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Continuity and Interpolation techniques for Computer Graphics

Continuity and interpolation have been crucial topics for computer graphics since its very beginnings. Every time we want to interpolate values across some area, we need to take a set of samples over that interpolating region. However, interpolating samples faithfully allowing the results to closely match the underlying functions can be a tricky task as the functions to sample could not be smooth and, in the worst case, it could be even impossible when they are not continuous. In those situations bringing the required continuity is not an easy task, and much work has been done to solve this problem. In this paper, we focus on the state of the art in continuity and interpolation in three stages of the real-time rendering pipeline. We study these problems and their current solutions in texture space (2D), object space (3D) and screen space. With this review of the literature in these areas, we hope to bring new light and foster research in these fundamental, yet not completely solved problems in computer graphics

We would like to thank the people that helped this work to become true, in particular the ViRVIG-GGG members. This work was partially funded by the TIN2013-47137-C2-2-P project from Ministerio de Economia y Competitividad, Spain

© Computer Graphics Forum, 2015, vol.35, núm. 1, p. 309-322

Wiley

Manager: Ministerio de Economía y Competitividad (Espanya)
Author: González García, Francisco
Patow, Gustavo
Date: 2016 February
Abstract: Continuity and interpolation have been crucial topics for computer graphics since its very beginnings. Every time we want to interpolate values across some area, we need to take a set of samples over that interpolating region. However, interpolating samples faithfully allowing the results to closely match the underlying functions can be a tricky task as the functions to sample could not be smooth and, in the worst case, it could be even impossible when they are not continuous. In those situations bringing the required continuity is not an easy task, and much work has been done to solve this problem. In this paper, we focus on the state of the art in continuity and interpolation in three stages of the real-time rendering pipeline. We study these problems and their current solutions in texture space (2D), object space (3D) and screen space. With this review of the literature in these areas, we hope to bring new light and foster research in these fundamental, yet not completely solved problems in computer graphics
We would like to thank the people that helped this work to become true, in particular the ViRVIG-GGG members. This work was partially funded by the TIN2013-47137-C2-2-P project from Ministerio de Economia y Competitividad, Spain
Format: application/pdf
Citation: 024601
ISSN: 0167-7055 (versió paper)
1467-8659 (versió electrònica)
Document access: http://hdl.handle.net/10256/12094
Language: eng
Publisher: Wiley
Collection: MINECO/PE 2014-2015/TIN2013-47137-C2-2-P
Reproducció digital del document publicat a: http://dx.doi.org/10.1111/cgf.12727
Articles publicats (D-IMAE)
Is part of: © Computer Graphics Forum, 2015, vol.35, núm. 1, p. 309-322
Rights: Tots els drets reservats
Subject: Infografia
Computer graphics
Visualització (Informàtica)
Information display systems
Interpolació (Matemàtica)
Interpolation
Title: Continuity and Interpolation techniques for Computer Graphics
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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