基于草图的可变形曲线网络表面设计

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本文主要探讨了基于草图的可塑曲线网络在表面设计中的应用，由Güney Orbay和Levent Burak Karan两位来自卡内基梅隆大学机械工程系的研究者提出。他们开发了一种新的三维表面建模方法，该方法允许用户通过绘制曲线网络来创建和修改平滑表面，实现了草图与生成表面之间的双向通信。在这个创新的方法中，用户设计的曲线网络起到了关键作用，它作为一个控制框架，用于生成一个细分表面。细分表面的设计理念是根据用户提供的曲线网络实时调整，同时尽可能减少整个表面的曲率变化，以保持表面的平滑性。这种设计技术特别适用于自由形式建模和工业产品设计领域，因为它提供了高度灵活性和精确控制。作者强调，通过独立控制表面公平性，用户可以根据设计需求对曲线网络进行调整，以确保生成的表面下层结构既美观又符合工程标准。这种技术不仅简化了三维设计过程，还能提高设计者的创作效率，对于那些追求精细控制和流畅曲线形态的设计师来说，无疑是一大进步。该文于2012年5月3日首次接收，经过修订后于同年8月1日重新提交，并于8月28日接受。最终，文章于9月14日在线发布。关键词包括"基于草图的三维设计"、"自由形式建模"、"表面设计"、"细分表面"以及"工业产品设计"，这些都是本文核心研究内容的体现。 Sketch-based malleable curve networks 提供了一种新颖且实用的工具，将传统的草图设计与现代计算机辅助设计技术相结合，极大地扩展了设计师在创建复杂表面时的创造力和精确度。这对于提升产品设计的质量和效率具有重要意义。

2. User-controlled surface fairing of subdivision surfaces in the

presence of creases and geometric constraints.

3. Two-way curve/surface communication where curve con-

straints and surface smoothness can control surfaces and

curves, respectively.

Fig. 3 shows two example designs modeled by our approach.

2. Related work

Current commercial modeling packages provide the means for

designing curves and surfaces, and implement geometric opera-

tions with which a wide variety of shapes can be achieved [2–7].

Although effective for surface design, the manipulators for local

and volumetric editing require the user to achieve and preserve

smooth surfaces manually (Fig. 4a, b). A lack of direct control on

the fairness of the surface makes it challenging for the user to

establish the key feature curves, while producing smooth surfaces

from these curves (Fig. 1). As a result, much effort is spent on

surface manipulation to achieve fair surfaces that result in the

desired feature curves, rather than directly prescribing such

curves, from which suitable surfaces can be generated.

Recent studies [10,11] on sketch-based modeling have pro-

posed methods to create and modify smooth surfaces using

sketching. In free-form surface modeling, these systems seek a

fast transformation from 2D to 3D using a simple base surface

instantiation, followed by an iterative modiﬁcation of the geo-

metry with pen strokes [8,12–15]. Alternatively, a number of

systems have been proposed that involve primitive sketching,

followed by gestural interactions that implement common CAD

operations [10]. A common feature in both approaches is that the

sketched strokes are used either to deﬁne an initial starting shape

such as a contour or silhouette, or to iteratively modify an

existing shape. While these approaches can produce smooth

surfaces, the created surfaces are similarly controlled through

the curves (Fig. 4c, d) rather than a direct shape control of the

surfaces. These approaches still require the user to iteratively

search for suitable curve conﬁgurations that lead to desirably

smooth surfaces.

Among the sketch-based blob creation and modiﬁcation

methods that have been proposed recently [8,12,13,16,17], Fiber-

mesh by Nealen et al. [8] is closely related to our work. It

produces a curvature minimizing closed mesh that interpolates

user-drawn contour and feature curves. While our approach

shares a similar goal of producing energy minimizing surfaces

such as those in Fibermesh [18–20], it differs from these

approaches in a number of ways. First, the curvature variation

minimization approach in Fibermesh produces a single, unique

mesh surface from the set of input curves. The user modiﬁes this

surface by modifying the curves. By contrast, our approach

permits greater latitude in surface modeling by allowing the user

to (1) construct a precise surface topology through a curve

network rather than through an iterative curve addition on a

base surface, (2) explore different surface geometries on the same

curve network through the use of free curves and independent

surface fairing. Moreover, during surface modiﬁcations, in con-

trast to Fibermesh’s pick/drag based interactions, we utilize

sketched strokes to directly deﬁne and modify the shapes of

curves. We also use a subdivision surface representation which allows

the control of the shape through a coarse control mesh but produces

high complexity sampling at low cost. Fibermesh, on the other hand,

uses a mesh representation which requires the coordinates of all

vertices to be calculated for each modiﬁcation on the curves.

Works of Nasri et al. [21] and Bein et al. [22] also originate

from a similar motivation. Nasri et al. [21] uses polygonal

complexes to create models that have user-deﬁned outer con-

tours, followed by subdivision for surfacing. However, the pro-

duced geometries are limited to ﬂat inﬂated models. Bein et al.

[22] present sketch-based tools for creating subdivision surfaces

using operators such as extrusion, revolution, and lofting. The

shape is controlled through vertex/edge additions and vertex/face

dragging. Similar to other sketch-based tools, maintaining the

crease curves

Fig. 3. Various results obtained by our approach. Note the feature crease curves and the transitions between smooth and discontinuous regions. The smooth regions far

from crease curves are designed and maintained using our approach.

Fig. 4. Current modeling software presents tools to locally modify surfaces

including (a) modiﬁcations using control points and (b) deformation lattices

(Rhinoceros 3D [5]). Recent advances in sketch-based methods utilize modiﬁca-

tions to the curves using (c) pick/drag (Fibermesh [8]) and (d) modiﬁer strokes

(SketchCAD [9]). However, surfaces are still manipulated indirectly through the

curves, preventing a direct control of surface fairness.

G. Orbay, L.B. Kara / Computers & Graphics 36 (2012) 916–929918

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