Isometric projection is a method for representing visually three-dimensional objects in two dimensions in technical and technical drawings. This is an axonometric projection in which the three coordinate axes look the same for sorting and the angle between them is 120 degrees.
Video Isometric projection
Overview
The term "isometric" comes from the Greek for "equal size", which reflects that the scale along each axis of the projection is the same (unlike other forms of graphical projection).
An isometric view of an object can be obtained by selecting the viewing direction such that the angle between the projection of x , y , and z axes are all the same, or 120 °. For example, with a cube, this is done by first looking directly into one face. Next, the cube is rotated  ± 45  ° about the vertical axis, followed by a rotation of about 35,264  ° (precisely the arc 3 or arctan 1 / ? 2 , related to the Magic angle) about the horizontal axis. Note that with the cube (see figure) the resulting 2D image perimeter is a perfect regular hex: all black lines have the same length and all the faces of the cube are the same area. Isometric graph paper can be placed under a sheet of normal drawing paper to help achieve the effects without calculation.
Similarly, an isometric view can be obtained in 3D scenes. Starting with the camera parallel to the floor and parallel to the coordinate axis, it is first rotated vertically (around the horizontal axis) about 35,264  ° as above, then  ± 45  ° around the vertical axis.
Another way of isometric projection can be visualized is to consider the inner view of the cubic room starting at the upper corner and looking towards the opposite and lower angles. The x -axis extends diagonally down and right, y -axis extends diagonally down and left, and z -axis straight to the top. The depth is also indicated by the height in the image. The lines drawn along the axis are at 120 ° to each other.
The term "isometric" is often incorrectly used to refer to the projection of axonometry, in general. However, there are actually three types of axonometric projection: isometric, dimetric and trimetric.
Maps Isometric projection
Rotation angle
Of the two angles required for isometric projection, the second value may appear to be contrary to intuition and deserves further explanation. Let us imagine a cube with a long side 2, and its center is positioned on the origin axis. We can calculate the length of the line from its center to the center of each edge as ? 2 using Pythagoras' theorem. By rotating the cube 45 Â ° at x -axis, the point (1, 1, 1) will be (1, 0, ? 2 ) as illustrated in the diagram. The second rotation aims to bring the same point on positive z -axis and therefore it is necessary to rotate the same value as arctangent 1 / ? 2 which is approximately 35.264 Â °.
Math
7 other possibilities are obtained by turning to the opposite side or not, and then reversing the direction of the view or not.
History and limits
First formalized by Professor William Farish (1759-1837), the concept of isometry has existed in rough empirical form for centuries. From the mid-19th century, isometry became "an invaluable tool for engineers, and soon axonometry and isometry were incorporated in the curriculum of architectural training courses in Europe and the US". According to Jan Krikke (2000), "axonometry comes from China, whose function in Chinese art is similar to the linear perspective in European art." Axonometry and its accompanying grammar have taken on a new meaning with the emergence of visual computing.
Like all parallel projection types, objects drawn with isometric projection do not appear larger or smaller because they extend closer to or away from the viewer. While advantageous for architectural drawings where measurements need to be taken directly, the result is a perceived distortion, unlike a perspective projection, not how human vision or photography usually works. It can also easily produce situations where depth and altitude are difficult to measure, as shown in the illustration on the right. This may appear to create paradoxical or impossible forms, such as the Penrose ladder.
Usage in video games and pixel art
Isometric graphs were regularly used in video games during the 1980s and 1990s, as these techniques provide limited 3D effects that can be achieved with limited microcomputer resources in this day and age. This style is also used for sprites and pixel art, achieving a distinctive style that is still used in retrogaming.
See also
- Graphical projection
References
External links
- Isometric Projection
Source of the article : Wikipedia
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