Head Mounted Display Optics I!
|
|
|
- Logan Griffin
- 5 years ago
- Views:
Transcription
1 ! Head Mounted Display Optics I! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 7! stanford.edu/class/ee267/!!
2 ! Logistics! HW3 is probably the longest homework, so get started asap if you have not done so already! What is MAR (minimum angle of resolution)?! Conflicting definitions of whether it s the visual angle of 1 pixel or 1 cycle (=2 pixels) for consistency, we use the same definition as in Guenther et al., which is 2 pixels! all hardware for HW4 will be given out in lab/office hours on Friday, 10-11:30am, Packard 001!
3 Lecture Overview! 1. stereo rendering for HMDs! 2. lens distortion correction using GLSL!
4 1. Stereo Rendering for HMDs! All Current-generation VR HMDs are Simple Magnifiers!
5 Image Formation! HMD! micro display! lens! Side View!
6 Image Formation! HMD! micro display! h' lens! f d ' d eye Side View! eye relief!
7 virtual image! Image Formation! HMD! h world origin is in the center of the virtual image!! micro display! h' lens! f d ' d Side View! d eye eye relief!
8 virtual image! Image Formation! h Gaussian thin lens formula:! 1 d + 1 d ' = 1 f d = 1 1 f 1 d ' micro display! h' HMD! lens! f d ' d Side View! d eye eye relief!
9 virtual image! Image Formation! h Gaussian thin lens formula:! 1 d + 1 d ' = 1 f Magnification:! M = f f d ' d = 1 1 f 1 d ' h = Mh' micro display! h' HMD! d ' lens! f d Side View! d eye eye relief!
10 virtual image! Image Formation! view frustum symmetric! h y z world origin is in the center of the virtual image!! d Side View! d eye eye relief!
11 virtual image! Image Formation! view frustum symmetric! near clipping plane! h y z d Side View! d eye eye relief!
12 virtual image! Image Formation! h y z view frustum symmetric! top! bottom! near clipping plane! z near d Side View! d eye eye relief!
13 virtual image! Image Formation! h similar triangles:! top = z near bottom = z near h ( ) 2 d + d eye h ( ) 2 d + d eye view frustum symmetric! top! bottom! near clipping plane! z near d Side View! d eye eye relief!
14 Image Formation! HMD! ipd! w' d ' d eye Top View! eye relief!
15 Image Formation Left Eye! HMD! w' 2 ipd/2! d eye Top View! eye relief!
16 virtual image! Image Formation Left Eye! HMD! w 1 x z ipd/2! w 2 d Top View! d eye eye relief!
17 virtual image! Image Formation Left Eye! w 1 x w 1 = M ipd 2 HMD! z ipd/2! w 2 w 2 = M w' ipd 2 d d eye eye relief! Top View!
18 virtual image! Image Formation Left Eye! w 1 x view frustum asymmetric! near clipping plane! z near z w 2 d d eye eye relief! Top View!
19 virtual image! Image Formation Left Eye! w 1 x view frustum asymmetric! near clipping plane! z near z right! left! w 2 d d eye eye relief! Top View!
20 virtual image! Image Formation Left Eye! w 1 similar triangles:! right = z near w 1 d + d eye view frustum asymmetric! near clipping plane! z near right! w 2 left = z near w 2 d + d eye d left! d eye eye relief! Top View!
21 w 2 virtual image! x w 2 = M Image Formation Right Eye! w' ipd 2 view frustum asymmetric! w 1 z w 1 = M ipd 2 d Top View! d eye eye relief!
22 w 2 virtual image! similar triangles:! Image Formation Right Eye! right = z near w 2 d + d eye view frustum asymmetric! right! z near left! w 1 left = z near w 1 d + d eye d Top View! d eye eye relief!
23 View Matrix - Lookat! center point (right eye)! eye position (right eye)! h ipd! center point (right eye)! d Top View! eye position (left eye)! d eye eye relief!
24 Prototype Specs View-Master Deluxe VR Viewer!! roughly follows Google Cardboard 2.0:! lenses focal length: 40 mm! lenses diameter: 34 mm! inter-lens distance: 64 mm! screen to lens distance: 39 mm! eye relief: 18 mm! Topfoison 6 LCD: width mm, height 74.5 mm; either 1920x1080 pixels (1080p) or 2650x1440 pixels (2K)!
25 ! Image Formation! use these formulas to compute the perspective matrix in WebGL! you can use:! THREE.Matrix4().makePerspective(left,right,top,bottom,near,far) THREE.Matrix4().lookAt(eye,center,up) that s all you need to render stereo images on the HMD!
26 Image Formation for More Complex Optics! especially important in free-form optics, off-axis optical configurations & AR! use ray tracing some nonlinear mapping from view frustum to microdisplay pixels! much more computationally challenging & sensitive to precise calibration; our HMD and most magnifier-based designs will work with what we discussed so far!
27 2. Lens Distortion Correction! All lenses introduce image distortion, chromatic aberrations, and other artifacts we need to correct for them as best as we can in software!
28 Lens Distortion! grid seen through HMD lens! lateral (xy) distortion of the image! chromatic aberrations: distortion is wavelength dependent!! image from:
29 Lens Distortion! Pincussion Distortion! Barrel Distortion!
30 Lens Distortion! Pincussion Distortion! optical! Barrel Distortion! digital correction!
31 image from: Lens Distortion!
32 Lens Distortion! x u, y u undistorted point!
33 Lens Distortion! x u, y u undistorted point! ( ) ( ) x d x u 1+ K 1 r 2 + K 2 r 4 y d y u 1+ K 1 r 2 + K 2 r 4 ( x c, y c ) x d, y d K 1,K 2 r x c, y c distorted point coordinates! distortion coefficients! normalized distance from center! center of optical axis! Barrel Distortion! digital correction!
34 Lens Distortion! x d, y d K 1,K 2 r x c, y c x u, y u undistorted point! ( ) ( ) x d x u 1+ K 1 r 2 + K 2 r 4 y d y u 1+ K 1 r 2 + K 2 r 4 distorted point coordinates! distortion coefficients! normalized distance from center! center of optical axis! NOTES:! center is assumed to be the center point (on optical axis) on screen! distortion is radially symmetric around center point! easy to get confused!! can implement in fragment shader (not super efficient, but easier for us)!
35 Normalizing r! x u, y u undistorted point! ( ) ( ) x d x u 1+ K 1 r 2 + K 2 r 4 y d y u 1+ K 1 r 2 + K 2 r 4 un-normalized radial distance from center:! ( ) 2 + ( y u y c ) 2 r! 2 = x u x c x c, y c center! r! Calculate in metric units, e.g. mm. Need physical size of the pixels of your screen for this!
36 virtual image! Normalizing r! r! r = r! d in mm mm view frustum symmetric! r! distance of a pixel from center point in mm! d distance to lens in mm!! r normalized, unit-less distance! that we use for distortion!! d Side View!
37 Lens Distortion Center Point! x c, y c right eye! h ipd! x c, y c left eye! d Top View! d eye eye relief!
38 Lens Distortion Correction Example! stereo rendering without lens distortion correction!
39 Lens Distortion Correction Example! stereo rendering with lens distortion correction!
40 How to Render into Different Parts of the Window?! WebGLRenderer.setViewport(x,y,width,height) x,y lower left corner; width, height viewport size! width2 height2 height1 (x2,y2) (x3,y3) height3 (x1,y1) width1 width3
41 Microdisplays!
42 Liquid Crystal Display (LCD) - Subpixels! IPS! wikipedia! S-IPS! IPS! TN subpixels!
43 wikipedia! LCD!
44 LCD Backlight! wikipedia! extremetech.com!
45 Liquid Crystal on Silicon (LCoS)! basically a reflective LCD! standard component in projectors and head mounted displays! used e.g. in google glass!
46 Organic Light Emitting Diodes (OLED)! lightrabbit.co.uk!
47 Digital Micromirror Device (DMD)! developed by Texas Instruments! MEMS device! binary states (e.g. +/- 10 degrees)! gray-level through pulse width modulation (PWM)! Texas Instruments!
48 B. T. Schowengerdt, R. Johnston, C.D. Melville, E.J. Seibel. 3D Displays Using Scanning Laser Projection. SID 2012.!
49 Next Lecture: HMD Displays Optics II! advanced VR & AR optics! microdisplays! drawing from Google Glass patent!
The Graphics Pipeline and OpenGL IV: Stereo Rendering, Depth of Field Rendering, Multi-pass Rendering!
! The Graphics Pipeline and OpenGL IV: Stereo Rendering, Depth of Field Rendering, Multi-pass Rendering! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 6! stanford.edu/class/ee267/!!
The Graphics Pipeline and OpenGL I: Transformations!
! The Graphics Pipeline and OpenGL I: Transformations! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 2! stanford.edu/class/ee267/!! Logistics Update! all homework submissions:
The Graphics Pipeline and OpenGL I: Transformations!
! The Graphics Pipeline and OpenGL I: Transformations! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 2! stanford.edu/class/ee267/!! Albrecht Dürer, Underweysung der Messung mit
LIGHT & OPTICS. Fundamentals of Physics 2112 Chapter 34 1
LIGHT & OPTICS Fundamentals of Physics 22 Chapter 34 Chapter 34 Images. Two Types of Images 2. Plane Mirrors 3. Spherical Mirrors 4. Images from Spherical Mirrors 5. Spherical Refracting Surfaces 6. Thin
Paraxial into real surfaces
Paraxial into real surfaces Curvature, Radius Power lens and mirrors lens maker equation mirror and lens in contact Principle planes Real Surfaces Refractive via Fermat s Principle Calculate optical path
Rigid Body Motion and Image Formation. Jana Kosecka, CS 482
Rigid Body Motion and Image Formation Jana Kosecka, CS 482 A free vector is defined by a pair of points : Coordinates of the vector : 1 3D Rotation of Points Euler angles Rotation Matrices in 3D 3 by 3
Models and Architectures
Models and Architectures Objectives Learn the basic design of a graphics system Introduce graphics pipeline architecture Examine software components for an interactive graphics system 1 Image Formation
WORCESTER POLYTECHNIC INSTITUTE
WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT Optical Metrology and NDT ME-593L, C 2018 Lecture 03 January 2018 Lasers sources Some operating characteristics: laser modes Schematic
Essential Physics I. Lecture 13:
Essential Physics I E I Lecture 13: 11-07-16 Reminders No lecture: Monday 18th July (holiday) Essay due: Monday 25th July, 4:30 pm 2 weeks!! Exam: Monday 1st August, 4:30 pm Announcements 250 word essay
Displays which can see. Adrian Travis Microsoft
Displays which can see Adrian Travis Microsoft Contents In praise of projection Wedge projection Window-like displays 3D displays Visionaries want offices to have wall-sized displays so that staff work
PH 222-2A Spring 2015
PH 222-2A Spring 2015 Images Lectures 24-25 Chapter 34 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 3 Chapter 34 Images One of the most important uses of the basic laws governing light
Camera model and multiple view geometry
Chapter Camera model and multiple view geometry Before discussing how D information can be obtained from images it is important to know how images are formed First the camera model is introduced and then
Dispersion (23.5) Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 17
Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 17 Dispersion (23.5) The speed of light in a material depends on its wavelength White light is a mixture of wavelengths
CSE 167: Lecture #4: Vertex Transformation. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012
CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2012 Announcements Project 2 due Friday, October 12
Lecture PowerPoint. Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli
Lecture PowerPoint Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the
Chapter 34. Images. In this chapter we define and classify images, and then classify several basic ways in which they can be produced.
Chapter 34 Images One of the most important uses of the basic laws governing light is the production of images. Images are critical to a variety of fields and industries ranging from entertainment, security,
Welcome to: Physics I. I m Dr Alex Pettitt, and I ll be your guide!
Welcome to: Physics I I m Dr Alex Pettitt, and I ll be your guide! Physics I: x Mirrors and lenses Lecture 13: 6-11-2018 Last lecture: Reflection & Refraction Reflection: Light ray hits surface Ray moves
Optics Course (Phys 311) Geometrical Optics Refraction through Lenses
Optics Course (Phys ) Geometrical Optics Refraction through Lenses Lecturer: Dr Zeina Hashim Slide 1 Objectives covered in this lesson : 1. Refraction through single spherical refracting surfaces. 2. Lenses:
Lecture 3 Sections 2.2, 4.4. Mon, Aug 31, 2009
Model s Lecture 3 Sections 2.2, 4.4 World s Eye s Clip s s s Window s Hampden-Sydney College Mon, Aug 31, 2009 Outline Model s World s Eye s Clip s s s Window s 1 2 3 Model s World s Eye s Clip s s s Window
Lecture 2: Digital Drawing. Computer Graphics and Imaging UC Berkeley CS184/284
Lecture 2: Digital Drawing Computer Graphics and Imaging UC Berkeley CS184/284 Today: Rasterizing Triangles into Pixels Life of Pi (2012) Drawing Machines CNC Sharpie Drawing Machine Aaron Panone with
ENGINEERING Electrical Engineering
ENGINEERING Electrical Engineering Virtual Reality EE 267, Spring 2017 Assignment 3 due 4/27/2017 at 11:59 PM Topics: Foveated Rendering, Depth of Field, Stereo Rendering, Anaglyph 3D Students should use
For 3CCD/3CMOS/4CCD Line Scan Cameras. Designed to be suitable for PRISM based 3CCD/CMOS/4CCD line scan cameras
BV-L series lenses For 3CCD/3CMOS/4CCD Line Scan Cameras Common Features Designed to be suitable for PRISM based 3CCD/CMOS/4CCD line scan cameras New optics design to improve the longitudinal chromatic
AP Physics: Curved Mirrors and Lenses
The Ray Model of Light Light often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric
Lumaxis, Sunset Hills Rd., Ste. 106, Reston, VA 20190
White Paper High Performance Projection Engines for 3D Metrology Systems www.lumaxis.net Lumaxis, 11495 Sunset Hills Rd., Ste. 106, Reston, VA 20190 Introduction 3D optical metrology using structured light
Orthogonal Projection Matrices. Angel and Shreiner: Interactive Computer Graphics 7E Addison-Wesley 2015
Orthogonal Projection Matrices 1 Objectives Derive the projection matrices used for standard orthogonal projections Introduce oblique projections Introduce projection normalization 2 Normalization Rather
Prospective Novel 3D Display Technology Development
1 Prospective Novel 3D Display Technology Development Yasuhiro Takaki Institute of Engineering Tokyo University of Agriculture and Technology TUAT 2 Tokyo University of Agriculture and Technology http://www.tuat.ac.jp
Chapter 34: Geometrical Optics
Chapter 34: Geometrical Optics Mirrors Plane Spherical (convex or concave) Lenses The lens equation Lensmaker s equation Combination of lenses E! Phys Phys 2435: 22: Chap. 34, 3, Pg Mirrors New Topic Phys
Thin Lenses. Lecture 23. Chapter 34. Ray Optics. Physics II. Course website:
Lecture 23 Chapter 34 Physics II Ray Optics Thin Lenses Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 34: Section 34.5-6 Thin Lenses There
Introduction, Overview, Fast Forward!
Introduction, Overview, Fast Forward! EE367/CS448I: Computational Imaging and Display! stanford.edu/class/ee367! Lecture 1! Gordon Wetzstein! Stanford University! Image: National Geographic! Nature!
Introduction to 3D Machine Vision
Introduction to 3D Machine Vision 1 Many methods for 3D machine vision Use Triangulation (Geometry) to Determine the Depth of an Object By Different Methods: Single Line Laser Scan Stereo Triangulation
CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation
CSE 167: Introduction to Computer Graphics Lecture #4: Vertex Transformation Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2013 Announcements Project 2 due Friday, October 11
Pipeline Operations. CS 4620 Lecture Steve Marschner. Cornell CS4620 Spring 2018 Lecture 11
Pipeline Operations CS 4620 Lecture 11 1 Pipeline you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX PROCESSING TRANSFORMED GEOMETRY conversion of primitives to pixels RASTERIZATION
CSE452 Computer Graphics
CSE45 Computer Graphics Lecture 8: Computer Projection CSE45 Lecture 8: Computer Projection 1 Review In the last lecture We set up a Virtual Camera Position Orientation Clipping planes Viewing angles Orthographic/Perspective
CIS 580, Machine Perception, Spring 2015 Homework 1 Due: :59AM
CIS 580, Machine Perception, Spring 2015 Homework 1 Due: 2015.02.09. 11:59AM Instructions. Submit your answers in PDF form to Canvas. This is an individual assignment. 1 Camera Model, Focal Length and
Refraction at a single curved spherical surface
Refraction at a single curved spherical surface This is the beginning of a sequence of classes which will introduce simple and complex lens systems We will start with some terminology which will become
Three-dimensional directional display and pickup
Three-dimensional directional display and pickup Joonku Hahn NCRCAPAS School of Electrical Engineering Seoul National University CONTENTS I. Introduction II. Three-dimensional directional display 2.1 Uniform
Pipeline Operations. CS 4620 Lecture 14
Pipeline Operations CS 4620 Lecture 14 2014 Steve Marschner 1 Pipeline you are here APPLICATION COMMAND STREAM 3D transformations; shading VERTEX PROCESSING TRANSFORMED GEOMETRY conversion of primitives
Light: Geometric Optics (Chapter 23)
Light: Geometric Optics (Chapter 23) Units of Chapter 23 The Ray Model of Light Reflection; Image Formed by a Plane Mirror Formation of Images by Spherical Index of Refraction Refraction: Snell s Law 1
Vision Review: Image Formation. Course web page:
Vision Review: Image Formation Course web page: www.cis.udel.edu/~cer/arv September 10, 2002 Announcements Lecture on Thursday will be about Matlab; next Tuesday will be Image Processing The dates some
Robot Vision: Camera calibration
Robot Vision: Camera calibration Ass.Prof. Friedrich Fraundorfer SS 201 1 Outline Camera calibration Cameras with lenses Properties of real lenses (distortions, focal length, field-of-view) Calibration
One or more objects A viewer with a projection surface Projectors that go from the object(s) to the projection surface
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
Chapter 33 Continued Properties of Light. Law of Reflection Law of Refraction or Snell s Law Chromatic Dispersion Brewsters Angle
Chapter 33 Continued Properties of Light Law of Reflection Law of Refraction or Snell s Law Chromatic Dispersion Brewsters Angle Dispersion: Different wavelengths have different velocities and therefore
zspace Developer SDK Guide - Introduction Version 1.0 Rev 1.0
zspace Developer SDK Guide - Introduction Version 1.0 zspace.com Developer s Guide Rev 1.0 zspace, Inc. 2015. zspace is a registered trademark of zspace, Inc. All other trademarks are the property of their
C P S C 314 S H A D E R S, O P E N G L, & J S RENDERING PIPELINE. Mikhail Bessmeltsev
C P S C 314 S H A D E R S, O P E N G L, & J S RENDERING PIPELINE UGRAD.CS.UBC.C A/~CS314 Mikhail Bessmeltsev 1 WHAT IS RENDERING? Generating image from a 3D scene 2 WHAT IS RENDERING? Generating image
Rendering Objects. Need to transform all geometry then
Intro to OpenGL Rendering Objects Object has internal geometry (Model) Object relative to other objects (World) Object relative to camera (View) Object relative to screen (Projection) Need to transform
CSE 167: Lecture #7: Color and Shading. Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011
CSE 167: Introduction to Computer Graphics Lecture #7: Color and Shading Jürgen P. Schulze, Ph.D. University of California, San Diego Fall Quarter 2011 Announcements Homework project #3 due this Friday,
Today. Rendering pipeline. Rendering pipeline. Object vs. Image order. Rendering engine Rendering engine (jtrt) Computergrafik. Rendering pipeline
Computergrafik Today Rendering pipeline s View volumes, clipping Viewport Matthias Zwicker Universität Bern Herbst 2008 Rendering pipeline Rendering pipeline Hardware & software that draws 3D scenes on
Draw a diagram showing the fibre and the path of the ray of light. Describe one use of optical fibres in medicine. You may draw a diagram.
1 (a) (i) A ray of light passes through a length of curved optical fibre. Draw a diagram showing the fibre and the path of the ray of light. [1] Describe one use of optical fibres in medicine. You may
Overview of Projections: From a 3D world to a 2D screen.
Overview of Projections: From a 3D world to a 2D screen. Lecturer: Dr Dan Cornford d.cornford@aston.ac.uk http://wiki.aston.ac.uk/dancornford CS2150, Computer Graphics, Aston University, Birmingham, UK
The Lens. Refraction and The Lens. Figure 1a:
Lenses are used in many different optical devices. They are found in telescopes, binoculars, cameras, camcorders and eyeglasses. Even your eye contains a lens that helps you see objects at different distances.
Graphics Systems and Models
Graphics Systems and Models 2 nd Week, 2007 Sun-Jeong Kim Five major elements Input device Processor Memory Frame buffer Output device Graphics System A Graphics System 2 Input Devices Most graphics systems
CS 498 VR. Lecture 19-4/9/18. go.illinois.edu/vrlect19
CS 498 VR Lecture 19-4/9/18 go.illinois.edu/vrlect19 Review from previous lectures Image-order Rendering and Object-order Rendering Image-order Rendering: - Process: Ray Generation, Ray Intersection, Assign
34.2: Two Types of Image
Chapter 34 Images 34.2: Two Types of Image For you to see an object, your eye intercepts some of the light rays spreading from the object and then redirect them onto the retina at the rear of the eye.
Pipeline Operations. CS 4620 Lecture 10
Pipeline Operations CS 4620 Lecture 10 2008 Steve Marschner 1 Hidden surface elimination Goal is to figure out which color to make the pixels based on what s in front of what. Hidden surface elimination
Viewing. Part II (The Synthetic Camera) CS123 INTRODUCTION TO COMPUTER GRAPHICS. Andries van Dam 10/10/2017 1/31
Viewing Part II (The Synthetic Camera) Brownie camera courtesy of http://www.geh.org/fm/brownie2/htmlsrc/me13000034_ful.html 1/31 The Camera and the Scene } What does a camera do? } Takes in a 3D scene
Assignment 1 due 4/13/2017 at 11:59PM Topic: Getting Started with WebGL and Transformations
Virtual Reality EE 267, Spring 2017 Assignment 1 due 4/13/2017 at 11:59PM Topic: Getting Started with WebGL and Transformations Students should use Javascript for this assignment, building on top of the
Inside VR on Mobile. Sam Martin Graphics Architect GDC 2016
Inside VR on Mobile Sam Martin Graphics Architect GDC 2016 VR Today Emerging technology Main mobile VR ecosystems Google Cardboard Samsung GearVR In this talk: Latency Multiple views Performance tuning
Seeing the world through a depth-sensing camera
Seeing the world through a depth-sensing camera Copyright 2014 pabr@pabr.org All rights reserved. In this project we attach a depth-sensing camera to a head-mounted stereoscopic display (think: Kinect
Introduction to Computer Vision. Introduction CMPSCI 591A/691A CMPSCI 570/670. Image Formation
Introduction CMPSCI 591A/691A CMPSCI 570/670 Image Formation Lecture Outline Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic
CS230 : Computer Graphics Lecture 6: Viewing Transformations. Tamar Shinar Computer Science & Engineering UC Riverside
CS230 : Computer Graphics Lecture 6: Viewing Transformations Tamar Shinar Computer Science & Engineering UC Riverside Rendering approaches 1. image-oriented foreach pixel... 2. object-oriented foreach
Design and prototype of an augmented reality display with per-pixel mutual occlusion capability
Design and prototype of an augmented reality display with per-pixel mutual occlusion capability Item Type Article Authors Wilson, Austin; Hua, Hong Citation Design and prototype of an augmented reality
Jump Stitch Metadata & Depth Maps Version 1.1
Jump Stitch Metadata & Depth Maps Version 1.1 jump-help@google.com Contents 1. Introduction 1 2. Stitch Metadata File Format 2 3. Coverage Near the Poles 4 4. Coordinate Systems 6 5. Camera Model 6 6.
Rendering. Converting a 3D scene to a 2D image. Camera. Light. Rendering. View Plane
Rendering Pipeline Rendering Converting a 3D scene to a 2D image Rendering Light Camera 3D Model View Plane Rendering Converting a 3D scene to a 2D image Basic rendering tasks: Modeling: creating the world
Rasterization Overview
Rendering Overview The process of generating an image given a virtual camera objects light sources Various techniques rasterization (topic of this course) raytracing (topic of the course Advanced Computer
Introduction to Computer Graphics with WebGL
Introduction to Computer Graphics with WebGL Ed Angel Professor Emeritus of Computer Science Founding Director, Arts, Research, Technology and Science Laboratory University of New Mexico Models and Architectures
CMPSCI 670: Computer Vision! Image formation. University of Massachusetts, Amherst September 8, 2014 Instructor: Subhransu Maji
CMPSCI 670: Computer Vision! Image formation University of Massachusetts, Amherst September 8, 2014 Instructor: Subhransu Maji MATLAB setup and tutorial Does everyone have access to MATLAB yet? EdLab accounts
Evening s Goals. Mathematical Transformations. Discuss the mathematical transformations that are utilized for computer graphics
Evening s Goals Discuss the mathematical transformations that are utilized for computer graphics projection viewing modeling Describe aspect ratio and its importance Provide a motivation for homogenous
CS 112 The Rendering Pipeline. Slide 1
CS 112 The Rendering Pipeline Slide 1 Rendering Pipeline n Input 3D Object/Scene Representation n Output An image of the input object/scene n Stages (for POLYGON pipeline) n Model view Transformation n
On Fig. 7.1, draw a ray diagram to show the formation of this image.
1- A small object is placed 30 cm from the centre of a convex lens of focal length 60 cm An enlarged image is observed from the other side of the lens (a) On Fig 71, draw a ray diagram to show the formation
Viewing with Computers (OpenGL)
We can now return to three-dimension?', graphics from a computer perspective. Because viewing in computer graphics is based on the synthetic-camera model, we should be able to construct any of the classical
On the Midterm Exam. Monday, 10/17 in class. Closed book and closed notes. One-side and one page cheat sheet is allowed. A calculator is allowed
On the Midterm Exam Monday, 1/17 in class Closed book and closed notes One-side and one page cheat sheet is allowed A calculator is allowed Covers the topics until the class on Wednesday, 1/12 Take-home
Lens Design I. Lecture 3: Properties of optical systems II Herbert Gross. Summer term
Lens Design I Lecture 3: Properties of optical systems II 205-04-27 Herbert Gross Summer term 205 www.iap.uni-jena.de 2 Preliminary Schedule 3.04. Basics 2 20.04. Properties of optical systems I 3 27.05.
Chapter 36. Image Formation
Chapter 36 Image Formation Apr 22, 2012 Light from distant things We learn about a distant thing from the light it generates or redirects. The lenses in our eyes create images of objects our brains can
CMSC427 Transformations II: Viewing. Credit: some slides from Dr. Zwicker
CMSC427 Transformations II: Viewing Credit: some slides from Dr. Zwicker What next? GIVEN THE TOOLS OF The standard rigid and affine transformations Their representation with matrices and homogeneous coordinates
Chapter 7: Geometrical Optics
Chapter 7: Geometrical Optics 7. Reflection at a Spherical Surface L.O 7.. State laws of reflection Laws of reflection state: L.O The incident ray, the reflected ray and the normal all lie in the same
Chapter 7: Geometrical Optics. The branch of physics which studies the properties of light using the ray model of light.
Chapter 7: Geometrical Optics The branch of physics which studies the properties of light using the ray model of light. Overview Geometrical Optics Spherical Mirror Refraction Thin Lens f u v r and f 2
Computer Graphics and Visualization. Graphics Systems and Models
UNIT -1 Graphics Systems and Models 1.1 Applications of computer graphics: Display Of Information Design Simulation & Animation User Interfaces 1.2 Graphics systems A Graphics system has 5 main elements:
Algebra Based Physics
Slide 1 / 66 Slide 2 / 66 Algebra Based Physics Geometric Optics 2015-12-01 www.njctl.org Table of ontents Slide 3 / 66 lick on the topic to go to that section Reflection Spherical Mirror Refraction and
Exercise 12 Geometrical and Technical Optics WS 2013/2014
Exercise 12 Geometrical and Technical Optics WS 213/214 Slide projector and Köhler illumination In this exercise a simplified slide projector (or LCD projector) will be designed and simulated with ray
Physics 1202: Lecture 18 Today s Agenda
Physics 1202: Lecture 18 Today s Agenda Announcements: Team problems today Team 10: Alisha Kumar, Adam Saxton, Alanna Forsberg Team 11: Riley Burns, Deanne Edwards, Shauna Bolton Team 12: Kervell Baird,
Optics Course (Phys 311) Geometrical Optics Refraction through Lenses
Optics Course (Phys ) Geometrical Optics Refraction through Lenses Lecturer: Dr Zeina Hashim Slide 1 Objectives covered in this lesson : 1. The refracting power of a thin lens. 2. Thin lens combinations.
SID Display Week Yasuhiro Takaki. Institute of Symbiotic and Technology. Tokyo Univ. of Agri. & Tech.
Three-Dimensional i Displays: Present and Future Yasuhiro Takaki Institute of Symbiotic and Technology Tokyo University it of Agriculture and Technology 1 Outline 1. Introduction 2. Human Factors 3. Current
Name Componon 2.8/28 Name Componon 2.8/28. [mm] Working distance [mm] - 77 AoV [ ] 54
![Name Componon 2.8/28 Name Componon 2.8/28. [mm] Working distance [mm] - 77 AoV [ ] 54](/thumbs/96/127778053.jpg "Name Componon 2.8/28 Name Componon 2.8/28. [mm] Working distance [mm] - 77 AoV [ ] 54")
The is a 28 mm focal length, macro lens with 3 mm image circle (for F/# 2.8 only for 2/3 sensor recommended) for large format sensors and short working distance. This macro lens is developed and corrected
Chapter 26 Geometrical Optics
Chapter 26 Geometrical Optics 1 Overview of Chapter 26 The Reflection of Light Forming Images with a Plane Mirror Spherical Mirrors Ray Tracing and the Mirror Equation The Refraction of Light Ray Tracing
Extended Fractional View Integral Photography Using Slanted Orthogonal Lenticular Lenses
Proceedings of the 2 nd World Congress on Electrical Engineering and Computer Systems and Science (EECSS'16) Budapest, Hungary August 16 17, 2016 Paper No. MHCI 112 DOI: 10.11159/mhci16.112 Extended Fractional
Light: Geometric Optics
Light: Geometric Optics 23.1 The Ray Model of Light Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization,
Realistic Lens Distortion Rendering
Realistic Lens Distortion Rendering Martin Lambers Computer Graphics Group University of Siegen Hoelderlinstrasse 3 57076 Siegen martin.lambers@ uni-siegen.de Hendrik Sommerhoff Computer Graphics Group
Victor S. Grinberg Gregg W. Podnar M. W. Siegel
Geometry of binocular imaging II : The augmented eye Victor S. Grinberg Gregg W. Podnar M. W. Siegel Robotics Institute, School of Computer Science, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh,
Models and The Viewing Pipeline. Jian Huang CS456
Models and The Viewing Pipeline Jian Huang CS456 Vertex coordinates list, polygon table and (maybe) edge table Auxiliary: Per vertex normal Neighborhood information, arranged with regard to vertices and
CS 563 Advanced Topics in Computer Graphics Stereoscopy. by Sam Song
CS 563 Advanced Topics in Computer Graphics Stereoscopy by Sam Song Stereoscopy Introduction Parallax Camera Displaying and Viewing Results Stereoscopy What is it? seeing in three dimensions creates the
Understanding Variability
Understanding Variability Why so different? Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic aberration, radial distortion
Final Exam. Today s Review of Optics Polarization Reflection and transmission Linear and circular polarization Stokes parameters/jones calculus
Physics 42200 Waves & Oscillations Lecture 40 Review Spring 206 Semester Matthew Jones Final Exam Date:Tuesday, May 3 th Time:7:00 to 9:00 pm Room: Phys 2 You can bring one double-sided pages of notes/formulas.
Classical and Computer Viewing. Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico
Classical and Computer Viewing Adapted From: Ed Angel Professor of Emeritus of Computer Science University of New Mexico Planar Geometric Projections Standard projections project onto a plane Projectors
Overview. Augmented reality and applications Marker-based augmented reality. Camera model. Binary markers Textured planar markers
Augmented reality Overview Augmented reality and applications Marker-based augmented reality Binary markers Textured planar markers Camera model Homography Direct Linear Transformation What is augmented
Three Main Themes of Computer Graphics
Three Main Themes of Computer Graphics Modeling How do we represent (or model) 3-D objects? How do we construct models for specific objects? Animation How do we represent the motion of objects? How do
2D rendering takes a photo of the 2D scene with a virtual camera that selects an axis aligned rectangle from the scene. The photograph is placed into
2D rendering takes a photo of the 2D scene with a virtual camera that selects an axis aligned rectangle from the scene. The photograph is placed into the viewport of the current application window. A pixel
Inertial Measurement Units I!
! Inertial Measurement Units I! Gordon Wetzstein! Stanford University! EE 267 Virtual Reality! Lecture 9! stanford.edu/class/ee267/!! Lecture Overview! coordinate systems (world, body/sensor, inertial,
Overview of Active Vision Techniques
SIGGRAPH 99 Course on 3D Photography Overview of Active Vision Techniques Brian Curless University of Washington Overview Introduction Active vision techniques Imaging radar Triangulation Moire Active
Waves & Oscillations
Physics 42200 Waves & Oscillations Lecture 40 Review Spring 2016 Semester Matthew Jones Final Exam Date:Tuesday, May 3 th Time:7:00 to 9:00 pm Room: Phys 112 You can bring one double-sided pages of notes/formulas.
Plano-Convex Lenses. Read further. Catalog Items BK7 Plano-Convex Lenses. Description. Standard specifications. Features.
Plano-Convex Lenses (PCX) PCX positive focal length lenses have flat surface on one side and spherical surface on the other. They are used for focusing beams in telescopes, collimators or condenser systems,