{
  "id": "1504.02628",
  "version": "v1",
  "published": "2015-04-10T10:06:41.000Z",
  "updated": "2015-04-10T10:06:41.000Z",
  "title": "B-spline-like bases for $C^3$ quintics on the Powell-Sabin 12-split",
  "authors": [
    "Tom Lyche",
    "Georg Muntingh"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NA",
    "math.CO"
  ],
  "abstract": "For the space of $C^3$ quintics on the Powell-Sabin 12-split of a triangle, we determine explicitly the six symmetric simplex spline bases that reduce to a B-spline basis on each edge, have a positive partition of unity, a Marsden identity, and domain points with an intuitive control net. For one of these bases we derive $C^0$, $C^1$, $C^2$ and $C^3$ conditions on the control points of two splines on adjacent macrotriangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-10T10:06:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A15",
      "65D07",
      "65D17"
    ],
    "keywords": [
      "b-spline-like bases",
      "powell-sabin",
      "symmetric simplex spline bases",
      "b-spline basis",
      "marsden identity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150402628L"
    }
  }
}