Applying these principles, we develop the … is not an inherent part of the final form. Alternative methods … results[9]) to achieve the final form. The final Surface Drawing was …

The state of the art in three-dimensional modeling can represent a variety of complex smooth surfaces. When artists and designers create shapes with these techniques, we observe that often the method of surface representation restricts the ways in which a shape can be modeled. Consider traditional spline-based modeling[8]. While splines can represent many different shapes, a user often has to think of the most efficient way to represent a shape before begin- ningthemodeling process. Changing directions midway through the design process often requires such a drastic change in the underlying placement of patches that the user must return to the drawing board, essentially starting from scratch[9]. The traditional shape modeling approach of the graphics and CAGD communities is fundamentally different from the approach taken by the artistic community. Consider the perhaps simplest of all modeling tools: the pencil. It is an extraordinarily effec- tiveconduitfor artistic expression. Part of the reason for this is its simplicity. Another reason for its success is the close relation between an artist’sperceptionand action and the forms the pencil produces. This link yields direct control overall aspects of form. Surface Drawing, which we introduce, provides direct control over three-dimensional space in the same way a pencil commands two- dimensional space. Considerthe Pencil. To better understand whataperceptual, creative computer model- ingtoolmightbe, consider an exemplary traditional tool: the pencil. The movements of the hand across the page are closely tied to the resulting lines that are displayed. This single tool can be used to make a range of shapes, from simple to intricate. The pencil does not require the user to work withina mathematical structure. The pencil does not force images to be understood through primitives that are not related to the drawing task. The pencil allows highly complex shapes to be directly created without tedious editing. The pencil allows the creation and viewing of drawings in their full dimension. Users are presented with direct control over the lines they are making, and nothing more. The pencil is successful because it allows users to think perceptually about a drawing as it is being constructed. Surface Drawing. The goal of the Surface Drawing approach is to extend the tra- ditionalsystemof drawing lines with a pencil to the creation of freeform surfaces. As discussed in Section 2.1 the pencil is an ex- cellenttoolfor perceptual thinking. The key to understandinga pencil is to analyze the way in which it is used by experts. Figure 3 shows how a trained artist holds a pencil. Note that the contact between the pencil and the paper (two-dimensional space) is in the form of a line . Surface Drawing is an extension of this metaphor where the contact between the user and three-dimensional space isa plane . There is an interesting connection between this view of drawing and manifold theory (see[1]). Drawing with a pencil is much like adding locally one-dimensional coordinate patches to a one-manifold…

Source: http://www.multires.caltech.edu/

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