符号几何
Version 10 adds broad support for geometric computation, with the key element being that of geometric region. Geometric regions can be created by using special regions such as circle, using formulas, using meshes containing collections of simple regions, or combining other regions through Boolean combinations and transformations. Several standard properties can be directly computed for every region, such as membership tests, measure (e.g. length, area, volume), centroid, nearest points, etc. Regions can also be used as specifications for many high-level solvers, including optimization, algebraic equation solving, integration, and partial differential equation solving.
- 作为 Wolfram 语言的主要要素引入几何区域.
- 完全支持多种基础和常见的特殊区域. »
- 完全支持隐式和显式（参数）公式区域. »
- 完全支持一维、二维和三维中的基于网格的区域. »
- 完全支持如布尔组合和变换等导出的区域. »
- 支持任何区域的（近似、精确和带参数）计算测度（长度、面积、体积等）.
- 支持任何区域的（近似、精确和带参数）几何中心计算.
- 支持从一点到任何区域的（近似、精确和带参数）最近点、距离和符号距离的计算.
- 支持任何区域的隶属关系和条件测试.
- 支持在任何区域上的（近似、精确和带参数）积分.
- 支持使用有限元求解偏微分方程和区域上的偏微分方程组.
- 支持使用区域约束（近似和精确）的最优化.
- 支持以区域约束求解方程（近似和精确）、不等式和量词（精确并带参数）.
- 支持任何小于嵌入维数的几何维数区域，例如点、曲线和三维曲面或包括混合维数元素的区域.
- 支持非流形区域. 实际上，对流形区域没有任何需要.
- 支持在任何维数中的特殊和公式区域.
- 从含有 Delaunay 三角网格、Voronoi 田形网格和凸包的点集进行自动区域创建.
- 将二维和三维图形自动离散化为基于网格的区域.
- 将任何一维、二维和三维嵌入区域自动离散化为基于网格的区域.
- 对一维、二维和三维中的基于网格的区域自动三角剖分.
Related Examples
相关函数EmptyRegion 
FullRegion Interval Point Line InfiniteLine HalfLine SSSTriangle SASTriangle ASATriangle AASTriangle Triangle Rectangle Parallelogram Polygon InfinitePlane HalfPlane Tetrahedron Hexahedron Pyramid Prism Cuboid Parallelepiped Simplex ConicHullRegion Circle Disk Sphere Circumsphere Ball Ellipsoid Cylinder Cone ImplicitRegion ParametricRegion MeshRegionQ MeshRegion BoundaryMeshRegionQ BoundaryMeshRegion DelaunayMesh VoronoiMesh ConvexHullMesh DiscretizeGraphics BoundaryDiscretizeGraphics DiscretizeRegion BoundaryDiscretizeRegion TriangulateMesh BoundaryMesh MaxCellMeasure MeshQualityGoal MeshRefinementFunction HighlightMesh MeshCellStyle MeshCellLabel MeshCellCount MeshCoordinates MeshCells MeshCellIndex MeshPrimitives DimensionalMeshComponents ConnectedMeshComponents RegionBoundary RegionUnion RegionIntersection RegionDifference RegionSymmetricDifference BooleanRegion RegionProduct TransformedRegion InverseTransformedRegion RegionQ ConstantRegionQ BoundedRegionQ Element RegionMember RegionBounds RegionDimension RegionEmbeddingDimension RegionMeasure ArcLength Area Volume RegionCentroid RegionDistance SignedRegionDistance RegionNearest Integrate NIntegrate NDSolve Solve NSolve Reduce FindInstance Resolve Minimize Maximize MinValue MaxValue ArgMin ArgMax NMinimize NMaximize NMinValue NMaxValue NArgMin NArgMax FindMinimum FindMaximum FindMinValue FindMaxValue FindArgMin FindArgMax Indexed
FullRegion Interval Point Line InfiniteLine HalfLine SSSTriangle SASTriangle ASATriangle AASTriangle Triangle Rectangle Parallelogram Polygon InfinitePlane HalfPlane Tetrahedron Hexahedron Pyramid Prism Cuboid Parallelepiped Simplex ConicHullRegion Circle Disk Sphere Circumsphere Ball Ellipsoid Cylinder Cone ImplicitRegion ParametricRegion MeshRegionQ MeshRegion BoundaryMeshRegionQ BoundaryMeshRegion DelaunayMesh VoronoiMesh ConvexHullMesh DiscretizeGraphics BoundaryDiscretizeGraphics DiscretizeRegion BoundaryDiscretizeRegion TriangulateMesh BoundaryMesh MaxCellMeasure MeshQualityGoal MeshRefinementFunction HighlightMesh MeshCellStyle MeshCellLabel MeshCellCount MeshCoordinates MeshCells MeshCellIndex MeshPrimitives DimensionalMeshComponents ConnectedMeshComponents RegionBoundary RegionUnion RegionIntersection RegionDifference RegionSymmetricDifference BooleanRegion RegionProduct TransformedRegion InverseTransformedRegion RegionQ ConstantRegionQ BoundedRegionQ Element RegionMember RegionBounds RegionDimension RegionEmbeddingDimension RegionMeasure ArcLength Area Volume RegionCentroid RegionDistance SignedRegionDistance RegionNearest Integrate NIntegrate NDSolve Solve NSolve Reduce FindInstance Resolve Minimize Maximize MinValue MaxValue ArgMin ArgMax NMinimize NMaximize NMinValue NMaxValue NArgMin NArgMax FindMinimum FindMaximum FindMinValue FindMaxValue FindArgMin FindArgMax Indexed参见 10 的新功能
