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The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors are equal to 1, we have directional scaling. In the case where v x = v y = v z = k, scaling increases the area of any surface by a factor of k 2 and the volume of any solid object by a factor of k 3.
An architect's scale is a specialized ruler designed to facilitate the drafting and measuring of architectural drawings, such as floor plans and Multi-view orthographic projections. Because the scale of such drawings is often smaller than life-size, an architect's scale features multiple units of length and proportional length increments. [1]
Another way isometric projection can be visualized is by considering a view within a cubical room starting in an upper corner and looking towards the opposite, lower corner. The x-axis extends diagonally down and right, the y-axis extends diagonally down and left, and the z-axis is straight up. Depth is also shown by height on the image.
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Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. [1] In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale.
In an orthogonal coordinate system the lengths of the basis vectors are known as scale factors. The scale factors for the elliptic coordinates ( μ , ν ) {\displaystyle (\mu ,\nu )} are equal to h μ = h ν = a sinh 2 μ + sin 2 ν = a cosh 2 μ − cos 2 ν . {\displaystyle h_{\mu }=h_{\nu }=a{\sqrt {\sinh ^{2}\mu +\sin ^{2 ...
Oblique drawing is also the crudest "3D" drawing method but the easiest to master. One way to draw using an oblique view is to draw the side of the object in two dimensions, i.e. flat, and then draw the other sides at an angle of 45°, but instead of drawing the sides full size they are only drawn with half the depth creating 'forced depth ...
The size of an angle is formalized as an angular measure. In Euclidean geometry, angles are used to study polygons and triangles, as well as forming an object of study in their own right. [43] The study of the angles of a triangle or of angles in a unit circle forms the basis of trigonometry. [58]