Shape and form (visual arts)

In the visual arts, shape is a flat, enclosed area of an artwork created through lines, textures, colours or an area enclosed by other shapes for example triangles circles and squares. Likewise, a form can refer to a three-dimensional composition or object within a three-dimensional composition.

The outline of an enclosed 2D object

A form is an artist's way of using elements of art, principles of design, and media. Element of art that is three-dimensional and encloses space. Like a shape, a form has length and width, but it also has depth. Forms are either geometric or free-form. usually a form gives an idea of how a shape looks like

Geometric shapes are precise edged and mathematically consistent curves, they are pure forms and so consist of circles, squares, spirals, triangles, while geometric forms are simple volumes, such as cubes, cylinders and pyramids. They generally dominate architecture, technology, industry and crystalline structures.

In contrast, organic shapes are free-form, unpredictable and flowing in appearance. These shapes, as well as organic forms, visually suggest the natural world of animals, plants, sky, sea, etc... The addition of organic shapes to a composition dominated by geometric structures can add unpredictable energy.

Definitions:

Rectilinear- characterized by straight lines.

Curvilinear- consisting of or bounded by curved lines: a curvilinear figure.

Examples:

Rectilinear- http://mathworld.wolfram.com/RectilinearCrossingNumber.html

Curvilinear- http://www.marklaurence.com/articles/discourse_on_curves.html

A positive shape is a shape, that has details inside it, such as an outline of a human, with body features. While, a negative shape is a shape without any details; it's just an outline.

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Wikipedia