I am working on a project where I want to model a dandelion  seeds in 3D.

I have a sketch working where the seeds can be drawn and move around in 2D, but I have run into problems trying to take it into 3D.

The source files for the 2D sketch are available here:
http://www.larsjessen.dk/dandelion/dandelionSeeds2D.zip

I have made a sketch to test that the wings of the seed are drawn at the right angle in relation to the seed's stem end point, but can't seem to get it right. I have included my code below and the source can also be downloaded at
http://www.larsjessen.dk/dandelion/angleTest7.zip
which includes the vecmath.jar
I am basically trying to find the correct angles that I need to rotate to draw things correctly in relation to the seed stem vector. Do you have any suggestions?

import javax.vecmath.*;
import processing.opengl.*;

Vector3f centerToStem, stem, wing;
Point3f center, stemStart, stemEnd;
float seedLength = 30.0f;

void setup(){
 size(1024,768,OPENGL);
 center = new Point3f(width/2, height/2, 0);
 stemStart = new Point3f();
 stemEnd = new Point3f();
 centerToStem = new Vector3f();
 stem = new Vector3f();
 wing = new Vector3f();
 stemStart.z = 0;
}

void draw(){
 background(255);
 
 //update points
 stemStart.x = mouseX;
 stemStart.y = mouseY;
   
 noStroke();
 fill(255,0,0);
 ellipse(center.x,center.y,10,10);
 pushMatrix();
 translate(stemStart.x,stemStart.y,stemStart.z);
 ellipse(0,0,5,5);
 popMatrix();

 centerToStem.x = stemStart.x - center.x;
 centerToStem.y = stemStart.y - center.y;
 centerToStem.z = stemStart.z - center.z;
 
 float ratio = seedLength/centerToStem.length();
 //println(ratio);
 stemEnd.x = centerToStem.x*ratio + stemStart.x;
 stemEnd.y = centerToStem.y*ratio + stemStart.y;
 stemEnd.z = centerToStem.z*ratio + stemStart.z;
 stroke(0,0,255);
 line(stemStart.x,stemStart.y,stemStart.z,stemEnd.x,stemEnd.y,stemEnd.z);
 
 translate(stemEnd.x,stemEnd.y,stemEnd.z);
 stem.x = stemEnd.x - stemStart.x;
 stem.y = stemEnd.y - stemStart.y;
 stem.z = stemEnd.z - stemStart.z;
 
 Vector3f zxProjection = new Vector3f(stem.x,0,stem.z);
 float Zrotation = stem.angle(zxProjection);
 
 if(stem.x<0 && stem.y>0) Zrotation = PI - Zrotation;
 if(stem.x<0 && stem.y<0) Zrotation = PI + Zrotation;
 if(stem.x>0 && stem.y<0) Zrotation = -Zrotation;
 rotateZ(Zrotation);
 println(Zrotation);
 
 Vector3f xAxis = new Vector3f(1,0,0);
 float Yrotation = zxProjection.angle(xAxis);
 if(stem.x<0 && stem.z>0) Yrotation = PI - Yrotation;
 if(stem.x<0 && stem.z<0) Yrotation = PI + Yrotation;
 if(stem.x>0 && stem.z<0) Yrotation = -Yrotation;
 if(stem.z == 0) Yrotation = 0;
 println(Yrotation);
 rotateY(Yrotation);
 
 stroke(0,255,0);
 for(int i = 0; i < 10; i++){
   pushMatrix();
   rotateX(TWO_PI*i/10);
   line(0,0,10,25);
   popMatrix();
 }
}


void keyPressed(){
 if(keyCode == UP){
   stemStart.z = stemStart.z + 1;
 }
 else if(keyCode == DOWN){
   stemStart.z = stemStart.z - 1;
 }
}