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Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1] The theoretical basis for descriptive geometry is provided by planar geometric projections.
Mathematics in art: Albrecht Dürer's copper plate engraving Melencolia I, 1514. Mathematical references include a compass for geometry, a magic square and a truncated rhombohedron, while measurement is indicated by the scales and hourglass. [1] Wireframe drawing [2] of a vase as a solid of revolution [2] by Paolo Uccello. 15th century
Fine art: Use of group theory, self-replicating shapes in art [21] [22] Escher, M. C. 1898–1972: Fine art: Exploration of tessellations, hyperbolic geometry, assisted by the geometer H. S. M. Coxeter [19] [23] Farmanfarmaian, Monir: 1922–2019: Fine art: Geometric constructions exploring the infinite, especially mirror mosaics [24] Ferguson ...
Stereotomy is strongly associated with stonecutting and has a very long history. Descriptive geometry can be considered as an evolution of streotomy. [3] In technical drawing stereotomy is sometimes referred to as descriptive geometry, and "is concerned with two-dimensional representations of three dimensional objects. Plane projections and ...
The Rytz’s axis construction is a basic method of descriptive geometry to find the axes, the semi-major axis and semi-minor axis and the vertices of an ellipse, starting from two conjugated half-diameters. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or by hand (see ellipse).
In painting, photography, graphical perspective and descriptive geometry, a picture plane is an image plane located between the "eye point" (or oculus) and the object being viewed and is usually coextensive to the material surface of the work.
Descriptive geometry customarily relies on obtaining various views by imagining an object to be stationary and changing the direction of projection (viewing) in order to obtain the desired view. See Figure 1. Using the rotation technique above, note that no orthographic view is available looking perpendicularly at any of the inclined surfaces.
Artists may choose to "correct" perspective distortions, for example by drawing all spheres as perfect circles, or by drawing figures as if centered on the direction of view. In practice, unless the viewer observes the image from an extreme angle, like standing far to the side of a painting, the perspective normally looks more or less correct.