Geometric and Analytical Investigation of Lambda-Modified Catmull-Rom Splines with Applications to Robotic Path Planning

Geometric and Analytical Investigation of Lambda-Modified Catmull-Rom Splines with Applications to Robotic Path Planning | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 4 July 2025 V1 Latest version Share on Geometric and Analytical Investigation of Lambda-Modified Catmull-Rom Splines with Applications to Robotic Path Planning Authors : gülden altay suroğlu 0000-0003-1976-3465 [email protected] and Zeynep ALTAY Authors Info & Affiliations https://doi.org/10.22541/au.175160890.08096968/v1 207 views 166 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Catmull-Rom splines are widely used in computer graphics and animation for defining smooth trajectories that pass through given control points. In this study, we investigate a new class of splines derived by modifying the tangent vectors of Catmull-Rom splines using a λ parameter. The λ parameter serves as a geometric control, adjusting the stiffness and turning behavior of the spline. It is numerically and graphically demonstrated that this modification preserves both C¹ and G¹ continuity. Furthermore, Catmull- Rom splines generated with various λ values are compared, and an application to sample path design is presented to illustrate the practical implications of the proposed method. Supplementary Material File (gulden altay suroglu paper.docx) Download 210.57 KB Information & Authors Information Version history V1 Version 1 04 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords catmull-rom spline parametric curve modeling spline curves Authors Affiliations gülden altay suroğlu 0000-0003-1976-3465 [email protected] Firat Universitesi Matematik Bolumu View all articles by this author Zeynep ALTAY Firat Universitesi Matematik Bolumu View all articles by this author Metrics & Citations Metrics Article Usage 207 views 166 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation gülden altay suroğlu, Zeynep ALTAY. Geometric and Analytical Investigation of Lambda-Modified Catmull-Rom Splines with Applications to Robotic Path Planning. Authorea . 04 July 2025. DOI: https://doi.org/10.22541/au.175160890.08096968/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.175160890.08096968/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'a0067c8fea6c1640',t:'MTc3OTU2NDc0Ng=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();