Concepts inLaplacian lines for real-time shape illustration
Laplacian matrix
In the mathematical field of graph theory the Laplacian matrix, sometimes called admittance matrix or Kirchhoff matrix, is a matrix representation of a graph. Together with Kirchhoff's theorem it can be used to calculate the number of spanning trees for a given graph. The Laplacian matrix can be used to find many other properties of the graph; see spectral graph theory.
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Real-time computing
In computer science, real-time computing (RTC), or reactive computing, is the study of hardware and software systems that are subject to a "real-time constraint"¿ e.g. operational deadlines from event to system response. Real-time programs must guarantee response within strict time constraints. Often real-time response times are understood to be in the order of milliseconds and sometimes microseconds.
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Illustration
An illustration is a rendition that is created to elucidate or dictate sensual information (such as a story, poem or newspaper article).
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Laplace operator
In mathematics the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ¿·¿, ¿ or ¿. The Laplacian ¿¿(p) of a function ¿ at a point p, up to a constant depending on the dimension, is the rate at which the average value of ¿ over spheres centered at p, deviates from ¿(p) as the radius of the sphere grows.
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Edge detection
Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction, which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in 1D signals is known as step detection.
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Image processing
In imaging science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or a set of characteristics or parameters related to the image. Most image-processing techniques involve treating the image as a two-dimensional signal and applying standard signal-processing techniques to it.
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Zero crossing
Zero-crossing is a commonly used term in electronics, mathematics, and image processing. In mathematical terms, a "zero-crossing" is a point where the sign of a function changes (e.g. from positive to negative), represented by a crossing of the axis (zero value) in the graph of the function.
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Line drawing algorithm
A line drawing algorithm is a graphical algorithm for approximating a line segment on discrete graphical media. On discrete media, such as pixel-based displays and printers, line drawing requires such an approximation (in nontrivial cases). On continuous media, by contrast, no algorithm is necessary to draw a line. For example, oscilloscopes use natural phenomena to draw lines and curves.
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