page_title: Superquadrics
hierarchical_section_title: Superquadrics
caption_attribution_description: English: Examples of some superquadrics.
context_page_description: In mathematics, the superquadrics or super-quadrics are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs.
  The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics.
  Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. However, the supertoroids are not superquadrics as defined above; and, while some superquadrics are superellipsoids, neither family is contained in the other.
  Comprehensive coverage of geometrical properties of superquadrics and a method of their recovery from range images is covered in a monograph.
context_section_description: In mathematics, the superquadrics or super-quadrics (also superquadratics)  are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs.
  The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. 
  Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. However, the (proper) supertoroids are not superquadrics as defined above; and, while some superquadrics are superellipsoids, neither family is contained in the other.
  Comprehensive coverage of geometrical properties of superquadrics and a method of their recovery from range images is covered in a monograph .
caption: Some superquadrics.
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