Concepts inSkeleton extraction by mesh contraction
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware. The development of computer graphics has made computers easier to interact with, and better for understanding and interpreting many types of data. Developments in computer graphics have had a profound impact on many types of media and have revolutionized animation, movies and the video game industry.
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Implicit and explicit functions
The implicit function theorem provides a link between implicit and explicit functions. It states that if the equation R(x, y) = 0 satisfies some mild conditions on its partial derivatives, then one can in principle solve this equation for y, at least over some small interval. Geometrically, the graph defined by R(x,y) = 0 will overlap locally with the graph of an equation y = f(x).
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Topology
Topology (from the Greek ¿¿¿¿¿, ¿place¿, and ¿¿¿¿¿, ¿study¿) is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736.
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Skeleton
The skeleton (From Greek ¿¿¿¿¿¿¿¿, skeletos = "dried-body", "mummy") is the body part that forms the supporting structure of an organism. There are two different skeletal types: the exoskeleton, which is the stable outer shell of an organism, and the endoskeleton, which forms the support structure inside the body. In a figurative sense, skeleton can refer to technology that supports a structure such as a building.
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Animation
The bouncing ball animation (below) consists of these six frames. This animation moves at 10 frames per second. Animation is the rapid display of a sequence of images of 2-D or 3-D artwork or model positions to create an illusion of movement. The effect is an optical illusion of motion due to the phenomenon of persistence of vision, and can be created and demonstrated in several ways.
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Geometry
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early as Thales (6th Century BC).
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