Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from http://reference.wolfram.com/language/ref/BoundaryMeshRegion.html below:

BoundaryMeshRegion—Wolfram Language Documentation

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technology expertise.

• Data & Computational Intelligence
• Model-Based Design
• Algorithm Development
• Wolfram|Alpha for Business
• Blockchain Technology
• Education Technology
• Quantum Computation

WolframConsulting.com

• See Also
  • MeshRegion
  • BoundaryDiscretizeRegion
  • BoundaryDiscretizeGraphics
  • ConvexHullMesh
  • BoundaryMesh
  • FindMeshDefects
  • BoundaryMeshRegionQ
  • MeshCellCount
  • MeshCoordinates
  • MeshCells
  • MeshCellIndex
  • MeshPrimitives
  • Printout3D
  • Formats
  • 3DS
  • BYU
  • X3D
• Related Guides
  • Mesh-Based Geometric Regions
  • Geometric Computation
  • Partial Differential Equations
  • Polyhedra
  • 3D Printing
• Workflows
  • Make a 3D Printout

BoundaryMeshRegion[{p₁,p₂,…},{bcell₁[{i₁,…}],bcell₂[{j₁,…}],…}]

yields a mesh with boundary cells bcell_j, where coordinates given as integer i are taken to be p_i, where the cells together represent a closed curve, surface, etc.

BoundaryMeshRegion[…,{…,w_i[bcell_i[…]],…}]

yields a mesh with cell properties defined by the symbolic wrapper w_i.

BoundaryMeshRegion[…,boundary₁,boundary₂,…]

yields a mesh from multiple boundaries boundary_i.

• BoundaryMeshRegion is also known as a boundary representation.
• BoundaryMeshRegion can represent a piecewise linear and full-dimensional region embedded in dimension 1, 2, or 3.
• BoundaryMeshRegion[…] displays in a notebook as a plot of a boundary mesh region.
• BoundaryMeshRegion is typically constructed using functions such as ConvexHullMesh, BoundaryMesh, BoundaryDiscretizeRegion, and BoundaryDiscretizeGraphics.
• The boundary cells need to represent a closed curve or surface without self-intersections.
• In BoundaryMeshRegion[{p₁,p₂,…},b₁,b₂,…], the boundary curves or surfaces b_i should not cross themselves or each other.
• In BoundaryMeshRegion[{p₁,p₂,…},b₁,b₂,…], a point p is considered to be in the region enclosed by the boundary curves or surfaces b_i if any infinite ray starting at p crosses the set of boundaries b_i an odd number of times.
• The following special wrappers w_i can be used for boundary faces:
• Labeled[cell,…] display the cell with labeling Style[cell,…] show the cell with the specified style Annotation[cell,name->value] associate the annotation name->value with cell
• Each cell in a BoundaryMeshRegion is given a unique MeshCellIndex of the form {d,i}, where d is the geometric dimension and i is the index.
• For purposes of selecting cells of a BoundaryMeshRegion, the following cell specifications may be used:
• {d,i} cell with index i of dimension d {d,ispec} cells with index specification ispec of dimension d {dspec,…} cells of dimensions given by dspec h[{i₁,…}] explicit cell with head h and vertex indices i₁, … {c₁,c₂,…} list of explicit cells c_i
• The index specification ispec can have the following form:
• i cell index i {i₁,i₂,…} cells with indices i_k All all cells patt cells with indices matching the pattern patt
• The dimension specification dspec can have the following form:
• d explicit dimension d All all dimensions from 0 to geometric dimension of region patt dimensions matching the pattern patt
• BoundaryMeshRegion contains cells of maximal dimension n-1, where n is the embedding dimension.
• BoundaryMeshRegion is always converted to an optimized representation and treated as raw by functions like AtomQ for purposes of pattern matching.
• BoundaryMeshRegion has the same options as Graphics for embedding dimension two, and the same options as Graphics3D for embedding dimension three, with the following additions and changes:
• Possible settings for PlotTheme include common base themes, font features themes, and size features themes.
• Mesh feature themes affect the plot of mesh cells. Themes include:
• Rendering feature themes affect the rendering of meshes. Themes include:
• Style and other specifications for cells are effectively applied in the order MeshCellStyle, Style, and other wrappers, with later specifications overriding earlier ones.
• Label style and other specifications for cell labels are effectively applied in the order MeshCellLabel and Labeled, with later specifications overriding earlier ones.
• BoundaryMeshRegion can be used with functions such as RegionMember, RegionDistance, RegionMeasure, and NDSolve.

Specify an interval from its boundary points:

It is full dimensional:

The region is bounded:

The length and centroid:

Check point membership:

Specify a triangle from its closed boundary curve:

It is full dimensional:

The region is bounded:

The area and centroid:

Check point membership:

Specify a tetrahedron from its closed boundary surface:

It is full dimensional:

The region is bounded:

The volume and centroid:

Check point membership:

Specify a 2D region from multiple closed boundary curves:

Find its area:

Specify a 3D region from multiple closed boundary surfaces:

Find its volume:

Specify an interval from its boundary points:

Label the points with HighlightMesh:

It is full dimensional:

The region is bounded:

The length and centroid:

Check point membership:

Specify a 1D region from multiple boundary points:

Apply Style to boundary points:

Label boundary points:

Specify a triangle from its closed boundary curve:

Label the segments with HighlightMesh:

It is full dimensional:

The region is bounded:

The area and centroid:

Check point membership:

Specify a 2D region from multiple closed boundary curves:

Label the points with their corresponding indexes with HighlightMesh:

Apply Style to specific boundary lines:

Label specific boundary lines:

Specify a tetrahedron from its closed boundary surface:

Label the segments with HighlightMesh:

It is full dimensional:

The region is bounded:

The volume and centroid:

Check point membership:

Specify a 3D region from multiple closed boundary surfaces:

Apply Style to specific boundary faces:

Label specific boundary faces:

Use a theme to draw 0D cells:

Use a theme to draw 1D cells or a wireframe:

Use a theme to draw 2D cells:

Use a theme to draw sampled points from mesh cells:

Use a theme to smooth the shading:

Use a theme to draw normals for each 2D cell:

Specify the position to be aligned in 3D Inset, using coordinates:

Draw all the axes:

Draw the axis, but not the axis:

Choose the bounding box edges automatically to draw the axes:

Choose the bounding box edges automatically to draw the axes:

Place a label for the axis:

Specify a label for each axis:

Determine where the axes cross automatically:

Specify the axes' origin explicitly:

Specify the overall axes style, including the ticks and the tick labels:

Specify the style of each axis:

Specify the style of each axis:

Align the center of a graphic with the baseline of the text:

Specify the baseline of a graphic as a fraction of the height by using Scaled:

Use the axis of a graphic as the baseline:

Set the starting style:

Set multiple starting styles:

Draw the edges of the bounding box:

Do not draw the edges of the bounding box:

Specify the ratios between the bounding box edges:

Use the actual coordinate values for the ratios:

Use dashed lines for the bounding box:

Draw a disk above the graphic, including the axes:

Put grids on every face of a 3D graphic:

Put grids on both ‐ faces:

Put face grids on the plane:

On the plane, put grid lines on , , and :

Specify the overall style of face grids:

Draw a frame around the whole graphic:

Draw a frame on the left and the right edges:

Specify frame labels for the bottom and the left edges:

Specify labels for each edge:

Specify the overall frame style:

Specify the style of each frame edge:

Put a frame, but no ticks:

Tick mark labels on the bottom and the left frame edges:

Frame ticks on the bottom and the right edges:

Specify frame tick and frame tick label style:

Specify frame tick style for each edge:

Put grids across a 2D graphic:

Draw grid lines at specific positions:

Specify the style of each grid:

Specify the overall grid style:

Allow no margins outside of ImageSize:

Have 20-point margins on all sides:

Draw grid lines at specific positions:

Leave no padding outside of the plot range:

Leave enough padding for all objects and labels that are present:

Specify the same padding for all sides in printer's points:

Specify the same padding for all sides in printer's points:

Use predefined symbolic sizes:

Use an explicit image width:

Use an explicit image width and height:

Specify the overall style of all the label-like elements:

Ambient light is uniformly applied to all the surfaces in the scene:

Directional lights with different colors:

Point lights with different colors:

Spotlights with different colors:

MeshCellLabel can be used to label parts of a BoundaryMeshRegion:

MeshCellLabel can reveal a cell's index with "Index", "CellIndex", or "Cell":

Any expression can be used as a label:

Label all cells with tooltips:

All can be used to specify all cells:

By default, all cells are labeled:

Label all cells of a given dimension:

Label specific vertices and edges of a polygon:

Alternatively, you can specify a head and indices:

Specify a list of cell indices to label:

Label cells whose dimensions match a pattern:

Label cells whose indices match a pattern:

Wrappers have precedence over options:

All can be used to specify all cells:

By default, all cells are styled:

Style all cells of a given dimension:

Style specific vertices and edges of a polygon:

Alternatively, you can specify a head and indices:

Specify a list of cell indices to style:

Style cells whose dimensions match a pattern:

Style cells whose indices match a pattern:

Style with graphics directives appropriate for the dimension of the components:

Wrappers have precedence over options:

Display a label on the top of the graphic in TraditionalForm:

Use Style and other typesetting functions to modify how the label appears:

Display all objects:

Explicitly choose and ranges:

Force clipping at the PlotRange:

PlotRange->s is equivalent to PlotRange->{{-s, s}, {-s, s}}:

Allow graphics objects to spread beyond PlotRange:

Clip all graphics objects at PlotRange:

Include coordinate unit of padding on all sides:

Include padding using Scaled coordinates:

Specify different padding on each side:

The contents of a graphic use the whole region:

Limit the contents of the graphic to the middle half of the region in each direction:

ImagePadding can also be used to add padding around a graphic:

Use a common based theme:

Use a monochrome theme:

Use a theme to draw 0D cells:

Use a theme to draw 1D cells or a wireframe:

Use a theme to draw 2D cells:

Use a theme to draw sampled points from mesh cells:

Use a theme to draw points as spheres and lines as tubes:

Use a theme to smooth shading:

Use a theme to draw normals for each 2D cell:

Define a simple graphic to use as a background:

Use it in multiple boundary mesh regions:

Specify that vertical frame labels should be rotated:

Specify that vertical frame labels should not be rotated:

Make a sequence of images be consistently sized, independent of orientation:

Without SphericalRegion, each image is made as big as possible:

Draw the axes, but not tick marks:

Place tick marks automatically:

Draw tick marks at the specific positions:

Specify the styles of the ticks and tick labels:

Specify the styles of and axis ticks separately:

Use a specific angle for a simulated camera:

Place the top-right corner of the object at the center of the final image:

Orthographic view of a mesh region from the negative direction:

Specify the view point using the special scaled coordinates:

Use symbolic view points:

Specify orthographic views:

By default, the range is sufficient to include all the objects:

Specify the minimum and maximum distances from the camera to be included:

Specify the view vectors using ordinary coordinates:

Use the axis direction as the vertical direction in the final image:

Various views of vertical directions:

Non-intersecting polygons are also BoundaryMeshRegion:

The resulting regions can be used for computing:

The area approaches as the number of sides goes to infinity:

Build a BoundaryMeshRegion in 2D with multiple rectangular holes. The coordinates for the inner rectangles:

The indexes for the inner rectangle closed curves:

Generating an outer rectangle with × inner rectangle closed curves:

The resulting mesh can be used for computing:

Non-intersecting polyhedra are also a BoundaryMeshRegion:

The Archimedean or semi-regular polyhedra:

Color the faces based on the number of vertices:

Color the faces of Archimedean polyhedra:

Build a BoundaryMeshRegion with multiple voids by using multiple inner cuboid boundaries. The coordinates for the inner cuboids:

The indexes for inner cuboid closed surfaces:

Generating an outer cuboid with ×× inner cuboid surfaces:

The resulting region can be used for computing:

Construct a cuboid boundary mesh with rectangular tunnels through it. You can construct it as the product of a 2D boundary mesh with an interval. Using the same construction as for constructing the polygon with holes above for the 2D boundary mesh:

The resulting boundary representation for a polygon with × holes:

Compute the Cartesian product with an interval:

Style it so that you can only see the boundary surfaces:

You can still compute with this region:

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4