Bayram, BengüÖztürk, GünayUgail, HassanEarnshaw, R. A.Qahwaji, R. S. R.Willis, P. J.2022-04-212022-04-212009Arslan, K. vd. (2009). "On spherical product surfaces in E3". ed. Hassan Ugail. vd. 2009 International Conference on Cyberworlds, 132-137.978-1-4244-4864-7https://doi.org/10.1109/CW.2009.64https://ieeexplore.ieee.org/document/5279659http://hdl.handle.net/11452/25961Bu çalışma, 07-11 Eylül 2009 tarihleri arasında Bradford[İngiltere]’da düzenlenen International Conference on Cyberworlds (CW 2009)’da bildiri olarak sunulmuştur.In the present study we consider spherical product surfaces X = alpha circle times beta of two 2D curves in E-3. We prove that if a spherical product surface patch X = alpha circle times beta has vanishing Gaussian curvature K (i.e. a flat surface) then either alpha or beta is a straight line. Further, we prove that if alpha(u) is a straight line and beta(v) is a 2D curve then the spherical product is a non-minimal and flat surface. We also prove that if beta(v) is a straight line passing through origin and alpha(u) is any 2D curve (which is not a line) then the spherical product is both minimal and flat. We also give some examples of spherical product surface patches with potential applications to visual cyberworlds.eninfo:eu-repo/semantics/closedAccessFunction based geometry modellingMinimal surfacesSpherical product surfaceRangeSuperquadrisModelsComputer scienceEngineeringRoboticsSpheresCyberworldsFlat surfacesGaussian curvaturesMinimal surfacesPotential applicationsProduct surfaceStraight linesTwo dimensionalProceedings Paper0002743261000192-s2.0-72349094419132137Computer science, artificial intelligenceComputer science, information systemsComputer science, theory & methodsEngineering, electrical & electronicRoboticsPlant Morphology; Botanists; Metaheuristics