Levent, AkinSahin, Bayram2024-08-042024-08-0420191683-35111683-6154https://hdl.handle.net/11616/102470In this paper, we investigate geometric properties of such curves. We construct a new curve by using curves based on new basis with beta functions satisfying various continuity condition and check shape properties. As an interesting property of such curves, we show that the curves based on new basis with beta functions do not have loops which is a useful property for CAGD systems. Since Pythagoren hodograph curves are also important in various CAD applications, we find certain conditions for Pythagorean Hodograph for the curves based on new basis with beta functions.eninfo:eu-repo/semantics/closedAccessBezier Curvesthe Beta FunctionHodograph CurvesArticle1817994WOS:000469247000007Q1