Further Development

The key for real-time non-photo-realistic computer graphics often lies in finding its silhouette (see Figure ). Mathematically, a silhouette edge is defined as edge connecting front-facing and back-facing polygons. An approach that uses a fast probabilistic identification of silhouette edges in object space in order to render line-art in real time was presented by Markosian et al. [#!CONF_CG_INTERACTIVE-2!#].

Figure: A probabilistically rendered silhouette (using the approach by the Markosian et al.)

Interframe coherence of the silhouette edges and a fast visibility determination based on Appel's hidden-line algorithm [#!appel67invisibility!#] is used to speed up the drawing process. The algorithm identifies large (and therefore more significant) silhouettes with higher probability than smaller ones. Only a small fraction of silhouette edges needs to be examined, which further adds to the speed. A method for rendering silhouettes purely in screen space is discussed in [#!raskar99image!#]. A hybrid approach that uses both object space and screen space was introduced by Northrup et al. [#!SYMP_NPAR-2000-8!#]. It first finds the silhouette in object space and then continues to analyze the projection of these silhouette edges, producing smooth stroke paths in screen space which are then rendered.

Winkenbach and Salesin [#!winkenback90parametric!#] propose a pen-and-ink system specificly for parametric surfaces (see Figure ).

Figure: Parametric surface rendered normally (left) and with constant-density hatching (right)
Figure: Pencil Illustration

The central problem the approach addresses is how to maintain constant tone over a surface which is bent, thus leading to the accumulation of more strokes (Fig. , left). The solution lies in what the authors call constant-density hatching, a technique with which the stroke thickness is adjusted to give the same tone over the surface (Fig. , right).

The physical simulation of graphite pencil drawing is subject to the work by Sousa and Buchanan [#!EVL-1999-365!#]. They propose a rendering framework that encapsulates three levels of drawing: First, there is the simulation of the drawing materials (low level): The distribution of lead particles over a piece of paper is computed, with multiple layers being rendered above each other. Furthermore, different pencil hardnesses, pencil tip shapes as well as the structure of the drawing paper is taken into account (refer to Figure ). At medium level, the simulation deals with the placement of the strokes and drawing of outlines. Composition of the scene and rendering as a whole is dealt with at high level.

Figure: A stack of books rendered with various line directions

Line direction is a critical factor in hatching. Girshik et al. [#!SYMP_NPAR-2000-7!#] have provided evidence that line direction affects surface perception (e.g. curvature of a surface). Salisbury et al. [#!CONF_CG_INTERACTIVE-3!#] have therefore proposed a system for creating pen-and-ink style renderings with orientatable strokes. By aligning the direction field with the surface orientation, a more expressive appearance of pen-and-ink illustrations can be achieved (see Figure ).

Praun, Hoppe et al. [#!EVL-2001-153!#] present an approach which manages to produce hatched illustrations in real-time. Producing an animation out of a set of individually hatched images poses the following problems:

• There is only limited time for the computation of each rendered image
• The strokes need to be frame-to-frame coherent, or else the animation will have a flickery look
• The strokes need to maintain the desired tone even if the object moves toward or away from the camera. This is done by varying the density and width of the desired strokes.

The approach pre-renders hatch strokes into a sequence of mip-mapped images corresponding to different tones (Tonal Art Maps, TAMs), which are then used to texture the surfaces (see Figure ).

Figure: Tonal Art Maps: Strokes in lighter images are subsets of those in darker ones.

Figure: Blending TAM images on a triangle

A triangle is drawn by blending several TAM images over each other using multi-texturing (see Figure ). Each texture image is weighted using the lighting computed at the vertices. Thus, tones can be varied over each triangle. The use of Real-Time hatched illustrations for 3D gaming has been researched by Freudenberg et al. Their approach uses a per-object specification of rendering style in order to optimize performance. Previous work on the subject [#!SYMP_INTACT_3D-2001-1!#] focused on intercepting OpenGL calls in order to replace them with sketched-style rendering calls. However, frame-to-frame coherence could not be reached with this method, resulting in a fuzzy and disturbing look. The approach leaves the specification of discontinuities on the 3D mesh to the artist, and introduces various simplifications in determining the visibility of the silhouette edges. Surface detail is added via mip-mapping (Hatch Maps and Ink Maps), with smaller images containing fewer lines in order to achieve constant tonality. Conventional shading is used for colorization of the objects.