Microscopic Structural Modeling of Colored Pencil Drawings

Modeling paper microstructure
As the look & feel of CPDs stems primarily from the ``texture'' of papers, faithful modeling of papers' 3D microstructure is crucial.

Fig. 1 illustrates a microscopic vertical cut view of a piece of paper. Papers are generally composed of multiple layers of globally-oriented, but locally-random sparse fiber nets, whose spaces are filled partially with talc for surface smoothness. A fiber net is modeled geometrically by instantiating defaced, napped and constricted cylinders. On the other hand, a constrained blobby approach is taken to model the distribution of talc. Such a microstructure of papers is then 3D scan converted into a thin volume model, whose field value indicates the density of a paper component or pigment. The resulting paper volume is volumetrically ray traced to simulate paper semitransparency and subsurface scattering (Fig. 2). A volume visualization and graphics software system called VolVis ver. 2.0 [2] is used for the purpose of rendering.

Modeling pigment distribution
Pigment distribution is modeled based on the paper microstructure model described above. Many chinks left in the layered structure of papers are the most dominant factor in governing how pigment is distributed (Fig. 1). The offset distance accessibility (ODA) [3] is calculated to approximately locate the chinks in the paper volume, where fractions of pigment can be distributed, by accounting for the pencil point's shape, pressure, and stroke as well as pigment fragility. Here again, the geometry of pigment peeled off from a pencil and deposited into the paper volume is modeled by the collision detected blobby model, and then 3D scan converted into the paper volume.

Fig. 3 shows three perspective views of the microstructure of a square piece of paper, (a) drawing without pigment; (b) virtual effect of graphitizer; and (c) drawing with a single color of pigment. The graphitizer is a well-known tool commonly used in the paper science for evaluating the texture of papers by press coating a special kind of pigment uniformly on pieces of paper. It can be seen also here from the center and right images respectively that the virtual graphitizer reveals the fiber nets more clearly, while in the regular drawing, most of the pigment is accumulated in the concave regions lying on the fore side of fibers with locally maximal height with respect to the pencil stroke direction. Furthermore, in both cases, it is revealed that pigment is more likely to be attached onto surface areas covered with talc, because these relatively flat areas possess lower ODA values, and talc has a relatively high pigment-adsorption rate (Fig. 1). Such pigment distribution patterns qualitatively coincide with physically observed ones. An example of macroscopic view of the resultant CPD is shown in Fig. 4.

Modeling pigment redistribution with water
Currently, our interest is drawn also to yet another principal CPD operation, namely, redistributing pigment with water (Fig. 2). Using water-soluble colored pencils, spreading and blending of pigment with water can yield a sense of smooth color fading and blending, and hence play a key role in depicting objects in a precise and natural manner.

A 3D extension of the LIC (Line Integral Convolution) algorithm [4], combined with the ODA concept could be the best candidate for calculating the effect of spreading and blending of brush-reachable pigments with water on or near the surface of the paper volume.

Fig. 1: Paper microstructure and pigment distribution

Fig. 2: Relationships among CPD models

Fig 3: Microscopic images of paper microstructure

(a) drawing: without pigment	(b) graphitizer	(c) drawing: with single color of pigment

Fig 4: Macroscopic image of paper microstructure

Arrow depicts the primary direction of pencil stroke.