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3D projection
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display.
3D objects are largely displayed on two-dimensional mediums (such as paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in engineering drawing, drafting, and computer graphics. Projections can be calculated through employment of mathematical analysis and formulae, or by using various geometric and optical techniques.
In order to display a three-dimensional (3D) object on a two-dimensional (2D) surface, a projection transformation is applied to the 3D object using a projection matrix. This transformation removes information in the third dimension while preserving it in the first two. See Projective Geometry for more details.
If the size and shape of the 3D object should not be distorted by its relative position to the 2D surface, a parallel projection may be used.
Examples of parallel projections:
If the 3D perspective of an object should be preserved on a 2D surface, the transformation must include scaling and translation based on the object's relative position to the 2D surface. This process is called perspective projection. Examples of perspective projections:
In parallel projection, the lines of sight from the object to the projection plane are parallel to each other. Thus, lines that are parallel in three-dimensional space remain parallel in the two-dimensional projected image. Parallel projection also corresponds to a perspective projection with an infinite focal length (the distance from a camera's lens and focal point), or "zoom".
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3D projection
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display.
3D objects are largely displayed on two-dimensional mediums (such as paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in engineering drawing, drafting, and computer graphics. Projections can be calculated through employment of mathematical analysis and formulae, or by using various geometric and optical techniques.
In order to display a three-dimensional (3D) object on a two-dimensional (2D) surface, a projection transformation is applied to the 3D object using a projection matrix. This transformation removes information in the third dimension while preserving it in the first two. See Projective Geometry for more details.
If the size and shape of the 3D object should not be distorted by its relative position to the 2D surface, a parallel projection may be used.
Examples of parallel projections:
If the 3D perspective of an object should be preserved on a 2D surface, the transformation must include scaling and translation based on the object's relative position to the 2D surface. This process is called perspective projection. Examples of perspective projections:
In parallel projection, the lines of sight from the object to the projection plane are parallel to each other. Thus, lines that are parallel in three-dimensional space remain parallel in the two-dimensional projected image. Parallel projection also corresponds to a perspective projection with an infinite focal length (the distance from a camera's lens and focal point), or "zoom".