A strictly 0D MeshRegion is a point set:

Label the points with HighlightMesh:

A strictly 1D MeshRegion is a collection of line segments:

Label the segments with HighlightMesh:

A MeshRegion can combine elements of different dimensions:

Separate them with DimensionalMeshComponents:

A strictly 0D MeshRegion is a point set:

Label the points with HighlightMesh:

A strictly 1D MeshRegion is a collection of line segments:

Label the segments with HighlightMesh:

A strictly 2D MeshRegion is a collection of polygonal faces:

Label the faces with HighlightMesh:

A MeshRegion can combine elements of different dimensions:

Separate them with DimensionalMeshComponents:

A strictly 0D MeshRegion is a point set:

Label the points with HighlightMesh:

A strictly 1D MeshRegion is a collection of line segments:

Label the segments with HighlightMesh:

A strictly 2D MeshRegion is a collection of polygonal faces:

Label the faces with HighlightMesh:

A strictly 3D MeshRegion is a collection of polyhedral volumes:

Polyhedral volume cells include Tetrahedron, Prism, Pyramid, and Hexahedron:

A MeshRegion can combine elements of different dimensions:

MeshCellLabel can be used to label the parts of a MeshRegion:

The labels do not have to be strings:

Labeled can be used as a wrapper to label cells when constructing a MeshRegion:

The labels do not need to be strings:

MeshCellMarker can be used to mark parts of a MeshRegion:

MeshCellStyle can be used to set the Style of components of a MeshRegion:

Style can be used as a wrapper to style cells when constructing a MeshRegion:

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 shading:

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

Embedding dimension:

Geometric dimension:

Point membership test:

Visualize it:

Measure is ArcLength for a 1D mesh, Area for a 2D mesh, and Volume for a 3D mesh:

Compute and visualize the centroids of each:

Distance from a point:

Visualize it:

Signed distance from a point:

Visualize it:

Nearest point in the region:

Visualize it:

A MeshRegion is always bounded:

Get its bounds:

Visualize the bounding box:

Integrate over a MeshRegion:

MeshCellCount returns the number of cells matching a given dimension or cell specification:

Get the number of 1D cells:

When no cell specification is given, the value for each dimension is returned:

MeshCells returns the cells in the mesh matching a given dimension or cell specification:

Get the 1D cells:

Individual cell indices or sets of cell indices can be used:

MeshCellIndex gets the index of a cell or set of cells in a mesh:

MeshCoordinates gets the coordinates of the mesh:

This list of coordinates is what the MeshCells refer to:

MeshPrimitives returns the primitives that make up the mesh:

Individual cell indices or sets of cell indices can be used:

DimensionalMeshComponents separates out components of a mesh with different dimensions:

ConnectedMeshComponents separates out components of a mesh based on connectivity:

MeshCellMeasure can be used to get the measures of a set of cells in a mesh:

The appropriate measure is used for each dimension:

MeshCellCentroid can be used to get the centroids of a set of cells in a mesh:

Visualize it:

MeshCellQuality can be used to get the quality of a set of cells in a mesh:

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

Use numerical values for AspectRatio:

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 a background color:

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 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:

MeshCellHighlight allows you to specify highlighting for parts of a MeshRegion:

By making faces transparent, the internal structure of a 3D MeshRegion can be seen:

Individual cells can be highlighted using their cell index:

Or by the cell itself:

MeshCellLabel can be used to label parts of a MeshRegion:

Label the vertices and edges of a polygon:

Individual cells can be labeled using their cell index:

Or by the cell itself:

MeshCellMarker can be used to assign values to parts of a MeshRegion:

Use MeshCellLabel to show the markers:

MeshCellShapeFunction allows you to specify functions for parts of a MeshRegion:

Individual cells can be drawn using their cell index:

Or by the cell itself:

MeshCellStyle allows you to specify styling for parts of a MeshRegion:

By making faces transparent, the internal structure of a 3D MeshRegion can be seen:

Individual cells can be styled using their cell index:

Or by the cell itself:

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 1 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:

Define a simple graphic to use as a background:

Use it in multiple 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 no tick marks:

Place tick marks automatically:

Draw tick marks at 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:

Extract the lines from a MeshRegion to make a wireframe mesh:

The indices given in MeshCells correspond to MeshCoordinates:

Compare properties:

Compute the perimeter of a regular polygon:

Compute perimeter lengths:

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

Create a mesh region of a Koch curve using a Lindenmayer system:

Define a function for interpreting characters in the production string to coordinates using turtle graphics:

Initial parameters for interpreting the production string:

Compute coordinates of the Koch curve from the production string:

Generate mesh regions from the coordinates:

Find a formula for the length of the Koch curve at iteration :

Convert a graph to a MeshRegion:

Some 2D embedded graphs:

You can compute with these as geometric regions:

Some 3D embedded graphs:

You can still compute with them:

You can, for instance, compute the curve integral across these curves:

Create a surface mesh by extruding a 2D curve mesh:

Some examples with planar layouts:

You can compute with the resulting regions, in this case computing surface integrals:

Directly generate a rectangular grid mesh. Here IndexFlatten flattens out the position index in the same way that Flatten would flatten it:

Alternatively, generate the same mesh region as the product of 1D meshes:

Generalize the direct method above to generate a mesh region corresponding to a pattern matrix:

Some simple patterns:

More involved patterns:

Directly generate a rectangular grid mesh. Here IndexFlatten flattens out the position index in the same way that Flatten would flatten it:

Alternatively, generate the same mesh region as the product of 1D meshes:

Generalize the direct method above to generate a mesh region corresponding to a pattern matrix:

A simple pattern:

More involved patterns:

Use the idea above to construct a Seidel mesh, i.e. a mesh region with tunnels going in every direction without crossing:

By converting to a boundary mesh and styling it, it becomes easier to comprehend: