SURF Surface-Plot
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Hi there,
I plotted something in a regualr 3D plot. Now my task is to code a surface-plot of the exact same thing.
So that the it's not just connected points, as in my actual plot, but a whole surface around the lines.
I hope that somebody can understand my problem and help me with it.
n = 3;
n1 = n-1;
a = 20;
b = 10;
P = [0 b;0 0;a 0];
T = 15;
H = 8;
R = 2;
h = 6;
syms t s(t)
B = bernsteinMatrix(n1,t);
bezierCurve = B*P;
s(t) = int(norm(diff(bezierCurve)),0,t);
snum = linspace(0,s(1),T);
for i = 1:T
tnum(i) = vpasolve(snum(i)==s(t),t);
end
px = double(subs(bezierCurve(:,1),t,tnum)).';
py = zeros(T,1);
pz = double(subs(bezierCurve(:,2),t,tnum)).';
normalToCurve = diff(bezierCurve)*[0 1;-1 0];
normalToCurve = normalToCurve/norm(normalToCurve);
newNormalToCurve = [double(subs(normalToCurve(1),t,tnum))' double(subs(normalToCurve(2),t,tnum))'];
newNormalToCurvex = newNormalToCurve(:,1);
newNormalToCurvez = newNormalToCurve(:,2);
%%%%%%%%%%%Obere Linie
for i = 1:T
S = double(s((i-1)/(T-1)));
d = R*(1-S/double(s(1)))+(H/2)*S/double(s(1));
delta(i) = d;
end
delta = delta';
pxnew1 = px+newNormalToCurvex.*delta;
pznew1 = pz+newNormalToCurvez.*delta;
for i = 1:T
S = double(s((i-1)/(T-1)));
rhilfe = (h/2)*S/double(s(1));
r(i) = rhilfe;
end
r = r';
pynew1a = - r;
pynew1b = r;
%%%%%%%%%%Untere Linie
delta = - delta;
pxnew2 = px+newNormalToCurvex.*delta;
pznew2 = pz+newNormalToCurvez.*delta;
pynew2a = pynew1a;
pynew2b = pynew1b;
%%%%%%%%%%seitliche Linien (schwarz)
for i = 1:T
S = double(s((i-1)/(T-1)));
chilfe = R*(1-S/double(s(1)))+(h/2)*S/double(s(1));
c(i) = chilfe;
end
for i = 1:T
S = double(s((i-1)/(T-1)));
lhilfe = H/2*S/double(s(1));
l(i) = lhilfe;
end
l = l';
c = c';
pynew3 = ones(T,1).*c;
pxnew3a = px-newNormalToCurvex.*l;
pxnew3b = px+newNormalToCurvex.*l;
pznew3a = pz-newNormalToCurvez.*l;
pznew3b = pz+newNormalToCurvez.*l;
pynew3a = pynew3;
pynew3b = -pynew3;
%%%%%%%%%%%%4Ecken
%%%vorne links/rechts (magenta)
Rnewx = R*cos(pi/4);
Rnewy = R*cos(pi/4);
for i = 1:T
S = double(s((i-1)/(T-1)));
jhilfe = Rnewx*(1-S/double(s(1)))+(H/2)*S/double(s(1));
j(i) = jhilfe;
end
for i = 1:T
S = double(s((i-1)/(T-1)));
ehilfe = Rnewy*(1-S/double(s(1)))+(h/2)*S/double(s(1));
e(i) = ehilfe;
end
j = j';
e = e';
pxnew4 = px+newNormalToCurvex.*j;
pznew4 = pz+newNormalToCurvez.*j;
pynew4a = -ones(T,1).*e;
pynew4b = ones(T,1).*e;
%%%%%vorne links/recht(grün)
pxnew5 = px-newNormalToCurvex.*j;
pznew5 = pz-newNormalToCurvez.*j;
pynew5a = pynew4a;
pynew5b = pynew4b;
%%%%%%%%%%PLOTS
plot3(px,py,pz,'b-')
axis equal
axis tight
grid on
hold on
plot3(pxnew1,pynew1a,pznew1,'r-')
plot3(pxnew1,pynew1b,pznew1,'r-')
plot3(pxnew2,pynew1a,pznew2,'r-')
plot3(pxnew2,pynew1b,pznew2,'r-')
plot3(pxnew3a,pynew3a,pznew3a,'k-')
plot3(pxnew3b,pynew3a,pznew3b,'k-')
plot3(pxnew3a,pynew3b,pznew3a,'k-')
plot3(pxnew3b,pynew3b,pznew3b,'k-')
plot3(pxnew4,pynew4a,pznew4,'m-')
plot3(pxnew4,pynew4b,pznew4,'m-')
plot3(pxnew5,pynew5a,pznew5,'g-')
plot3(pxnew5,pynew5b,pznew5,'g-')
hold off
pxgesamt = [px;pxnew1; pxnew1; pxnew2; pxnew2; pxnew3a;pxnew3b;pxnew3a;pxnew3b;pxnew4; pxnew4; pxnew5; pxnew5];
pygesamt = [py;pynew1a;pynew1b;pynew2a;pynew2b;pynew3a;pynew3a;pynew3b;pynew3b;pynew4a;pynew4b;pynew5a;pynew5b];
pzgesamt = [pz;pznew1; pznew1; pznew2; pznew2; pznew3a;pznew3b;pznew3a;pznew3b;pznew4; pznew4; pznew5; pznew5];
pgesamt = [pxgesamt pygesamt pzgesamt];
surf([pxgesamt pygesamt pzgesamt]) %%%% that obviously does not work
0 个评论
采纳的回答
Star Strider
2022-11-15
Concatenate the column vectors horizontally (to create matrices) instead of vertically (to create column vectors) and it sort of works.
There are still some ptoblems. I leave the resolutions of those to you.
I also used the three column vectors with griddata to create matrices from them using interpolation. You can experiment with that as well.
I’m not certain how to resolve the inconsistiencies in creating matrices from the vectors so that the surf provides a more pleasing and representative appearance. Therea are several interpolation techniques to experiment with.
n = 3;
n1 = n-1;
a = 20;
b = 10;
P = [0 b;0 0;a 0];
T = 15;
H = 8;
R = 2;
h = 6;
syms t s(t)
B = bernsteinMatrix(n1,t);
bezierCurve = B*P;
s(t) = int(norm(diff(bezierCurve)),0,t);
snum = linspace(0,s(1),T);
for i = 1:T
tnum(i) = vpasolve(snum(i)==s(t),t);
end
px = double(subs(bezierCurve(:,1),t,tnum)).';
py = zeros(T,1);
pz = double(subs(bezierCurve(:,2),t,tnum)).';
normalToCurve = diff(bezierCurve)*[0 1;-1 0];
normalToCurve = normalToCurve/norm(normalToCurve);
newNormalToCurve = [double(subs(normalToCurve(1),t,tnum))' double(subs(normalToCurve(2),t,tnum))'];
newNormalToCurvex = newNormalToCurve(:,1);
newNormalToCurvez = newNormalToCurve(:,2);
%%%%%%%%%%%Obere Linie
for i = 1:T
S = double(s((i-1)/(T-1)));
d = R*(1-S/double(s(1)))+(H/2)*S/double(s(1));
delta(i) = d;
end
delta = delta';
pxnew1 = px+newNormalToCurvex.*delta;
pznew1 = pz+newNormalToCurvez.*delta;
for i = 1:T
S = double(s((i-1)/(T-1)));
rhilfe = (h/2)*S/double(s(1));
r(i) = rhilfe;
end
r = r';
pynew1a = - r;
pynew1b = r;
%%%%%%%%%%Untere Linie
delta = - delta;
pxnew2 = px+newNormalToCurvex.*delta;
pznew2 = pz+newNormalToCurvez.*delta;
pynew2a = pynew1a;
pynew2b = pynew1b;
%%%%%%%%%%seitliche Linien (schwarz)
for i = 1:T
S = double(s((i-1)/(T-1)));
chilfe = R*(1-S/double(s(1)))+(h/2)*S/double(s(1));
c(i) = chilfe;
end
for i = 1:T
S = double(s((i-1)/(T-1)));
lhilfe = H/2*S/double(s(1));
l(i) = lhilfe;
end
l = l';
c = c';
pynew3 = ones(T,1).*c;
pxnew3a = px-newNormalToCurvex.*l;
pxnew3b = px+newNormalToCurvex.*l;
pznew3a = pz-newNormalToCurvez.*l;
pznew3b = pz+newNormalToCurvez.*l;
pynew3a = pynew3;
pynew3b = -pynew3;
%%%%%%%%%%%%4Ecken
%%%vorne links/rechts (magenta)
Rnewx = R*cos(pi/4);
Rnewy = R*cos(pi/4);
for i = 1:T
S = double(s((i-1)/(T-1)));
jhilfe = Rnewx*(1-S/double(s(1)))+(H/2)*S/double(s(1));
j(i) = jhilfe;
end
for i = 1:T
S = double(s((i-1)/(T-1)));
ehilfe = Rnewy*(1-S/double(s(1)))+(h/2)*S/double(s(1));
e(i) = ehilfe;
end
j = j';
e = e';
pxnew4 = px+newNormalToCurvex.*j;
pznew4 = pz+newNormalToCurvez.*j;
pynew4a = -ones(T,1).*e;
pynew4b = ones(T,1).*e;
%%%%%vorne links/recht(grün)
pxnew5 = px-newNormalToCurvex.*j;
pznew5 = pz-newNormalToCurvez.*j;
pynew5a = pynew4a;
pynew5b = pynew4b;
%%%%%%%%%%PLOTS
plot3(px,py,pz,'b-')
axis equal
axis tight
grid on
hold on
plot3(pxnew1,pynew1a,pznew1,'r-')
plot3(pxnew1,pynew1b,pznew1,'r-')
plot3(pxnew2,pynew1a,pznew2,'r-')
plot3(pxnew2,pynew1b,pznew2,'r-')
plot3(pxnew3a,pynew3a,pznew3a,'k-')
plot3(pxnew3b,pynew3a,pznew3b,'k-')
plot3(pxnew3a,pynew3b,pznew3a,'k-')
plot3(pxnew3b,pynew3b,pznew3b,'k-')
plot3(pxnew4,pynew4a,pznew4,'m-')
plot3(pxnew4,pynew4b,pznew4,'m-')
plot3(pxnew5,pynew5a,pznew5,'g-')
plot3(pxnew5,pynew5b,pznew5,'g-')
hold off
% Matrices —
pxgesamt = [px, pxnew1, pxnew1, pxnew2, pxnew2, pxnew3a, pxnew3b, pxnew3a, pxnew3b, pxnew4, pxnew4, pxnew5, pxnew5];
pygesamt = [py, pynew1a, pynew1b, pynew2a, pynew2b, pynew3a, pynew3a, pynew3b, pynew3b, pynew4a, pynew4b, pynew5a, pynew5b];
pzgesamt = [pz, pznew1, pznew1, pznew2, pznew2, pznew3a, pznew3b, pznew3a, pznew3b, pznew4, pznew4, pznew5, pznew5];
% Column Vectors
pxgesamtv = [px;pxnew1; pxnew1; pxnew2; pxnew2; pxnew3a;pxnew3b;pxnew3a;pxnew3b;pxnew4; pxnew4; pxnew5; pxnew5];
pygesamtv = [py;pynew1a;pynew1b;pynew2a;pynew2b;pynew3a;pynew3a;pynew3b;pynew3b;pynew4a;pynew4b;pynew5a;pynew5b];
pzgesamtv = [pz;pznew1; pznew1; pznew2; pznew2; pznew3a;pznew3b;pznew3a;pznew3b;pznew4; pznew4; pznew5; pznew5];
% pgesamt = [pxgesamt pygesamt pzgesamt];
%
figure
surfc(pxgesamt, pygesamt, pzgesamt) %%%% that obviously does not work
colormap(turbo)
xlabel('pxgesamt')
ylabel('pygesamt')
zlabel('pzgesamt')
axis('equal')
N = numel(pxgesamtv);
N = ceil(N/5)
xv = linspace(min(pxgesamtv), max(pxgesamtv), N);
yv = linspace(min(pygesamtv), max(pygesamtv), N);
[X, Y] = ndgrid(xv, yv);
Z = griddata(pxgesamtv,pygesamtv, pzgesamtv, X, Y);
figure
surfc(X, Y, Z, 'EdgeAlpha',0.25)
grid on
colormap(turbo)
xlabel('pxgesamt')
ylabel('pygesamt')
zlabel('pzgesamt')
axis('equal')
.
4 个评论
Star Strider
2022-11-15
As always, my pleasure!
I wasn’t certain what it was supposed to look like.
.
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