Faramarz F. Samavati

Technical Section: Sketch-based modeling: A survey

User interfaces in modeling have traditionally followed the WIMP (Window, Icon, Menu, Pointer) paradigm. Though functional and very powerful, they can also be cumbersome and daunting to a novice user, and creating a complex model requires considerable expertise and effort. A recent trend is toward more accessible and natural interfaces, which has lead to sketch-based interfaces for modeling (SBIM). The goal is to allow sketches-hasty freehand drawings-to be used in the modeling process, from rough model creation through to fine detail construction. Mapping a 2D sketch to a 3D modeling operation is a difficult task, rife with ambiguity. To wit, we present a categorization based on how a SBIM application chooses to interpret a sketch, of which there are three primary methods: to create a 3D model, to add details to an existing model, or to deform and manipulate a model. Additionally, in this paper we introduce a survey of sketch-based interfaces focused on 3D geometric modeling applications. The canonical and recent works are presented and classified, including techniques for sketch acquisition, filtering, and interpretation. The survey also provides an overview of some specific applications of SBIM and a discussion of important challenges and open problems for researchers to tackle in the coming years.

Sketch-based modeling with few strokes

We present a novel sketch-based system for the interactive modeling of a variety of free-form 3D objects using just a few strokes. Our technique is inspired by the traditional illustration strategy for depicting 3D forms where the basic geometric forms of the subjects are identified, sketched and progressively refined using few key strokes. We introduce two parametric surfaces, rotational and cross sectional blending, that are inspired by this illustration technique. We also describe orthogonal deformation and cross sectional oversketching as editing tools to complement our modeling techniques. Examples with models ranging from cartoon style to botanical illustration demonstrate the capabilities of our system.

Reversing subdivision rules: local linear conditions and observations on inner products

Abstract In a previous work (Samavati and Bartels, Comput. Graphics Forum 18 (1998) 97–119) we investigated how to reverse subdivision rules using global least-squares fitting. This led to multiresolution structures that could be viewed as semiorthogonal wavelet systems whose inner product was that for finite-dimensional Cartesian vector space. We produced simple and sparse reconstruction filters, but had to appeal to matrix factorization to obtain an efficient, exact decomposition. We also made some observations on how the inner product that defines the semiorthogonality influences the sparsity of the reconstruction filters. In this work we carry the investigation further by studying biorthogonal systems based upon subdivision rules and local least-squares fitting problems that reverse the subdivision. We are able to produce multiresolution structures for some common univariate subdivision rules that have both sparse reconstruction and decomposition filters. Three will be presented here – for quadratic and cubic B-spline subdivision and for the four-point interpolatory subdivision of Dyn et al. We observe that each biorthogonal system we produce can be interpreted as a semiorthogonal system with an inner product induced on the multiresolution that is quite different from that normally used. Some examples of the use of this approach on images, curves, and surfaces are given.

Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least-Squares Data Fitting

This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, least‐squares data fitting, and wavelets. We show how least‐squares data fitting can be used to “reverse” a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization.

Single camera flexible projection

We introduce a flexible projection framework that is capable of modeling a wide variety of linear, nonlinear, and hand-tailored artistic projections with a single camera. This framework introduces a unified geometry for all of these types of projections using the concept of a flexible viewing volume. With a parametric representation of the viewing volume, we obtain the ability to create curvy volumes, curvy near and far clipping surfaces, and curvy projectors. Through a description of the frameworks geometry, we illustrate its capabilities to recreate existing projections and reveal new projection variations. Further, we apply two techniques for rendering the frameworks projections: ray casting, and a limited GPU based scanline algorithm that achieves real-time results.

Precise Ink Drawing of 3D Models

Drawings made with precise pen strokes accurately reveal the geometric forms that give subjects their characteristicshape. We present a system for non‐photorealistic rendering of precise drawing strokes over dense 3Dtriangle meshes with arbitrary topology. During an automatic pre‐process, we construct an extended version ofthe edge‐buffer data structure to allow the calculation of shape measures at each mesh edge, by adapting numericalmethods used in geomorphology. At runtime, feature edges related to shape measures are extracted andrendered as strokes with varying thickness and pen marking styles. Stroke thickness is automatically adjusted byconsidering surface curvature. Pen marking styles and visual effects of ink distribution are both controlled by theuser. We demonstrate precise drawing strokes over complex meshes revealing a variety of shape characteristics.

Multiresolution Surfaces having Arbitrary Topologies by a Reverse Doo Subdivision Method

We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models (Samavati and Bartels, Computer Graphics Forum, 18(2):97–119, June 1999). As a result, semiorthogonal wavelet systems have also been generated. To construct a multiresolution surface of an arbitrary topology, however, biorthogonal wavelets are needed. In Bartels and Samavati (Journal of Computational and Applied Mathematics, 119:29–67, 2000) we introduced local least squares models for reversing subdivision rules to construct multiresolution curves and tensor product surfaces, noticing that the resulting wavelets were biorthogonal (under an induced inner product). Here, we construct multiresolution surfaces of arbitrary topologies by locally reversing the Doo subdivision scheme. In a Doo subdivision, a coarse surface is converted into a fine one by the contraction of coarse faces and the addition of new adjoining faces. We propose a novel reversing process to convert a fine surface into a coarse one plus an error. The conversion has the property that the subdivision of the resulting coarse surface is locally closest to the original fine surface, in the least squares sense, for two important face geometries. In this process, we first find those faces of the fine surface which might have been produced by the contraction of a coarse face in a Doo subdivision scheme. Then, we expand these faces. Since the expanded faces are not necessarily joined properly, several candidates are usually at hand for a single vertex of the coarse surface. To identify the set of candidates corresponding to a vertex, we construct a graph in such a way that any set of candidates corresponds to a connected component. The connected components can easily be identified by a depth first search traversal of the graph. Finally, vertices of the coarse surface are set to be the average of their corresponding candidates, and this is shown to be equivalent to local least squares approximation for regular arrangements of triangular and quadrilateral faces.

L-SYSTEM DESCRIPTION OF SUBDIVISION CURVES

In recent years, subdivision has emerged as a major geometric modeling technique. Algorithms for generating subdivision curves are often specified in terms of iterated matrix multiplication. Each multiplication maps a globally indexed sequence of points that represents a coarser approximation of the curve onto a longer sequence that represents a finer approximation. Unfortunately, this use of matrices and indices obscure the local and stationary character of typical subdivision rules. We introduce parametric context-sensitive L-systems with affine geometry interpretation as an alternative technique for specifying and generating subdivision curves. This technique is illustrated using Chaikin, cubic B-spline, and Dyn-Levin-Gregory (4-point) subdivision schemes as examples. L-systems formalize subdivision algorithms in an intuitive, concise, index-free manner, reflecting the parallel and local character of these algorithms. Furthermore, L-system specification of subdivision algorithms directly leads to their computer implementation.

TERRAIN SYNTHESIS BY-EXAMPLE

Synthesizing terrain or adding detail to terrains manually is a long and tedious process. With procedural synthesis methods this process is faster but more difficult to control. This paper presents a new technique of terrain synthesis that uses an existing terrain to synthesize new terrain. To do this we use multi-resolution analysis to extract the high-resolution details from existing models and apply them to increase the resolution of terrain. Our synthesized terrains are more heterogeneous than procedural results, are superior to terrains created by texture transfer, and retain the large-scale characteristics of the original terrain.

Sketch-based Interfaces and Modeling

The field of sketch-based interfaces and modeling (SBIM) is concerned with developing methods and techniques to enable users to interact with a computer through sketching - a simple, yet highly expressive medium. SBIM blends concepts from computer graphics, human-computer interaction, artificial intelligence, and machine learning. Recent improvements in hardware, coupled with new machine learning techniques for more accurate recognition, and more robust depth inferencing techniques for sketch-based modeling, have resulted in an explosion of both sketch-based interfaces and pen-based computing devices. Presenting the first coherent, unified overview of SBIM, this unique text/reference bridges the two complementary research areas of user interaction (sketch-based interfaces), and graphical modeling and construction (sketch-based modeling). The book discusses the state of the art of this rapidly evolving field, with contributions from an international selection of experts. Also covered are sketch-based systems that allow the user to manipulate and edit existing data - from text, images, 3D shapes, and video - as opposed to modeling from scratch. Topics and features: reviews pen/stylus interfaces to graphical applications that avoid reliance on user interface modes; describes systems for diagrammatic sketch recognition, mathematical sketching, and sketch-based retrieval of vector drawings; examines pen-based user interfaces for engineering and educational applications; presents a set of techniques for sketch recognition that rely strictly on spatial information; introduces the Teddy system; a pioneering sketching interface for designing free-form 3D models; investigates a range of advanced sketch-based systems for modeling and designing 3D objects, including complex contours, clothing, and hair-styles; explores methods for modeling from just a single sketch or using only a few strokes. This text is an essential resource for researchers, practitioners and graduate students involved in human-factors and user interfaces, interactive computer graphics, and intelligent user interfaces and AI.