Topology-constrained synthesis of vector patterns

Abstract

Decorative patterns are observed in many forms of art, typically enriching the visual aspect of otherwise simple shapes. Such patterns are especially difficult to create, as they often exhibit intricate structural details and at the same time have to precisely match the size and shape of the underlying geometry. In the field of Computer Graphics, several approaches have been proposed to automatically synthesize a decorative pattern along a curve, from an example. This empowers non expert users with a simple brush metaphor, allowing them to easily paint complex structured decorations. We extend this idea to the space of design and fabrication. The major challenge is to properly account for the topology of the produced patterns. In particular, our technique ensures that synthesized patterns will be made of exactly one connected component, so that once printed they form a single object. To achieve this goal we propose a two steps synthesis process, first synthesizing the topology of the pattern and later synthesizing its exact geometry. We introduce topology descriptors that efficiently capture the topology of the pattern synthesized so far. We propose several applications of our method, from designing objects using synthesized patterns along curves and within rectangles, to the decoration of surfaces with a dedicated smooth frame interpolation. Using our technique, designers paint structured patterns that can be fabricated into solid, tangible objects, creating unusual and surprising designs of lamps, chairs and laces from examples.

A survey of the state-of-the-art in patch-based synthesis

“…In cases where the pattern is fairly regular and self-similar, Zhou et al [78] showed that a simpler dynamic programming technique can be used to synthesize patterns along curves. Later, Zhou et al [79] showed that decorative patterns can be synthesized with better controls over topology (e.g., number of holes and connected components), by first synthesizing the topology using a topological descriptor, and then synthesizing the pattern itself. This latter work also demonstrated design of 3D patterns, which we discuss next.…”

State of the Art in Methods and Representations for Fabrication-Aware Design

“…To address this, a method for topology‐constrained pattern synthesis was proposed by Zhou et al [ZJL14]. Given a 2D exemplar, the method strives to tile it along a curve in a fabricable manner.…”

Fabricable tile decors

“…Several recent works consider the problem of decorating surfaces to turn them into printable objects, with the same purpose of customization for 3D printing. Zhou et al [2014] synthesize connected patterns along curves, and use their approach to model fabricable 3D objects. Dumas et al [2015] modify texture synthesis to account for structure and rigidity, and synthesize printable 3D patterns that cover a base surface.…”