In “rectangular” form the vector’s length and direction are denoted in terms of its horizontal and vertical span, the first number representing the the horizontal (“real”) and the second number (with the “j” prefix) representing the vertical (“imaginary”) dimensions.
The horizontal component is referred to as the real component, since that dimension is compatible with normal, scalar (“real”) numbers. The vertical component is referred to as the imaginary component, since that dimension lies in a different direction, totally alien to the scale of the real numbers. (Figure below )
Vector compass showing real and imaginary axes
The “real” axis of the graph corresponds to the familiar number line we saw earlier: the one with both positive and negative values on it. The “imaginary” axis of the graph corresponds to another number line situated at 90 ^{ o } to the “real” one. Vectors being twodimensional things, we must have a twodimensional “map” upon which to express them, thus the two number lines perpendicular to each other: (Figure below )
Vector compass with real and imaginary (“j”) number lines.
Either method of notation is valid for complex numbers. The primary reason for having two methods of notation is for ease of longhand calculation, rectangular form lending itself to addition and subtraction, and polar form lending itself to multiplication and division. Conversion between the two notational forms involves simple trigonometry. To convert from polar to rectangular, find the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle. This may be understood more readily by drawing the quantities as sides of a right triangle, the hypotenuse of the triangle representing the vector itself (its length and angle with respect to the horizontal constituting the polar form), the horizontal and vertical sides representing the “real” and “imaginary” rectangular components, respectively: (Figure below )
Magnitude vector in terms of real (4) and imaginary (j3) components.
To convert from rectangular to polar, find the polar magnitude through the use of the Pythagorean Theorem (the polar magnitude is the hypotenuse of a right triangle, and the real and imaginary components are the adjacent and opposite sides, respectively), and the angle by taking the arctangent of the imaginary component divided by the real component:
A grid is a structure with a
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used to align negative space in designs.
Using a grid makes content appear to flow more naturally on your page.
Grids divide horizontal space into indivisible units called "columns". All columns in a grid must specify their width as proportion of the total available row width.
All grid systems choose an arbitrary column count to allow per row. Semantic's default theme uses 16 columns .
The example below shows four
four wide
columns will fit in the first row,
16 / 4 = 4
, and three various sized columns in the second row.
2 + 8 + 6 = 16
The default column count, and other arbitrary features of grids can be changed by adjusting Semantic UI's underlying theming variables .
Rows are groups of columns which are aligned horizontally.
Rows can either be
explicit
, marked with an additional
row
element, or
implicit
, automatically occurring when no more space is left in a previous row.
After each group of columns vertical spacing is added to separate each group of columns, creating vertical rhythm.
Grid columns are separated by areas of white space referred to as "gutters". Gutters improve legibility by providing, negative space between page elements.
Gutters remain a constant size regardless of the width of the grid, or how many columns are in a row. To increase the size of gutters in a particular grid, you can use a
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variation.
Since all grid columns include gutters, grids use negative margins to make sure that the first and last columns sit flush with content outside the grid.
In the following example, you can see even though the top row has padding, the
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still sits flush with the edge of the grid.
In some cases, like when a column or row is
colored
, you may want to avoid using negative margins. You can do this by using a
padded grid
variation.
Grids are fluid and will automatically flow in size to take the maximum available width.
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are elements designed to limit page content to a reasonable maximum width for display based on the size of the user's screen.
Created at CIID byArvind Sanjeev, Lumen is a mixed reality storytelling device that lets users explore AR/VR content without being confined to headsets or mobile devices. It uses machine learning and projection mapping to provide interactive media in the physical world by overlaying a layer of digital content on top of it.
The project explores the future implications of media without screens to see how people may interact with the environment around them. Lumen consists of a laser projector in combination with a camera and depth sensors and relies on the yolo darknet machine learning platform to classify objects which is then processed by the onboard algorithm that generates stories on top of the classified objects through projection mapping.
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Arvind Sanjeev
Editorinchief at CreativeApplications.Net, cofounder and editorial director at HOLO Magazine , director of platform at and researcher/lecturer at the University of Westminster, London.
Freelance Creative Technologist (FramerJS) at IXDS GmbH
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Research and Teaching Assistant at Film University Babelsberg KONRAD WOLF
Junior Interaction Designer / Developer at Random42
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