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

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

Answer 1

[Youssef Khmou]

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)

[Huseyin Eldem]

thanks so much. I can draw arc with above code. But I couldn't draw for several points (example 200 points). Please help me.

Answer 2

[Huseyin Eldem]

thanks so much. I can draw arc with above code. But I couldn't draw for several points (example 200 points). Please help me.

[Youssef Khmou]

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]

Hello there can you help me with this one please y=x/(x2+1)

Answer 3

[Huseyin Eldem]

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...

[Youssef Khmou]

ok good, did you try the last code? it must work very well then .

Answer 4

[Huseyin Eldem]

didn't work :(

[Youssef Khmou]

ok can you upload the 200 points ? or copy and paste them here ?

Answer 5

[ChristianW]

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]

Thanks Christian. It works.

Answer 6

[Huseyin Eldem]

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
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0,70454379  -0,335523451  -0,625333561    1
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0,110644762  0,317270008  -0,941858524    1
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-0,574024499  0,097254016  0,813042146    1
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0,350214448  -0,629254956  -0,693821332    1
-0,859896171  -0,510468971  -7,05E-05    1
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0,763373354  -0,46228893  -0,451165233    1
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0,453736216  -0,879319521  0,144639646    1
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0,521503928  -0,012667887  -0,853154838    1
0,228584446  0,122274253  0,965814764    1
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0,40611889  0,321828134  0,855274283    1
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0,244169456  -0,508940251  0,825445999    1
0,970143405  0,094187317  0,223496135    1
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0,148034944  -0,511561538  0,846398516    1

[Youssef Khmou]

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

...