在处理中渲染极地正二十面体时遇到问题 [英] Problems rendering a Polar Zonohedron in Processing

问题描述

我最近一直在研究Zonohedrons，而罗伯·贝尔做的很漂亮.我玩过免费的 Polar Zonohedron Sketchup插件，并考虑过使用

I've recently been looking into Zonohedrons and Rob Bell made beautiful ones. I had a play with the free Polar Zonohedron Sketchup Plugin and thought about playing with the geometry using Processing. So far I've open up the plugin/Ruby script and tried to port it directly, but I am not experienced with Ruby and have been using the Sketchup Ruby API reference.

代码的几何部分大部分在polar_zonohedron函数中:

The geometry part of the code is mostly in the polar_zonohedron function:

def polar_zonohedron #frequency, pitch = atan(sqrt(2)/2), len = 1.0 # frequency,pitch,length

  mo = Sketchup.active_model
  mo.start_operation "polar_zonohedron"

  prompts = ["Frequency", "Pitch in radians", "Length"]
  values = [8, "atan( sqrt(2)/2 )", 12.inch]
  results = inputbox prompts, values, "Polar Zonohedron"

  return if not results # This means that the user canceld the operation

  ents = mo.active_entities
  grp = ents.add_group
  ents = grp.entities

  grp.frequency = results[0]
  grp.pitch = eval( results[1] )
  grp.length = results[2]

  pts=[]

  #we begin by setting pts[0] to the origin
  pts[0] = Geom::Point3d.new(0,0,0)

  vector = Geom::Vector3d.new(cos(grp.pitch),0,sin(grp.pitch) ) #tilt pitch vector up the xz plane
  vector.length = grp.length

  #Using the origin as the initial generator we iterate thru each zone of the zonohedron
  #our first task is to define the four points of the base rhomb for this zone
  #at the end the pts[3] becomes our new origin for the rhomb of the next zone
  1.upto(grp.frequency-1){ |i| 
    p_rotate = Geom::Transformation.rotation( pts[0] , Geom::Vector3d.new(0,0,1), i*2*PI/grp.frequency )

    #obtain the other three points of the rhomb face
    pts[1] = pts[0].transform vector
    pts[3] = pts[1].transform( p_rotate )
    pts[2] = pts[3].transform( vector )

    #we now have the 4 points which make this zone's base rhomb
    #so we rotate around the origin frequency times making a star pattern of faces
    0.upto(grp.frequency-1){ |j| 
      f_rotate = Geom::Transformation.rotation( Geom::Point3d.new(0,0,0) , Geom::Vector3d.new(0,0,1), j*2*PI/grp.frequency )     
      ents.add_face( pts.collect{|p| p.transform(f_rotate)} )
    }

    #set the origin for the rhomb of the next zone
    pts[0] = pts[3]
  }

  mo.commit_operation
end

我已经了解了循环，但是对转换有点困惑:

I've understood the loops but am slightly confused by transforms:

pts[1] = pts[0].transform vector
pts[3] = pts[1].transform( p_rotate )
pts[2] = pts[3].transform( vector )

据我所知pts[1]是pts[0]和vector的媒介成瘾， pts[3]是pts[1]乘以p_rotate旋转矩阵. pts[2]还会加(在pts[3]和vector之间)吗?

As far as I can tell pts[1] is the vector addiction of pts[0] and vector, and pts[3] is pts[1] multiplied by the p_rotate rotation matrix. Would pts[2] also be an addition (between pts[3] and vector )?

这是到目前为止我的尝试:

Here's what my attempt looks like so far:

//a port attempt of Rob Bell's polar_zonohedron.rb script - http://zomebuilder.com/

int frequency = 3;
float pitch   = atan(sqrt(2)/2);
float length  = 24;

ArrayList<Face> faces = new ArrayList<Face>(); 

void setup(){
  size(400,400,P3D);
  strokeWeight(3);
  setupZome();
}
void setupZome(){
  faces.clear();
  PVector[] pts = new PVector[4];
  pts[0] = new PVector();

  PVector vector = new PVector(cos(pitch),0,sin(pitch));
  vector.mult(length);

  for(int i = 1 ; i < frequency; i++){
    PMatrix3D p_rotate = new PMatrix3D();
    p_rotate.rotate(i * TWO_PI / frequency,  0,0,1);
    //PVector v = new PVector();
    //p_rotate.mult(pts[0],v);
    //pts[0] = v;

    pts[1] = PVector.add(pts[0],vector);
    pts[3] = new PVector();
    p_rotate.mult(pts[1],pts[3]);
    pts[2] = PVector.add(pts[3],vector);

    for(int j = 0; j < frequency; j++){
      PMatrix3D f_rotate = new PMatrix3D();
      f_rotate.rotate(j*2*PI/frequency , 0,0,1);

      Face f = new Face();
      for(PVector pt : pts){
        PVector p = new PVector();
        f_rotate.mult(pt,p);
        f.add(p.get());
      }
      faces.add(f);
    }

    pts[0] = pts[3];
  } 
}
void draw(){
  background(255);
  lights();

  translate(width * .5, height * .5,0);
  rotateY(map(mouseX,0,width,-PI,PI));
  rotateX(map(mouseY,0,height,-PI,PI));
  drawAxes(100);
  pushMatrix();
  translate(0,0,-frequency * length * .25);
  for(Face f : faces){
    beginShape(mousePressed ? QUADS : POINTS);
      for(PVector p : f.pts) vertex(p.x,p.y,p.z);
    endShape();
  }
  popMatrix(); 
}
void keyPressed(){
  if(keyCode == UP  && frequency < 32) frequency++;
  if(keyCode == DOWN && frequency > 2) frequency--;
  setupZome(); 
}
void drawAxes(int size){
  stroke(192,0,0);
  line(0,0,0,size,0,0);
  stroke(0,192,0);
  line(0,0,0,0,size,0);
  stroke(0,0,192);  
  line(0,0,0,0,0,size);
}
class Face{
  ArrayList<PVector> pts = new ArrayList<PVector>();
  Face(){}
  void add(PVector p){
    if(pts.size() <= 4) pts.add(p);
  }
}

我觉得我已经接近了，但是我弄错了循环条件和顶点索引. 有关如何解决此问题的任何提示?

I feel I'm close, but I'm getting the loop conditionals and vertex indices wrong. Any tips on how to fix this?

推荐答案

我非常亲密，但是没有注意所有细节. 事实证明，如果不增加p_rotate上的旋转，我将获得正确的网格:

I was very close, but not paying attention to all the details. Turns out I get the correct mesh if I don't increment the rotation on p_rotate:

p_rotate.rotate(TWO_PI / frequency,  0,0,1);

代替

p_rotate.rotate(i * TWO_PI / frequency,  0,0,1);

这是完整的代码清单:

//a port attempt of Rob Bell's polar_zonohedron.rb script - http://zomebuilder.com/

int frequency = 3;
float pitch   = atan(sqrt(2)/2);
float length  = 24;

ArrayList<Face> faces = new ArrayList<Face>(); 

void setup(){
  size(400,400,P3D);
  strokeWeight(3);
  setupZome();
}
void setupZome(){
  faces.clear();
  PVector[] pts = new PVector[4];
  pts[0] = new PVector();

  PVector vector = new PVector(cos(pitch),0,sin(pitch));
  vector.mult(length);

  for(int i = 1 ; i < frequency-1; i++){
    PMatrix3D p_rotate = new PMatrix3D();
    p_rotate.rotate(TWO_PI / frequency,  0,0,1);

    pts[1] = PVector.add(pts[0],vector);
    pts[3] = new PVector();
    p_rotate.mult(pts[1],pts[3]);
    pts[2] = PVector.add(pts[3],vector);

    for(int j = 0; j < frequency; j++){
      PMatrix3D f_rotate = new PMatrix3D();
      f_rotate.rotate(j*2*PI/frequency , 0,0,1);

      Face f = new Face();
      for(PVector pt : pts){
        PVector p = new PVector();
        f_rotate.mult(pt,p);
        f.add(p.get());
      }
      faces.add(f);
    }

    pts[0] = pts[3];
  } 
}
void draw(){
  background(255);
  lights();

  translate(width * .5, height * .5,0);
  rotateY(map(mouseX,0,width,-PI,PI));
  rotateX(map(mouseY,0,height,-PI,PI));
  drawAxes(100);
  pushMatrix();
  translate(0,0,-frequency * length * .25);
  for(Face f : faces){
    beginShape(mousePressed ? QUADS : POINTS);
      for(PVector p : f.pts) vertex(p.x,p.y,p.z);
    endShape();
  }
  popMatrix(); 
}
void keyPressed(){
  if(keyCode == UP  && frequency < 32) frequency++;
  if(keyCode == DOWN && frequency > 3) frequency--;
  setupZome(); 
}
void drawAxes(int size){
  stroke(192,0,0);
  line(0,0,0,size,0,0);
  stroke(0,192,0);
  line(0,0,0,0,size,0);
  stroke(0,0,192);  
  line(0,0,0,0,0,size);
}
class Face{
  ArrayList<PVector> pts = new ArrayList<PVector>();
  Face(){}
  void add(PVector p){
    if(pts.size() <= 4) pts.add(p);
  }
}

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