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Parallelogram—Wolfram Language Documentation

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• See Also
  • Rectangle
  • Polygon
  • Parallelepiped
  • Cuboid
  • MeshRegion
• Related Guides
  • Graphics Objects
  • Basic Geometric Regions
  • Plane Geometry
  • Polygons

Parallelogram[p,{v₁,v₂}]

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

• Parallelogram is also known as rhomboid and rhombus.
• Parallelogram represents , where the vectors v_i have to be linearly independent.
• Parallelogram[] is equivalent to Parallelogram[{0,0},{{1,0},{1,1}}].
• CanonicalizePolygon can be used to convert a parallelogram to an explicit Polygon object.
• Parallelogram can be used as a geometric region and graphics primitive.
• Parallelogram can be used in Graphics.
• In graphics, the point p and vectors v_i can be Scaled and Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, EdgeForm, Opacity, and color.

A standard parallelogram:

Different styles applied to a parallelogram:

Compute the Area of a parallelogram:

Centroid:

A standard parallelogram:

A parallelogram with specified origin and directions:

Color directives specify the face color:

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

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:

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:

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