a b s t r a c tWe present a method for generating surface crack patterns that appear in materials such as mud, ceramic glaze, and glass. To model these phenomena, we build upon existing physically based methods. Our algorithm generates cracks from a stress field defined heuristically over a triangle discretization of the surface. The simulation produces cracks by evolving this field over time. The user can control the characteristics and appearance of the cracks using a set of simple parameters. By changing these parameters, we have generated examples similar to a variety of crack patterns found in the real world. We assess the realism of our results by comparison with photographs of real-world examples. Using a physically based approach also enables us to generate animations similar to time-lapse photography.

We present a new algorithm for unfolding planar polygonal linkages without self-intersection based on following the gradient flow of a "repulsive" energy function. This algorithm has several advantages over previous methods. (1) The output motion is represented explicitly and exactly as a piecewise-linear curve in angle space. As a consequence, an exact snapshot of the linkage at any time can be extracted from the output in strongly polynomial time (on a real RAM supporting arithmetic, radicals, and trigonometric functions). (2) Each linear step of the motion can be computed exactly in O(n 2 ) time on a real RAM where n is the number of vertices. (3) We explicitly bound the number of linear steps (and hence the running time) as a polynomial in n and the ratio between the maximum edge length and the initial minimum distance between a vertex and an edge. (4) Our method is practical and easy to implement. We provide a publicly accessible Java applet [1] that implements the algorithm.

Anisotropic energies are indispensable when simulating realistic phenomena such as muscles [Lee et al. 2018], plants [Wang et al.

We present a novel method for stably simulating stylized curly hair that addresses artistic needs and performance demands, both found in the production of feature films. To satisfy the artistic requirement of maintaining the curl's helical shape during motion, we propose a hair model based upon an extensible elastic rod. We introduce a novel method for stably computing a frame along the hair curve, essential for stable simulation of curly hair. Our hair model introduces a novel spring for controlling the bending of the curl and another for maintaining the helical shape during extension. We also address performance concerns often associated with handling hairhair contact interactions by efficiently parallelizing the simulation. To do so, we present a novel algorithm for pruning both hair-hair contact pairs and hair particles. Our method is in use on a full length feature film and has proven to be robust and stable over a wide range of animated motion and on a variety of hair styles, from straight to wavy to curly.

This paper describes an algorithm for generating a guaranteed-intersection-free interpolation sequence between any pair of compatible polygons. Our algorithm builds on prior results from linkage unfolding, and if desired it can ensure that every edge length changes monotonically over the course of the interpolation sequence. The computational machinery that ensures against self-intersection is independent from a distance metric that determines the overall character of the interpolation sequence. This decoupled approach provides a powerful control mechanism for determining how the interpolation should appear, while still assuring against intersection and guaranteeing termination of the algorithm. Our algorithm also allows additional control by accommodating a set of algebraic constraints that can be weakly enforced throughout the interpolation sequence.