proyector 3d de gir horitzontal

k·<( cos(s)(c_{1}+(-1)a_{1})+sin(s)(c_{3}+(-1)a_{3}) ),(c_{2}+(-1)a_{2}),...
...( (-1)sin(s)(c_{1}+(-1)a_{1})+cos(s)(c_{3}+(-1)a_{3}) )>=...
...i·<cos(s),0,(-1)sin(s)>+j·<0,1,0>+<sin(s),0,cos(s)>


k=( 1/(c_{3}+(-1)a_{3}) )
i=( (c_{1}+(-1)a_{1}) )/(c_{3}+(-1)a_{3})
j=( (c_{2}+(-1)a_{2}) )/(c_{3}+(-1)a_{3})


si s=0 ==>...
...k·<(c_{1}+(-1)a_{1}),(c_{2}+(-1)a_{2}),(c_{3}+(-1)a_{3})>=...
...i·<1,0,0>+j·<0,1,0>+<0,0,1>
...[ i·<x,0,0>+j·<0,y,0>+<0,0,z> ]


k=( 1/(c_{3}+(-1)a_{3}) )
i=( (c_{1}+(-1)a_{1}) )/(c_{3}+(-1)a_{3})
j=( (c_{2}+(-1)a_{2}) )/(c_{3}+(-1)a_{3})


si s=(pi/2) ==>...
...k·<(c_{3}+(-1)a_{3}),(c_{2}+(-1)a_{2}),(-1)(c_{1}+(-1)a_{1})>=...
...i·<1,0,0>+j·<0,1,0>+<0,0,1>
...[ i·<z,0,0>+j·<0,y,0>+<0,0,(-x)> ]


k=( (-1)/(c_{1}+(-1)a_{1}) )
i=( (-1)(c_{3}+(-1)a_{3}) )/(c_{1}+(-1)a_{1})
j=( (-1)(c_{2}+(-1)a_{2}) )/(c_{1}+(-1)a_{1})


si s=(-1)(pi/2) ==>...
...k·<(-1)(c_{3}+(-1)a_{3}),(c_{2}+(-1)a_{2}),(c_{1}+(-1)a_{1})>=...
...i·<1,0,0>+j·<0,1,0>+<0,0,1>
...[ i·<(-z),0,0>+j·<0,y,0>+<0,0,x> ]


k=( 1/(c_{1}+(-1)a_{1}) )
i=( (-1)(c_{3}+(-1)a_{3}) )/(c_{1}+(-1)a_{1})
j=( (c_{2}+(-1)a_{2}) )/(c_{1}+(-1)a_{1})










k·<f(s),g(s),d_{s}[f(s)]>=...
...i·<1,0,0>+j·<0,1,0>+<0,0,1>


f(s) = cos(s)(c_{1}+(-1)a_{1})+sin(s)(c_{3}+(-1)a_{3})
d_{s}[f(s)] = (-1)sin(s)(c_{1}+(-1)a_{1})+cos(s)(c_{3}+(-1)a_{3})






si s=(pi/4) ==>...
...k·<(2^{(1/2)}/2)( (c_{1}+(-1)a_{1})+(c_{3}+(-1)a_{3}) ),...
...( (2^{(1/2)}/2)+(2^{(1/2)}/2) )(c_{2}+(-1)a_{2}),...
...(2^{(1/2)}/2)( (c_{3}+(-1)a_{3})+(-1)(c_{1}+(-1)a_{1}) )>=...
...i·<1,0,0>+j·<0,1,0>+<0,0,1>
...[ i·<(2^{(1/2)}/2)x+(2^{(1/2)}/2)z,0,0>+...
...j·<0,(2^{(1/2)}/2)y+(2^{(1/2)}/2)y,0>+...
...<0,0,(2^{(1/2)}/2)z+(2^{(1/2)}/2)(-x)> ]


k=( 1/( (c_{3}+(-1)a_{3})+(-1)(c_{1}+(-1)a_{1}) ) )
i=( ( (c_{1}+(-1)a_{1})+(c_{3}+(-1)a_{3}) ) )/( (c_{3}+(-1)a_{3})+(-1)(c_{1}+(-1)a_{1}) )
j=( 2(c_{2}+(-1)a_{2}) )/( (c_{3}+(-1)a_{3})+(-1)(c_{1}+(-1)a_{1}) )


si s=(pi/6) ==>...
...k·<( (1/2)(c_{1}+(-1)a_{1})+(3^{(1/2)}/2)·(c_{3}+(-1)a_{3}) ),...
...( (1/2)+(3^{(1/2)}/2) )(c_{2}+(-1)a_{2}),...
...( (1/2)(c_{3}+(-1)a_{3})+(-1)(3^{(1/2)}/2)·(c_{1}+(-1)a_{1}) )>=...
...i·<1,0,0>+j·<0,1,0>+<0,0,1>
...[ i·<(1/2)x+(3^{(1/2)}/2)z,0,0>+...
...j·<0,(1/2)y+(3^{(1/2)}/2)y,0>+...
...<0,0,(1/2)z+(3^{(1/2)}/2)(-x)> ]


k=( 1/( (1/2)(c_{3}+(-1)a_{3})+(-1)(3^{(1/2)}/2)·(c_{1}+(-1)a_{1}) )
i=( ( (1/2)(c_{1}+(-1)a_{1})+(3^{(1/2)}/2)(c_{3}+(-1)a_{3}) ) )·...
(1/( (1/2)(c_{3}+(-1)a_{3})+(-1)(3^{(1/2)}/2)·(c_{1}+(-1)a_{1}) ) )
j=( ((1/2)+(3^{(1/2)}/2))(c_{2}+(-1)a_{2}) )/( (1/2)(c_{3}+(-1)a_{3})+(-1)(3^{(1/2)}/2)·(c_{1}+(-1)a_{1}) )




En ser un gir hi ha una component ortogonal a les y.