title":"Comput. Ind."},{"key":"ref_13","first-page":"S41","article-title":"Research and application of computer aided design system for product innovation","volume":"19","author":"Li","year":"2019","journal-title":"J. Comput. Methods Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.compind.2009.05.011","article-title":"Computer aided innovation\u2013State of the art from a new product development perspective","volume":"60","author":"Kohn","year":"2009","journal-title":"Comput. Ind."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/j.compind.2009.05.012","article-title":"An ontological basis for computer aided innovation","volume":"60","author":"Cavallucci","year":"2009","journal-title":"Comput. Ind."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.compind.2009.05.010","article-title":"The future of computer-aided innovation","volume":"60","author":"Leon","year":"2009","journal-title":"Comput. Ind."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.tsc.2018.11.007","article-title":"Improving creative self-efficacy and performance through computer-aided design application","volume":"31","author":"Chang","year":"2019","journal-title":"Think. Skills Creat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1016\/j.compind.2009.05.018","article-title":"Computer-aided sketching as a tool to promote innovation in the new product development process","volume":"60","author":"Company","year":"2009","journal-title":"Comput. Ind."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"103198","DOI":"10.1016\/j.compind.2020.103198","article-title":"Reducing human effort in engineering drawing validation","volume":"117","author":"Rica","year":"2020","journal-title":"Comput. Ind."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.destud.2019.11.003","article-title":"A 3D shape generative method for aesthetic product","volume":"66","year":"2020","journal-title":"Des. Stud."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1145\/3355089.3356533","article-title":"OpenSketch: A richly-annotated dataset of product design sketches","volume":"38","author":"Gryaditskaya","year":"2019","journal-title":"ACM Trans. Graph."},{"key":"ref_22","first-page":"707","article-title":"Traditional product representations and new digital tools in the dimensioning activity: A designers\u2019 point of view on difficulties and needs","volume":"21","author":"Ranger","year":"2018","journal-title":"Des. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/09544828.2019.1617413","article-title":"Influence of sketching instruction on elementary students\u2019 design cognition: A study of three sketching approaches","volume":"30","author":"Sung","year":"2019","journal-title":"J. Eng. Des."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.cad.2019.04.003","article-title":"Sketch-based retrieval and instantiation of parametric parts","volume":"113","author":"Zeng","year":"2019","journal-title":"Comput. Aided Des."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"102789","DOI":"10.1016\/j.cad.2019.102789","article-title":"3D computational sketch synthesis framework: Assisting design exploration through generating variations of user input sketch and interactive 3D model reconstruction","volume":"120","author":"Ban","year":"2020","journal-title":"Comput. Aided Des."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1017\/S0890060416000512","article-title":"Sketching in three dimensions: A beautification scheme","volume":"31","author":"Shankar","year":"2017","journal-title":"Ai Edam Artif. Intell. Eng. Des. Anal. Manuf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.cag.2019.03.017","article-title":"Progressive sketching with instant previewing","volume":"81","author":"Wang","year":"2019","journal-title":"Comput. Graph. UK"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1016\/j.patcog.2012.11.006","article-title":"New method to find corner and tangent vertices in sketches using parametric cubic curves approximation","volume":"46","author":"Albert","year":"2013","journal-title":"Pattern Recognit."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cag.2016.05.013","article-title":"Detecting mirror symmetry in single-view wireframe sketches of polyhedral shapes","volume":"59","author":"Plumed","year":"2016","journal-title":"Comput. Graph. UK"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.cag.2015.07.013","article-title":"Coincidence condition of two B\u00e9zier curves of an arbitrary degree","volume":"54","author":"Chen","year":"2016","journal-title":"Comput. Graph."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"444","DOI":"10.5951\/MT.54.6.0444","article-title":"The problem of Apollonius","volume":"54","year":"1961","journal-title":"Math. Teach."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/0025570X.1983.11977025","article-title":"Apollonius by Inversion","volume":"56","author":"Bruen","year":"1983","journal-title":"Math. Mag."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Meskens, A., and Tytgat, P. (2017). The Genesis of Geometry. Exploring Classical Greek Construction Problems with Interactive Geometry Software, Birkh\u00e4user. Compact Textbooks in Mathematics.","DOI":"10.1007\/978-3-319-42863-5"},{"key":"ref_34","unstructured":"D\u00f6rrie, H. (1965). The tangency problem of Apollonius. 100 Great Problems of Elementary Mathematics: Their History and Solutions, Dover."},{"key":"ref_35","unstructured":"Hern\u00e1ndez-Abad, F., Hern\u00e1ndez-Abad, V., and Ochoa-Vives, M. (1996). Lugares Geom\u00e9tricos: Su Aplicaci\u00f3n a Tangencias, Ediciones UPC. (In Spanish)."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s004070100046","article-title":"Textual note on a (problem of) geometric place in Aristotle\u2019s Meteorologica (III. 5, 375 b 16-376 b 22)","volume":"56","author":"Vitrac","year":"2002","journal-title":"Arch. Hist. Exact Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/cae.20344","article-title":"Educational software to learn the essentials of engineering graphics","volume":"20","year":"2012","journal-title":"Comput. Appl. Eng. Educ."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/7\/1181\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:49:11Z","timestamp":1760176151000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/7\/1181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,16]]},"references-count":37,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["sym12071181"],"URL":"https:\/\/doi.org\/10.3390\/sym12071181","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,7,16]]}}}