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Polynomial texture mapping (PTM), also known as Reflectance Transformation Imaging (RTI), is a technique of imaging and interactively displaying objects under varying lighting conditions to reveal surface phenomena. The data acquisition method is Single Camera Multi Light (SCML). [1]
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Affine texture mapping linearly interpolates texture coordinates across a surface, and so is the fastest form of texture mapping. Some software and hardware (such as the original PlayStation ) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them.
RTI was invented by Tom Malzbender and Dan Gelb, research scientists at Hewlett-Packard Labs. A landmark paper describing these first tools and methods, named Polynomial Texture Mapping (PTM), was published in 2001." [19] RTI has several applications for cultural heritage.
UV mapping is the 3D modeling process of projecting a 3D model's surface to a 2D image for texture mapping. The letters "U" and "V" denote the axes of the 2D texture because "X", "Y", and "Z" are already used to denote the axes of the 3D object in model space, while "W" (in addition to XYZ) is used in calculating quaternion rotations, a common ...
The Phong reflection model was developed by Bui Tuong Phong at the University of Utah, who published it in his 1975 Ph.D. dissertation. [1] [2] It was published in conjunction with a method for interpolating the calculation for each individual pixel that is rasterized from a polygonal surface model; the interpolation technique is known as Phong shading, even when it is used with a reflection ...
During the texture mapping process for any arbitrary 3D surface, a texture lookup takes place to find out where on the texture each pixel center falls. For texture-mapped polygonal surfaces composed of triangles typical of most surfaces in 3D games and movies, every pixel (or subordinate pixel sample) of that surface will be associated with some triangle(s) and a set of barycentric coordinates ...
When V, W are finite-dimensional vector spaces and are viewed as algebraic varieties, then a polynomial mapping is precisely a morphism of algebraic varieties. One fundamental outstanding question regarding polynomial mappings is the Jacobian conjecture , which concerns the sufficiency of a polynomial mapping to be invertible.