Journal Article10.1145/3973.3976
Incremental linear interpolation
51
TL;DR: Two incremental linear interpolation algorithms are derived and analyzed for speed and accuracy and a new algorithm is shown to achieve perfect accuracy and, depending on the underlying processor, may be faster than the fixed-point algorithm.
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Abstract: Two incremental linear interpolation algorithms are derived and analyzed for speed and accuracy. The first is a version of a “simple” digital differential analyzer (DDA) employing fixed-point arithmetic, whereas the second is a new algorithm that uses only integral arithmetic and is a generalization of Bresenham's line-drawing algorithm. The new algorithm is shown to achieve perfect accuracy and, depending on the underlying processor, may be faster than the fixed-point algorithm.
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Citations
Quad-Mesh Generation and Processing: A Survey
David Bommes,Bruno Levy,Nico Pietroni,Enrico Puppo,Cláudio T. Silva,Marco Tarini,Denis Zorin +6 more
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Spectral convergence of the connection Laplacian from random samples
Amit Singer,Hau-Tieng Wu +1 more
TL;DR: This paper proves that the eigenvectors and eigenvalues of these Laplacians converge in the limit of infinitely many independent random samples, and generalizes the spectral convergence results to the case where the data points are sampled from a non-uniform distribution, and for manifolds with and without boundary.
121
Patch-Collaborative Spectral Point-Cloud Denoising
TL;DR: A new framework for point cloud denoising by patch‐collaborative spectral analysis is presented, which competes favourably with state‐of‐the‐art approaches, and extends patch‐based algorithms from the image processing domain to point clouds of arbitrary sampling.
•Posted Content
Spectral Convergence of the connection Laplacian from random samples
Amit Singer,Hau-Tieng Wu +1 more
TL;DR: In this paper, a unified framework for approximating other connection Laplacians over the manifold by considering its principle bundle structure was presented, and it was shown that the eigenvectors and eigenvalues of these LaplACians converge in the limit of infinitely many independent random samples.
78
Continuous shading of curved surfaces
Henri Gouraud
- 01 Jan 1982
TL;DR: In this paper, a procedure for computing shaded pictures of curved surfaces is presented, where the surface is approximated by small polygons in order to solve easily the hidden-parts problem, but the shading of each polygon is computed so that the discontinuities of shade are eliminated across the surface and a smooth appearance is obtained.
60
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TL;DR: The principles of interactive computer graphics are discussed in this article, where the authors propose a set of principles for the development of computer graphics systems, including the principles of Interactive Computer Graphics (ICG).
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Continuous shading of curved surfaces
Henri Gouraud
- 01 Jul 1998
TL;DR: The surface is approximated by small polygons in order to solve easily the hidden-parts problem, but the shading of each polygon is computed so that discontinuities of shade are eliminated across the surface and a smooth appearance is obtained.
624
Using program transformations to derive line-drawing algorithms
TL;DR: The transformations are used to derive several highly parallel variants of Bresenham's algorithm, designed for use on displays that can generate more than one pixel at a time.
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