| """Generate deterministic isometric voxel-structure reasoning datasets.""" |
| from __future__ import annotations |
| import argparse,json,math,random |
| from collections import Counter |
| from pathlib import Path |
| from PIL import Image,ImageDraw |
| try: |
| from tqdm import tqdm |
| except ImportError: |
| def tqdm(x,**_):return x |
| BG="#F1EFE8";SCALE_AA=3 |
| DATASET_VERSION="cube-structure-2.0.0" |
| RAMPS={"A":{"top":"#BFD2D6","left":"#8FB2BA","right":"#6F98A3"},"B":{"top":"#D3CBC0","left":"#AA998A","right":"#86766A"}};EDGE="#26383D" |
|
|
| def iso_project(x,y,z):return((x-y)*.8660254,(x+y)*.5-z) |
| def gravity_valid(cubes): |
| s=set(cubes);return all(z==0 or (x,y,z-1) in s for x,y,z in s) |
| def cube_hidden(cube,cubes,viewpoint=0): |
| """Exact full-projection occlusion along the fixed isometric viewing ray.""" |
| x,y,z=cube;s=set(cubes);dx,dy=(1,1) if viewpoint==0 else (-1,-1) |
| return any((x+dx*k,y+dy*k,z+k) in s for k in range(1,12)) |
| def face_count(cube,cubes,viewpoint=0): |
| if cube_hidden(cube,cubes,viewpoint):return 0 |
| x,y,z=cube;s=set(cubes);dx,dy=(1,1) if viewpoint==0 else (-1,-1) |
| return int((x,y,z+1) not in s)+int((x+dx,y,z) not in s)+int((x,y+dy,z) not in s) |
| def visibility(cubes,viewpoint=0):return {c:face_count(c,cubes,viewpoint)>0 for c in cubes} |
|
|
| def generate_valid_structure(num_cubes,rng): |
| base_n=rng.randint(4,min(10,num_cubes));foot={(0,0)} |
| while len(foot)<base_n: |
| x,y=rng.choice(tuple(foot));dx,dy=rng.choice([(1,0),(-1,0),(0,1),(0,-1)]);foot.add((x+dx,y+dy)) |
| heights={p:1 for p in foot};remaining=num_cubes-base_n |
| while remaining: |
| candidates=[p for p,h in heights.items() if h<6];p=rng.choice(candidates);heights[p]+=1;remaining-=1 |
| cubes={(x,y,z) for (x,y),height in heights.items() for z in range(height)};assert len(cubes)==num_cubes and gravity_valid(cubes);return cubes |
| def assign_clusters(cubes,two): |
| if not two:return {c:"A" for c in cubes} |
| xs=sorted({c[0] for c in cubes});pivot=xs[len(xs)//2];out={c:("A" if c[0]<pivot else "B") for c in cubes} |
| if len(set(out.values()))<2: |
| ordered=sorted(cubes);out={c:("A" if i<len(ordered)//2 else "B") for i,c in enumerate(ordered)} |
| return out |
|
|
| def face_vertices(c,face,viewpoint=0): |
| x,y,z=c;dx,dy=(1,1) if viewpoint==0 else (-1,-1) |
| if face=="top":return [(x,y,z+1),(x+1,y,z+1),(x+1,y+1,z+1),(x,y+1,z+1)] |
| if face=="right": |
| xx=x+1 if dx==1 else x;return [(xx,y,z),(xx,y+1,z),(xx,y+1,z+1),(xx,y,z+1)] |
| yy=y+1 if dy==1 else y;return [(x,yy,z),(x+1,yy,z),(x+1,yy,z+1),(x,yy,z+1)] |
| def visible_faces(cubes): |
| s=set(cubes);faces=[] |
| for c in cubes: |
| if cube_hidden(c,s,0):continue |
| x,y,z=c |
| if (x,y,z+1) not in s:faces.append((c,"top")) |
| if (x+1,y,z) not in s:faces.append((c,"right")) |
| if (x,y+1,z) not in s:faces.append((c,"left")) |
| return sorted(faces,key=lambda f:(sum(f[0]),f[0][2],{"left":0,"right":1,"top":2}[f[1]])) |
| def render(path,size,cubes,clusters,line_width): |
| w,h=size;faces=visible_faces(cubes);raw=[iso_project(*v) for c,f in faces for v in face_vertices(c,f)];minx,maxx=min(x for x,y in raw),max(x for x,y in raw);miny,maxy=min(y for x,y in raw),max(y for x,y in raw);scale=min((w-64)/(maxx-minx),(h-64)/(maxy-miny));ox=w/2-scale*(minx+maxx)/2;oy=h/2-scale*(miny+maxy)/2 |
| im=Image.new("RGB",(w*SCALE_AA,h*SCALE_AA),BG);d=ImageDraw.Draw(im) |
| for c,f in faces: |
| pts=[((ox+scale*x)*SCALE_AA,(oy+scale*y)*SCALE_AA) for x,y in [iso_project(*v) for v in face_vertices(c,f)]];d.polygon(pts,fill=RAMPS[clusters[c]][f]);d.line(pts+[pts[0]],fill=EDGE,width=max(2,round(line_width*SCALE_AA)),joint="curve") |
| im.resize((w,h),Image.Resampling.LANCZOS).save(path,"PNG") |
|
|
| def make_questions(iid,meta,rng): |
| layers={int(k):v for k,v in meta["cubes_per_layer"].items()};maxn=max(layers.values());best=min(z for z,n in layers.items() if n==maxn);qs=[ |
| {"question_id":iid+"_q1","question_text":"How many cubes make up this structure in total? Answer with a number in curly brackets, e.g. {12}.","question_type":"total_cube_count","ground_truth":str(meta["total_cube_count"]),"answer_format":"numeric","difficulty_level":1}, |
| {"question_id":iid+"_q2","question_text":"How many cubes are touching the ground (bottom layer)? Answer with a number in curly brackets, e.g. {5}.","question_type":"base_layer_count","ground_truth":str(meta["base_layer_count"]),"answer_format":"numeric","difficulty_level":2}] |
| pool=["layers","largest"]+(["cluster"] if meta["color_cluster_count"]==2 else []);t=rng.choice(pool) |
| if t=="layers":text="How many total layers (levels of height) does this structure have? Answer with a number in curly brackets, e.g. {3}.";gt=str(meta["max_height"]);typ="max_height" |
| elif t=="largest":text="Which layer (counting from the ground as layer 1) has the most cubes? Answer with a number in curly brackets, e.g. {2}.";gt=str(best+1);typ="largest_layer" |
| else:cluster=rng.choice(["A","B"]);text=f"How many cubes are in the {cluster} color cluster?";gt=str(meta["cluster_counts"][cluster]);typ="cluster_cube_count" |
| qs.append({"question_id":iid+"_q3","question_text":text,"question_type":typ,"ground_truth":gt,"answer_format":"numeric","difficulty_level":3}) |
| t="hidden" |
| if t=="hidden":text="How many cubes in this structure are completely hidden from view? Answer with a number in curly brackets, e.g. {2}.";gt=str(meta["hidden_cube_count"]);typ="hidden_cube_count";fmt="numeric" |
| elif t=="stable":text="Is this structure physically stable—does every cube have support beneath it with no floating cubes? Answer yes or no.";gt="yes";typ="physical_stability";fmt="yes_no" |
| else:text="If this structure were rotated 180 degrees around the vertical axis, how many currently-hidden cubes would become visible? Answer with a number in curly brackets, e.g. {3}.";gt=str(meta["hidden_to_visible_180"]);typ="hidden_to_visible_180";fmt="numeric" |
| qs.append({"question_id":iid+"_q4","question_text":"How many cubes are completely hidden from the current view? Answer with a number.","question_type":"hidden_cube_count","ground_truth":str(meta["hidden_cube_count"]),"answer_format":"numeric","difficulty_level":4}) |
| qs.append({"question_id":iid+"_q5","question_text":"If this structure were rotated 180 degrees around the vertical axis, how many currently-hidden cubes would become visible? Answer with a number in curly brackets, e.g. {3}.","question_type":"hidden_to_visible_180","ground_truth":str(meta["hidden_to_visible_180"]),"answer_format":"numeric","difficulty_level":5});return qs |
| def generate_one(i,images): |
| iid=f"cube_structure_{i:04d}";target_hidden,target_level5=((0,0),(1,1),(2,2))[(i-1)%3] |
| for attempt in range(10000): |
| rng=random.Random(f"cube-structure-v2:{i}:{attempt}");size=(rng.randint(400,430),rng.randint(400,430));total=rng.randint(8,22);cubes=generate_valid_structure(total,rng);vis=visibility(cubes,0);ambiguous=any(z>0 and not vis.get((x,y,z-1),True) for x,y,z in cubes) |
| if ambiguous:continue |
| opp=visibility(cubes,180);hidden_count=sum(not vis[c] for c in cubes);level5_count=sum(not vis[c] and opp[c] for c in cubes) |
| if (hidden_count,level5_count)!=(target_hidden,target_level5):continue |
| two=rng.random()<.25;clusters=assign_clusters(cubes,two);line_width=round(rng.uniform(.5,1),2);render(images/f"{iid}.png",size,cubes,clusters,line_width) |
| from validate_cube_dataset import png_faces_match |
| with Image.open(images/f"{iid}.png") as source:probe=source.convert("RGB");probe.load() |
| if png_faces_match(probe,cubes,clusters):break |
| else:raise RuntimeError(f"unable to generate unambiguous cube structure {i}") |
| hidden=[c for c in cubes if not vis[c]];layers=Counter(z for x,y,z in cubes);cluster_counts=Counter(clusters.values());cluster_hidden=Counter(clusters[c] for c in cubes if not vis[c]) |
| records=[] |
| for c in sorted(cubes): |
| fc=face_count(c,cubes,0);status="fully_hidden" if fc==0 else ("fully_visible" if fc==3 else "partially_occluded");records.append({"x":c[0],"y":c[1],"z":c[2],"visibility":status,"visible":fc>0,"visible_face_count":fc,"color_cluster":clusters[c]}) |
| meta={"total_cube_count":total,"visible_cube_count":sum(vis.values()),"hidden_cube_count":len(hidden),"base_layer_count":layers[0],"max_height":max(layers)+1,"cubes_per_layer":{str(z):layers[z] for z in sorted(layers)},"color_cluster_count":2 if two else 1,"cluster_counts":dict(cluster_counts),"hidden_members_per_cluster":{name:cluster_hidden.get(name,0) for name in cluster_counts},"has_ambiguous_visual_floater":False,"hidden_to_visible_180":sum(not vis[c] and opp[c] for c in cubes)};difficulty=round(min(1,.3*(total-8)/14+.3*len(hidden)/max(1,total)+.2*(meta["max_height"]-1)/5+.1*two),4) |
| return {"dataset_version":DATASET_VERSION,"vertical_axis":"z","coordinate_frame":"right-handed voxel coordinates (x,y,z)","render_frame":"isometric projection with screen vertical component -z","rotation_axis_level5":"z","generation_attempt":attempt,"id":iid,"image_path":f"images/{iid}.png","canvas_size":list(size),**meta,"line_width_px":line_width,"seed":i,"difficulty_score":difficulty,"cubes":records,"questions":make_questions(iid,meta,rng)} |
| def generate_dataset(n=3000,output_dir="cube_structure_dataset"): |
| out=Path(output_dir);images=out/"images";images.mkdir(parents=True,exist_ok=True) |
| with (out/"annotations.jsonl").open("w",encoding="utf-8",newline="\n") as f: |
| for i in tqdm(range(1,n+1),desc="Generating cube structures"):f.write(json.dumps(generate_one(i,images),sort_keys=True,separators=(",",":"))+"\n") |
| from validate_cube_dataset import validate;checked,issues=validate(out);assert not issues,issues[:10];print(f"Validated {checked} images in {out.resolve()}") |
| def main(): |
| p=argparse.ArgumentParser();p.add_argument("--n",type=int,default=3000);p.add_argument("--output-dir",default="cube_structure_dataset");p.add_argument("--sample",action="store_true");a=p.parse_args();generate_dataset(5 if a.sample else a.n,a.output_dir) |
| if __name__=="__main__":main() |
|
|
