This paper introduces a new kind of mosaic, called Jigsaw Image Mosaic (JIM), where image tiles of arbitrary shape are used to compose the final picture. The generation of a Jigsaw Image Mosaic is a solution to the following problem: given an arbitrarily-shaped container image and a set of arbitrarily-shaped image tiles, fill the container as compactly as possible with tiles of similar color to the container taken from the input set while optionally deforming them slightly to achieve a more visually-pleasing effect. We approach the problem by defining a mosaic as the tile configuration that minimizes a mosaicing energy function. We introduce a general energy-based framework for mosaicing problems that extends some of the existing algorithms such as Photomosaics and Simulated Decorative Mosaics. We also present a fast algorithm to solve the mosaicing problem at an acceptable computational cost. We demonstrate the use of our method by applying it to a wide range of container images and tiles.

2.2m triangles: 300 rows, 900 columns, 16.9 s 388k triangles: 432 rows, 864 columns, 13.5 s 869k triangles: 100 rows, 200 columns, 3.8 s Figure 1: In the above images, over 1.9 million surface samples are shaded from over 100 thousand point lights in a few seconds. This is achieved by sampling a few hundred rows and columns from the large unknown matrix of surface-light interactions. AbstractRendering complex scenes with indirect illumination, high dynamic range environment lighting, and many direct light sources remains a challenging problem. Prior work has shown that all these effects can be approximated by many point lights. This paper presents a scalable solution to the many-light problem suitable for a GPU implementation. We view the problem as a large matrix of samplelight interactions; the ideal final image is the sum of the matrix columns. We propose an algorithm for approximating this sum by sampling entire rows and columns of the matrix on the GPU using shadow mapping. The key observation is that the inherent structure of the transfer matrix can be revealed by sampling just a small number of rows and columns. Our prototype implementation can compute the light transfer within a few seconds for scenes with indirect and environment illumination, area lights, complex geometry and arbitrary shaders. We believe this approach can be very useful for rapid previewing in applications like cinematic and architectural lighting design.

Tangles are complex patterns, which are often used to decorate the surface of real-world artisanal objects. They consist of arrangements of simple shapes organized into nested hierarchies, obtained by recursively splitting regions to add progressively finer details. In this article, we show that 3D digital shapes can be decorated with tangles by working interactively in the intrinsic metric of the surface. Our tangles are generated by the recursive application of only four operators, which are derived from tracing the isolines or the integral curves of geodesics fields generated from selected seeds on the surface. Based on this formulation, we present an interactive application that lets designers model complex recursive patterns directly on the object surface without relying on parametrization. We reach interactive speed on meshes of a few million triangles by relying on an efficient approximate graph-based geodesic solver.