{
  "title": "cone sparse height-map stack · base stack v3",
  "meta": "sparse stack using source base geometry: cone",
  "camera": {
    "position": [
      5.2,
      4.2,
      6.3
    ],
    "target": [
      0.0,
      1.0584,
      0.0
    ],
    "orthoSize": 3.4311999999999996
  },
  "vertices": {
    "P0": [
      0.58,
      0.02,
      0.58
    ],
    "P": [
      0.58,
      2.74,
      0.58
    ]
  },
  "faces": [],
  "edges": [],
  "aux_lines": [
    {
      "points": [
        "P0",
        "P"
      ],
      "color": "#d97400",
      "dash": true,
      "depthTest": false,
      "width": 4.0
    }
  ],
  "aux_faces": [],
  "aux_points": [
    "P"
  ],
  "labels": [
    {
      "text": "P",
      "point": "P",
      "offset": [
        0.08,
        0.12,
        0.08
      ],
      "kind": "aux"
    }
  ],
  "primitives": [
    {
      "type": "cone",
      "center": [
        -0.58,
        0.41,
        -1.74
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        1.74,
        0.41,
        -1.74
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        1.74,
        1.25,
        -1.74
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#f2c94c",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        -1.74,
        0.41,
        -0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        -0.58,
        0.41,
        -0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        -0.58,
        1.25,
        -0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#f2c94c",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        1.74,
        0.41,
        -0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        0.58,
        0.41,
        0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        0.58,
        1.25,
        0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#f2c94c",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        0.58,
        2.09,
        0.58
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#95d5b2",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        -1.74,
        0.41,
        1.74
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        -1.74,
        1.25,
        1.74
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#f2c94c",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    },
    {
      "type": "cone",
      "center": [
        0.58,
        0.41,
        1.74
      ],
      "radius": 0.42,
      "height": 0.82,
      "axis": "y",
      "color": "#8ecae6",
      "opacity": 0.42,
      "edgeColor": "#202326",
      "width": 2.1,
      "role": "base_stack"
    }
  ],
  "height_map": [
    [
      0,
      1,
      0,
      2
    ],
    [
      1,
      2,
      0,
      1
    ],
    [
      0,
      0,
      3,
      0
    ],
    [
      2,
      0,
      1,
      0
    ]
  ],
  "base_unit": "cone",
  "qa_seeds": [
    {
      "task": "GE3D_BASE_STACK_TOTAL_COUNT",
      "question": "How many cones are in the stack?",
      "answer": 13,
      "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": 8,
      "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": 4,
      "evidence": "Count columns whose height is two or more."
    },
    {
      "task": "GE3D_BASE_STACK_EMPTY_POSITIONS",
      "question": "How many ground positions are empty?",
      "answer": 8,
      "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": 5,
      "evidence": "For each column, count all layers above the ground layer."
    }
  ],
  "_augmentation": "base_stack_v3",
  "_hide_meta_panel": true,
  "_id": "base_stack_v3_cone",
  "_model": "rule_base_stack_v3"
}