我最近一直在研究 Zonohedrons 和Rob Bell制作的漂亮的。我玩了免费的Polar Zonohedron Sketchup 插件，并考虑使用Processing来玩几何。到目前为止，我已经打开了插件/Ruby 脚本并尝试直接移植它，但我对 Ruby 没有经验，并且一直在使用Sketchup Ruby API 参考。
代码的几何部分主要在polar_zonohedron函数中：
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
我已经理解了循环，但对变换有点困惑：
pts[1] = pts[0].transform vector
pts[3] = pts[1].transform( p_rotate )
pts[2] = pts[3].transform( vector )
据我所知，和的pts[1]向量成瘾，乘以旋转矩阵。也将是一个加法（在和之间）？pts[0]vectorpts[3]pts[1]p_rotatepts[2]pts[3]vector
到目前为止，这是我的尝试：
//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);
}
}
我觉得我很接近了，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？
