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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
Orthogonal functions are necessary for transforms such as the FFT, or the DCT. orthogonal transform a transform whose basis functions are orthogonal. The transform matrix of a discrete orthogonal transform is an orthogonal matrix. Sometimes orthogonal transform is used to refer to a unitary transform. Orthogonal real transforms exhibit the property of energy conservation. orthogonal wavelet wavelet functions that form orthogonal basis by translation and dilation of a mother wavelet. orthographic projection a form of projection in which the rays forming an image are modeled as moving along parallel paths on their way to the image plane: usually the paths are taken to be orthogonal to the image plane. Orthographic projection suppresses information on depth in the scene. A limiting case of perspective projection. orthonormal functions an orthogonal signal set f m (t) on [t1 , t2 ] such that
Manipulate View
Published in Tamara Munzner, Visualization Analysis and Design, 2014
With the project design choice, all items are shown, but without the information for specific dimensions chosen to exclude. For instance, the shadow of an object on a wall or floor is a projection from 3D to 2D. There are many types of projection; some retain partial information about the removed dimensions, while others eliminate that completely. A very simple form of projection is orthographic projection: for each item the values for excluded dimensions are simply dropped, and no information about the eliminated dimensions is retained. In the case of orthographic projection from 3D to 2D, all information about depth is lost. Projections are often used via multiple views, where there can be a view for each possible combination of dimensions. For instance, standard architectural blueprints show the three possible views for axis-aligned 2D views of a 3D XYZ scene: a floor plan for the XY dimensions, a side view for YZ, and a front view for XZ. A more complex yet more familiar form of projection is the standard perspective projection, which also projects from 3D to 2D. This transformation happens automatically in our eyes and is mathematically modeled in the perspective transformation used in the computer graphics virtual camera. While a great deal of information about depth is lost, some is retained through the perspective distortion foreshortening effect, where distant objects are closer together on the image plane than nearby objects would be. Many map projections from the surface of the Earth to 2D maps have been proposed by cartographers, including the well-known Mercator projection. These projections transform from a curved to a flat space, and most of the design choices when creating them concern whether distorting angles or areas is less problematic for the intended abstract task.1
Design and graphical communication
Published in Mike Tooley, Engineering GCSE, 2012
When you produced the simple GA and detail drawings in 1.3 you made use of a basic drawing technique called orthographic projection. Orthographic projection is used to represent 3D solids on the 2D surface of a sheet of drawing paper so that all the dimensions are true length and all the surfaces are true to shape. To achieve this when surfaces are inclined to the vertical or the horizontal we have to make use of additional auxiliary views, but more about these later. Let us keep things simple for the moment.
Three-dimensional angularity characterization of coarse aggregates based on experimental comparison of selected methods
Published in Particulate Science and Technology, 2022
Huaiying Fang, Hejun Zhu, Jianhong Yang, Xiaoyu Huang, Xiang Hu
A VHX-6000 digital microscope (Keyence, Japan) was used to measure the 3D contours of the CA. It mainly comprises a main frame, VH-Z20T camera shot, XY platform, Z platform, and controller, as shown in Figure 3. The resolution and moving speed of the XY platform were respectively 1 µm and 20 mm/s while that of the Z platform were respectively 0.1 µm and 17 mm/s. In recording surface data of the CA, the magnification of the VH-Z20T camera shot was set to 50 times and the resolution of the XY platform was 4.4 µm. The digital microscope took an image with 1600 × 1200 pixels and thus needed to perform 3D image jointing when measuring CAs (to give a maximum size of 20,000 × 20,000 pixels). Figure 4 was a flowchart of the detection process. The CA was first placed in the middle of the XY platform. The moving range of the XY platform was ±50 mm, and the XY platform could be controlled by the controller to select the orthographic projection area of the CA. The distance between the VH-Z20T camera shot and the XY platform was then adjusted, and the automatic focusing function was turned on to set the highest and lowest values of the CA in turn. The 3D contours of the CA were finally obtained by 3 D image jointing and converted into 3D data points.
Fine scale optical remote sensing experiment of mixed stand over complex terrain (FOREST) in the Genhe Reserve Area: objective, observation and a case study
Published in International Journal of Digital Earth, 2021
Biao Cao, Jianbo Qi, Erxue Chen, Qing Xiao, Qinhuo Liu, Zengyuan Li
The sun zenith and azimuth angles (42.3°, 163.0°) were calculated by the Sun Position Calculator tool of LESS based on the flight date, time, and geographical position of KEA. The sensor was set to orthographic projection with view zenith angle equal to zero. This simulation took around 50 min on a laptop with 16 GB memory and 8 cores. Four reflectance images were simulated for comparison with the LiCHy-Hyperspectral measured image. Figure 15a-b illustrates the LESS simulated results using the individual-tree approach while Figure 15c-d shows the results using the voxel-based approach. It can be found that the results of the voxel-based approach were brighter than the corresponding image of the individual-tree approach and closer to the LiCHy-Hyperspectral measured images. However, the simulated images are much more homogeneous than the airborne measured images. We can obtain the reflectance difference between the measured and simulated results in the two bands. Figure 15e-h show the reflectance bias histograms for Figure 15a-d, respectively. It can be found that the simulated results of the individual-tree approach were overall underestimated whereas the histogram of the reflectance bias of the voxel-based approach simulated results was close to the normal distribution.
A mirror in the sky: assessment of an augmented reality method for depicting navigational information
Published in Ergonomics, 2020
Adam J. Reiner, Justin G. Hollands, Greg A. Jamieson, Sabah Boustila
The simulation was rendered using Unity 5, which ran on an Intel Core i7-6700HQ CPU MSI laptop computer with 2.60 GHz core using an NVIDIA GeForce GTX 1060 graphics card. For the MitS display, we used the testbed settings created by the developers. A map was projected onto a virtual hemispheric dome with a radius of 1050 m using an orthographic projection centred at the participant’s position. The self-marker was not presented directly above the participant at the centre of the dome, but rather at an offset such that the marker was presented at a 45° visual angle from the horizon, to make it easier for the user to see. The rest of the map was compressed to compensate for the offset, such that the map’s projection was no longer orthographic (similar to dome with offset in Figure 2). The Map presentation showed the map tilted at a 30° angle. This was intended to simulate a smartphone or GPS device which is often held in front of the user at an angle.