Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called ‘biogeom’ that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. ‘biogeom’ includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. ‘biogeom’ can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world.

中文翻译：

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'biogeom'：用于模拟和拟合自然形状的 R 包

许多自然物体在单个平面中表现出径向或轴向对称性。然而，缺乏用于模拟和拟合此类物体形状的通用工具。在此，我们展示了一个名为“biogeom”的 R 包，它模拟和拟合自然界中发现的许多形状。该软件包包含新颖的通用参数方程，可生成鸟蛋、花朵、线性和披针形叶子、种子、海星和树轮的轮廓，以及三个生长速率方程，可生成卵形叶子的轮廓和个体发育曲线动物和植物。“biogeom”包括几个经验数据集，包括鸟蛋、水果、披针形和卵形叶子、树木年轮、种子和海星的边界坐标。该包还可以应用于与数据集中类似的其他种类的自然形状。此外，该软件包包括从三个增长率方程导出的 S 形曲线，可用于模拟动植物生长轨迹并预测与最大增长率相关的时间。“biogeom”可以量化自然轮廓的种内或种间相似性，它提供形状的定量信息和形状的个体发生修饰，对生命世界的生长和形式具有重要的生态和进化意义。