en
und dkrit
an für die Hesse'sche Normalform der zur x-z-Ebene
parallelen Ebene y = 3
.
en = [0 1 0], dkrit = 3
z = exp(i*26*pi/2) = exp(i*13*pi) = exp(i*pi) = -1
u = [q ; 2 ; -2]
,
und v = [q ; 2 ; 4]
zueinander orthogonal sind.
q*q + 4 - 8 = 0 ; q = 2
A = [-4 -4 0]' B = [4 -4 0]' S = [0 0 5]' SA = A - S SB = B - S w = acosd(SA'*SB/(norm(SA)*norm(SB))) %SA = -4 -4 -5 %SB = 4 -4 -5 %w = 63.9856
xc = 3, yc = 0, r = 3 w0 = -pi/2 gh = 4/2 n = 2 t = 0:pi/200:n*2*pi; x = r*cos(t+w0) + xc; y = r*sin(t+w0) + yc; z = gh*t/(2*pi); plot3(x,y,z) hold on axis equal PSE = [3 3 3; -3 -3 -3; 0 2 4] plot3(PSE(1,:),PSE(2,:), PSE(3,:),'ko') PM = [3 3 ; 3 3 ; 1 3] plot3(PM(1,:),PM(2,:), PM(3,:),'ko') P1 = [0 0 1.5]' plot3(P1(1),P1(2), P1(3),'ro') P2 = [0 0 3.5]' plot3(P2(1),P2(2), P2(3),'ro') plot3([0 0],[0 0],[ 0 4],'r') box on view(11,22) hold off
A = [0 0 0]' , B = [4 0 0]' C = [4 -3 0]' , D = [0 -3 0]' E = [0 0 3.2]' , F = [4 0 3.2]' G = [4 -3 3.2]' , H = [0 -3 3.2]' u = G - B v = D - B N = cross(u,v) lN = norm(N) en1 = N/lN dkrit1 = en1'*B % Distanztests A H F dA = en1'*A-dkrit1 dF = en1'*F-dkrit1 dH = en1'*H-dkrit1 %u = 0 -3.0000 3.2000 %v = -4 -3 0 %N = 9.6000 -12.8000 -12.0000 %lN = 20 %en1 = 0.4800 -0.6400 -0.6000 %dkrit1 = 1.9200 %dA = -1.9200 %dF = -1.9200 %dH = -1.9200 en2 = en1 dkrit2 = en2'*A % = 0
Koi = [2 6 6 2 2; 0 0 4 4 0; 1 1 1 1 1] Trax = [1 0 -4; 0 1 0 ; 0 0 1] Mx = [-1 0 0; 0 1 0; 0 0 1] Trbx = [1 0 4; 0 1 0 ; 0 0 1] Tray = [1 0 0; 0 1 -2 ; 0 0 1] My = [1 0 0; 0 -1 0; 0 0 1] Trby = [1 0 0; 0 1 2 ; 0 0 1] Ttot = Trby * My * Tray * Trbx * Mx * Trax Kof = Ttot*Koi