A Bidirectional Deposition Model of Wax Crayons Dave Rudolf dave.rudolf@usask.ca David Mould mould@cs.usask.ca Eric Neufeld eric@cs.usask.ca Department of Computer Science University of Saskatchewan Abstract We present a physically-inspired model of wax crayons, which synthesizes drawings from collections of user- specified strokes. Paper is represented by a height-field texture, and a crayon is modelled with a 2D mask that evolves as it interacts with the paper. The amount of wax deposition is computed based on the crayon contact profile, contact force, and friction. Previously deposited wax is smeared by crayon action, based on wax softness and contact information. Deposited wax can also be carved from the paper by the crayon and redeposited at another location. The distributed wax is rendered using a simplified Kubelka-Monk model, which approximates light transmission and scattering effects. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Gen- eration I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism: Color, shading, shadowing, and texture Keywords: nonphotorealistic rendering, procedural textures, interactive techniques 1. Introduction Recent years have seen a proliferation of nonphotorealistic rendering styles, such as oil painting, pen-and-ink illustra- tion, and copperplate engraving, among others. One thread of research has involved simulating specific traditional me- dia, such as watercolours or pencils. In this paper, we de- scribe a drawing primitive designed to mimic wax crayons. Wax crayons possess certain characteristics that make them challenging to model. The crayon contact area is large enough that the paper cannot be treated as flat over the re- gion of contact. The softness of wax is such that a substan- tial quantity of wax adheres to the page, and that previously deposited wax can be smeared and carved away by the ac- tion of later crayon strokes. However, wax is much more vis- cous than paints and inks, and so its interactions are differ- ent than these other media. Also, the crayon footprint can change shape over a short period of time, changing substan- tially even within a single stroke. Many different colours of wax crayon are commonly in use, and the interaction be- tween multiple translucent materials offers a rendering chal- lenge. We present a method for simulating wax crayons based on a physically-inspired model of wax deposition, smearing, and redeposition. Drawings are based on a collection of user- specified strokes; the effect at each point along a crayon’s stroke is treated by first computing the crayon’s contact pro- file, then depositing wax from the crayon to the paper, updat- ing the crayon shape, smearing and possibly carving previ- ously deposited wax. The final distribution of wax is ren- dered with a simplified Kubelka-Monk model, which ac- counts for light transmission and scattering through multiple layers of wax. Wax crayons are archetypally associated with a certain highly simplified drawing style. Despite the occasionally onerous physical simulation we describe, we have endeav- oured to retain a sense of fun in the project, and we hope that this carries through in the childish artistic style of the images we present. 2. Previous Work Originally, nonphotorealistic rendering (NPR) branched from work in image processing and pattern recognition circles. The earliest work in NPR consisted of specialized dithering techniques [VdMG91, VB99]. Edge detection