Deep Shadow Maps

Total Page:16

File Type:pdf, Size:1020Kb

Deep Shadow Maps Deep Shadow Maps Tom Lokovic Eric Veach Pixar Animation Studios£ Abstract We introduce deep shadow maps, a technique that produces fast, high-quality shadows for primitives such as hair, fur, and smoke. Unlike traditional shadow maps, which store a single depth at each pixel, deep shadow maps store a representation of the fractional visibility through a pixel at all possible depths. Deep shadow maps have several advantages. First, they are prefiltered, which allows faster shadow lookups and much smaller memory footprints than regular shadow maps of similar quality. Second, they support shad- ows from partially transparent surfaces and volumetric objects such as fog. Third, they handle important cases of motion blur at no extra cost. The algorithm is simple to implement and can be added easily Figure 1: Hair rendered with and without self-shadowing. to existing renderers as an alternative to ordinary shadow maps. 1 Introduction through dense hair and fog. Compared to ordinary shadow maps, deep shadows have the fol- Rendering hair, fur, and smoke is difficult because accurate self- lowing advantages: shadowing is so important to their appearance [2]. To demonstrate ¯ They support semitransparent surfaces and volumetric primi- this, Figure 1 shows a small patch of curly hair rendered both with tivessuchassmoke. and without shadows. Notice that the shadows cast by portions of the hair onto itself have a great influence on the overall illumination ¯ For high-quality shadows, they are smaller than equivalent and apparent realism of the rendering. shadow maps by an order of magnitude and are significantly Traditional shadow maps [11] need very high resolutions to cap- faster to access. ture this type of self-shadowing accurately. Many more depth sam- ples must also be accessed during shadow lookups to compensate ¯ Unlike ordinary shadow maps, they support mip-mapping. for the higher frequencies in the shadow map. This is especially ob- This can dramatically reduce lookup costs when objects are vious in animations, where inadequate sampling results in sparkling viewed over a wide range of scales. (a distracting artifact caused by rapidly changing noise patterns). In addition, deep shadow maps can efficiently support high- Furthermore, shadow maps cannot handle volumetric effects quality motion blurred shadows. While this effect is also possible such as clouds or smoke. Traditional approaches such as integrating with ordinary shadow maps, the large filter widths required have the atmospheric density along each shadow ray are very inefficient, made this technique quite expensive in the past. simply because there can be a large number of shadow tests along In the following section, we discuss previous work and explain each primary ray. why traditional shadow maps are not appropriate for fine geome- We propose a new type of shadow map to solve these problems, try such as hair and fur. Section 3 defines deep shadow maps and the deep shadow map. Rather than storing a single depth at each presents algorithms for creating and using them, while Section 4 pixel, a deep shadow map stores a fractional visibility function (or describes their advantages and limitations. We then discuss some simply visibility function) that records the approximate amount of of the more practical implementation issues, and present the results light that passes through the pixel and penetrates to each depth. The from several experiments. visibility function takes into account not only the opacities of the surfaces and volume elements encountered, but also their coverage of the pixel’s filter region. This allows deep shadow maps to ac- 2 Background and Related Work curately represent the partial attenuation that occurs as light passes Traditional shadow maps [11] are generated by placing a camera £ email: [email protected], [email protected] (the shadow camera) at the light source origin such that the ob- jects casting shadows are within the field of view. The result is a Permission to make digital or hard copies of part or all of this work or rectangular array of pixels where each pixel stores the depth of the personal or classroom use is granted without fee provided that copies are not closest visible surface. To determine whether a given point È is in made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to shadow, it is transformed into the coordinate system of the shadow republish, to post on servers, or to redistribute to lists, requires prior specific camera and its depth is compared to the corresponding value from permission and/or a fee. the shadow map. Higher-quality antialiased shadows are possible SIGGRAPH 2000, New Orleans, LA USA with percentage closer filtering [9], which examines depth sam- ples within a given filter region and computes the fraction that are © ACM 2000 1-58113-208-5/00/07 ...$5.00 closer than a given depth Þ . This process relies heavily on stratified sampling [7], both in generating the original shadow map and in selecting a random subset of the depth samples for filtering. 385 N N ::: classic survey is [13]). Ray casting can generate accurate shadows, ::: ::::::::: but on furry objects with millions of hairs it is too expensive in :::::: :::::: terms of time and memory. This is particularly true when hair re- :::::::::::: ::::: ceives shadows from fog or smoke, since ray marching is performed ::::::::::::: :::::: once for every hair sample. It is also difficult, other than by using ::::::: :::: an expensive area light source, to “soften” shadows for artistic pur- ::::::: ::: poses. In the case of standard shadow maps this can be achieved ::: :::::: by simply increasing the filter width. Kajiya and Kay used ray-cast ::: :::::: shadows on a volumetric hair representation [2], but their rendering ::::: :::::: times were relatively long. ::: ::::::: :::: Another possible approach to hair self-shadowing is to precom- :::: :::: pute the shadow density as a 3D texture. This technique has been used with some success for clouds (e.g. [3]) and for hybrid volume (a) (b) and surface rendering of medical datasets [5]. The main drawback Figure 2: Variance contributions to stratified sampling. (a) When a of this approach is that 3D textures have a relatively coarse resolu- =¾ ½ tion, and in particular they have limited range and low accuracy in ´Æ µ single silhouette edge passes through the filter region, Ç sam- ples contribute to the variance. (b) When the filter region is covered Þ (which creates bias problems). A 3D texture with sufficient detail to capture accurate surface shadows of complex geometry would be with fine geometry, all Æ samples contribute to the variance, resulting in a much larger expected error. prohibitively large. Multi-layer Z-buffers [6] and layered depth images [10] store in- formation at multiple depths per pixel, but are geared toward ren- dering opaque surfaces from new viewpoints rather than shadow While shadow maps are very good for rendering shadows of evaluation. Keating and Max [4] apply multi-layer depth images to large objects, they do not work as well for finely detailed geom- the problem of shadow penumbras, but their technique otherwise etry such as hair. This is because stratified sampling does not work has the same limitations as ordinary shadow maps. very well when there are many discontinuities crossing the filter re- gion [7]. As a result, many more samples are required in order to 3 Deep Shadow Maps reduce noise artifacts such as sparkling to an acceptable level. To understand why this is so, consider Figure 2a. Here we show 3.1 Definition an isolated silhouette edge crossing the filter region for a shadow Ô Ô Æ ¢ Æ lookup, evaluated using Æ samples jittered over a grid. A deep shadow map is a rectangular array of pixels in which every The depth of each sample is obtained from the shadow map (whose pixel stores a visibility function. Intuitively, a visibility function is resolution may be much finer than the sample grid). Using per- defined by considering a beam of light that starts at the shadow cam- centage closer filtering, each sample contributes either 0 or 1 to era origin and passes through the given pixel. The function value the average shadow value depending on the relative Þ values of the at a given depth is simply the fraction of the beam’s initial power shadow map and the test point È . that penetrates to that depth. Note that the beam is not necessar- In this situation, observe that the only samples that contribute to ily square; it can be shaped and weighted according to any desired the variance are the ones whose cells are crossed by the silhouette pixel filter. Figure 3 gives several examples, showing how visibility ½=¾ ´Æ µ edge. There are only Ç of these, and further analysis [7] functions can account for semitransparent surfaces, pixel coverage, ¿=4 and smoke. Each visibility function starts off with a value of 1, and ´Æ µ shows that the expected error in this case is Ç . Thus strat- ification yields much better results near large silhouette edges than decreases with depth as various types of blockers are encountered. unstratified Monte Carlo sampling, which has an expected error of If all light is blocked, the function drops off to a value of 0. ½=¾ To make this definition more precise, consider a ray that starts ´Æ µ Ç . Ü; Ý µ at the shadow camera origin and passes through the point ´ on In the case of hair or fur, however, the filter region is crossed by the image plane. Some fraction of the light emitted along this ray many silhouette edges (see Figure 2b). In this case, every one of the will be attenuated by surfaces or by volumetric scattering and ab- Æ cells is crossed by an edge, and the corresponding expected error sorption.
Recommended publications
  • Using Typography and Iconography to Express Emotion
    Using typography and iconography to express emotion (or meaning) in motion graphics as a learning tool for ESL (English as a second language) in a multi-device platform. A thesis submitted to the School of Visual Communication Design, College of Communication and Information of Kent State University in partial fulfillment of the requirements for the degree of Master of Fine Arts by Anthony J. Ezzo May, 2016 Thesis written by Anthony J. Ezzo B.F.A. University of Akron, 1998 M.F.A., Kent State University, 2016 Approved by Gretchen Caldwell Rinnert, M.G.D., Advisor Jaime Kennedy, M.F.A., Director, School of Visual Communication Design Amy Reynolds, Ph.D., Dean, College of Communication and Information TABLE OF CONTENTS TABLE OF CONTENTS .................................................................................... iii LIST OF FIGURES ............................................................................................ v LIST OF TABLES .............................................................................................. v ACKNOWLEDGEMENTS ................................................................................ vi CHAPTER 1. THE PROBLEM .......................................................................................... 1 Thesis ..................................................................................................... 6 2. BACKGROUND AND CONTEXT ............................................................. 7 Understanding The Ell Process ..............................................................
    [Show full text]
  • 3D Graphics Fundamentals
    11BegGameDev.qxd 9/20/04 5:20 PM Page 211 chapter 11 3D Graphics Fundamentals his chapter covers the basics of 3D graphics. You will learn the basic concepts so that you are at least aware of the key points in 3D programming. However, this Tchapter will not go into great detail on 3D mathematics or graphics theory, which are far too advanced for this book. What you will learn instead is the practical implemen- tation of 3D in order to write simple 3D games. You will get just exactly what you need to 211 11BegGameDev.qxd 9/20/04 5:20 PM Page 212 212 Chapter 11 ■ 3D Graphics Fundamentals write a simple 3D game without getting bogged down in theory. If you have questions about how matrix math works and about how 3D rendering is done, you might want to use this chapter as a starting point and then go on and read a book such as Beginning Direct3D Game Programming,by Wolfgang Engel (Course PTR). The goal of this chapter is to provide you with a set of reusable functions that can be used to develop 3D games. Here is what you will learn in this chapter: ■ How to create and use vertices. ■ How to manipulate polygons. ■ How to create a textured polygon. ■ How to create a cube and rotate it. Introduction to 3D Programming It’s a foregone conclusion today that everyone has a 3D accelerated video card. Even the low-end budget video cards are equipped with a 3D graphics processing unit (GPU) that would be impressive were it not for all the competition in this market pushing out more and more polygons and new features every year.
    [Show full text]
  • Flood Insurance Rate Map (FIRM) Graphics Guidance
    Guidance for Flood Risk Analysis and Mapping Flood Insurance Rate Map (FIRM) Graphics November 2019 Requirements for the Federal Emergency Management Agency (FEMA) Risk Mapping, Assessment, and Planning (Risk MAP) Program are specified separately by statute, regulation, or FEMA policy (primarily the Standards for Flood Risk Analysis and Mapping). This document provides guidance to support the requirements and recommends approaches for effective and efficient implementation. The guidance, context, and other information in this document is not required unless it is codified separately in the aforementioned statute, regulation, or policy. Alternate approaches that comply with all requirements are acceptable. For more information, please visit the FEMA Guidelines and Standards for Flood Risk Analysis and Mapping webpage (www.fema.gov/guidelines-and-standards-flood-risk-analysis-and- mapping). Copies of the Standards for Flood Risk Analysis and Mapping policy, related guidance, technical references, and other information about the guidelines and standards development process are all available here. You can also search directly by document title at www.fema.gov/library. FIRM Graphics November 2019 Guidance Document 6 Page i Document History Affected Section or Date Description Subsection This guidance has been revised to align various November descriptions and specifications to standard operating Sections 4.3 and 5.2 2019 procedures, including labeling of structures and application of floodway and special floodway notes. FIRM Graphics November
    [Show full text]
  • Introduction to Scalable Vector Graphics
    Introduction to Scalable Vector Graphics Presented by developerWorks, your source for great tutorials ibm.com/developerWorks Table of Contents If you're viewing this document online, you can click any of the topics below to link directly to that section. 1. Introduction.............................................................. 2 2. What is SVG?........................................................... 4 3. Basic shapes............................................................ 10 4. Definitions and groups................................................. 16 5. Painting .................................................................. 21 6. Coordinates and transformations.................................... 32 7. Paths ..................................................................... 38 8. Text ....................................................................... 46 9. Animation and interactivity............................................ 51 10. Summary............................................................... 55 Introduction to Scalable Vector Graphics Page 1 of 56 ibm.com/developerWorks Presented by developerWorks, your source for great tutorials Section 1. Introduction Should I take this tutorial? This tutorial assists developers who want to understand the concepts behind Scalable Vector Graphics (SVG) in order to build them, either as static documents, or as dynamically generated content. XML experience is not required, but a familiarity with at least one tagging language (such as HTML) will be useful. For basic XML
    [Show full text]
  • An Online System for Classifying Computer Graphics Images from Natural Photographs
    An Online System for Classifying Computer Graphics Images from Natural Photographs Tian-Tsong Ng and Shih-Fu Chang fttng,[email protected] Department of Electrical Engineering Columbia University New York, USA ABSTRACT We describe an online system for classifying computer generated images and camera-captured photographic images, as part of our effort in building a complete passive-blind system for image tampering detection (project website at http: //www.ee.columbia.edu/trustfoto). Users are able to submit any image from a local or an online source to the system and get classification results with confidence scores. Our system has implemented three different algorithms from the state of the art based on the geometry, the wavelet, and the cartoon features. We describe the important algorithmic issues involved for achieving satisfactory performances in both speed and accuracy as well as the capability to handle diverse types of input images. We studied the effects of image size reduction on classification accuracy and speed, and found different size reduction methods worked best for different classification methods. In addition, we incorporated machine learning techniques, such as fusion and subclass-based bagging, in order to counter the effect of performance degradation caused by image size reduction. With all these improvements, we are able to speed up the classification speed by more than two times while keeping the classification accuracy almost intact at about 82%. Keywords: Computer graphics, photograph, classification, online system, geometry features, classifier fusion 1. INTRODUCTION The level of photorealism capable by today’s computer graphics makes distinguishing photographic and computer graphic images difficult.
    [Show full text]
  • Graphics Formats and Tools
    Graphics formats and tools Images à recevoir Stand DRG The different types of graphics format Graphics formats can be classified broadly in 3 different groups -Vector - Raster (or bitmap) - Page description language (PDL) Graphics formats and tools 2 Vector formats In a vector format (revisable) a line is defined by 2 points, the text can be edited Graphics formats and tools 3 Raster (bitmap) format A raster (bitmap) format is like a photograph; the number of dots/cm defines the quality of the drawing Graphics formats and tools 4 Page description language (PDL) formats A page description language is a programming language that describes the appearance of a printed page at a higher level than an actual output bitmap Adobe’s PostScript (.ps), Encapsulated PostScript (.eps) and Portable Document Format (.pdf) are some of the best known page description languages Encapsulated PostScript (.eps) is commonly used for graphics It can contain both unstructured vector information as well as raster (bitmap) data Since it comprises a mixture of data, its quality and usability are variable Graphics formats and tools 5 Background Since the invention of computing, or more precisely since the creation of computer-assisted drawing (CAD), two main professions have evolved - Desktop publishing (DTP) developed principally on Macintosh - Computer-assisted drawing or design (CAD) developed principally on IBM (International Business Machines) Graphics formats and tools 6 Use of DTP applications Used greatly in the fields of marketing, journalism and industrial design, DTP applications fulfil the needs of various professions - from sketches and mock-ups to fashion design - interior design - coachwork (body work) design - web page design -etc.
    [Show full text]
  • Interactive Topographic Web Mapping Using Scalable Vector Graphics
    University of Nebraska at Omaha DigitalCommons@UNO Student Work 12-1-2003 Interactive topographic web mapping using scalable vector graphics Peter Pavlicko University of Nebraska at Omaha Follow this and additional works at: https://digitalcommons.unomaha.edu/studentwork Recommended Citation Pavlicko, Peter, "Interactive topographic web mapping using scalable vector graphics" (2003). Student Work. 589. https://digitalcommons.unomaha.edu/studentwork/589 This Thesis is brought to you for free and open access by DigitalCommons@UNO. It has been accepted for inclusion in Student Work by an authorized administrator of DigitalCommons@UNO. For more information, please contact [email protected]. INTERACTIVE TOPOGRAPHIC WEB MAPPING USING SCALABLE VECTOR GRAPHICS A Thesis Presented to the Department of Geography-Geology and the Faculty of the Graduate College University of Nebraska in Partial Fulfillment of the Requirements for the Degree Master of Arts University of Nebraska at Omaha by Peter Pavlicko December, 2003 UMI Number: EP73227 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation WWisMng UMI EP73227 Published by ProQuest LLC (2015). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 THESIS ACCEPTANCE Acceptance for the faculty of the Graduate College, University of Nebraska, in Partial fulfillment of the requirements for the degree Master of Arts University of Nebraska Omaha Committee ----------- Uf.A [JL___ Chairperson.
    [Show full text]
  • Rendering Synthetic Objects Into Real Scenes
    ToappearintheSIGGRAPH98conferenceproceedings RenderingSyntheticObjectsintoRealScenes: BridgingTraditionalandImage-basedGraphicswithGlobalIllumination andHighDynamicRangePhotography PaulDebevec UniversityofCaliforniaatBerkeley 1 ABSTRACT 1Introduction Renderingsyntheticobjectsintoreal-worldscenesisanimportant Wepresentamethodthatusesmeasuredsceneradianceandglobal applicationofcomputergraphics,particularlyinarchitecturaland illuminationinordertoaddnewobjectstolight-basedmodelswith visualeffectsdomains.Oftentimes,apieceoffurniture,aprop,or correctlighting.Themethodusesahighdynamicrangeimage- adigitalcreatureoractorneedstoberenderedseamlesslyintoa basedmodelofthescene,ratherthansyntheticlightsources,toil- realscene.Thisdif®culttaskrequiresthattheobjectsbelitcon- luminatethenewobjects.Tocomputetheillumination,thesceneis sistentlywiththesurfacesintheirvicinity,andthattheinterplayof consideredasthreecomponents:thedistantscene,thelocalscene, lightbetweentheobjectsandtheirsurroundingsbeproperlysimu- andthesyntheticobjects.Thedistantsceneisassumedtobepho- lated.Speci®cally,theobjectsshouldcastshadows,appearinre¯ec- tometricallyunaffectedbytheobjects,obviatingtheneedforre- tions,andrefract,focus,andemitlightjustasrealobjectswould. ¯ectancemodelinformation.Thelocalsceneisendowedwithes- timatedre¯ectancemodelinformationsothatitcancatchshadows andreceivere¯ectedlightfromthenewobjects.Renderingsare createdwithastandardglobalilluminationmethodbysimulating Distant theinteractionoflightamongstthethreecomponents.Adifferen- Scene tialrenderingtechniqueallowsforgoodresultstobeobtainedwhen
    [Show full text]
  • Applied Art and Design (AAD) 1
    Applied Art and Design (AAD) 1 AAD 0053. Publication Design II APPLIED ART AND DESIGN Units: 3 Prerequisite: Completion of AAD 52, 54 or 62 with grade of "C" or better (AAD) Hours: 72 (36 lecture, 36 activity) Page layout for developing and producing high-quality multi-page AAD 0012. Visual Communication documents. Emphasis on publication design, production, typography, Units: 3 graphics, and pre-press. Includes research and application of effective Also known as COMM 12 magazine layout concepts, cover design, grid theory, graphics, text Hours: 54 lecture elements and printing standards and processes. (CSU) Study of visual communication including design principles, aesthetics, AAD 0054. Typography visual perception, non-verbal messages, relationship to verbal Units: 3 communication, audience analysis, mass media and persuasion. Prerequisite: Completion of AAD 52, 53, 61, 62, or 75 with grade of "C" or Historical overview of visual media as well as current trends and better technology. (C-ID JOUR 170) (CSU, UC) Advisory: Completion of AAD 60 with grade of "C" or better AAD 0020. Portfolio Development and Presentation Hours: 72 (36 lecture, 36 activity) Units: 3 A professional and historical approach to understanding typographic Advisory: Completion of AAD 70, 75, or 85 with grade of "C" or better principles and form, effects of type on the style and communication Hours: 72 (36 lecture, 36 activity) in print and screen. Includes study of historical and contemporary Function and use of the portfolio as a marketing device for artists and graphics and typographic design, conceptualizing, developing and designers. Styles, materials, resources in portfolio design. Evaluation of refining typographical forms, methods for analyzing typographic usage, professional goals and image building.
    [Show full text]
  • Graphics and Visualization (GV)
    1 Graphics and Visualization (GV) 2 Computer graphics is the term commonly used to describe the computer generation and 3 manipulation of images. It is the science of enabling visual communication through computation. 4 Its uses include cartoons, film special effects, video games, medical imaging, engineering, as 5 well as scientific, information, and knowledge visualization. Traditionally, graphics at the 6 undergraduate level has focused on rendering, linear algebra, and phenomenological approaches. 7 More recently, the focus has begun to include physics, numerical integration, scalability, and 8 special-purpose hardware, In order for students to become adept at the use and generation of 9 computer graphics, many implementation-specific issues must be addressed, such as file formats, 10 hardware interfaces, and application program interfaces. These issues change rapidly, and the 11 description that follows attempts to avoid being overly prescriptive about them. The area 12 encompassed by Graphics and Visual Computing (GV) is divided into several interrelated fields: 13 • Fundamentals: Computer graphics depends on an understanding of how humans use 14 vision to perceive information and how information can be rendered on a display device. 15 Every computer scientist should have some understanding of where and how graphics can 16 be appropriately applied and the fundamental processes involved in display rendering. 17 • Modeling: Information to be displayed must be encoded in computer memory in some 18 form, often in the form of a mathematical specification of shape and form. 19 • Rendering: Rendering is the process of displaying the information contained in a model. 20 • Animation: Animation is the rendering in a manner that makes images appear to move 21 and the synthesis or acquisition of the time variations of models.
    [Show full text]
  • 3D Computer Graphics Compiled By: H
    animation Charge-coupled device Charts on SO(3) chemistry chirality chromatic aberration chrominance Cinema 4D cinematography CinePaint Circle circumference ClanLib Class of the Titans clean room design Clifford algebra Clip Mapping Clipping (computer graphics) Clipping_(computer_graphics) Cocoa (API) CODE V collinear collision detection color color buffer comic book Comm. ACM Command & Conquer: Tiberian series Commutative operation Compact disc Comparison of Direct3D and OpenGL compiler Compiz complement (set theory) complex analysis complex number complex polygon Component Object Model composite pattern compositing Compression artifacts computationReverse computational Catmull-Clark fluid dynamics computational geometry subdivision Computational_geometry computed surface axial tomography Cel-shaded Computed tomography computer animation Computer Aided Design computerCg andprogramming video games Computer animation computer cluster computer display computer file computer game computer games computer generated image computer graphics Computer hardware Computer History Museum Computer keyboard Computer mouse computer program Computer programming computer science computer software computer storage Computer-aided design Computer-aided design#Capabilities computer-aided manufacturing computer-generated imagery concave cone (solid)language Cone tracing Conjugacy_class#Conjugacy_as_group_action Clipmap COLLADA consortium constraints Comparison Constructive solid geometry of continuous Direct3D function contrast ratioand conversion OpenGL between
    [Show full text]
  • Guidance for Flood Risk Analysis and Mapping
    Guidance for Flood Risk Analysis and Mapping Flood Insurance Rate Map (FIRM) Graphics December 2020 Requirements for the Federal Emergency Management Agency (FEMA) Risk Mapping, Assessment, and Planning (Risk MAP) Program are specified separately by statute, regulation, or FEMA policy (primarily the Standards for Flood Risk Analysis and Mapping). This document provides guidance to support the requirements and recommends approaches for effective and efficient implementation. The guidance, context, and other information in this document is not required unless it is codified separately in the aforementioned statute, regulation, or policy. Alternate approaches that comply with all requirements are acceptable. For more information, please visit the FEMA Guidelines and Standards for Flood Risk Analysis and Mapping webpage (www.fema.gov/flood-maps/guidance-partners/guidelines-standards). Copies of the Standards for Flood Risk Analysis and Mapping policy, related guidance, technical references, and other information about the guidelines and standards development process are all available here. You can also search directly by document title at www.fema.gov/multimedia-library. FIRM Graphics December 2020 Guidance Document 6 Page i Table of Revisions The following summary of changes details revisions to this document subsequent to its most recent version in November 2019. Affected Section or Date Description Subsection December Section 1 Added section for Automated Map Production 2020 December Sections 6.7 and 6.8 Added evaluation lines for 2D modeling
    [Show full text]