{
  "title": "cube complex floating stack · base stack v4 floating",
  "meta": "sparse stack using source base geometry: cube",
  "camera": {
    "position": [
      5.2,
      4.2,
      6.3
    ],
    "target": [
      0.0,
      1.848,
      0.0
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    "orthoSize": 4.316000000000001
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  "vertices": {
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      0.02,
      0.54
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    "P": [
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      0.54
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    "P1": [
      0.65,
      3.52,
      0.11
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    "P2": [
      1.51,
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    "P3": [
      1.51,
      3.52,
      0.97
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    "P4": [
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    "F0_base": [
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      -1.62
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    "F0_top": [
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      -1.62
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    "F1_base": [
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    "F1_top": [
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      2.78,
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    "F2_base": [
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      0.54
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    "F2_top": [
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      0.54
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    "F3_base": [
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    "F3_top": [
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      -0.54
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    "F4_base": [
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      1.62
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    "F4_top": [
      -2.16,
      3.66,
      1.62
    ]
  },
  "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"
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      "color": "#d03030",
      "dash": false,
      "depthTest": false,
      "width": 3.8
    },
    {
      "points": [
        "F0_base",
        "F0_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F1_base",
        "F1_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F2_base",
        "F2_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F3_base",
        "F3_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
    },
    {
      "points": [
        "F4_base",
        "F4_top"
      ],
      "color": "#6d2eb8",
      "dash": true,
      "depthTest": false,
      "width": 2.2,
      "opacity": 0.5
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  ],
  "aux_faces": [
    {
      "points": [
        "P1",
        "P2",
        "P3",
        "P4"
      ],
      "color": "#d03030",
      "opacity": 0.24,
      "role": "base_geo_overlap",
      "occlude": false
    }
  ],
  "aux_points": [
    "P",
    "F0_top",
    "F1_top",
    "F2_top"
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  "labels": [
    {
      "text": "P",
      "point": "P",
      "offset": [
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        0.08
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      "kind": "aux"
    },
    {
      "text": "F1",
      "point": "F0_top",
      "offset": [
        0.07,
        0.12,
        0.07
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      "kind": "aux"
    },
    {
      "text": "F2",
      "point": "F1_top",
      "offset": [
        0.07,
        0.12,
        0.07
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      "kind": "aux"
    },
    {
      "text": "F3",
      "point": "F2_top",
      "offset": [
        0.07,
        0.12,
        0.07
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      "kind": "aux"
    }
  ],
  "primitives": [
    {
      "type": "box",
      "center": [
        -2.16,
        0.43,
        -1.62
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      "size": [
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        0.86,
        0.86
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      "color": "#8ecae6",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
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      "size": [
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      "color": "#8ecae6",
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      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
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      "color": "#f2c94c",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
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      "color": "#8ecae6",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
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        -0.54
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      "size": [
        0.86,
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        0.86
      ],
      "color": "#8ecae6",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
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        -0.54
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      "size": [
        0.86,
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        0.86
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      "color": "#f2c94c",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
        -1.08,
        2.19,
        -0.54
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      "size": [
        0.86,
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        0.86
      ],
      "color": "#95d5b2",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
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      "size": [
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        0.86
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      "color": "#8ecae6",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
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        -0.54
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      "size": [
        0.86,
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      "color": "#8ecae6",
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      "edgeColor": "#202326",
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    {
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      "edgeColor": "#202326",
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    {
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      "color": "#8ecae6",
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      "role": "base_stack"
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    {
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    },
    {
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    {
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      "color": "#8ecae6",
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      "edgeColor": "#202326",
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      "role": "base_stack"
    },
    {
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      "role": "base_stack"
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    {
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    {
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    {
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      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
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      "color": "#f2c94c",
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    {
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      "color": "#f2c94c",
      "opacity": 0.4,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
        -1.08,
        3.07,
        -1.62
      ],
      "size": [
        0.86,
        0.86,
        0.86
      ],
      "color": "#c77dff",
      "opacity": 0.48,
      "edgeColor": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
        2.16,
        2.19,
        -1.62
      ],
      "size": [
        0.86,
        0.86,
        0.86
      ],
      "color": "#56cfe1",
      "opacity": 0.48,
      "edgeColor": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
        0.0,
        3.95,
        0.54
      ],
      "size": [
        0.86,
        0.86,
        0.86
      ],
      "color": "#f4a261",
      "opacity": 0.48,
      "edgeColor": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
        1.08,
        3.95,
        -0.54
      ],
      "size": [
        0.86,
        0.86,
        0.86
      ],
      "color": "#ff7aa2",
      "opacity": 0.48,
      "edgeColor": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "box",
      "center": [
        -2.16,
        3.07,
        1.62
      ],
      "size": [
        0.86,
        0.86,
        0.86
      ],
      "color": "#c77dff",
      "opacity": 0.48,
      "edgeColor": "#6d2eb8",
      "width": 2.1,
      "role": "base_stack"
    }
  ],
  "height_map": [
    [
      1,
      0,
      2,
      1,
      0
    ],
    [
      0,
      3,
      1,
      0,
      2
    ],
    [
      2,
      1,
      0,
      4,
      1
    ],
    [
      0,
      2,
      1,
      0,
      2
    ]
  ],
  "floating_units": [
    {
      "x": 1,
      "z": 0,
      "layer": 3
    },
    {
      "x": 4,
      "z": 0,
      "layer": 2
    },
    {
      "x": 2,
      "z": 2,
      "layer": 4
    },
    {
      "x": 3,
      "z": 1,
      "layer": 4
    },
    {
      "x": 0,
      "z": 3,
      "layer": 3
    }
  ],
  "base_unit": "cube",
  "qa_seeds": [
    {
      "task": "GE3D_BASE_STACK_TOTAL_COUNT",
      "question": "How many cubes are in the stack?",
      "answer": 28,
      "evidence": "Sum all nonzero column heights and any explicitly floating solids."
    },
    {
      "task": "GE3D_BASE_STACK_MAX_HEIGHT",
      "question": "What is the maximum number of base solids in one vertical position?",
      "answer": 4,
      "evidence": "Count stacked and floating solids at each vertical grid position."
    },
    {
      "task": "GE3D_BASE_STACK_TOP_COLUMN_COUNT",
      "question": "How many vertical positions reach the highest occupied layer?",
      "answer": 2,
      "evidence": "Count positions whose highest occupied layer equals the scene maximum."
    },
    {
      "task": "GE3D_BASE_STACK_HIGHEST_LAYER",
      "question": "What is the highest occupied layer number if the ground layer is layer 1?",
      "answer": 5,
      "evidence": "Find the largest occupied layer index and convert it to one-based numbering."
    },
    {
      "task": "GE3D_BASE_STACK_OCCUPIED_POSITIONS",
      "question": "How many ground positions are occupied by at least one base solid?",
      "answer": 13,
      "evidence": "Count nonzero cells in the ground height map."
    },
    {
      "task": "GE3D_BASE_STACK_MARKED_COLUMN_HEIGHT",
      "question": "How many base solids are in the marked vertical position P?",
      "answer": 4,
      "evidence": "The orange dashed line and P label mark the selected column."
    },
    {
      "task": "GE3D_BASE_STACK_TALL_COLUMN_COUNT",
      "question": "How many occupied vertical positions contain at least two base solids?",
      "answer": 7,
      "evidence": "Count vertical positions with two or more occupied layers."
    },
    {
      "task": "GE3D_BASE_STACK_EMPTY_POSITIONS",
      "question": "How many ground positions are empty?",
      "answer": 7,
      "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": 15,
      "evidence": "For each column, count all layers above the ground layer."
    },
    {
      "task": "GE3D_BASE_STACK_THIRD_LEVEL_COLUMN_COUNT",
      "question": "How many vertical positions have a solid on the third layer or higher?",
      "answer": 7,
      "evidence": "Count positions whose highest occupied layer is at least the third layer."
    },
    {
      "task": "GE3D_BASE_STACK_FLOATING_COUNT",
      "question": "How many base solids are floating above a gap or empty cell?",
      "answer": 5,
      "evidence": "Count solids listed in the nonphysical floating layer set."
    },
    {
      "task": "GE3D_BASE_STACK_FLOATING_POSITION_COUNT",
      "question": "How many grid positions contain at least one floating solid?",
      "answer": 5,
      "evidence": "Count distinct grid positions used by floating solids."
    },
    {
      "task": "GE3D_BASE_STACK_HIGHEST_FLOATING_LAYER",
      "question": "What is the highest layer number occupied by a floating solid?",
      "answer": 5,
      "evidence": "Find the maximum floating layer index and convert it to one-based numbering."
    }
  ],
  "_augmentation": "base_stack_v4",
  "_hide_meta_panel": true,
  "_id": "base_stack_v4_cube",
  "_model": "rule_base_stack_v4"
}