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Index › Programming Questions & Help › OpenGL and 3D Libraries › Arc between two points in 3D?

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Arc between two points in 3D?? (Read 1192 times)

seltar

Arc between two points in 3D??
Dec 6^th, 2005, 8:40pm

I have to calculate an arced path for a point, from one point to another.

The points are positioned in a spherical maner, and the arc should be pointing away from (0,0,0)..
Code:


   ,'`,
  *a | '
   \ |D \
    \|   |
 C---*---'--- midpoint 
   ...\  '
   ....\ '
   .....*b

C is the crossproduct
D is the up angle.. the direction of the point, away from the center of the sphere of points

any help on this matter would be grately appreciated

I'm bored, therefore I program
http://seltar.org > seltar's special place
http://snippet.seltar.org > seltar's snippet palace
http://libraries.seltar.org > seltar's libraries

_alcys_ YaBB Newbies Offline Posts: 12	Re: Arc between two points in 3D?? Reply #1 - Dec 8^th, 2005, 5:28pm Let V1 and V2 two vectors. If V1.length=V2.length=r then alpha=Math.acos( dot(V1/r,V2/r)) (radians) arc=alpha*r.

seltar

Re: Arc between two points in 3D??
Reply #2 - Dec 9^th, 2005, 5:17pm

That wasn't very explanatory for me unfortunatly..

I need x,y,z variables ..
i have this function, which does the job, but not rotated correctly:

Code:


void drawArc(P a, P b, int step, int maxstep)
{
  float x, y, z;
  P C = a.CenterPoint(b); // the centerpoint of a and b
  C.draw(2); // draws the current centerpoint size 2
  float div = PI/maxstep; // number of steps
  for(int i = 0; i < maxstep; i++)
  {
    pushMatrix();
    translate(C.x,C.y,C.z); // so it rotates around C
    stroke(0,255,0);
    x = (cos(div*i)*(C.Distance(b)));
    y = (sin(div*i)*(C.Distance(b)));
    z = 0;
    point(x,y,z);  
    popMatrix();
  }
}

Basicly, all i need to get this to work is:
total Centerpoint (0,0,0)
Point 1
Point 2
CenterPoint

Then to get the direction of the arc i take
CenterPoint+CenterPoint/10 // since it's away from (0,0,0)

That's about where it stops for me..
I did some rotating with rotateX,Y,Z but couldn't really see what angles to calculate to get the correct rotation.

again, any pointers would be greatly appreciated

-seltar

I'm bored, therefore I program
http://seltar.org > seltar's special place
http://snippet.seltar.org > seltar's snippet palace
http://libraries.seltar.org > seltar's libraries

st33d

Re: Arc between two points in 3D??
Reply #3 - Dec 9^th, 2005, 7:27pm

I was going to pick it out of the code for you and explain it properly but I really should be cracking on with my thesis.

http://www.hardcorepawn.com/Anenome/

JohnG's anenome has a cylinder building class which uses calculations of pitch and heading to work out the trigonometry. You might want to experiment by pulling the equations out of his class and experimenting with them. They're pretty solid for modelling trajectory as I've used the cylinder builder for a project that exports .obj files.

Another idea would be to model your arc using a bezier curve. You could then track points along that arc using bezierPoint(). That would be the least headache method.

_alcys_

Re: Arc between two points in 3D??
Reply #4 - Dec 9^th, 2005, 10:20pm

please see:
http://www.alcys.com/p5/TracerArc/applet/index.html

Code:



public void tracerArc(Vecteur v1,Vecteur v2){
  Vecteur v3=new Vecteur(); 
  float angle=(float)Math.acos(v2.dot(v1)/v2.dot(v2));
  for(float t=0;t<=1;t+=0.05f){
    v3=Vecteur.comb(sin((1-t)*angle)/sin(angle),v1,sin(t*angle)/sin(angle),v2);
  line(0,0,0,v3.x,v3.y,v3.z);
  }
  
}

seltar Senior Member Offline Posts: 475	Re: Arc between two points in 3D?? Reply #5 - Dec 10^th, 2005, 12:23am Thank you both so much! I got it working using the bezierPoint(); you can see it in action here: http://seltar.wliia.org/sketch.php?pid=33 woohoo -seltar
	« Last Edit: Dec 10^th, 2005, 4:06pm by seltar » I'm bored, therefore I program http://seltar.org > seltar's special place http://snippet.seltar.org > seltar's snippet palace http://libraries.seltar.org > seltar's libraries

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