{ "title": "cube irregular three-level stack ยท base stack v3", "meta": "sparse stack using source base geometry: cube", "camera": { "position": [ 5.2, 4.2, 6.3 ], "target": [ 0.0, 1.1088, 0.0 ], "orthoSize": 3.2592000000000003 }, "vertices": { "P0": [ -0.54, 0.02, -0.54 ], "P": [ -0.54, 2.86, -0.54 ], "P1": [ -0.97, 2.64, -0.97 ], "P2": [ -0.11, 2.64, -0.97 ], "P3": [ -0.11, 2.64, -0.11 ], "P4": [ -0.97, 2.64, -0.11 ] }, "faces": [], "edges": [], "aux_lines": [ { "points": [ "P0", "P" ], "color": "#d97400", "dash": true, "depthTest": false, "width": 4.0 }, { "points": [ "P1", "P2" ], "color": "#d03030", "dash": false, "depthTest": false, "width": 3.8 }, { "points": [ "P2", "P3" ], "color": "#d03030", "dash": false, "depthTest": false, "width": 3.8 }, { "points": [ "P3", "P4" ], "color": "#d03030", "dash": false, "depthTest": false, "width": 3.8 }, { "points": [ "P4", "P1" ], "color": "#d03030", "dash": false, "depthTest": false, "width": 3.8 } ], "aux_faces": [ { "points": [ "P1", "P2", "P3", "P4" ], "color": "#d03030", "opacity": 0.24, "role": "base_geo_overlap", "occlude": false } ], "aux_points": [ "P" ], "labels": [ { "text": "P", "point": "P", "offset": [ 0.08, 0.12, 0.08 ], "kind": "aux" } ], "primitives": [ { "type": "box", "center": [ -1.62, 0.43, -1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 0.54, 0.43, -1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 0.54, 1.31, -1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#f2c94c", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 1.62, 0.43, -1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -0.54, 0.43, -0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -0.54, 1.31, -0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#f2c94c", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -0.54, 2.19, -0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#95d5b2", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 0.54, 0.43, -0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -1.62, 0.43, 0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -1.62, 1.31, 0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#f2c94c", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -0.54, 0.43, 0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 1.62, 0.43, 0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 1.62, 1.31, 0.54 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#f2c94c", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ -0.54, 0.43, 1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 0.54, 0.43, 1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#8ecae6", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" }, { "type": "box", "center": [ 0.54, 1.31, 1.62 ], "size": [ 0.86, 0.86, 0.86 ], "color": "#f2c94c", "opacity": 0.4, "edgeColor": "#202326", "width": 2.1, "role": "base_stack" } ], "height_map": [ [ 1, 0, 2, 1 ], [ 0, 3, 1, 0 ], [ 2, 1, 0, 2 ], [ 0, 1, 2, 0 ] ], "base_unit": "cube", "qa_seeds": [ { "task": "GE3D_BASE_STACK_TOTAL_COUNT", "question": "How many cubes are in the stack?", "answer": 16, "evidence": "Sum all nonzero column heights in the sparse height map." }, { "task": "GE3D_BASE_STACK_MAX_HEIGHT", "question": "What is the maximum number of base solids in a vertical column?", "answer": 3, "evidence": "Find the tallest stack column." }, { "task": "GE3D_BASE_STACK_TOP_COLUMN_COUNT", "question": "How many columns reach the highest level?", "answer": 1, "evidence": "Count columns whose height equals the maximum height." }, { "task": "GE3D_BASE_STACK_OCCUPIED_POSITIONS", "question": "How many ground positions are occupied by at least one base solid?", "answer": 10, "evidence": "Count nonzero cells in the height map." }, { "task": "GE3D_BASE_STACK_MARKED_COLUMN_HEIGHT", "question": "How many base solids are in the marked column P?", "answer": 3, "evidence": "The orange dashed line and P label mark the selected column." }, { "task": "GE3D_BASE_STACK_TALL_COLUMN_COUNT", "question": "How many occupied columns contain at least two base solids?", "answer": 5, "evidence": "Count columns whose height is two or more." }, { "task": "GE3D_BASE_STACK_EMPTY_POSITIONS", "question": "How many ground positions are empty?", "answer": 6, "evidence": "Count cells in the sparse height map with height zero." }, { "task": "GE3D_BASE_STACK_ABOVE_GROUND_COUNT", "question": "How many base solids are above the first layer?", "answer": 6, "evidence": "For each column, count all layers above the ground layer." } ], "_augmentation": "base_stack_v3", "_hide_meta_panel": true, "_id": "base_stack_v3_cube", "_model": "rule_base_stack_v3" }