球面 Voronoi 图：可拖拽点的范区划分
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该范例演示如何在球面上用一组可拖拽点生成 Voronoi 图，从而观察每个点对应的“最近区域”随点移动而实时变化。核心数学概念包括球面几何、Voronoi 划分（最近点/支配区域）、球面上的距离分区，以及与单位圆/反射等相关的几何直观（图中可体现分割边界与对称结构）。作图要点：利用 GeoGebra 的 Sequence 生成点集合，并通过 Zip 将若干对象批量封装；先构造 Sphere（球体）与 PointIn（在球面/空间中取点/筛选点）；再用 Midpoint 计算中点或用于构造分割边界的辅助几何量；相关对象如 N（点数）、M、Lm、O（原点/参考点）、Pname/PMname（点命名）、Cols/colP（颜色管理）以及一系列 C1…C29（分界/区域相关对象）支撑整个球面 Voronoi 的生成与更新。适合高中到大学的几何建模与可视化教学，也可用于计算几何、空间数据分析的入门演示与课堂实验。
GeoGebra 命令及参数
Sequence(1, M) → LmZip("sphere" + (Text[m]), m, Lm) → SnameZip("C" + (Text[m]), m, Lm) → PnameZip("M" + (Text[m]), m, Lm) → PMnameZip(random(), k, Lm) → ColsSphere(O, 1) → sPointIn(s) → C1PointIn(s) → C2PointIn(s) → C3PointIn(s) → C4PointIn(s) → C5PointIn(s) → C6PointIn(s) → C7PointIn(s) → C8PointIn(s) → C9PointIn(s) → C10PointIn(s) → C11PointIn(s) → C12PointIn(s) → C13PointIn(s) → C14PointIn(s) → C15PointIn(s) → C16PointIn(s) → C17PointIn(s) → C18PointIn(s) → C19PointIn(s) → C20PointIn(s) → C21PointIn(s) → C22PointIn(s) → C23PointIn(s) → C24PointIn(s) → C25PointIn(s) → C26PointIn(s) → C27PointIn(s) → C28PointIn(s) → C29PointIn(s) → C30PointIn(s) → C31PointIn(s) → C32PointIn(s) → C33PointIn(s) → C34PointIn(s) → C35PointIn(s) → C36PointIn(s) → C37PointIn(s) → C38PointIn(s) → C39PointIn(s) → C40PointIn(s) → C41PointIn(s) → C42PointIn(s) → C43PointIn(s) → C44PointIn(s) → C45PointIn(s) → C46PointIn(s) → C47PointIn(s) → C48PointIn(s) → C49PointIn(s) → C50Midpoint(C1, O) → M1Midpoint(C2, O) → M2Midpoint(C3, O) → M3Midpoint(C4, O) → M4Midpoint(C5, O) → M5Midpoint(C6, O) → M6Midpoint(C7, O) → M7Midpoint(C8, O) → M8Midpoint(C9, O) → M9Midpoint(C10, O) → M10Midpoint(C11, O) → M11Midpoint(C12, O) → M12Midpoint(C13, O) → M13Midpoint(C14, O) → M14Midpoint(C15, O) → M15Midpoint(C16, O) → M16Midpoint(C17, O) → M17Midpoint(C18, O) → M18Midpoint(C19, O) → M19Midpoint(C20, O) → M20Midpoint(C21, O) → M21Midpoint(C22, O) → M22Midpoint(C23, O) → M23Midpoint(C24, O) → M24Midpoint(C25, O) → M25Midpoint(C26, O) → M26Midpoint(C27, O) → M27Midpoint(C28, O) → M28Midpoint(C29, O) → M29Midpoint(C30, O) → M30Midpoint(C31, O) → M31Midpoint(C32, O) → M32Midpoint(C33, O) → M33Midpoint(C34, O) → M34Midpoint(C35, O) → M35Midpoint(C36, O) → M36Midpoint(C37, O) → M37Midpoint(C38, O) → M38Midpoint(C39, O) → M39Midpoint(C40, O) → M40Midpoint(C41, O) → M41Midpoint(C42, O) → M42Midpoint(C43, O) → M43Midpoint(C44, O) → M44Midpoint(C45, O) → M45Midpoint(C46, O) → M46Midpoint(C47, O) → M47Midpoint(C48, O) → M48Midpoint(C49, O) → M49Midpoint(C50, O) → M50Sphere(M1, 1 / 2) → sphere1Sphere(M2, 1 / 2) → sphere2Sphere(M3, 1 / 2) → sphere3Sphere(M4, 1 / 2) → sphere4Sphere(M5, 1 / 2) → sphere5Sphere(M6, 1 / 2) → sphere6Sphere(M7, 1 / 2) → sphere7Sphere(M8, 1 / 2) → sphere8Sphere(M9, 1 / 2) → sphere9Sphere(M10, 1 / 2) → sphere10Sphere(M11, 1 / 2) → sphere11Sphere(M12, 1 / 2) → sphere12Sphere(M13, 1 / 2) → sphere13Sphere(M14, 1 / 2) → sphere14Sphere(M15, 1 / 2) → sphere15Sphere(M16, 1 / 2) → sphere16Sphere(M17, 1 / 2) → sphere17Sphere(M18, 1 / 2) → sphere18Sphere(M19, 1 / 2) → sphere19Sphere(M20, 1 / 2) → sphere20Sphere(M21, 1 / 2) → sphere21Sphere(M22, 1 / 2) → sphere22Sphere(M23, 1 / 2) → sphere23Sphere(M24, 1 / 2) → sphere24Sphere(M25, 1 / 2) → sphere25Sphere(M26, 1 / 2) → sphere26Sphere(M27, 1 / 2) → sphere27Sphere(M28, 1 / 2) → sphere28Sphere(M29, 1 / 2) → sphere29Sphere(M30, 1 / 2) → sphere30Sphere(M31, 1 / 2) → sphere31Sphere(M32, 1 / 2) → sphere32Sphere(M33, 1 / 2) → sphere33Sphere(M34, 1 / 2) → sphere34Sphere(M35, 1 / 2) → sphere35Sphere(M36, 1 / 2) → sphere36Sphere(M37, 1 / 2) → sphere37Sphere(M38, 1 / 2) → sphere38Sphere(M39, 1 / 2) → sphere39Sphere(M40, 1 / 2) → sphere40Sphere(M41, 1 / 2) → sphere41Sphere(M42, 1 / 2) → sphere42Sphere(M43, 1 / 2) → sphere43Sphere(M44, 1 / 2) → sphere44Sphere(M45, 1 / 2) → sphere45Sphere(M46, 1 / 2) → sphere46Sphere(M47, 1 / 2) → sphere47Sphere(M48, 1 / 2) → sphere48Sphere(M49, 1 / 2) → sphere49Sphere(M50, 1 / 2) → sphere50Zip((sin((π * random())) * cos(((2 * π) * random()))), k, Lm) → LxZip((sin((π * random())) * sin(((2 * π) * random()))), k, Lm) → LyZip(cos((π * random())), k, Lm) → LzPointIn(s) → C51PointIn(s) → C52PointIn(s) → C53PointIn(s) → C54PointIn(s) → C55PointIn(s) → C56PointIn(s) → C57PointIn(s) → C58PointIn(s) → C59PointIn(s) → C60PointIn(s) → C61PointIn(s) → C62PointIn(s) → C63PointIn(s) → C64PointIn(s) → C65PointIn(s) → C66PointIn(s) → C67PointIn(s) → C68PointIn(s) → C69PointIn(s) → C70PointIn(s) → C71PointIn(s) → C72PointIn(s) → C73PointIn(s) → C74PointIn(s) → C75PointIn(s) → C76PointIn(s) → C77PointIn(s) → C78PointIn(s) → C79PointIn(s) → C80PointIn(s) → C81PointIn(s) → C82PointIn(s) → C83PointIn(s) → C84PointIn(s) → C85PointIn(s) → C86PointIn(s) → C87PointIn(s) → C88PointIn(s) → C89PointIn(s) → C90PointIn(s) → C91PointIn(s) → C92PointIn(s) → C93PointIn(s) → C94PointIn(s) → C95PointIn(s) → C96PointIn(s) → C97PointIn(s) → C98PointIn(s) → C99PointIn(s) → C100Midpoint(C51, O) → M51Midpoint(C52, O) → M52Midpoint(C53, O) → M53Midpoint(C54, O) → M54Midpoint(C55, O) → M55Midpoint(C56, O) → M56Midpoint(C57, O) → M57Midpoint(C58, O) → M58Midpoint(C59, O) → M59Midpoint(C60, O) → M60Midpoint(C61, O) → M61Midpoint(C62, O) → M62Midpoint(C63, O) → M63Midpoint(C64, O) → M64Midpoint(C65, O) → M65Midpoint(C66, O) → M66Midpoint(C67, O) → M67Midpoint(C68, O) → M68Midpoint(C69, O) → M69Midpoint(C70, O) → M70Midpoint(C71, O) → M71Midpoint(C72, O) → M72Midpoint(C73, O) → M73Midpoint(C74, O) → M74Midpoint(C75, O) → M75Midpoint(C76, O) → M76Midpoint(C77, O) → M77Midpoint(C78, O) → M78Midpoint(C79, O) → M79Midpoint(C80, O) → M80Midpoint(C81, O) → M81Midpoint(C82, O) → M82Midpoint(C83, O) → M83Midpoint(C84, O) → M84Midpoint(C85, O) → M85Midpoint(C86, O) → M86Midpoint(C87, O) → M87Midpoint(C88, O) → M88Midpoint(C89, O) → M89Midpoint(C90, O) → M90Midpoint(C91, O) → M91Midpoint(C92, O) → M92Midpoint(C93, O) → M93Midpoint(C94, O) → M94Midpoint(C95, O) → M95Midpoint(C96, O) → M96Midpoint(C97, O) → M97Midpoint(C98, O) → M98Midpoint(C99, O) → M99Midpoint(C100, O) → M100Sphere(M51, 1 / 2) → sphere51Sphere(M52, 1 / 2) → sphere52Sphere(M53, 1 / 2) → sphere53Sphere(M54, 1 / 2) → sphere54Sphere(M55, 1 / 2) → sphere55Sphere(M56, 1 / 2) → sphere56Sphere(M57, 1 / 2) → sphere57Sphere(M58, 1 / 2) → sphere58Sphere(M59, 1 / 2) → sphere59Sphere(M60, 1 / 2) → sphere60Sphere(M61, 1 / 2) → sphere61Sphere(M62, 1 / 2) → sphere62Sphere(M63, 1 / 2) → sphere63Sphere(M64, 1 / 2) → sphere64Sphere(M65, 1 / 2) → sphere65Sphere(M66, 1 / 2) → sphere66Sphere(M67, 1 / 2) → sphere67Sphere(M68, 1 / 2) → sphere68Sphere(M69, 1 / 2) → sphere69Sphere(M70, 1 / 2) → sphere70Sphere(M71, 1 / 2) → sphere71Sphere(M72, 1 / 2) → sphere72Sphere(M73, 1 / 2) → sphere73Sphere(M74, 1 / 2) → sphere74Sphere(M75, 1 / 2) → sphere75Sphere(M76, 1 / 2) → sphere76Sphere(M77, 1 / 2) → sphere77Sphere(M78, 1 / 2) → sphere78Sphere(M79, 1 / 2) → sphere79Sphere(M80, 1 / 2) → sphere80Sphere(M81, 1 / 2) → sphere81Sphere(M82, 1 / 2) → sphere82Sphere(M83, 1 / 2) → sphere83Sphere(M84, 1 / 2) → sphere84Sphere(M85, 1 / 2) → sphere85Sphere(M86, 1 / 2) → sphere86Sphere(M87, 1 / 2) → sphere87Sphere(M88, 1 / 2) → sphere88Sphere(M89, 1 / 2) → sphere89Sphere(M90, 1 / 2) → sphere90Sphere(M91, 1 / 2) → sphere91Sphere(M92, 1 / 2) → sphere92Sphere(M93, 1 / 2) → sphere93Sphere(M94, 1 / 2) → sphere94Sphere(M95, 1 / 2) → sphere95Sphere(M96, 1 / 2) → sphere96Sphere(M97, 1 / 2) → sphere97Sphere(M98, 1 / 2) → sphere98Sphere(M99, 1 / 2) → sphere99Sphere(M100, 1 / 2) → sphere100
AI 绘图提示语参考
画一个单位球面上的球面 Voronoi 图。先放置球心参考点并画出以它为中心、半径为1的球。随后在球面上生成一组可拖拽的“站点”（数量为若干个），让它们作为距离判定依据。用球面度量将球面划分为多个区域，每个区域由距离其最近的站点主导；同时建立若干由站点与球面几何关系确定的分界结构，使区域能随站点拖动实时更新。最后给不同区域上色以强调细胞分割效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。