P P Ó P. r r t r r r s 1. r r ó t t ó rr r rr r rí st s t s. Pr s t P r s rr. r t r s s s é 3 ñ

P P Ó P r r t r r r s 1 r r ó t t ó rr r rr r rí st s t s Pr s t P r s rr r t r s s s é 3 ñ í sé 3 ñ 3 é1 r

P P Ó P str r r r t é t r r r s 1 t r P r s rr 1 1 s t r r ó s r s st rr t s r t s rr s r q s rr r str 2 r s rr t s r ést st r r s st s rr t q t s q t s rr s 1 P r s 1 1 étr r t r s s s é 3 ñ í sé 3 ñ 3 é1 r 1 r s

P Ó P Ó P Ó Ó é1 r P P Ó P P r r s t r q q t r t t t r r r s 1 2ó s t s t r t s tr st rt é 2 s t r t r s s 2 rr s r s s s r r s r 2 t t s r t r 2 r s r q s t s st s r s ó q st r s s s é 3 ñ í sé 3 ñ 3 r t r s

rt st r t r ó s rr r s r r ó t st t t P té rt r t s 2 t s r r 2 r t t s s q r str s s q 1 í t t s ó 1 s s r s s té 2 r s s s s q r t t s t r r ó s r st r rt té rá t rs r ó é s r r ó t st t t P té s t s át 3 s é 1t s ó

r t s s r t r s P r s 2 2 s s s r t s rr st r 2 t sí s r t ó r ó r s 2 rs P r 2 r t t s s s 3 r P r s 2 2 t ó t s rít s s rr st tr tt P r s rr

r tr ó r st t s P rt s t s ás q Pr 2 s Pr 2 s P r s s P 2 r 2 rr t s t s 1 á s s r t s ñ t 1 tr P q t 1 tr 1 tr t r2 P q t Pr t P q t s 1 s r s r t r P r r r P q t P r r r P q t 1 tr r 2 r P t r P q t 1 tr r t r t s r ó s r r t 1 r t s r s Pr s P rs t s étr

P rs t P rs t P rs t s t s Pr s P rs t s étr P rs t P rs t P rs t s t s á s s s r s t s s s 2 r t r r t r s s r í str ó t tr s r r ó t t r ó s r s s str ó s t s

r s s s r ó s étr s s r 2 t r s s Pr 2 s 1 étr s rt s s Pr 2 s 1 étr s s P rs t t r s st r t 1 tr 1 tr r 1 tr t r r r r ó t 1t r ó t 1t r s s t r rr s t s s 1 s r s r t r s r r q P r r r P r r s r s r s P r r r P r P r P r r 1 tr r 2 r r ó s s P t r

1 tr r t r 1 tr r t s t t r s s r st r t t

ít tr ó r st t st t s r tr t r t r r r s 1 q s s rr ó r rí r r ó t r t q r t t ó s s 1 étr s s s s r r s rr 1 rt r t r t r ó t s st s r s st t s ó ít s r r ít tr t r s s r ó r 2 t t t rí trás ést r r s tér s 2 t 1t s s r s s t s r 2 t t s r ó r t t t r r ít tr t r s t s t s t s t rt ít r s s s s r 2 t sí tr t r s P r ú t é r s t t r t s s s s 2 í s ás q tr t t ú r ñ s 2 q s s é r s r r s tr s s 2 r s r s s r t q s t r s stá r r ó s s r s r s t rá s s s r rá s q ú t t 3 t r 2 r tr st s ó s tr tr s s s s ❼ á r s s s r t s s r ❼ s r á r s 2 q s t s s r

P Ó ❼ ér r r r r rs s té s 2 r 2 s q s r s r t r r s ó r s s r r t é r ó r t t r r s ó ❼ 1 P á s s s r ❼ rst P rs P á r s ó r t st r ❼ r P rs P á r st r t st r t s s r r r s 1 rst rs t r rs r s s ás s r s s P rt s t t ás s t s r q st t t s r

P t s t s q t r tú s r r s stá s t s q t r q ést s t s s rt í t s s r tr s r ó t rá s 2 s r r s s t s t r r s P r t st r ss s s t t s r s s ñ r s q r s rá s 2 s 2 r r r s q s q r r s r t s 2 ó r q t rr t t s ás q t t s t ás t str ó t r r s ó s r s t r t q s t s t s s r s r 2 r s t r 2 ó té t 3 st r s ó s ñ r s 2 r r r s t r ás r s s r ó 2 q s r s í t s s r tr s r ó q s r s s s r t r s r s r r r ó s étr P r r r q s st s é r t s q t r 2 r t s r s q s r r s t t r r s ó Pr 2 s r 2 ó s r r ó s s s s r s r 2 t r s r s r r s ú t

P Ó r s s r 2 t r s t r 2 t s rt s ó t s r st s r r s t r r t s r t s 2 s s ést s Pr 2 s r s s í s s ó t r 2 ó s r s tr sí Pr 2 s rs t r q s t s st t s r ás q ñ s q s t s r s Pr 2 s P r s s st r 2 t r t s s tr r 2 ó t s r t s s r r s tr sí s 3 ést s t s ó s 1 étr s Pr r s ó t r q s r s s s s s st q r r s t ó t st rs s rt rá s s st t r r s t r t s étr s t r s r 2 s t r t s á s 1 étr s 1 étr s r r s s r 2 s 1 étr s s r t ríst s st t s s s r r t ríst s r s s r r s s r r ést s s rá st rs s 2 s s 1 trí rt 2 1 trí rt 1 trí rt r t s r 2 s s étr s rt s s á s s r

P étr s rt s s á s s r r étr s rt s s á s r t s r s étr étr r étr r s Pr 2 s 1 étr s rt s 1 trí r 2 ó 1 étr s r t q r s r ést r s Pr 2 s 1 étr s s rt rá s s r 2 s rt rá s rs t s t s s ést s r r s s t s r r s r rs t t r q s t s s s ás q ñ s q t s r s

P Ó r P rs t t t r r s t r q s r t r r s ó s ó q s t s t t s r s í r s r r t s st s tr 2 r r s s r t s s r s s P 2 r 2 rr t s t s s r r t r s t t ás s s 2 r s r s t s rt r é s s s r t r s r q q r ó s rr t s r t t t t s s r s s s t 3 r t 2 ás r r s s s s t ú s s 2 s s r t t s 2 t s r t st r r rt r r r rr t q r t s s rr 1 1 s r r s ñ r s s t r t s t ó s t 2 s s r r t ú s rt r rá s r str t s r r t q t st r t ríst

ít á s s r t s rr r t r r r s s 1 P r 3 r t r r t s s s t s s í s r t r r s ó s s Pr r s r r s r s t rr Pr r s r s r t 1t r s s r t rr r r s r q t s t r t r st s t r t rá r ❼ r ó r t t rr ❼ ó s í t s t s r s q q r s r st rr t t s s r r 3 st s 1 étr t r ó t r ó t s st t r r s t rá r s t 1t q r í s t rá 2 t r í r s t á s q rs t 1 étr s r 3 ést r r s q s r r í s t r r t s t s r s t s s t s s r s r t q t r tú t rr

P P r r s

ít s ñ st s ó s s r rá r r q tr t s s r r s ét s t r t 2 q s r ó r r r t r sí r s t té 2 r q tr s t 1 tr r q s ó ést t 1 tr r q r s rs t 1 étr r s r s str t r r st r t

P Ñ P q t 1 tr r 1 tr 1 tr t r2 s s á r s á r s t só s s s r t r q r s t s r t r 2 r r r 3 r t s s r 1 tr r s r r á r t r s ét s r s st r r s r r t s s tr t r s t s étr

P P P q t Pr t r 1 tr st q t s r r ó r ó r r r s t ó s r s r r r ó r t q r s s s s ó r 2 t r s s t r tá r r ó s q r r r r t r r

P Ñ r t r r r P s r t r r s r t t r rt s st t s r r t 1t q r r s t st r r r ó t 1t s s r s r r rr 2 s s r s s r r r r ó t 1t r s t s s r ó s r

P P r s t r rr s s ó r t r stá r r s s s 2 r s 1 s q r st s s s s s rt s t s r r 2 q s t 3 s r s rr t s r r 3 í str ó s á s s r s r ó rt r ó ó str r s s s tér s r s s s t r ó r str ó s r r t r r r s t s s s rí r r s t s

P Ñ s t 1 ó tr s s r r r á s tr ést s r P q t s r s q t s stá r rr t s r ó 2 s t rá s 1 s r 1 s r s r r ó s t r s 2 tr s r s tr s s r 2 s r

P r 1 s r r t s r r ó s t s q s rá r t s r r ó s s r t r q 2 s r r s r r s r t r s t r r s r t r s r t r s á s 2 s s q s t r s t s r r s r t r P r t r q r t r r s á s s r t r r q s r ú t r r r 3q r r ú t r r r r r ú t r r r

P Ñ r s r r q P r r r P r r r r s r r r s r r s s á s r s r r r r P r r r

P P r á s r r r t t s r t s P r r r r r P r r s r s r s s s r r r s á s ést s é r r 1 r 2 t t só s t 3 r st t t s s s s tr s r ó tr s s t s r s

P Ñ P q t P r r r r P r r r st q t s t 3 s t s P r r r r r r 3 r r r s t r 1 1 st s s r r t á s r s s s s q s rá t ó r s rt t r r tr r st t P r P r r s 3 s r r r s r ú r s s r s r s s s s r s s 3 s t P r r r stá t 3 r t s str r s t s q s tr t

P P r P r P r t 2 r P r t t s 3 r

P Ñ r P r P r r t 2 r t 3 r t 3 s r r s q s t r r P r r

P P P q t 1 tr r r 1 tr r r s r s r t r s s 2 t r s rt str r s t s t s 2 tr í t s r r ó s r r ó s r s s r s rr t s r r 3 2 s s s r r r str r r s q r r s t t r í 2 r í s rr t s r r 3 s r r r r r r s rs t s 1 étr s

P Ñ s s s r s r rr str t r ár r r r q s r s r t s s r s r 2 r r s s rr t s r r 3 r r r r r s t ó st 2 s r s r 1 r st r r s t ó r r t s t s t s t s 2 tr í t s P r á s φ 2 θ s r r t r s r a = ax,ay = sin(φ),cos(φ) b = bx,by = sin(φ+θ),cos(φ+θ) s s s r s r t s s r r ó r P = α a+β b P = px,py s q r t 2 α β ú r s r s s s st s r r ax = sin(φ) 0 t r s s s t s r s β = py ay ax px by ay ax bx α = px ax bx py ay ax px ax by ay ax bx s r t r ó by ay ax bx = 0 by = ay ax bx by bx = ay ax cot(φ+θ) = cot(φ) rí s q θ = 0 s r s s r < 2π rí s ó s st st r q s t r s s rí s

P P s P rt r ax = sin(φ) = 0 β = px bx α = y by bx px ay s ax = sin(φ) = 0 φ = 0 φ = π r t t ay = cos(φ) = 1 ay = cos(φ) = 1 r α t r rs r 2 s bx = sin(φ+θ) = 0 r 3 t t r r t s q by = sin(φ+θ) = 1 ó by = sin(φ+θ) = 1 rí q s t r s s s 2 r t t t r ó s st s r s φ 2 θ s r s α 2 β s ás r tr ó st s r s 2 t s r t r ést t s t r r q s s r t r s r 2 r 2 r r s t q r s t r s r r rs r str t r ár r r 2 r r r s r r ó s s q s

P Ñ r r ó s s

P P P t r P t r r s t q r r s t t r t s s s 2 s t s r r s t ó t 3 r ó s r r r s s s r P t r P q t 1 tr r t r r 1 tr r t r s q t q rt t r s t s t s tr str 1 étr 1 tr r t 1 tr r t r rt t r ó r s r t q s t ét s r q s r t r q q r ó t ñ r 2 r ó r t q tr t r r r s r r r s t ó s ó 2 t s r t s s r s s r t t é s r t s s ó t t s s ó q s t r r ó tr t st t s sí s t r t r r s ó s r t s r t s ó s s 1 3 2 s r t t s ó 2

P Ñ r 1 tr r t r

ít t s r ó s r r t 1 1 t r r t s s s 2 tr s r 1 s t ést s s t t t s r r ó r r t t r r á1 r s s t s r s s r s r r t s s 2 1 r s r st r é t r t r t rá s r s r ú s r t s r s rá r s s r s r t s s étr 2 s r s s r s s r 3 rá tr s r s s rá s á s q t t r t 3 r s t s ést r s r r s s P q ñ s s s s r s s 2 r s t 3 rá rr t r t r r r t 2 t r t 3 s t 3 rá q 1 t t t s 2 t r s r s r ú t r s s r s r s s 2

Pr s P P Ó P rs t s étr s s s t t s s r P rs t s s s t t s s r P rs t s s s t t s s r

P P rs t s s s t t s s r s t s 3 r s t s ést r s q s P q ñ r r t r 2 r r s r r t r 2 r r s r r r t r 2 r r s 2 r r r t r 2 r r Pr s P rs t s étr s s s t t s s r P rs t s s s t t s s r

P P Ó P rs t s s s t t s s r P rs t s s s t t s s r s t s 3 r s t s ést r s q s P q ñ r r t r 2 r r s r r t r 2 r r s r r r t r 2 r r s 2 r r r t r 2 r r á s s s r s t s r s t s st s r s s q t stá ás s s q ñ s 2 q s r s r 2 r r t r s t s s s s r t 2 q s t r s r s r s t st s

r s t t r s

P P Ó

ít s s 2 r t r r t r 3 s r t 2 r t s r s t r r t t r s rr r s rr t r s t 3 s ñ r t t t r r r t 3 r t t s q ést t 3 r rí r t t t t 2 r r t s s t r r s r r 1 ó tr s 2 st r r s r ás r t ó s s r r ó s r s t s t r s rr t r r r ó ést s r rí st t r t t s r r á s s s t r r r 2 r r r s t s s s r rí á r ó s s r ó rá s r r r t r r s ó s s ár s 2 t r s t s r ó t r t í r s t s r ó t ó ést s r r r t s s r s str r s st r q r s s r ó st s t r r s ó st r 2 t t é t 3 r r rá t r s t s á s s t r 2 á r str r r ó q t s rr s t át t s st t t t s r r s r s s s r s 2 r s s r tr r r t t r s t ñ q ñ s r s s t s s r q s t s ést tr s 3 r 2 q t r s 1 étr s r s t 1t r t r t s t s s str t r

P

r í r Pr 2 t t r r tt r r r t t r Pr 2 s r s t r r tt s r Pr 2 r Pr 2 t r r tt s r s s s 7 Pr 2 r 2 t t t t t r r r 2 r tt r r 2 r r ss t t t s r r r t s t r t r r r s t r s s r tt s t r r r s t t r s s r tt t t t str s t r s s r tt s s str2 str é1 t r s s r tt s s s t r t 1 t r t r tt 1 r t r t r t r 2 r2 r ss r tt t t s r t rt s t s r t r t r s r P r t P tr t s t r st t r tt st t r t r st t r t rt tr r tr s tr s tr s P 2 r r t t t st s t r r tt 1 r ts s r t s st t st s t st s st t r r tt r st s s st t r t t r tt t t r 1 s

t r ts r t r r tt r P t s t r r tt 1 t t t r1 t r r r tt r1 r t r t 1 r s t r s t r r s r tt r s 1 r 1 r st r 1 st t r sst r tt r s 1 r 1 t 1 r r s t r r s r r tt r s 1 r 1 t t P rt 1 t r r r tt s t t t r2 r s r tt r2 r s t r tt t t

é str ó st s ó s rá tr ó s t t tr s r r t ó r s s rr t r r ó s r s r s ás r r q s t s s q r r s t r s t r í st s q t r s r s t r s 2 t ñ s r t s s s t r ás tr s r t 1t r s s t r s á s q s s t s s q t s 3 s s s r s r ú t r 2 s t r s r ú t r q t s 3 s r q s r s r ú t r 2 s t r s r ú t r q t s 3 s 3q r q s r s r ú t r 2 s t r s r ú t r s s q r ú ás tr s r t r í r t r r q 3 s q é s ó t r í s q r r s t r í

ó t t P Ó P r ú t s t s r s q t ú t t q 1t s 1 tr r t st s r r s r r t q s s 2 t s rt r 1 1 tr 1 tr r t r 1 tr r t rt r 1 ss t 1t s 1 tr r t 4 r s r r r s r r t r s r r r r t sp r r s r q t st t r q t ss t t 4 s r s t 1 s t 2 s 1P t r q t tr tr t tr t tr s s r 1 s s r 2 s s 1 t2 1 s s 1 t2 2 s r s r r s 6 rr t t 4 s 1 1 s 1 6 t s t tr tr tr 4 t 4 2 6 s 1 s r ss 4 2 6 s 4 2 6 6 rr t r r 4 t r s r r 4 t sp r 6 r r s 1 2s stpr ss P 4 t r s tr 6 1 2s st s P 4 t r s s s t r s r s 6 t r s 4 r s 6 6

P t t r s 4 r t 1P t 1P t r 2 r 1P t 1P t r r 1P t 1P t r r 1 s r ss 4 r 1P t 1 s 1 1 1 s 2 2 t t r 2 r 1 s t2 1 t s s s t2 2 t s s 6 6 t s t s r s 4 4 r r tr s r 4 t sp r 6 s 4 t sp r 6 6 6 6 st t t str ó s 3 r st ó r rt s rt r 1 1 tr 1 tr r t r 1 tr r t rt r 1 q í st s rt st rt ó t s s 1 tr s r t q t s s r s t s t s t 1 ss t 1t s 1 tr r t 4 st r 1 tr r t q í st s 1t t 1 tr s r t r r t 3 r s s é t s r s r r r s r r t r s r r r r t sp r r s r q t st t r q t ss t t 4 s r s t 1 s t 2

P Ó s 1P t r q t tr tr t tr t tr s s r 1 s s r 2 s s 1 t2 1 s s 1 t2 2 s r s r r s 6 st r ó 3 ó r s r ó r s r st t s rt t r t s r str t r 1 tr r t t é st s r s s t r 2 t 1 r ú t st s r s ís q t é stá t s 1 ú ó q sté t s s r t 2 q ést tr t s s rt t r t r q t r r r r s r r r r r t str ó í t s s r rr t t 4 s 1 1 s 1 6 t s t tr tr tr 4 t 4 2 6 s 1 s r ss 4 2 6 s 4 2 6 6 st ó t t q í st s r ó s r t s r s r ét t 1 tr r t q st stá s st t t r s s rt r st t st s á r s s 2 r r s q s stá r áq st s s rr t r r 4 t r s r r 4 t sp r 6 r r s 1 2s stpr ss P 4 t r s tr 6 1 2s st s P 4 t r s s s t r s r s 6 t r s 4 r s 6 6 t t r s 4 r t 1P t 1P t r 2 r 1P t 1P t

P r r 1P t 1P t r r 1 s r ss 4 r 1P t 1 s 1 1 1 s 2 2 t t r 2 r 1 s t2 1 t s s s t2 2 t s s 6 6 t s t s r s 4 4 r r tr s r 4 t sp r 6 s 4 t sp r 6 6 6 st t t t P r ú t r s r t t t s r s r ét r r q st s st t t r s r t s r t s t ést t t s r r q st s s s t2 3 t2 ú 1 ó s ét s r t t r r á s t s r r s t t r t é t s áq st s r ó r ó s r t r s t s st s tr s r r s s r r s r rt r 1 rt st t s t st t t t t r r ss 1t s 1 4 t 4 r r s r t st t t 6 6 2 r r st r st s r rt r 1 1 tr 1 tr r rt r 1 1 tr 1 tr t r2 rt st t s P 2 r t rt r 1 ss t st t t 1t s 1 t t 4 s r r 2 s 2 t t t str r r 2 ss

P Ó s r r 2 s 2 t t t str r t r 2 ss s r t t r r ss s r r rt r r rt ss s r rs r r rs r ss rr t r t 4 1 s s rs r r t r2 1 tr t r2 1 tr t r2 t r2 t s r t r r r rt r rt r t r2 t s s tr s t r2 t s tr t P s t r2 t s r tr t P t P s tr t r2 t s q t P tr t r2 t s q t P tr t r2 t s q t P r t r 2 r 2 1 st t r q t t t t q t 1 r q t str 2 6 6 st st r s s s r s r s st r rt r 1 1 tr 1 tr t r2 rt r 1 1 tr 1 tr r rt st t s P 2 r t rt r 1 st s rt st rt ó s s s 1 tr t r2 r r ó s r t r t t q s r r t t 1 ss t st t t 1t s 1 t t 4 st r ó s

P r s s r t st t t q 1t s 1 t t 1 t t s s 1 r r s r s r r 2 s 2 t t t str r r 2 ss s r r 2 s 2 t t t str r t r 2 ss s r t t r r ss s r r rt r r rt ss s r rs r r rs r ss st r ó r s r s rt s s r s r r í 2 t r í s á s s 2 á rs r rr t r t 4 st ét r t ét r t s r r ó s r 1 s s rs r r t r2 1 tr t r2 1 tr t r2 st 3 ó t s 3 rs r 2 s r á r t s r t r r r rt r rt st s r t r q st st s t s r t r q r s s q s r t 3 r s r t s s r s r t s s r s t s r st ét t r2 t s s tr s t r2 t s tr t P s t r2 t s r tr t P t P s tr t r2 t s q t P tr t r2 t s q t P tr t r2 t s q t P st ó r r 3 t s r r r 3 st s s r r 3 r t ó r s s s r s r ú t 2 π/360 s ó ó 3q r t s t s tr s r s r r 3 s s r r s t s r t s r s t r ó r r 2 t r 2 1 st t r q t t t t q t 1 r q t

P Ó str 2 st ñ t t P r ú t r s á s r s t 1t rá tr ñ s s r 2 r s t t t q t s r t s ó rr s s s t s s q q r s s r r s ó á r t t ét str ó 2 s t 3 r r str r s r st r r s s str ó s r r s r st r s s 1 tr r r st r t t 1t 1 tr r t

P r t t s t s st s t s t rí s st r s t ér s t t r r r 3 s étr ó r t r2 t s s tr s st ó r r 3

P Ó 13 ó r t r2 t s q t P s st ó r r 3

P tr s s s