PUZZLE #5088: Bezier Curve (diff 5)

bezier learn difficulty: 5/7 compute author: system unsolved

A 4-point Bezier curve traversing a 11x11 grid. Evaluate at given t-values.

DATA

Grid	['G', 'E', 'T', 'B', 'D', 'A', 'E', 'C', 'T', 'C', 'D'], ['S', 'N', 'F', 'D', 'T', 'H', 'G', 'L', 'E', 'F', 'Y'], ['B', 'M', 'Q', 'S', 'R', 'J', 'M', 'C', 'E', 'N', 'B'], ['M', 'O', 'G', 'O', 'M', 'O', 'H', 'D', 'G', 'H', 'W'], ['S', 'N', 'E', 'L', 'L', 'U', 'O', 'L', 'R', 'Y', 'F'], ['P', 'E', 'G', 'K', 'V', 'H', 'U', 'A', 'C', 'K', 'D'], ['M', 'O', 'J', 'F', 'L', 'S', 'P', 'R', 'I', 'T', 'Y'], ['D', 'U', 'U', 'A', 'C', 'R', 'T', 'V', 'A', 'K', 'M'], ['T', 'S', 'T', 'F', 'Q', 'X', 'B', 'T', 'G', 'O', 'T'], ['M', '_', 'C', 'L', 'Z', 'Z', 'X', 'S', 'T', 'H', 'N'], ['E', 'P', 'O', 'O', 'R', 'D', 'I', 'N', 'A', 'T', 'E']
Grid Size	`11`
Control Points	`[3, 6], [2, 3], [4, 0], [8, 1]`
T Values	`0.043, 0.087, 0.169, 0.289, 0.422, 0.476, 0.593, 0.64, 0.762, 0.867, 0.958, 1.042, 1.114, 1.119, 1.244, 1.336, 1.409, 1.472, 1.527, 1.578, 1.624, 1.667`
Num Control Points	`4`
Format	`Evaluate the Bezier curve at each t-value. The resulting (x,y) coordinates map to cells in the grid. The letters at those cells spell the answer.`
Method	`De Casteljau's algorithm`
Hint	`Bezier curve with 4 control points on a 11x11 grid. The curve may pass between grid cells — round to nearest integer.`
Answer Format	`comma-separated path coordinates`

{
  "type": "bezier",
  "grid": [
    [
      "G",
      "E",
      "T",
      "B",
      "D",
      "A",
      "E",
      "C",
      "T",
      "C",
      "D"
    ],
    [
      "S",
      "N",
      "F",
      "D",
      "T",
      "H",
      "G",
      "L",
      "E",
      "F",
      "Y"
    ],
    [
      "B",
      "M",
      "Q",
      "S",
      "R",
      "J",
      "M",
      "C",
      "E",
      "N",
      "B"
    ],
    [
      "M",
      "O",
      "G",
      "O",
      "M",
      "O",
      "H",
      "D",
      "G",
      "H",
      "W"
    ],
    [
      "S",
      "N",
      "E",
      "L",
      "L",
      "U",
      "O",
      "L",
      "R",
      "Y",
      "F"
    ],
    [
      "P",
      "E",
      "G",
      "K",
      "V",
      "H",
      "U",
      "A",
      "C",
      "K",
      "D"
    ],
    [
      "M",
      "O",
      "J",
      "F",
      "L",
      "S",
      "P",
      "R",
      "I",
      "T",
      "Y"
    ],
    [
      "D",
      "U",
      "U",
      "A",
      "C",
      "R",
      "T",
      "V",
      "A",
      "K",
      "M"
    ],
    [
      "T",
      "S",
      "T",
      "F",
      "Q",
      "X",
      "B",
      "T",
      "G",
      "O",
      "T"
    ],
    [
      "M",
      "_",
      "C",
      "L",
      "Z",
      "Z",
      "X",
      "S",
      "T",
      "H",
      "N"
    ],
    [
      "E",
      "P",
      "O",
      "O",
      "R",
      "D",
      "I",
      "N",
      "A",
      "T",
      "E"
    ]
  ],
  "grid_size": 11,
  "control_points": [
    [
      3,
      6
    ],
    [
      2,
      3
    ],
    [
      4,
      0
    ],
    [
      8,
      1
    ]
  ],
  "t_values": [
    0.043,
    0.087,
    0.169,
    0.289,
    0.422,
    0.476,
    0.593,
    0.64,
    0.762,
    0.867,
    0.958,
    1.042,
    1.114,
    1.119,
    1.244,
    1.336,
    1.409,
    1.472,
    1.527,
    1.578,
    1.624,
    1.667
  ],
  "num_control_points": 4,
  "format": "Evaluate the Bezier curve at each t-value. The resulting (x,y) coordinates map to cells in the grid. The letters at those cells spell the answer.",
  "method": "De Casteljau's algorithm",
  "hint": "Bezier curve with 4 control points on a 11x11 grid. The curve may pass between grid cells \u2014 round to nearest integer.",
  "answer_format": "comma-separated path coordinates"
}

author's note: Pool fill: bezier diff 5