Descriptive: Interactive 3D Shape Modeling from A Single Descriptive Sketch

Highlights

• Using descriptive style to enable the shape modeling from a single sketch.

• Extends the range and complexity of shapes that can be created from a sketch.

• No limitation on the nature of the object or the viewpoint of the sketch.

Abstract

In this paper, we present a sketch-based modeler that reconstructs a 3D shape by combining a single descriptive sketch and minimal user intervention. The user provides a single 2D drawing in the form of a descriptive sketch, where solid curves describe the visible silhouette, and dashed curves the hidden outline. The curves are partitioned into a set of closed curves in a semi-automatic manner, each of which is consolidated into a closed surface element by solving a constrained optimization problem. The final 3D shape is generated by assembling these surface elements. The algorithmic reconstruction is complemented by allowing users to optionally guide the shape computation or correct any inaccuracy. This is done by successively specifying different kinds of local constraints on sparsely selected points in rotated views, such as adjustment of volume thickness along the projection line, or curvature discontinuity. Consequently, the range and complexity of shapes that can be created from a single-view sketch are significantly extended. We evaluate our solution by reconstructing a wide range of 3D models from sketches of various sources, and visually comparing the reference models and the shapes reconstructed by users.

Introduction

The common goal of sketch-based modeling (SBM) is to enable users to create 3D shapes from the sketch, an intuitive and efficient tool for visual communication. The user draws a set of strokes describing a 3D object on the sketching plane, which the modeler takes as input to compute a corresponding shape whose silhouette matches the input strokes. In solving the ill-posed problem, most modelers make use of human perceptual principles that are supposedly shared between the designers drawing the 2D sketches and the viewers who interpret them to mentally build the 3D shape. Leveraging our natural and well-trained skill for drawing and interpreting sketches, such modelers offer several advantages over conventional 3D modeling tools (3DS Max, Maya), among which is the ability to allow almost anyone to create 3D shapes easily and efficiently.

On the other hand, the shapes created with sketch-based modeling tools possess limited complexity and expressivity, as it becomes difficult to cover the full functionalities as offered by general modeling tools using solely a sketch-based interaction scheme. This paper addresses such difficulty and proposes solutions that combine a comprehensive sketching style borrowed from the descriptive geometry and minimal user intervention borrowed from conventional geometric modeling tools. The general goal of our modeler, which we name as Descriptive, is to expand the range and complexity of shapes that can be created from a single-view sketch.

The main limitation originates from the inherent ambiguities of a 3D shape reconstruction problem from a 2D drawing, i.e. there exists an infinite number of 3D shapes that match a given drawing. This problem becomes even more challenging when the drawing contains hidden parts that need to be estimated both in 2D and 3D. Although several existing methods have adopted perceptive or model-specific priors to make the problem solvable, it is still hard to solve it algorithmically since it involves the semantic understanding of the drawing. For example, the hidden part of a given shape depends on whether it represents a human or a plant. Our strategy to solve this problem is two-fold. First, the user sketches descriptive curves containing the description of hidden outlines in a dashed line style, which not only drastically reduces the ambiguity about the hidden shape (Fig. 1(a)) but also provides partial information on relative placements of enclosed shapes along the depth. Such a design choice is inspired by descriptive geometry, where hidden outlines are drawn by dashed curves. Next, the user can guide the automatic reconstruction by successively specifying local geometric constraints on sparsely selected curve points, through commonly accepted user interfaces as in conventional modeling tools. Such combination of a single-view sketch and minimum local control appears to be an efficient yet flexible way to convey the information on the intended shape.

Fig. 1 illustrates the modeling workflow with our system. The user starts by sketching the outline of an object including occluded parts, using the descriptive drawing style (Fig. 1(a)). The user is free to choose an arbitrary view, although there seems to be viewpoints preferred by designers that expose the multiple sides of the object and minimize the variation between a 2D projection and its 3D counterpart. The curve segments are then assembled into a set of closed curves (Fig. 1(b)), whose 3D counterparts are computed to allow the user to inspect the 3D shape to be reconstructed. The user can add local geometric constraints either to guide the initial reconstruction, or to modify it (Fig. 1(c)). In any case, a closed surface is generated for each curve, whose union is computed to result in a shape in such a way that both the projective constraint (sketch) and the user-specified local constraints are satisfied (Fig. 1(d)). We demonstrate that our strategies can significantly extend the modeling power of SBM while still maintaining the intuitive, easy-to-use interface. The remainder of the paper is organized as follows: Section 2 reviews related work. Section 3 explains the workflow followed by the user. Sections 4 Surface generation from 3D curves, 5 3D reconstruction of 2D closed curves respectively describe our surface generation process from the 3D curves, and the computation of the 3D coordinates of those curves. Section 6 presents results and discussion, and Section 7 conclusion.