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Geometri Transformasi
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Geometri Transformasi

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  • 1. TransformasiOleh :Feli RamuryMaya SaftariNurul Fajriah
  • 2. Pendahuluan1. Konsep Felix Klein2. Geometr Transformasi
  • 3. Transformasi VektorTr a n s f o r ma s i i n ime n u n j u k k a n s u a t ut r a n s f o r ma s i l i n i e r .Tr a n s f o r ma s i l i n i e ra k a n t a mp a k t e r l i h a tj e l a s j i k a B = C d a n a k a nd i n y a t a k a n d a l a m b e n t u kA : B B y a n g d i s e b u td e n g a n o p e r a t o r l i n i e rp a d a B. Sa t u a l a s a nme n g a p a t r a n s f o r ma s it e r s e b u t d i k a t a k a n
  • 4. Gambar Points on a Line L1 a +tb a +b L1 a tb Diperpanjang sebesar t b 0
  • 5. Transformasi Linier dengan Matriks 1. I s o me t r i a r t i n y a b e r u k u r a n s a ma . 2. I n v a r i a n 3. I s o me t r i d a l a m g e o me t r i E u c l i d t e r d i r i d a r i 3 k a t e g o r i d a n k o mp o s i s i n y a : t r a n s l a s i , r o t a s i , d a n r e f l e k s i .
  • 6. Transformasi Affine1. T r a n s f o r ma s i a f f i n a d a l a h h u b u n g a n g e o me t r i y a n g me mp e r t a h a n k a n b e n t u k d a s a r d a n i n t e g r i t a s b a n g u n g e o me t r i . Tr a n s f o r ma s i a f f i n d a p a t b e r u p a r o t a s i , t r a n s l a s i , d a n d i l a t a s i .2. T r a n s f o r ma s i a f f i n e t i d a k me mp e r t a h a n k a n /
  • 7. Contoh Transformasi Affine
  • 8. The Group of Isometries ofThe Plane
  • 9. C h a p t e r 3.7, s e t i a pi s o me t r i d a r i R 2a d a l a h p r o d u k d a r is a t u , d u a , a t a u t i g ar e f l e k s i .M i s a l k a n f = r 1r 2r 3,Re f l e k s i d i o p e r a s i k a nd e n g a n d i r i n y ame n j a d i f u n g s ii d e n t i t a s , d i d a p a tf = r 1r 2r 3 r 3r 2r 1 = r 1r 2r 2r 1 = r 1r 1
  • 10. A t r a n s f o r ma t i o no f a s e t S i a af u n c t i o n f r o m St o S, a n d ac o l l e c t i o n G o ft r a n s f o r ma t i o nf o r ms a g r o u p i fi t h a s t h e t wop r o p e r t i e s :J i k a f d a n g b e r a d a d i G , ma k a b e g i t u j u g a f g
  • 11. Spherical GeometrySpherical Geometry adalah suatu geometri dua dimensi dari permukaan bola (sphere). Sphere adalah himpunan semua titik dalam ruang tiga dimensi yang merupakan jaraktetap dari suatu titik tertentu (disebut pusat).
  • 12. Great CircleO 1 Q θ P
  • 13. Great CircleGreat Circle Distance adalah lingkaran yang dibentukoleh perpotongan bola dan bidang melewati pusat.Sebuah lingkaran besar adalah lingkaran terbesaryang dapat ditarik pada suatu lingkungantertentu, dan jalur terpendek sepanjang bola antaradua titik adalah lingkaran besar.
  • 14. The Reflection “line” on The Sphere
  • 15. Representing Space Rotations byQuaternions 
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  • 18. Rotations of (i, j, k) –space
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  • 23. Terima Kasih