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well-formed_objects [2014/09/22 07:03]
ameya
well-formed_objects [2017/10/05 05:52] (current)
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 ===== Well-formed Objects ===== ===== Well-formed Objects =====
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-A **well-formed shape** is defined as a shape that is complete and without abberation. For example, a rubber-band stretched in the shape of a rectangle is well-formed. However, a set of four lines meeting at four corners may not be considered as a well-formed shape. For example, a set of four matchsticks put together in the shape of a rectangle does not create a well-formed shape, even if the corners are glued together. 
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-A typical CAD software has shapes built out of elements like points and lines. These are called **ill-formed** shapes. Likewise, when a shape is extruded to form a volume, it can either be a well-formed object or not. 
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-A typical surface modeling software has objects that are ill-formed. Multiple ill-formed shapes come together to form the faces of the volume (object). In case of solid modeling software, if the geometry of the object can further be sub-divided into further geometrical shapes and elements, then the objects are considered as ill-formed objects. However, if the objects in the solid modeling software are holistic in nature and cannot be further geometrically sub-divided,​ they are considered as **well-formed objects**. 
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 A **well-formed** shape is a complete, holistic shape. For example, a rubber-band stretched in the shape of a rectangle is a well-formed shape. However, a set of four lines meeting at four corners are not considered as a well-formed shape. For example, a set of four matchsticks put together in the shape of a rectangle does not create a well-formed shape, even if the corners are glued together. A **well-formed** shape is a complete, holistic shape. For example, a rubber-band stretched in the shape of a rectangle is a well-formed shape. However, a set of four lines meeting at four corners are not considered as a well-formed shape. For example, a set of four matchsticks put together in the shape of a rectangle does not create a well-formed shape, even if the corners are glued together.
  
-In CAD software, shapes are built out of elements like points and lines. Such shapes are ill-formed shapes. Similarly, when a shape is extruded to form a volume, it can either be a well-formed object or not. Multiple ill-formed shapes come together to form the faces of the volume. In solid modeling software, if an object can further be subdivided into other geometrical shapes and elements, ​ the objects are considered as ill-formed objects. However, the objects in the solid modeling software are holistic in nature and cannot be subdivided further geometrically. Therefore, these shapes are considered as well-formed objects.+In CAD software, shapes are built out of elements like points and lines. Such shapes are **ill-formed** shapes. Similarly, when a shape is extruded to form a volume, it can either be a well-formed object or not. Multiple ill-formed shapes come together to form the faces of the volume. In solid modeling software, if an object can further be subdivided into other geometrical shapes and elements, ​ the objects are considered as ill-formed objects. However, the objects in the solid modeling software are holistic in nature and cannot be subdivided further geometrically. Therefore, these shapes are considered as well-formed objects.
  

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Last modified: le 2017/10/05 05:52