{
  "_id": "6a1f1ecfb401979e7341ff81",
  "Package": "biogeom",
  "Type": "Package",
  "Title": "Biological Geometries",
  "Version": "1.5.1",
  "Date": "2026-04-16",
  "Authors@R": "c(person(given=\"Peijian\", family=\"Shi\", email=\"pjshi@njfu.edu.cn\", role=c(\"aut\", \"cre\")),\nperson(given=c(\"Johan\"), family=\"Gielis\", email=\"johan.gielis@uantwerpen.be\", role=c(\"aut\")),\nperson(given=c(\"Brady K.\"), family=\"Quinn\", email=\"brady.quinn@dfo-mpo.gc.ca\", role=c(\"aut\")))",
  "Author": "Peijian Shi [aut, cre], Johan Gielis [aut], Brady K. Quinn\n[aut]",
  "Maintainer": "Peijian Shi <pjshi@njfu.edu.cn>",
  "Description": "Is used to simulate and fit biological geometries.\n'biogeom' incorporates several novel universal parametric\nequations that can generate the profiles of bird eggs, flowers,\nlinear and lanceolate leaves, seeds, starfish, and tree-rings\n(Gielis (2003) <doi:10.3732/ajb.90.3.333>; Shi et al. (2020)\n<doi:10.3390/sym12040645>), three growth-rate curves\nrepresenting the ontogenetic growth trajectories of animals and\nplants against time, and the axially symmetrical and integral\nforms of all these functions (Shi et al. (2017)\n<doi:10.1016/j.ecolmodel.2017.01.012>; Shi et al. (2021)\n<doi:10.3390/sym13081524>). The optimization method proposed by\nNelder and Mead (1965) <doi:10.1093/comjnl/7.4.308> was used to\nestimate model parameters. 'biogeom' includes several real data\nsets of the boundary coordinates of natural shapes, including\navian eggs, fruit, lanceolate and ovate leaves, tree rings,\nseeds, and sea stars,and can be potentially applied to other\nnatural shapes. 'biogeom' can quantify the conspecific or\ninterspecific similarity of natural outlines, and provides\ninformation with important ecological and evolutionary\nimplications for the growth and form of living organisms.\nPlease see Shi et al. (2022) <doi:10.1111/nyas.14862> for\ndetails.",
  "License": "GPL (>= 2)",
  "NeedsCompilation": "no",
  "Packaged": {
    "Date": "2026-05-16 08:15:43 UTC",
    "User": "root"
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  "Repository": "https://cran.r-universe.dev",
  "Date/Publication": "2026-04-16 08:09:24 UTC",
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  "_file": "biogeom_1.5.1.tar.gz",
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  "_created": "2026-05-16T08:15:43.000Z",
  "_published": "2026-06-02T18:19:59.518Z",
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  "_buildurl": "https://github.com/r-universe/cran/actions/runs/25957033080",
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  "_commit": {
    "id": "d178b5e4cdc5713c5eb88beeee3772f05914c1ca",
    "author": "Peijian Shi <pjshi@njfu.edu.cn>",
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    "message": "version 1.5.1\n",
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  "_maintainer": {
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    "curveEPE",
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    "DEPE",
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    "EPE",
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    "fitGS",
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    "fitNRGE",
    "fitovate",
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    "MbetaE",
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    "SarabiaE",
    "SCSE",
    "SHE",
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    "SurfaceAreaAM",
    "SurfaceAreaEPE",
    "SurfaceAreaETE",
    "SurfaceAreaNRGE",
    "SurfaceAreaSGE",
    "TE",
    "TGE",
    "TSE",
    "VolumeAM",
    "VolumeEPE",
    "VolumeETE",
    "VolumeNRGE",
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      "title": "Boundary Data Adjustment of A Polygon",
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      "title": "Area Calculation for an Ovate Polygon",
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      "title": "Leaf Boundary Data of _Phyllostachys incarnata_ T. H. Wen (Poaceae: Bambusoideae)",
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      "title": "Biological Geometries",
      "topics": [
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      "title": "Drawing the Gielis Curve",
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      "title": "Drawing the Egg Shape Predicted by the Narushin-Romanov-Griffin Equation",
      "topics": [
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      ]
    },
    {
      "page": "curveovate",
      "title": "Drawing the Ovate Leaf-Shape Curve",
      "topics": [
        "curveovate"
      ]
    },
    {
      "page": "DEPE",
      "title": "Calculation of the First-Order Derivative of the Explicit Preston Equation",
      "topics": [
        "DEPE"
      ]
    },
    {
      "page": "DETE",
      "title": "Calculation of the First-Order Derivative of the Explicit Troscianko Equation",
      "topics": [
        "DETE"
      ]
    },
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      "title": "Calculation of the First-Order Derivative of the Narushin-Romanov-Griffin Equation",
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    },
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      "title": "Calculation of the First-Order Derivative of the Simplified Gielis Equation",
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    },
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      "title": "Egg Boundary Data of Nine Species of Birds",
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      ]
    },
    {
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      "title": "Calculation of the Ordinate For an Arbitrary Point on the Troscianko Curve in the Plane",
      "topics": [
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    },
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      "page": "fitAM",
      "title": "Fitting the 2-D Profiles of Apical Meristems",
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    },
    {
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      "title": "Data-Fitting Function for the Explicit Preston Equation",
      "topics": [
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    },
    {
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      "title": "Data-Fitting Function for the Explicit Troscianko Equation",
      "topics": [
        "fitETE"
      ]
    },
    {
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      "title": "Data-Fitting Function for the Gielis Equation",
      "topics": [
        "fitGE"
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    },
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      "title": "Data-Fitting Function for the Geometric Series of Size Distribution Measurements",
      "topics": [
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      ]
    },
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      "title": "Data-Fitting Function for the Rotated and Right-Shifted Lorenz Curve",
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    {
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      "topics": [
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    },
    {
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      "title": "Data-Fitting Function for the Sigmoid Growth Equation",
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      "topics": [
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    },
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      "title": "Calculation of Fractal Dimension of Lef Veins Based on the Box-Counting Method",
      "topics": [
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      ]
    },
    {
      "page": "GE",
      "title": "Calculation of the Polar Radius of the Gielis Curve",
      "topics": [
        "GE"
      ]
    },
    {
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      "title": "Boundary Data of the Side Projections of _Ginkgo biloba_ Seeds",
      "topics": [
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    },
    {
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      "topics": [
        "kp"
      ]
    },
    {
      "page": "LeafSizeDist",
      "title": "Leaf size distribution of _Shibataea chinensis_",
      "topics": [
        "LeafSizeDist"
      ]
    },
    {
      "page": "lmPE",
      "title": "Parameter Estimation for the Todd-Smart Equation",
      "topics": [
        "lmPE"
      ]
    },
    {
      "page": "lmTE",
      "title": "Parameter Estimation for the Troscianko Equation",
      "topics": [
        "lmTE"
      ]
    },
    {
      "page": "MbetaE",
      "title": "Modified Beta Equation",
      "topics": [
        "MbetaE"
      ]
    },
    {
      "page": "MBriereE",
      "title": "Modified Briere Equation",
      "topics": [
        "MBriereE"
      ]
    },
    {
      "page": "MLRFE",
      "title": "Modified Lobry-Rosso-Flandrois (LRF) Equation",
      "topics": [
        "MLRFE"
      ]
    },
    {
      "page": "MPerformanceE",
      "title": "Modified Performance Equation",
      "topics": [
        "MPerformanceE"
      ]
    },
    {
      "page": "Neocinnamomum",
      "title": "Leaf Boundary Data of Seven Species of _Neocinnamomum_",
      "topics": [
        "Neocinnamomum"
      ]
    },
    {
      "page": "NRGE",
      "title": "The Narushin-Romanov-Griffin Equation (NRGE)",
      "topics": [
        "NRGE"
      ]
    },
    {
      "page": "PE",
      "title": "Calculation of the Abscissa, Ordinate and Distance From the Origin For an Arbitrary Point on the Preston Curve",
      "topics": [
        "PE"
      ]
    },
    {
      "page": "PlanCoor",
      "title": "Extracts the Planar Coordinates the 2-D Profiles of Apical Meristems",
      "topics": [
        "PlanCoor"
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    },
    {
      "page": "SAMs",
      "title": "Boundary Data of Shoot Apical Meristems",
      "topics": [
        "SAMs"
      ]
    },
    {
      "page": "SarabiaE",
      "title": "Sarabia Equation",
      "topics": [
        "SarabiaE"
      ]
    },
    {
      "page": "SCSE",
      "title": "Sarabia-Castillo-Slottje Equation (SCSE)",
      "topics": [
        "SCSE"
      ]
    },
    {
      "page": "SHE",
      "title": "Sitthiyot-Holasut Equation",
      "topics": [
        "SHE"
      ]
    },
    {
      "page": "shoots",
      "title": "Height Growth Data of Bamboo Shoots",
      "topics": [
        "shoots"
      ]
    },
    {
      "page": "sigmoid",
      "title": "Sigmoid Growth Equation",
      "topics": [
        "sigmoid"
      ]
    },
    {
      "page": "starfish",
      "title": "Boundary Data of Eight Sea Stars",
      "topics": [
        "starfish"
      ]
    },
    {
      "page": "SurfaceAreaAM",
      "title": "Calculation of the Lateral Surface Area of an Apical meristem.",
      "topics": [
        "SurfaceAreaAM"
      ]
    },
    {
      "page": "SurfaceAreaEPE",
      "title": "Calculation of the Surface Area of An Egg Based on the Explicit Preston Equation",
      "topics": [
        "SurfaceAreaEPE"
      ]
    },
    {
      "page": "SurfaceAreaETE",
      "title": "Calculation of the Surface Area of An Egg Based on the Explicit Troscianko Equation",
      "topics": [
        "SurfaceAreaETE"
      ]
    },
    {
      "page": "SurfaceAreaNRGE",
      "title": "Calculation of the Surface Area of An Egg Based on the Narushin-Romanov-Griffin Equation",
      "topics": [
        "SurfaceAreaNRGE"
      ]
    },
    {
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