Draw an arc between two points --> (x1,y1,z1) and (x2,y2,z2)

28 次查看（过去 30 天）
Huseyin Eldem
Huseyin Eldem 2013-2-23
评论： Esther 2024-4-8
Hi. I have several points on the sphere. I want to combine these points with arc. I can draw these points with lines but I can't draw arcs Please help

请先登录，再回答此问题。

采纳的回答

Youssef Khmou
Youssef Khmou 2013-2-23
编辑：Youssef Khmou 2013-2-23
hi, you can try drawing a circle but restrict it into certain region,
I started a code, try to adjust/enhance it :
% Draw an arc between two points
p1=[-2 -2 -3];
p2=[10 15 20];
% Circle x²+y²+z²=Constant
%=> z=sqrt(Constant-x²-y²-);
Center=((p2+p1))./2;
xc=Center(1);
yc=Center(2);
zc=Center(3);
% Radius
R=norm((p2-p1))/2;
%Min=min(min(p1,p2));
%Max=max(max(p1,p2));
%x=linspace(Min,Max,20);
%y=linspace(Min,Max,20);
x=linspace(p1(1),p2(1),200);
y=linspace(p1(2),p2(2),200);
z=zc+sqrt((R^2)-((x-xc).^2)-((y-yc).^2));
figure, plot3(x,y,z), grid on, hold on
plot3(p1(1),p1(2),p1(3),'*','MarkerSize',10),
plot3(p2(1),p2(2),p2(3),'*','MarkerSize',10),
hold on, plot3(xc,yc,zc,'*','MarkerSize',10)
  1 个评论
Huseyin Eldem
Huseyin Eldem 2013-2-24
thanks so much. I can draw arc with above code. But I couldn't draw for several points (example 200 points). Please help me.

请先登录，再进行评论。

更多回答（5 个）

Huseyin Eldem
Huseyin Eldem 2013-2-24
thanks so much. I can draw arc with above code. But I couldn't draw for several points (example 200 points). Please help me.
  2 个评论
Youssef Khmou
Youssef Khmou 2013-2-24
编辑：Youssef Khmou 2013-2-24
hi Huseyin, then you didnt have to accept the answer because the problem is not solved yet , in the code above we used circle's equation, so to draw arc between 200 points, theirs coordinates must satisfy :
1<=i,j,k <=200 xi²+yi²+zi²=R²
IF the points do not satisfy the equation they dont BELONG to the arc :
ok lets try to draw an arc between 200 points : we generalize the above code :
clear, clc
p=round(10*randn(200,3));
% Circle x²+y²+z²=Constant
%=> z=sqrt(Constant-x²-y²-);
Center=((sum(p)))./2;
xc=Center(1);
yc=Center(2);
zc=Center(3);
% Radius
p2=max(p);
p1=min(p);
R=norm((p2-p1))/2;
%Min=min(min(p1,p2));
%Max=max(max(p1,p2));
%x=linspace(Min,Max,20);
%y=linspace(Min,Max,20);
x=linspace(p1(1),p2(1),200);
y=linspace(p1(2),p2(2),200);
z=zc+sqrt((R^2)-((x-xc).^2)-((y-yc).^2));
figure, plot3(x,y,z), grid on, hold on
plot3(p(:,1),p(:,2),p(:,3),'.')
As points do not satisfy the equation the line cant contain them all .
Esther
Esther 2024-4-8
Hello there can you help me with this one please y=x/(x2+1)

请先登录，再进行评论。

Huseyin Eldem
Huseyin Eldem 2013-2-24
Hi Youssef. Sorry I shouldn't accept the answers. I dont know. Coordinates of my points satisfy this equation. My points on a unit circle that radius r=1; so
xi²+yi²+zi²= 1 my points satisfy this equation exactly...
Huseyin Eldem
Huseyin Eldem 2013-2-25
didn't work :(
ChristianW
ChristianW 2013-2-25
编辑：ChristianW 2013-2-25
function test_sphere
n = 200;
THETA = rand(1,n)*2*pi;
PHI = rand(1,n)*2*pi;
R = 1.1*ones(1,n);
[x,y,z] = sph2cart(THETA,PHI,R);
acc = 10; % accuracy: ~ lines per arc
V = track_arc(x,y,z,acc);
plot3(x,y,z,'.r'); axis([-1 1 -1 1 -1 1]); axis square; hold on
plot3(V(1,:),V(2,:),V(3,:),'g')
sphere(31)
colormap([1 1 1]*0.1)
function V = track_arc(x,y,z,acc)
v1 = [x(1:end-1);y(1:end-1);z(1:end-1)]; % Vector from center to 1st point
v2 = [x(2:end);y(2:end);z(2:end)]; % Vector from center to 2nd point
r = sqrt(sum([x(1); y(1); z(1)].^2,1));
v3a = cross(cross(v1,v2),v1); % v3 lies in plane of v1 & v2 and is orthog. to v1
v3 = r*v3a./repmat(sqrt(sum(v3a.^2,1)),3,1); % Make v3 of length r
% Let t range through the inner angle between v1 and v2
tmax = atan2(sqrt(sum(cross(v1,v2).^2,1)),dot(v1,v2));
V = zeros(3,sum(round(tmax*acc))); % preallocate
k = 0; % index in v
for i = 1:length(tmax)
steps = round(tmax(i)*acc)+1; %Edited +1
k = (1:steps) + k(end);
t = linspace(0,tmax(i),steps);
V(:,k) = v1(:,i)*cos(t)+v3(:,i)*sin(t);
end
For the shortest great circle path, I modified code from Roger Stafford: http://www.mathworks.com/matlabcentral/newsreader/view_thread/277881
Huseyin Eldem
Huseyin Eldem 2013-2-25
For Example.
X Y Z R
0,355590319 -0,825650574 -0,438014446 1
0,770249008 -0,51787671 0,372182991 1
0,389588366 0,399438725 -0,8298612 1
0,850957663 -0,515047582 -0,102941943 1
-0,600938176 -0,659250233 0,451954024 1
0,155798226 0,109555927 -0,981694663 1
-0,067669882 0,373870581 -0,92500896 1
-0,945073428 -0,286727164 -0,156919565 1
0,894045248 -0,244541832 -0,375343025 1
0,939506811 -0,210695624 -0,270063522 1
0,333053848 0,507811942 0,794482326 1
0,797502364 -0,149055451 0,584613079 1
0,959983962 -0,264782366 0,09122001 1
-0,65966674 0,060786309 0,749096 1
0,145978188 -0,446595256 -0,882747441 1
0,360864688 0,446890562 0,818575288 1
-0,574482024 0,307594985 0,758522069 1
0,440997581 -0,258061866 0,859607589 1
0,171881804 -0,632864183 0,754943422 1
0,948105757 -0,246657847 0,200637433 1
-0,462783426 -0,687829262 0,559215887 1
0,232416051 0,053043441 -0,971168972 1
0,569384383 -0,79277486 0,217507347 1
0,502037406 -0,221031767 0,836124034 1
-0,127461455 -0,265374445 -0,955682992 1
0,003090819 -0,06350426 -0,997976781 1
-0,042343557 -0,980702139 0,190867329 1
-0,266574407 0,214318097 0,939683904 1
-0,405592374 -0,600682924 0,68896651 1
0,455800865 0,843943692 0,282850874 1
-0,260645438 -0,919667152 -0,29372825 1
0,719080503 0,145773573 0,679465448 1
-0,15964546 0,934723257 -0,317499229 1
0,754889146 0,225353585 -0,615920562 1
0,525811885 0,367732329 0,767003778 1
0,160574483 -0,322840865 0,932732336 1
-0,272763785 -0,755078476 0,596201655 1
-0,344671309 0,768513045 0,539063437 1
0,924612456 -0,29899926 0,235989935 1
0,976372458 0,214679929 -0,024685022 1
-0,246017293 0,099657412 0,964128566 1
-0,540166724 0,497386991 0,678841728 1
0,056963988 -0,582424454 -0,810886465 1
0,025685475 -0,087997291 0,995789502 1
0,085630278 0,204446505 -0,975125162 1
-0,747873978 0,04816384 -0,662091201 1
-0,941518833 0,335055515 0,035778327 1
-0,588009865 -0,771110351 -0,244199151 1
-0,171307305 -0,656312797 0,734783859 1
0,029197332 -0,991225023 0,128920402 1
-0,01883528 0,114157646 -0,99328408 1
-0,422855825 -0,89427415 -0,146515173 1
-0,560336444 -0,825603151 -0,066351389 1
0,347095121 0,567301365 0,74678922 1
0,732819277 0,679529154 0,034871695 1
-0,924956632 0,009507931 -0,379953718 1
0,818868822 -0,211654566 -0,533531814 1
-0,509153711 0,79801628 0,322385663 1
-0,786387246 -0,466855572 0,404525617 1
0,006183017 0,03723684 -0,99928734 1
0,000941658 -0,118278835 0,992979975 1
-0,011298248 0,352800191 -0,935630469 1
-0,26887209 -0,010068385 -0,963123267 1
-0,187912764 -0,567120412 -0,801912234 1
0,236235372 -0,193183166 0,952298857 1
0,709133615 -0,185443709 0,680250063 1
-0,831217773 -0,254090558 0,494484582 1
0,544092217 0,64624014 -0,535104981 1
0,24598342 0,335428005 0,909384523 1
-0,036219871 0,767194913 -0,640390573 1
0,177617534 -0,2771121 0,944277976 1
-0,023824448 0,885265118 -0,464476121 1
0,39295407 -0,919375947 0,018302096 1
0,026018937 0,639187245 -0,768610877 1
0,70454379 -0,335523451 -0,625333561 1
-0,175064729 0,24100762 -0,954603409 1
0,110644762 0,317270008 -0,941858524 1
-0,005906513 0,867305668 0,497740887 1
-0,605050212 -0,540523029 -0,584593103 1
-0,574024499 0,097254016 0,813042146 1
-0,057114923 0,076912538 0,995400596 1
0,350214448 -0,629254956 -0,693821332 1
-0,859896171 -0,510468971 -7,05E-05 1
-0,949699335 -0,306753661 0,063034636 1
0,255855389 -0,146590738 -0,955536067 1
-0,210116171 0,917264804 -0,338343721 1
0,042170011 -0,931496233 -0,361298294 1
0,010012473 -0,427246634 -0,904079678 1
-0,419341879 0,391583399 -0,819032862 1
-0,884248083 -0,401406601 -0,238700793 1
0,482980446 0,249365339 0,839372871 1
0,645445957 0,227576549 0,729114827 1
-0,342513349 -0,067118485 -0,937112434 1
0,016394353 -0,088454263 0,995945314 1
0,914807638 -0,402642275 0,031720402 1
0,344834644 0,366778212 0,864038663 1
-0,060766006 -0,028047621 -0,997757898 1
-0,770466341 0,150033806 -0,619573624 1
0,997203967 0,074713142 -0,00148165 1
-0,518330052 0,850356862 0,090703715 1
0,09760858 0,158571362 0,98251091 1
0,230996571 -0,808646216 -0,541047023 1
-0,04986827 0,123196615 0,991128523 1
-0,219005396 -0,039689194 0,974916101 1
0,50435989 0,860814842 -0,067962558 1
-0,23987377 -0,178884326 0,954180786 1
-0,044021151 0,538933851 -0,84119703 1
-0,307417731 -0,446768767 -0,840173796 1
-0,285347906 -0,710442163 -0,643310583 1
-0,0052681 -0,453583217 0,891198358 1
-0,834902034 0,268138484 -0,480666566 1
0,863013427 0,501795849 -0,058384514 1
0,01116895 0,084062236 -0,99639791 1
0,763373354 -0,46228893 -0,451165233 1
0,337864258 0,479949869 -0,809626992 1
0,453736216 -0,879319521 0,144639646 1
-0,949297751 -0,233227457 0,210804963 1
0,521503928 -0,012667887 -0,853154838 1
0,228584446 0,122274253 0,965814764 1
-0,380204133 0,143180701 0,913752759 1
0,40611889 0,321828134 0,855274283 1
0,915012486 -0,223338414 0,335964438 1
0,505091488 0,014711255 -0,86294042 1
0,090285256 -0,572121584 -0,815184314 1
0,077495522 -0,172200915 0,982008803 1
0,64484451 -0,698075264 0,311233809 1
0,859468343 0,504184664 -0,084332628 1
-0,780761524 0,568887158 0,258416031 1
-0,05460348 0,879322706 -0,473085657 1
0,28475396 -0,875101203 -0,391296647 1
-0,721371123 0,331656709 0,607970008 1
0,827061457 -0,52016068 0,213077952 1
0,02019571 0,044243655 0,998816616 1
-0,004334724 0,049856289 -0,998746995 1
0,305946474 0,397194017 0,865236192 1
0,214945282 0,247132782 0,944840682 1
0,627295276 -0,673983195 0,390188787 1
-0,511400863 -0,279910149 0,812477363 1
-0,950828379 -0,308019772 0,032391574 1
0,536820407 0,691658988 0,483147696 1
0,09129101 -0,120746884 -0,988476677 1
-0,178346176 -0,171865417 -0,968842051 1
-0,097624767 0,132691875 0,986337808 1
-0,731017924 -0,06099772 -0,679626421 1
-0,610327582 0,432921845 0,663384442 1
0,862260792 0,445961352 0,240051658 1
0,062601617 0,98672875 -0,149824604 1
0,127850711 0,12517801 -0,983862115 1
0,390041078 0,884625999 0,255548035 1
0,003357372 0,053111085 -0,998582966 1
-0,704474707 0,403192895 0,584081225 1
0,76802631 0,24770452 -0,590574345 1
0,709635274 -0,497301854 -0,499107849 1
0,933331392 -0,337430397 -0,122610114 1
-0,811162706 0,046614058 -0,582959857 1
-0,864268997 0,058450939 -0,499622447 1
-0,277999348 0,452253041 0,847457108 1
0,316739446 -0,22996099 0,920214141 1
-0,001967682 0,002115342 -0,999995827 1
0,392078574 0,329377897 0,858943882 1
0,019316813 -0,100398127 0,994759809 1
-0,755288038 0,626919029 -0,191082471 1
0,018924462 0,362172157 -0,931919092 1
-0,709662807 0,489410543 -0,50680965 1
0,462906359 0,320814076 0,826314729 1
0,61898671 0,675751324 0,400269411 1
0,927338518 -0,353407664 0,123070294 1
0,055478113 -0,015689903 -0,99833662 1
-0,420118936 -0,21475533 0,881691685 1
0,40789635 0,160844371 -0,898748939 1
0,085779152 0,89424808 -0,439274752 1
-0,558687286 0,737724015 0,378987855 1
0,244169456 -0,508940251 0,825445999 1
0,970143405 0,094187317 0,223496135 1
0,962147125 0,266620297 0,056449338 1
0,180259116 0,323017556 0,929067441 1
-0,56901041 -0,774091835 -0,277504927 1
-0,074744441 -0,647984142 0,757977454 1
-0,560248942 -0,748588197 0,354593902 1
-0,920635191 0,293236263 -0,257766054 1
-0,68031362 -0,206996033 0,703083225 1
-0,226978839 0,757737399 0,611812586 1
-0,031109524 -0,932583255 -0,359611832 1
0,277007889 0,686439582 0,672359524 1
-0,20279312 -0,483350164 -0,851614684 1
0,022086194 0,049755942 -0,998517174 1
-0,507906321 0,551291456 -0,661897953 1
-0,621316542 -0,626164943 0,471044817 1
0,182238677 -0,94796679 -0,261051777 1
0,289913195 0,16206205 0,943231801 1
0,262020733 -0,124534583 -0,956993351 1
0,059377576 -0,364328891 -0,929375469 1
-0,5398891 0,044908882 -0,8405373 1
-0,672004815 0,286508316 0,68287811 1
-0,903419216 0,313858849 -0,292106731 1
-0,024500295 0,06628335 0,997500002 1
-0,971170262 -0,0519697 0,232653118 1
-0,829947015 -0,056256514 0,554998339 1
0,200283695 -0,442631879 0,874050034 1
0,148034944 -0,511561538 0,846398516 1
  1 个评论
Youssef Khmou
Youssef Khmou 2013-2-25
hi, they numbers need more processing to convert them into Mat format, anyway try this with numbers :
X=reshape(x,20,10);
Y=reshape(y,20,10);
Z=reshape(z,20,10);
figure, surf(X,Y,Z), shading interp
If they satisfy the equation, them they must give a partial Sphere
...

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Surface and Mesh Plots 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by