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Axonometry
Axonometry is a graphical procedure belonging to descriptive geometry that generates a Planar graph, planar image of a three-dimensional object. The term "axonometry" means "to measure along Cartesian coordinate system, axes", and indicates that the Dimension, dimensions and Scaling (geometry), scaling of the coordinate axes play a crucial role. The result of an axonometric procedure is a uniformly-scaled parallel projection of the object. In general, the resulting parallel projection is oblique projection, oblique (the rays are not perpendicular to the image plane); but in special cases the result is orthographic projection, orthographic (the rays are perpendicular to the image plane), which in this context is called an Orthogonality, orthogonal axonometry. In technical drawing and in architecture, axonometric perspective is a form of Two-dimensional space, two-dimensional representation of Three-dimensional space, three-dimensional objects whose goal is to preserve the impressi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axonometric Projection
Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the object is rotated around one or more of its axes to reveal multiple sides.Gary R. Bertoline et al. (2002) ''Technical Graphics Communication''. McGraw–Hill Professional, 2002. , p. 330. Overview "Axonometry" means "to measure along the axes". In German literature, axonometry is based on Pohlke's theorem, such that the scope of axonometric projection could encompass ''every'' type of parallel projection, including not only orthographic projection (and multiview projection), but also oblique projection. However, outside of German literature, the term "axonometric" is sometimes used only to distinguish between orthographic views where the principal axes of an object are ''not'' orthogonal to the projection plane, and orthographic views in which the principal axes of the object ''are'' orthogonal to the projection plane. (In multiview projection thes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Projection
In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane, known as the ''projection plane'' or ''image plane'', where the '' rays'', known as '' lines of sight'' or ''projection lines'', are parallel to each other. It is a basic tool in descriptive geometry. The projection is called '' orthographic'' if the rays are perpendicular (orthogonal) to the image plane, and '' oblique'' or '' skew'' if they are not. Overview A parallel projection is a particular case of ''projection'' in mathematics and ''graphical projection'' in technical drawing. Parallel projections can be seen as the limit of a central or perspective projection, in which the rays pass through a fixed point called the ''center'' or ''viewpoint'', as this point is moved towards infinity. Put differently, a parallel projection corresponds to a perspective projection with an infinite focal length (the distance between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foreshortening
Linear or point-projection perspective () is one of two types of 3D projection, graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by station point, the eye. Perspective drawing is useful for representing a three-dimensional space, three-dimensional scene in a plane (mathematics), two-dimensional medium, like paper. It is based on the Magnification#Single lens, optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to , meaning that an object's dimensions Parallel (geometry), parallel to the line of sight appear shorter than its dimensions perpendicular to the line of sight. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pohlke's Theorem
Pohlke's theorem is the fundamental theorem of axonometry. It was established 1853 by the German painter and teacher of descriptive geometry Karl Wilhelm Pohlke. The first proof of the theorem was published 1864 by the German mathematician Hermann Amandus Schwarz, who was a student of Pohlke. Therefore the theorem is sometimes called theorem of Pohlke and Schwarz, too. The theorem *Three arbitrary line sections \overline O\overline U,\overline O\overline V,\overline O\overline W in a plane originating at point \overline O, which are not contained in a line, can be considered as the parallel projection of three edges OU,OV,OW of a cube. For a mapping of a unit cube, one has to apply an additional scaling either in the space or in the plane. Because a parallel projection and a scaling preserves ratios one can map an arbitrary point P=(x,y,z) by the axonometric procedure below. Pohlke's theorem can be stated in terms of linear algebra as: *Any Affine transformation, affine mapping ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relief
Relief is a sculpture, sculptural method in which the sculpted pieces remain attached to a solid background of the same material. The term ''wikt:relief, relief'' is from the Latin verb , to raise (). To create a sculpture in relief is to give the impression that the sculpted material has been raised above the background Plane (geometry), plane. When a relief is carved into a flat surface of stone (relief sculpture) or wood (relief carving), the field is actually lowered, leaving the unsculpted areas seeming higher. The approach requires chiselling away of the background, which can be time-intensive. On the other hand, a relief saves forming the rear of a subject, and is less fragile and more securely fixed than a sculpture in the round, especially one of a standing figure where the ankles are a potential weak point, particularly in stone. In other materials such as metal, clay, plaster stucco, ceramics or papier-mâché the form can be simply added to or raised up from the bac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' meaning "equal", and μέτρον ''metron'' meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion. Introduction Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional Euclidean space, two geometric figures are congruent if they are related by an isometry; the isometry that relates them is either a rigid motion (translation or rotati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Square
A set square or triangle (American English) is an object used in engineering and technical drawing, with the aim of providing a straightedge at a right angle or other particular planar angle to a baseline. Types The simplest form of set square is a triangular piece of transparent plastic (or formerly of polished wood) with the centre removed. More commonly the set square bears the markings of a ruler and a half circle protractor. The outer edges are typically bevelled. These set squares come in two usual forms, both right triangles: one with 90-45-45 degree angles, the other with 30-60-90 degree angles. Combining the two forms by placing the hypotenuses together will also yield 15° and 75° angles. They are often purchased in packs with protractors and compasses. Less commonly found is the adjustable set square. Here, the body of the object is cut in half and rejoined with a hinge marked with angles. Adjustment to the marked angle will produce any desired angl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
