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Line Drawings from 3D Models A Tutorial Other titles in Foundations and Trends R in Computer Graphics and Vision Publishing and Consuming 3D Content on the Web: A Survey Marco Potenziani, Marco Callieri, Matteo Dellepiane and Roberto Scopigno ISBN: 978-1-68083-536-6 Crowdsourcing in Computer Vision Adriana Kovashka, Olga Russakovsky, Li Fei-Fei and Kristen Grauman ISBN: 978-1-68083-212-9 The Path to Path-Traced Movies Per H. Christensen and Wojciech Jarosz ISBN: 978-1-68083-210-5 (Hyper)-Graphs Inference through Convex Relaxations and Move Making Algorithms Nikos Komodakis, M. Pawan Kumar and Nikos Paragios ISBN: 978-1-68083-138-2 Line Drawings from 3D Models A Tutorial Pierre Bénard LaBRI (UMR 5800, CNRS, Univ. Bordeaux) Inria Bordeaux Sud-Ouest [email protected] Aaron Hertzmann Adobe Research [email protected] Boston — Delft Foundations and Trends R in Computer Graphics and Vision Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is P. Bénard and A. Hertzmann. Line Drawings from 3D Models. Foundations and Trends R in Computer Graphics and Vision, vol. 11, no. 1-2, pp. 1–159, 2019. ISBN: 978-1-68083-591-5 c 2019 P. Bénard and A. Hertzmann All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged. Authorization does not extend to other kinds of copying, such as that for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. In the rest of the world: Permission to photocopy must be obtained from the copyright owner. Please apply to now Publishers Inc., PO Box 1024, Hanover, MA 02339, USA; Tel. +1 781 871 0245; www.nowpublishers.com; [email protected] now Publishers Inc. has an exclusive license to publish this material worldwide. Permission to use this content must be obtained from the copyright license holder. Please apply to now Publishers, PO Box 179, 2600 AD Delft, The Netherlands, www.nowpublishers.com; e-mail: [email protected] Foundations and Trends R in Computer Graphics and Vision Volume 11, Issue 1-2, 2019 Editorial Board Editor-in-Chief Brian Curless William T. Freeman Luc Van Gool University of Washington MIT KU Leuven and ETH Zurich Editors Marc Alexa Aaron Hertzmann Peter Shirley TU Berlin Adobe Research University of Utah Kavita Bala Hugues Hoppe Noah Snavely Cornel Microsoft Research Cornell Ronen Basri C. Karen Liu Stefano Soatto Weizmann Institute of Georgia Tech UCLA Science David Lowe Richard Szeliski Peter Belhumeur University of British Microsoft Research Columbia University Columbia Joachim Weickert Jitendra Malik Andrew Blake Saarland University Microsoft Research Berkeley Steve Marschner Song Chun Zhu Chris Bregler Cornell UCLA Facebook-Oculus Shree Nayar Andrew Zisserman Joachim Buhmann Columbia Oxford ETH Zurich James O’Brien Michael Cohen Berkeley Microsoft Research Tomas Pajdla Paul Debevec Czech Technical University USC Institute for Creative Technologies Pietro Perona California Institute of Julie Dorsey Technology Yale Marc Pollefeys Fredo Durand ETH Zurich MIT Jean Ponce Olivier Faugeras Ecole Normale Superieure INRIA Long Quan Rob Fergus HKUST NYU Cordelia Schmid Mike Gleicher INRIA University of Wisconsin Steve Seitz University of Washington Richard Hartley Australian National Amnon Shashua University Hebrew University Editorial Scope Topics Foundations and Trends R in Computer Graphics and Vision publishes survey and tutorial articles in the following topics: • Rendering • Motion estimation and registration • Shape • Stereo matching and • Mesh simplification reconstruction • Animation • 3D reconstruction and • Sensors and sensing image-based modeling • Image restoration and • Learning and statistical enhancement methods • Segmentation and grouping • Appearance-based matching • Feature detection and selection • Object and scene recognition • Color processing • Face detection and recognition • Texture analysis and synthesis • Activity and gesture recognition • Illumination and reflectance modeling • Image and video retrieval • Shape representation • Video analysis and event recognition • Tracking • Medical image analysis • Calibration • Robot localization and • Structure from motion navigation Information for Librarians Foundations and Trends R in Computer Graphics and Vision, 2019, Volume 11, 4 issues. ISSN paper version 1572-2740. ISSN online version 1572-2759. Also available as a combined paper and online subscription. Contents 1 Introduction2 1.1 Occluding contours..................... 3 1.2 How to use this tutorial................... 5 1.3 The importance of visualizations.............. 7 1.4 The science and perception of art.............. 8 1.5 Survey of feature curves................... 10 1.6 Brief history of 3D Non-Photorealistic Rendering..... 14 2 Image-Space Curves 17 2.1 Discussion and extensions.................. 20 3 Mesh Contours: Definition and Detection 24 3.1 Meshes............................ 24 3.2 Camera viewing....................... 25 3.3 Front faces and back faces................. 26 3.4 Mesh contours and boundaries............... 27 3.5 Generic position assumption................. 29 3.6 Contours are sparse..................... 30 3.7 Extraction algorithms.................... 30 4 Mesh Curve Visibility 37 4.1 Ray tests........................... 38 4.2 Concave and convex edges................. 39 4.3 Singular points........................ 39 4.4 Visibility for other curve types............... 43 4.5 View Graph data structures................. 43 4.6 Curve-based visibility algorithms.............. 46 4.7 Quantitative Invisibility................... 48 4.8 Planar Maps......................... 50 4.9 Non-orientable surfaces................... 51 5 Smooth Surfaces as Meshes 54 5.1 The ups and downs of mesh rendering for smooth surfaces 54 5.2 Interpolated Contours.................... 56 5.3 Planar Maps......................... 61 6 Fast Hardware-Based Extraction and Visibility 63 6.1 Two-pass hardware rendering................ 63 6.2 Contour extraction on the GPU............... 64 6.3 Hardware-accelerated visibility computation........ 65 6.4 Item buffer.......................... 67 6.5 Segment Atlas........................ 67 7 Parametric Surfaces: Contours and Visibility 70 7.1 Surface definition...................... 70 7.2 Contour definition...................... 72 7.3 Contour extraction...................... 75 7.4 Contour curvature...................... 76 7.5 Singular points........................ 78 7.6 Visibility computation.................... 81 8 Implicit Surfaces: Contours and Visibility 86 8.1 Surface definition...................... 86 8.2 Contour extraction...................... 87 8.3 Visibility........................... 93 8.4 Volumetric data....................... 94 9 Stylized Rendering and Animation 103 9.1 Stroke extraction...................... 103 9.2 Stroke rendering....................... 107 9.3 Topological simplification.................. 108 9.4 Object shading and texturing................ 112 9.5 Animation.......................... 113 10 Conclusion 118 10.1 Open research problems................... 119 Acknowledgements 121 Appendices 122 A Fundamentals of Differential Geometry 123 A.1 Geometry of surfaces.................... 123 A.2 Curvature.......................... 124 B Convex and Concave Contours 129 C Accurate Numerical Computation 132 C.1 Logical intersections..................... 132 C.2 Orientation test....................... 133 Line Drawings from 3D Models Pierre Bénard1 and Aaron Hertzmann2 1LaBRI – Inria; [email protected] 2Adobe Research; [email protected] ABSTRACT This tutorial describes the geometry and algorithms for gen- erating line drawings from 3D models, focusing on occluding contours. The geometry of occluding contours on meshes and on smooth surfaces is described in detail, together with al- gorithms for extracting contours, computing their visibil- ity, and creating stylized renderings and animations. Exact methods and hardware-accelerated fast methods are both described, and the trade-offs between different methods are discussed. The tutorial brings together and organizes mate- rial that, at present, is scattered throughout the literature. It also includes some novel explanations, and implementation tips. A thorough survey of the field of non-photorealistic 3D ren- dering is also included, covering other kinds of line drawings and artistic shading. Pierre Bénard and Aaron Hertzmann (2019), “Line Drawings from 3D Models”, Foundations and Trends R in Computer Graphics and Vision: Vol. 11, No. 1-2, pp 1–159. DOI: 10.1561/0600000075. 1 Introduction Humans have
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