Publication: Polyhedra metamorphosis using cubic symmetry in 3D interactive environment
Abstract
Çok Yüzlüler: yüzeyleri çokgenlerden oluşan, 3 boyutlu geometride üzerinde çok çalışılmış çekici bir konudur. Bunun en önemli nedeni çok yüzlünün taşıdığı yüksek seviyedeki simetridir. Kübik Simetri bu simetri tiplerinden birisi olup, tek bir şekili, belli bir yaklaşımla,birçok şekile dönüştürebilir. Kübik simetri, bir küre ve bir çekirdek noktası kullanılarak , sınırsız çok yüzlü üretilebilir. Bazı özel durumlar eşsiz çok yüzlülerin çıkarılmasını sağlar. Arşimet ve Platonik cisimleri gibi. Bu tezde özel bir metot kullanılarak 3 boyutlu uzayda çok yüzlülerin oluşturulması sağlanmaktadır. Kullanıcı etkileşimli bir ortam , bu çok yüzlülerin gösterimi ve doğalarının incelenmesi için son derece önemlidir. Bu yüzden bu çeşit bir 3 boyutlu ortam hazırlanmıştır. Kullanıcının etkilieşimini de sağlayan 3 boyutlu zahiri bir ortam öte yandan karmaşık bir iştir. Bu yüzden 3 boyutlu uzayda geometri işlemleri ve 3 boyutlu grafik motorlarının kullanımı tez de önemli bir yer teşkil eder. 3 boyutlu geometri ile ilgili olarak; 3 boyutlu noktalar , düzlemler, doğrular, noktaları düzlemler etrafında döndürmek gibi konular kullanılmıştır. 3 boyutlu Grafik Motoru ile ilgili olarak; umut vadeci bir motor olan Java3D kullanımıştır. Bu araçla 3 boyutlu uzayda nesne işleme işlemleri olan : nesne yaratımı, ekrana çizmesi, nesnenin bir kısmını gizlemek, boyutunu küçültüp büyütmek, çevirmek, gözlemcinin bakış noktasını değiştirmek gibi işlemler kolayca yapılmaktadır.
Polyhedron (plural Polyhedra) is a three dimensional (3D) solid composed of many polygons. It is a long-studied, charming subject in 3D geometry. The most important reason for this is the high degree of symmetry the Polyhedron holds. Cubic Symmetry is a one of these kinds of symmetries that leads a single shape to transform to many totally different yet familiar shapes with a certain approach. By using cubic symmetry, a sphere and a seed point unlimited number of Polyhedra can be generated. Some special cases leads to the unique polyhedra with their regularity including Platonic Solids, Archimedean Solids and so on. In this thesis a special approach is used to create Polyhedra in 3D Space. An interactive environment for visualization of Polyhedra would be very beneficial for the watchers to visualize and understand the 3D nature of the shapes, similarities between shapes, symmetries that a shape and so on. In this thesis such an interactive virtual environment is modeled and created. 3D Virtual Environment that also allows interaction with user is a challenging task however. A great deal of 3D Geometry Knowledge and effective use of 3D Graphics Engine is essential to create such an environment. Related with 3D Geometry; 3D Points, Planes, Lines, Revolving points around lines/ planes, getting symmetries are extensively used. Related with 3D Graphics Engine; A promising graphics engine called Java3D is used. With this tool the fundamental functions of 3D Object manipulation including; Object creation, drawing, clipping, scaling, revolving, changing the viewpoint and so on was implemented rather easily and effectively.
Polyhedron (plural Polyhedra) is a three dimensional (3D) solid composed of many polygons. It is a long-studied, charming subject in 3D geometry. The most important reason for this is the high degree of symmetry the Polyhedron holds. Cubic Symmetry is a one of these kinds of symmetries that leads a single shape to transform to many totally different yet familiar shapes with a certain approach. By using cubic symmetry, a sphere and a seed point unlimited number of Polyhedra can be generated. Some special cases leads to the unique polyhedra with their regularity including Platonic Solids, Archimedean Solids and so on. In this thesis a special approach is used to create Polyhedra in 3D Space. An interactive environment for visualization of Polyhedra would be very beneficial for the watchers to visualize and understand the 3D nature of the shapes, similarities between shapes, symmetries that a shape and so on. In this thesis such an interactive virtual environment is modeled and created. 3D Virtual Environment that also allows interaction with user is a challenging task however. A great deal of 3D Geometry Knowledge and effective use of 3D Graphics Engine is essential to create such an environment. Related with 3D Geometry; 3D Points, Planes, Lines, Revolving points around lines/ planes, getting symmetries are extensively used. Related with 3D Graphics Engine; A promising graphics engine called Java3D is used. With this tool the fundamental functions of 3D Object manipulation including; Object creation, drawing, clipping, scaling, revolving, changing the viewpoint and so on was implemented rather easily and effectively.