page_title: Geometric design
hierarchical_section_title: Geometric design
caption_attribution_description: English: 3D Curves, example
context_page_description: Geometrical design is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumesand is closely related to geometric modeling. Core problems are curve and surface modelling and representation. GD studies especially the construction and manipulation of curves and surfaces given by a set of points using polynomial, rational, piecewise polynomial, or piecewise rational methods. The most important instruments here are parametric curves and parametric surfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the level-set method.
  Application areas include shipbuilding, aircraft, and automotive industries, as well as architectural design. The modern ubiquity and power of computers means that even perfume bottles and shampoo dispensers are designed using techniques unheard of by shipbuilders of 1960s.
  Geometric models can be built for objects of any dimension in any geometric space. Both 2D and 3D geometric models are extensively used in computer graphics. 2D models are important in computer typography and technical drawing.
context_section_description: Geometrical design (GD) is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumesand is closely related to geometric modeling. Core problems are curve and surface modelling and representation. GD studies especially the construction and manipulation of curves and surfaces given by a set of points using polynomial, rational, piecewise polynomial, or piecewise rational methods. The most important instruments here are parametric curves and parametric surfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the level-set method.
  Application areas include shipbuilding, aircraft, and automotive industries, as well as architectural design. The modern ubiquity and power of computers means that even perfume bottles and shampoo dispensers are designed using techniques unheard of by shipbuilders of 1960s.
  Geometric models can be built for objects of any dimension in any geometric space. Both 2D and 3D geometric models are extensively used in computer graphics. 2D models are important in computer typography and technical drawing. 3D models are central to computer-aided design and manufacturing, and many applied technical fields such as geology and medical image processing.
  Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an algorithm. They are also contrasted with digital images and volumetric models; and with  mathematical models such as the zero set of an arbitrary polynomial. However, the distinction is often blurred: for instance, geometric shapes can be represented by objects; a digital image can be interpreted as a collection of colored squares; and geometric shapes such as circles are defined by implicit mathematical equations. Also, the modeling of fractal objects often requires a combination of geometric and procedural techniques.
  Geometric problems originating in architecture can lead to interesting research and results in geometry processing, computer-aided geometric design, and discrete differential geometry.
  In architecture, geometric design is associated with the pioneering explorations of Chuck Hoberman into transformational geometry as a design idiom, and applications of this design idiom within the domain of architectural geometry.
caption: 3D curves — Example 01
exif: {"Image Orientation": "Horizontal (normal)", "Image XResolution": "72", "Image YResolution": "72", "Image ResolutionUnit": "Pixels/Inch", "Image Software": "Adobe Photoshop 7.0", "Image DateTime": "2007:03:10 20:32:24", "Image ExifOffset": "156", "Thumbnail Compression": "JPEG (old-style)", "Thumbnail XResolution": "72", "Thumbnail YResolution": "72", "Thumbnail ResolutionUnit": "Pixels/Inch", "Thumbnail JPEGInterchangeFormat": "294", "Thumbnail JPEGInterchangeFormatLength": "3499", "EXIF ColorSpace": "Uncalibrated", "EXIF ExifImageWidth": "130", "EXIF ExifImageLength": "130"}