Functions
	figure (1)
id	bod1x ()
1/2	tec1 ()
1/2	bod1y ()
	if (imag(Ay(1))==0) reseni(1)
end	if (imag(Ay(2))==0) reseni(2)
end	if (imag(Ay(3))==0) reseni(3)
end	if (imag(Ay(4))==0) reseni(4)
	plot (bod1(1), bod1(2),'rx')
	plot (bod2(1), bod2(2),'rx') axis([0 11.5 0 7]) xlabel('x')
	ylabel ('y')
	title ('UPRAVENY kubicky spline z Matlabu')
	if (reseni(1)==1)%1.polynom X1
end	if (reseni(2)==1)%2.polynom X2
end	if (reseni(3)==1)%3.polynom X3
end	if (reseni(4)==1)%4.polynom X4
end	Y2 (i))
end	Y3 (i))
end	Y4 (i))
Variables
clear	all
	clc
pocita se segment trajektorie s nasledujicim	zadanim
pocita se segment trajektorie s nasledujicim tecen a krivosti	bod1 = [2,2]'
	bod2 = [8,6]'
	tecna1 = [1,0.02]'
	tecna2 = [1,0.01]'
	cur1 = 0.1
	Ax = -20
	bod1x = bod1(1)
	bod1y = bod1(2)
	bod2x = bod2(1)
	bod2y = bod2(2)
	tec1 = tecna1(2)/tecna1(1)
	tec2 = tecna2(2)/tecna2(1)
	Dy = [bod1y
	Cx = [1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)+1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2)
	Cy = [tec1(1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)+1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2))^(1/2))
	Bx = [bod2x-Ax-1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)-1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2)-bod1x
	By = [-tec2Ax-2tec2bod2x+tec2(1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)+1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2))^(1/2))+2tec2bod1x+3bod2y-2tec1(1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)+1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2))^(1/2))-3bod1y
	Ay = [-2bod2y+tec2Ax+2tec2bod2x-tec2(1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)+1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2))^(1/2))-2tec2bod1x+tec1(1/cur1((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)+1/cur1(-(2((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2tec1-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec2^2-((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2)tec1^2-6cur1tec2bod2y+2cur1tec1^2bod1x+2cur1tec1^2Ax+6cur1bod2ytec1+2cur1tec2tec1bod1x+2cur1tec2^2Ax-6cur1tec1bod1y+4cur1tec2^2bod2x-4cur1tec2^2bod1x+6cur1tec2bod1y-2cur1tec1^2bod2x-4cur1tec2Axtec1-2cur1tec2bod2xtec1)/(3tec1^2+3tec1^4+1+tec1^6)/((-2tec2tec1+tec2^2+tec1^2)/(3tec1^2+3tec1^4+1+tec1^6))^(1/2))^(1/2))+2*bod1y
	Dx
end vykresleni	splinu
hold	on
	t = 0:0.005:1
	Y1 = Ay(1)t.^3 + By(1)t.^2 + Cy(1)*t + Dy(1)
	Y2 = Ay(2)t.^3 + By(2)t.^2 + Cy(2)*t + Dy(2)
	Y3 = Ay(3)t.^3 + By(3)t.^2 + Cy(3)*t + Dy(3)
	Y4 = Ay(4)t.^3 + By(4)t.^2 + Cy(4)*t + Dy(4)
end for	i

Function Documentation

id bod1x ( ) [virtual]

1/2 bod1y ( ) [virtual]

figure ( 1 )

end if ( imag(Ay(4)) = =0 )

end if ( reseni(4) = =1 )

end if ( reseni(3) = =1 )

end if ( reseni(2) = =1 )

if ( imag(Ay(1)) = =0 )

end if ( imag(Ay(2)) = =0 )

if ( reseni(1) = =1 )

end if ( imag(Ay(3)) = =0 )

plot	(	bod1(1)	,
		bod1(2)	,
		'rx'
	)

plot	(	bod2(1)	,
		bod2(2)	,
		'rx'
	)

1/2 tec1 ( ) [virtual]

title ( 'UPRAVENY kubicky spline z Matlabu' )

end Y2 ( i )

end Y3 ( i )

end Y4 ( i )

ylabel ( 'y' )

Variable Documentation

clear all

Ax = -20

Ay = [-2*bod2y+tec2*Ax+2*tec2*bod2x-tec2*(1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)+1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2))-2*tec2*bod1x+tec1*(1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)+1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2))+2*bod1y

pocita se segment trajektorie s nasledujicim tecen a krivosti bod1 = [2,2]'

bod1x = bod1(1)

bod1y = bod1(2)

bod2 = [8,6]'

bod2x = bod2(1)

bod2y = bod2(2)

Bx = [bod2x-Ax-1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)-1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2)-bod1x

By = [-tec2*Ax-2*tec2*bod2x+tec2*(1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)+1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2))+2*tec2*bod1x+3*bod2y-2*tec1*(1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)+1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2))-3*bod1y

clc

cur1 = 0.1

Cx = [1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)+1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2)

Cy = [tec1*(1/cur1*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)+1/cur1*(-(2*((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2*tec1-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec2^2-((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2)*tec1^2-6*cur1*tec2*bod2y+2*cur1*tec1^2*bod1x+2*cur1*tec1^2*Ax+6*cur1*bod2y*tec1+2*cur1*tec2*tec1*bod1x+2*cur1*tec2^2*Ax-6*cur1*tec1*bod1y+4*cur1*tec2^2*bod2x-4*cur1*tec2^2*bod1x+6*cur1*tec2*bod1y-2*cur1*tec1^2*bod2x-4*cur1*tec2*Ax*tec1-2*cur1*tec2*bod2x*tec1)/(3*tec1^2+3*tec1^4+1+tec1^6)/((-2*tec2*tec1+tec2^2+tec1^2)/(3*tec1^2+3*tec1^4+1+tec1^6))^(1/2))^(1/2))

Dx

Initial value:

 subs(Dx)
Dy = subs(Dy)
Cx = subs(Cx)
Cy = subs(Cy)
Bx = subs(Bx)
By = subs(By)
Ay = subs(Ay)     
 
%vyber jednoho z reseni
reseni = [0,0,0,0]

Dy = [bod1y

end for i

Initial value:

1:size(t,2)-1
  if(reseni(1)==1)
    plot(X1(i),Y1(i))

hold on

end vykresleni splinu

t = 0:0.005:1

tec1 = tecna1(2)/tecna1(1)

tec2 = tecna2(2)/tecna2(1)

tecna1 = [1,0.02]'

tecna2 = [1,0.01]'

Y1 = Ay(1)*t.^3 + By(1)*t.^2 + Cy(1)*t + Dy(1)

Y2 = Ay(2)*t.^3 + By(2)*t.^2 + Cy(2)*t + Dy(2)

Y3 = Ay(3)*t.^3 + By(3)*t.^2 + Cy(3)*t + Dy(3)

Y4 = Ay(4)*t.^3 + By(4)*t.^2 + Cy(4)*t + Dy(4)

pocita se segment trajektorie s nasledujicim zadanim

Priklad3.m File Reference

Functions

Variables

Function Documentation

Variable Documentation