Parallelogram

Parallelogram[p,{v1,v2}]

represents a parallelogram with origin p and directions v1 and v2.

Details

Examples

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Basic Examples  (3)

A standard parallelogram:

Different styles applied to a parallelogram:

Compute the Area of a parallelogram:

Centroid:

Scope  (16)

Graphics  (6)

Specification  (2)

A standard parallelogram:

A parallelogram with specified origin and directions:

Styling  (2)

Color directives specify the face color:

FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

Coordinates  (2)

Use Scaled coordinates:

Use Offset coordinates:

Regions  (10)

Embedding dimension is the dimension of the space in which the vertices exist:

Geometric dimension is the dimensionality of the region itself:

Point membership test:

Get conditions for point membership:

Measure and centroid:

Distance from a point to a parallelogram:

Visualizing:

Signed distance to a parallelogram:

Visualizing:

Nearest point:

Visualizing:

A parallelogram is bounded and convex:

Compute a bounding box:

Integrate over a parallelogram:

Optimize over a parallelogram:

Solve equations in a parallelogram:

Applications  (5)

A rhombus is a parallelogram in which all edges are the same length:

Visualize:

A parallelogram with sides that form right angles is a rectangle:

Visualize:

Any rectangle can easily be converted to a parallelogram:

The area of a parallelogram can easily be computed from the direction vectors:

Simply treat the vectors as a matrix and take the absolute value of the determinant:

Compare with Area:

A Parallelogram can tile the plane:

Properties & Relations  (6)

Rectangle is a special case of Parallelogram:

Polygon is a generalization of Parallelogram:

Parallelepiped generalizes Parallelogram to any dimension:

ImplicitRegion can represent any parallelogram:

ParametricRegion can represent any parallelogram:

A parallelogram can be represented as the union of two triangles:

Introduced in 2014
 (10.0)
 |
Updated in 2019
 (12.0)