Stereoscopic 3D Visualization on Planar Displays Stefan Seipel 2016
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Chapter 3 Image Formation
This is page 44 Printer: Opaque this Chapter 3 Image Formation And since geometry is the right foundation of all painting, I have de- cided to teach its rudiments and principles to all youngsters eager for art... – Albrecht Durer¨ , The Art of Measurement, 1525 This chapter introduces simple mathematical models of the image formation pro- cess. In a broad figurative sense, vision is the inverse problem of image formation: the latter studies how objects give rise to images, while the former attempts to use images to recover a description of objects in space. Therefore, designing vision algorithms requires first developing a suitable model of image formation. Suit- able, in this context, does not necessarily mean physically accurate: the level of abstraction and complexity in modeling image formation must trade off physical constraints and mathematical simplicity in order to result in a manageable model (i.e. one that can be inverted with reasonable effort). Physical models of image formation easily exceed the level of complexity necessary and appropriate for this book, and determining the right model for the problem at hand is a form of engineering art. It comes as no surprise, then, that the study of image formation has for cen- turies been in the domain of artistic reproduction and composition, more so than of mathematics and engineering. Rudimentary understanding of the geometry of image formation, which includes various models for projecting the three- dimensional world onto a plane (e.g., a canvas), is implicit in various forms of visual arts. The roots of formulating the geometry of image formation can be traced back to the work of Euclid in the fourth century B.C. -
Canonical View Volumes
University of British Columbia View Volumes Canonical View Volumes Why Canonical View Volumes? CPSC 314 Computer Graphics Jan-Apr 2016 • specifies field-of-view, used for clipping • standardized viewing volume representation • permits standardization • restricts domain of z stored for visibility test • clipping Tamara Munzner perspective orthographic • easier to determine if an arbitrary point is perspective view volume orthographic view volume orthogonal enclosed in volume with canonical view y=top parallel volume vs. clipping to six arbitrary planes y=top x=left x=left • rendering y y x or y x or y = +/- z x or y back • projection and rasterization algorithms can be Viewing 3 z plane z x=right back 1 VCS front reused front plane VCS y=bottom z=-near z=-far x -z x z=-far plane -z plane -1 x=right y=bottom z=-near http://www.ugrad.cs.ubc.ca/~cs314/Vjan2016 -1 2 3 4 Normalized Device Coordinates Normalized Device Coordinates Understanding Z Understanding Z near, far always positive in GL calls • convention left/right x =+/- 1, top/bottom y =+/- 1, near/far z =+/- 1 • z axis flip changes coord system handedness THREE.OrthographicCamera(left,right,bot,top,near,far); • viewing frustum mapped to specific mat4.frustum(left,right,bot,top,near,far, projectionMatrix); • RHS before projection (eye/view coords) parallelepiped Camera coordinates NDC • LHS after projection (clip, norm device coords) • Normalized Device Coordinates (NDC) x x perspective view volume orthographic view volume • same as clipping coords x=1 VCS NDCS y=top • only objects -
A Geometric Correction Method Based on Pixel Spatial Transformation
2020 International Conference on Computer Intelligent Systems and Network Remote Control (CISNRC 2020) ISBN: 978-1-60595-683-1 A Geometric Correction Method Based on Pixel Spatial Transformation Xiaoye Zhang, Shaobin Li, Lei Chen ABSTRACT To achieve the non-planar projection geometric correction, this paper proposes a geometric correction method based on pixel spatial transformation for non-planar projection. The pixel spatial transformation relationship between the distorted image on the non-planar projection plane and the original projection image is derived, the pre-distorted image corresponding to the projection surface is obtained, and the optimal view position is determined to complete the geometric correction. The experimental results show that this method can achieve geometric correction of projective plane as cylinder plane and spherical column plane, and can present the effect of visual distortion free at the optimal view point. KEYWORDS Geometric Correction, Image Pre-distortion, Pixel Spatial Transformation. INTRODUCTION Projection display technology can significantly increase visual range, and projection scenes can be flexibly arranged according to actual needs. Therefore, projection display technology has been applied to all aspects of production, life and learning. With the rapid development of digital media technology, modern projection requirements are also gradually complicated, such as virtual reality presentation with a high sense of immersion and projection performance in various forms, which cannot be met by traditional plane projection, so non-planar projection technology arises at the right moment. Compared with traditional planar projection display technology, non-planar projection mainly includes color compensation of projected surface[1], geometric splicing and brightness fusion of multiple projectors[2], and geometric correction[3]. -
COMPUTER GRAPHICS COURSE Viewing and Projections
COMPUTER GRAPHICS COURSE Viewing and Projections Georgios Papaioannou - 2014 VIEWING TRANSFORMATION The Virtual Camera • All graphics pipelines perceive the virtual world Y through a virtual observer (camera), also positioned in the 3D environment “eye” (virtual camera) Eye Coordinate System (1) • The virtual camera or “eye” also has its own coordinate system, the eyeY coordinate system Y Eye coordinate system (ECS) Z eye X Y X Z Global (world) coordinate system (WCS) Eye Coordinate System (2) • Expressing the scene’s geometry in the ECS is a natural “egocentric” representation of the world: – It is how we perceive the user’s relationship with the environment – It is usually a more convenient space to perform certain rendering tasks, since it is related to the ordering of the geometry in the final image Eye Coordinate System (3) • Coordinates as “seen” from the camera reference frame Y ECS X Eye Coordinate System (4) • What “egocentric” means in the context of transformations? – Whatever transformation produced the camera system its inverse transformation expresses the world w.r.t. the camera • Example: If I move the camera “left”, objects appear to move “right” in the camera frame: WCS camera motion Eye-space object motion Moving to Eye Coordinates • Moving to ECS is a change of coordinates transformation • The WCSECS transformation expresses the 3D environment in the camera coordinate system • We can define the ECS transformation in two ways: – A) Invert the transformations we applied to place the camera in a particular pose – B) Explicitly define the coordinate system by placing the camera at a specific location and setting up the camera vectors WCSECS: Version A (1) • Let us assume that we have an initial camera at the origin of the WCS • Then, we can move and rotate the “eye” to any pose (rigid transformations only: No sense in scaling a camera): 퐌푐 퐨푐, 퐮, 퐯, 퐰 = 퐑1퐑2퐓1퐑ퟐ … . -
CS 4204 Computer Graphics 3D Views and Projection
CS 4204 Computer Graphics 3D views and projection Adapted from notes by Yong Cao 1 Overview of 3D rendering Modeling: * Topic we’ve already discussed • *Define object in local coordinates • *Place object in world coordinates (modeling transformation) Viewing: • Define camera parameters • Find object location in camera coordinates (viewing transformation) Projection: project object to the viewplane Clipping: clip object to the view volume *Viewport transformation *Rasterization: rasterize object Simple teapot demo 3D rendering pipeline Vertices as input Series of operations/transformations to obtain 2D vertices in screen coordinates These can then be rasterized 3D rendering pipeline We’ve already discussed: • Viewport transformation • 3D modeling transformations We’ll talk about remaining topics in reverse order: • 3D clipping (simple extension of 2D clipping) • 3D projection • 3D viewing Clipping: 3D Cohen-Sutherland Use 6-bit outcodes When needed, clip line segment against planes Viewing and Projection Camera Analogy: 1. Set up your tripod and point the camera at the scene (viewing transformation). 2. Arrange the scene to be photographed into the desired composition (modeling transformation). 3. Choose a camera lens or adjust the zoom (projection transformation). 4. Determine how large you want the final photograph to be - for example, you might want it enlarged (viewport transformation). Projection transformations Introduction to Projection Transformations Mapping: f : Rn Rm Projection: n > m Planar Projection: Projection on a plane. -
Interactive Volume Navigation
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 4, NO. 3, JULY-SEPTEMBER 1998 243 Interactive Volume Navigation Martin L. Brady, Member, IEEE, Kenneth K. Jung, Member, IEEE, H.T. Nguyen, Member, IEEE, and Thinh PQ Nguyen Member, IEEE Abstract—Volume navigation is the interactive exploration of volume data sets by “flying” the viewpoint through the data, producing a volume rendered view at each frame. We present an inexpensive perspective volume navigation method designed to be run on a PC platform with accelerated 3D graphics hardware. The heart of the method is a two-phase perspective raycasting algorithm that takes advantage of the coherence inherent in adjacent frames during navigation. The algorithm generates a sequence of approximate volume-rendered views in a fraction of the time that would be required to compute them individually. The algorithm handles arbitrarily large volumes by dynamically swapping data within the current view frustum into main memory as the viewpoint moves through the volume. We also describe an interactive volume navigation application based on this algorithm. The application renders gray-scale, RGB, and labeled RGB volumes by volumetric compositing, allows trilinear interpolation of sample points, and implements progressive refinement during pauses in user input. Index Terms—Volume navigation, volume rendering, 3D medical imaging, scientific visualization, texture mapping. ——————————F—————————— 1INTRODUCTION OLUME-rendering techniques can be used to create in- the views should be produced at interactive rates. The V formative two-dimensional (2D) rendered views from complete data set may exceed the system’s memory, but the large three-dimensional (3D) images, or volumes, such as amount of data enclosed by the view frustum is assumed to those arising in scientific and medical applications. -
Computer Graphicsgraphics -- Weekweek 33
ComputerComputer GraphicsGraphics -- WeekWeek 33 Bengt-Olaf Schneider IBM T.J. Watson Research Center Questions about Last Week ? Computer Graphics – Week 3 © Bengt-Olaf Schneider, 1999 Overview of Week 3 Viewing transformations Projections Camera models Computer Graphics – Week 3 © Bengt-Olaf Schneider, 1999 VieViewingwing Transformation Computer Graphics – Week 3 © Bengt-Olaf Schneider, 1999 VieViewingwing Compared to Taking Pictures View Vector & Viewplane: Direct camera towards subject Viewpoint: Position "camera" in scene Up Vector: Level the camera Field of View: Adjust zoom Clipping: Select content Projection: Exposure Field of View Computer Graphics – Week 3 © Bengt-Olaf Schneider, 1999 VieViewingwing Transformation Position and orient camera Set viewpoint, viewing direction and upvector Use geometric transformation to position camera with respect to the scene or ... scene with respect to the camera. Both approaches are mathematically equivalent. Computer Graphics – Week 3 © Bengt-Olaf Schneider, 1999 VieViewingwing Pipeline and Coordinate Systems Model Modeling Transformation Coordinates (MC) Modeling Position objects in world coordinates Transformation Viewing Transformation World Coordinates (WC) Position objects in eye/camera coordinates Viewing EC a.k.a. View Reference Coordinates Transformation Eye (Viewing) Perspective Transformation Coordinates (EC) Perspective Convert view volume to a canonical view volume Transformation Also used for clipping Perspective PC a.k.a. clip coordinates Coordinates (PC) Perspective Perspective Division Division Normalized Device Perform mapping from 3D to 2D Coordinates (NDC) Viewport Mapping Viewport Mapping Map normalized device coordinates into Device window/screen coordinates Coordinates (DC) Computer Graphics – Week 3 © Bengt-Olaf Schneider, 1999 Why a special eye coordinate systemsystem ? In prinicipal it is possible to directly project on an arbitray viewplane. However, this is computationally very involved. -
Documenting Carved Stones by 3D Modelling
Documenting carved stones by 3D modelling – Example of Mongolian deer stones Fabrice Monna, Yury Esin, Jérôme Magail, Ludovic Granjon, Nicolas Navarro, Josef Wilczek, Laure Saligny, Sébastien Couette, Anthony Dumontet, Carmela Chateau Smith To cite this version: Fabrice Monna, Yury Esin, Jérôme Magail, Ludovic Granjon, Nicolas Navarro, et al.. Documenting carved stones by 3D modelling – Example of Mongolian deer stones. Journal of Cultural Heritage, El- sevier, 2018, 34 (November–December), pp.116-128. 10.1016/j.culher.2018.04.021. halshs-01916706 HAL Id: halshs-01916706 https://halshs.archives-ouvertes.fr/halshs-01916706 Submitted on 22 Jul 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/328759923 Documenting carved stones by 3D modelling-Example of Mongolian deer stones Article in Journal of Cultural Heritage · May 2018 DOI: 10.1016/j.culher.2018.04.021 CITATIONS READS 3 303 10 authors, including: Fabrice Monna Yury Esin University -
CSCI 445: Computer Graphics
CSCI 445: Computer Graphics Qing Wang Assistant Professor at Computer Science Program The University of Tennessee at Martin Angel and Shreiner: Interactive Computer Graphics 7E © 1 Addison-Wesley 2015 Classical Viewing Angel and Shreiner: Interactive Computer Graphics 7E © 2 Addison-Wesley 2015 Objectives • Introduce the classical views • Compare and contrast image formation by computer with how images have been formed by architects, artists, and engineers • Learn the benefits and drawbacks of each type of view Angel and Shreiner: Interactive Computer Graphics 7E © 3 Addison-Wesley 2015 Classical Viewing • Viewing requires three basic elements • One or more objects • A viewer with a projection surface • Projectors that go from the object(s) to the projection surface • Classical views are based on the relationship among these elements • The viewer picks up the object and orients it how she would like to see it • Each object is assumed to constructed from flat principal faces • Buildings, polyhedra, manufactured objects Angel and Shreiner: Interactive Computer Graphics 7E © 4 Addison-Wesley 2015 Planar Geometric Projections • Standard projections project onto a plane • Projectors are lines that either • converge at a center of projection • are parallel • Such projections preserve lines • but not necessarily angles • Nonplanar projections are needed for applications such as map construction Angel and Shreiner: Interactive Computer Graphics 7E © 5 Addison-Wesley 2015 Classical Projections Angel and Shreiner: Interactive Computer Graphics 7E -
Openscenegraph 3.0 Beginner's Guide
OpenSceneGraph 3.0 Beginner's Guide Create high-performance virtual reality applications with OpenSceneGraph, one of the best 3D graphics engines Rui Wang Xuelei Qian BIRMINGHAM - MUMBAI OpenSceneGraph 3.0 Beginner's Guide Copyright © 2010 Packt Publishing All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews. Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the authors, nor Packt Publishing and its dealers and distributors will be held liable for any damages caused or alleged to be caused directly or indirectly by this book. Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information. First published: December 2010 Production Reference: 1081210 Published by Packt Publishing Ltd. 32 Lincoln Road Olton Birmingham, B27 6PA, UK. ISBN 978-1-849512-82-4 www.packtpub.com Cover Image by Ed Maclean ([email protected]) Credits Authors Editorial Team Leader Rui Wang Akshara Aware Xuelei Qian Project Team Leader Reviewers Lata Basantani Jean-Sébastien Guay Project Coordinator Cedric Pinson -
Lecture 16: Planar Homographies Robert Collins CSE486, Penn State Motivation: Points on Planar Surface
Robert Collins CSE486, Penn State Lecture 16: Planar Homographies Robert Collins CSE486, Penn State Motivation: Points on Planar Surface y x Robert Collins CSE486, Penn State Review : Forward Projection World Camera Film Pixel Coords Coords Coords Coords U X x u M M V ext Y proj y Maff v W Z U X Mint u V Y v W Z U M u V m11 m12 m13 m14 v W m21 m22 m23 m24 m31 m31 m33 m34 Robert Collins CSE486, PennWorld State to Camera Transformation PC PW W Y X U R Z C V Rotate to Translate by - C align axes (align origins) PC = R ( PW - C ) = R PW + T Robert Collins CSE486, Penn State Perspective Matrix Equation X (Camera Coordinates) x = f Z Y X y = f x' f 0 0 0 Z Y y' = 0 f 0 0 Z z' 0 0 1 0 1 p = M int ⋅ PC Robert Collins CSE486, Penn State Film to Pixel Coords 2D affine transformation from film coords (x,y) to pixel coordinates (u,v): X u’ a11 a12xa'13 f 0 0 0 Y v’ a21 a22 ya'23 = 0 f 0 0 w’ Z 0 0z1' 0 0 1 0 1 Maff Mproj u = Mint PC = Maff Mproj PC Robert Collins CSE486, Penn StateProjection of Points on Planar Surface Perspective projection y Film coordinates x Point on plane Rotation + Translation Robert Collins CSE486, Penn State Projection of Planar Points Robert Collins CSE486, Penn StateProjection of Planar Points (cont) Homography H (planar projective transformation) Robert Collins CSE486, Penn StateProjection of Planar Points (cont) Homography H (planar projective transformation) Punchline: For planar surfaces, 3D to 2D perspective projection reduces to a 2D to 2D transformation. -
Opensg Starter Guide 1.2.0
OpenSG Starter Guide 1.2.0 Generated by Doxygen 1.3-rc2 Wed Mar 19 06:23:28 2003 Contents 1 Introduction 3 1.1 What is OpenSG? . 3 1.2 What is OpenSG not? . 4 1.3 Compilation . 4 1.4 System Structure . 5 1.5 Installation . 6 1.6 Making and executing the test programs . 6 1.7 Making and executing the tutorials . 6 1.8 Extending OpenSG . 6 1.9 Where to get it . 7 1.10 Scene Graphs . 7 2 Base 9 2.1 Base Types . 9 2.2 Log . 9 2.3 Time & Date . 10 2.4 Math . 10 2.5 System . 11 2.6 Fields . 11 2.7 Creating New Field Types . 12 2.8 Base Functors . 13 2.9 Socket . 13 2.10 StringConversion . 16 3 Fields & Field Containers 17 3.1 Creating a FieldContainer instance . 17 3.2 Reference counting . 17 3.3 Manipulation . 18 3.4 FieldContainer attachments . 18 ii CONTENTS 3.5 Data separation & Thread safety . 18 4 Image 19 5 Nodes & NodeCores 21 6 Groups 23 6.1 Group . 23 6.2 Switch . 23 6.3 Transform . 23 6.4 ComponentTransform . 23 6.5 DistanceLOD . 24 6.6 Lights . 24 7 Drawables 27 7.1 Base Drawables . 27 7.2 Geometry . 27 7.3 Slices . 35 7.4 Particles . 35 8 State Handling 37 8.1 BlendChunk . 39 8.2 ClipPlaneChunk . 39 8.3 CubeTextureChunk . 39 8.4 LightChunk . 39 8.5 LineChunk . 39 8.6 PointChunk . 39 8.7 MaterialChunk . 40 8.8 PolygonChunk . 40 8.9 RegisterCombinersChunk .