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In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field (such as fluid motion) at high spatial resolutions. [1] The LIC technique was first proposed by Brian Cabral and Leith Casey Leedom in 1993.
Methods for visualizing vector fields include glyphs (graphical icons) such as arrows, streamlines and streaklines, particle tracing, line integral convolution (LIC) and topological methods. Later, visualization techniques such as hyperstreamlines [7] were developed to visualize 2D and 3D tensor fields.
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
In scientific visualization and computer graphics, volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field. A typical 3D data set is a group of 2D slice images acquired by a CT, MRI, or MicroCT scanner.
For a general discussion of the number of linear independent vector fields on a n-sphere, see the article vector fields on spheres. There is an interesting action of the circle group T on S 3 giving the 3-sphere the structure of a principal circle bundle known as the Hopf bundle. If one thinks of S 3 as a subset of C 2, the action is given by
A modern rendering of the Utah teapot, an iconic model in 3D computer graphics created by Martin Newell in 1975. Computer graphics is a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also ...
A vector field defines a direction and magnitude at each point in space. A field line is an integral curve for that vector field and may be constructed by starting at a point and tracing a line through space that follows the direction of the vector field, by making the field line tangent to the field vector at each point.
In scientific visualization a stream surface is the 3D generalization of a streamline. It is the union of all streamlines seeded densely on a curve. Like a streamline, a stream surface is used to visualize flows – three-dimensional flows in this case.