Datorgrafikas un attēlu apstrādes pamati

4. Matematiskie aprēķīni
Dots: α=120; {(x1,y1) = (8,8); (x2,y2) = (7,-6); (x3,y3) = (-13,-7); (x4,y4) = (-9,8)};
Formulas: X(new)=x*cos α - y*sin α, Y(new)=x*sin α + y*cos α;
Risinājums: cos(120)=(-1/2) ; sin(120)= (√3/2) ;
X1=8*(-0.5)-8*(√3/2)=-4-4*1.73=-10.9=-11
Y1=8*(√3/2)+ 8*(-0.5)=6.9-4=2.9=3
X2=7*(-0.5)-(-6)*(√3/2)=-3.5+5.2=1.7=2
Y2=7*(√3/2)+ (-6)*(-0.5)=6+3=9
X3=(-13)*(-0.5)-(-7)*(√3/2)=6.5+6=12.5=13
Y3=(-13)*(√3/2)+ (-7)*(-0.5)=-11.2+3.5=-7.7=-8
X4=(-9)*(-0.5)-8*(√3/2)=4.5-6.9=-2.4=-2
Y4=(-9)*(√3/2)+8*(-0.5)=-7.8-4=-11.8=-12
Atbilde: (x1,y1) = (-11,3); (x2,y2) = (2,9); (x3,y3) = (13,-8); (x4,y4) = (-2,-12);
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