Physically-Based Interactive Bi-Scale Material DesignHongzhi Wu Julie Dorsey Holly RushmeierComputer Graphics Group, Yale UniversityEditingSlidersLarge-ScaleViewSmall-ScaleViewbcdeaFigure 1: Bi-scale material design: large-scale appearance changes produced by editing of small-scale geometry (b & c), color (d) andBRDFs (e), using our interactive system (a), which quickly updates the appearance of the large-scale object after small-scale edits. Thesmall-scale details (rendered with a Lambertian BRDF for a better visualization) are shown in the bottom right corner of (b-e). In (d), thecolor of the small-scale side faces is adjusted to yellow. In (e), the small-scale material is changed from a measured silver-metallic-paint2BRDF to a Lambertian model.AbstractWe present the first physically-based interactive system to facilitatethe appearance design at different scales consistently, through ma-nipulations of both small-scale geometry and materials. The core ofour system is a novel reflectance filtering algorithm, which rapidlycomputes the large-scale appearance from small-scale details, byexploiting the low-rank structures of the Bidirectional Visible Nor-mal Distribution Function and pre-rotated BRDFs in the matrix for-mulation of our rendering problem. Our algorithm is three orders ofmagnitude faster than a ground-truth method. We demonstrate vari-ous editing results of different small-scale geometry with analyticaland measured BRDFs. In addition, we show the applications of oursystem to physical realization of appearance, as well as modelingof real-world materials using very sparse measurements.CR Categories: I.3.7 [Computer Graphics]: Three-DimensionalGraphics and Realism—Color, shading, shadowing, and textureKeywords: bi-scale, material editing, reflectance filtering, low-rank matrixLinks: DL PDF WEB VIDEO1 IntroductionThe appearance of materials can vary considerably when viewedat different scales. For example, individual grains of sand or fab-ric threads that are visible on close view merge into a material de-scribed by a single reflectance function when viewed from a dis-tance. Physically speaking, the large-scale appearance is uniquelydetermined by averaging the look of small-scale details [Brunetonand Neyret 2011]. Therefore, it would be desirable to build an edit-ing system for interactive appearance design at different scales, bymanipulating small-scale structures. This could be useful in appli-cations like building exterior design, where the user edits the looksof a building at different view distances.Existing interactive material editing systems (e.g. [Ben-Artzi et al.2006; Pellacini and Lawrence 2007]) focus on adjusting materialappearance only at a single scale. On the other hand, previouswork [Westin et al. 1992; Gondek et al. 1994], which computesrealistic large-scale appearance by simulating light interactions insmall-scale details, is too slow to provide interactive feedback.Although converting small-scale structures to large-scale appear-ance is essentially performing reflectance filtering, related tech-niques [Bruneton and Neyret 2011] are not suitable for our purpose,due to the lack of support for general geometry and materials [Hanet al. 2007], or costly computational overhead [Wu et al. 2009].This paper presents, to our knowledge, the first physically-based in-teractive bi-scale material editing system, which manipulates small-scale geometry and Bidirectional Reflectance Distribution Func-tions (BRDFs), to facilitate appearance design at two differentscales consistently. The user can freely change both small-scale ge-ometry and materials, then our system quickly computes the large-scale appearance to provide interactive visual feedback. As illus-trated in Fig. 1, various small-scale edits can have dramatic effectson appearance. We achieve an acceleration rate of over 5000:1,when compared with a ground-truth method similar to [Westin et al.1992], implemented on modern hardware. The key to the per-formance of our system is a novel reflectance filtering algorithm,which efficiently processes the Bidirectional Visible Normal Dis-tribution Function (BVNDF) and pre-rotated BRDFs, derived fromthe changing small-scale details. We observe and exploit the low-rank structures in both quantities to accelerate the large-scale ap-pearance computation, using Singular Value Decomposition (SVD)combined with the random projection method [Vempala 2004].Our system can also guide the physical realization of bi-scale ap-pearance, since the small-scale details are explicitly modeled. Inaddition, real-world materials can be approximately modeled bymimicking the small-scale details and then fine-tuning the large-scale appearance, using very few photographs. We believe that oursystem can be useful in many applications, including building exte-rior design, outdoor advertisements, physical realization of appear-ance as well as rapid material modeling in visual effects industry.In summary, the major contributions of this paper are:• We propose a novel form of interactive material design at twoscales, through the manipulation of both small-scale geome-try and materials. Our method is physically based so that thelarge-scale appearance is consistent with the small-scale de-tails.• We bridge the gap between interactive editing and previouswork on bi-scale material modeling [Westin et al. 1992], byusing a novel reflectance filtering algorithm, that rapidly com-putes large-scale appearance from changing small-scale de-tails.• Our system facilitates the design of physically realizable ma-terials, since we explicitly model small-scale details.• We propose a new modeling method for real-world materialswith very sparse measurements using bi-scale constraints.Terminology. We use the terms “small/large-scale” instead of“micro/milli-scale” as in some previous work, because we do notwant to impose tight limits on the absolute sizes of both scales.Our method will work as long as the ratio between the large and thesmall scale is big, and the small scale is greater than the wavelengthof light.2 Previous WorkInteractive Material Editing. There has been much research ef-fort devoted to interactive material editing in the past decade (e.g.[Ben-Artzi et al. 2006; Pellacini and Lawrence 2007]). Sophisti-cated methods are developed to achieve interactive or even real-time frame rates. However, no existing work considers the edit-ing of appearance at different scales. In comparison, our