Creating Animated Pop-up Books from the Motion of

Creating Animated Pop-up Books from the Motion of 3D Articulated Characters ∗

Conrado Ruiz Jr ∗ Sang N. Le ‡ School of Computing, National University of Singapore

‡

Kok-Lim Low ∗ Digipen Institute of Technology, Singapore

Figure 1: (Top) Input articulated character of a girl§ waving her hands. (Bottom) Actual pop-up design generated by the algorithm.

1

Introduction

Pop-up books are interesting books containing paper pieces that pop-out to form 3D structures when opened. But more than just depicting 3D objects, pop-up artists also use the movement of the paper pieces during the opening process to reproduce animations. Artists have used this technique to create pop-ups of persons swimming, running and objects peeping out. In this work, we study the movement of paper pieces in different pop-up mechanisms with the goal to use this knowledge to automatically design animated popups from the motion of articulated 3D models. There have been a few works that proposed approaches to automatically generate pop-up designs from 3D Models [Li et al. 2011; Ruiz et al. 2014]. In this work however, we take it even further. We not only want to produce a good representation of the 3D object but duplicate its movement as well. It is inspired by the work on kinematic synthesis for mechanical toys and characters [Coros et al. 2013]. Pop-ups themselves can be considered an articulated figure, with the paper patches as linkages and the hinges serving as the joints with 1 DOF. We therefore can consider this as a motion retargeting or simplification problem, in which the motion of articulated figure with multiple joints and linkages is given, and we try to find the best approximation using fewer joints and DOFs. Most artists have no innate knowledge of the kinematics of pop-up structures. They rely on a trial-and-error approach to produce the desired animation. This work aims to provide a more formal study of pop-up motion and propose an automated approach to animated pop-up design that has not been explored in any previous work.

2

Our Approach

Given an articulated 3D model, we first simplify its skeleton by grouping the links and joints into sets of linkage chains, considering only parts with animation. Each of the chains is then mapped to a specific pop-up mechanism. This is done by fitting the motion ∗ e-mail:{conrado,lowkl}@comp.nus.edu.sg; § 3D

Model modified from L. Kaplinski

‡ [email protected]

Figure 2: Pop-up mechanisms used to produce motion. (a) Floating layer and an angled v-fold (b) floating layer and a single patch (c) v-folds and a single patch (d) v-fold and step-fold. trajectory of the end effector of the chain, using forward kinematics, with the output motion of the pop-up mechanisms. We then generate a possible layout of all the mechanisms together. In some cases, modifications have to be made to some mechanisms to prevent intersections during folding. For example, a mechanism might be slightly moved or altered, or replaced with another type of mechanism. We use simulated annealing to search through the valid configuration space while trying to minimize the difference of the original input motion and the output motion of the entire pop-up structure. Once we have the layout and the linkage chains have been mapped to a specific mechanism, we then perform parameter optimization for each mechanism to give the best approximation of the original input motion. This is done by directly computing and iteratively searching for the optimal the parameters, i.e. orientation or lengths of the patches, in the mechanism. We use a specific perspective view when considering the animation. The paper patches are generated using an image-based approach from the specific viewpoint, with the rigging, skinning and depth information used to segment the 3D model into different 2D paper patches. Results show that common motions of articulated characters can be reproduced using paper pop-up animations. More complicated motion however, might be oversimplified but the approach can still produce valid working pop-up structures.

References C OROS , S., T HOMASZEWSKI , B., N ORIS , G., S UEDA , S., F OR BERG , M., S UMNER , R. W., M ATUSIK , W., AND B ICKEL , B. 2013. Computational design of mechanical characters. ACM Trans. Graph. 32, 4 (July), 83:1–83:12. L I , X.-Y., J U , T., G U , Y., AND H U , S.-M. 2011. A geometric study of v-style pop-ups: Theories and algorithms. ACM Trans. Graph. 30, 4 (July), 98:1–98:10. RUIZ , C. J., L E , S. N., Y U , J., AND L OW, K.-L. 2014. Multi-style Paper Pop-up Designs from 3D Models. Computer Graphics Forum 33, 2, 487–496.