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Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable examples include plane curves , space curves , polyhedra , ordinary differential equations , partial differential equations (particularly numerical solutions, as in fluid dynamics or minimal surfaces such as soap films ...
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Polynomial texture mapping may be used for detailed recording and documentation, 3D modeling, edge detection, and to aid the study of inscriptions, rock art [5] and other artefacts. [ 3 ] [ 6 ] It has been applied to hundreds of the Vindolanda tablets by the Centre for the Study of Ancient Documents at the University of Oxford in conjunction ...
Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low ...
A transition map provides a way of comparing two charts of an atlas. To make this comparison, we consider the composition of one chart with the inverse of the other. This composition is not well-defined unless we restrict both charts to the intersection of their domains of definition. (For example, if we have a chart of Europe and a chart of ...
A normal pointing to top right corner of the texture (1,1,0) is mapped to (255,255,128). Hence the top-right corner of an object is usually light yellow. The brightest part of a color map. A normal pointing to right of the texture (1,0,0) is mapped to (255,128,128). Hence the right edge of an object is usually light red.
In computer graphics, a procedural texture [1] is a texture created using a mathematical description (i.e. an algorithm) rather than directly stored data. The advantage of this approach is low storage cost, unlimited texture resolution and easy texture mapping . [ 2 ]
This atlas contains every chart that is compatible with the smooth structure. There is a natural one-to-one correspondence between smooth structures and maximal smooth atlases. Thus, we may regard a smooth structure as a maximal smooth atlas and vice versa. In general, computations with the maximal atlas of a manifold are rather unwieldy.