Reflection curves -- new computation and rendering techniques.
Ulmet, Dan-Eugen (2004)
International Journal of Mathematics and Mathematical Sciences
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Ulmet, Dan-Eugen (2004)
International Journal of Mathematics and Mathematical Sciences
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Szilvási-Nagy, Márta, Béla, Szilvia, Mátyási, Gyula (2008)
Annales Mathematicae et Informaticae
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Bohumil Cenkl (1960)
Commentationes Mathematicae Universitatis Carolinae
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O. Karwowski (1964)
Annales Polonici Mathematici
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Libuše Marková (1971)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica
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Ahmet Yücesan, Gözde Özkan, Yasemín Yay (2011)
Annales Polonici Mathematici
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We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases. ...