We proposean approach for modeling surface details such as scales, feathers, or thorns. These types of cellular textures require a representation with more detail than texture-mapping but are inconvenient to model with hand-crafted geometry. We generate patterns of geometric elements using a biologically -motivated cellular development simulation together with a constraint to keep the cells on a surface. The surface may be defined by an implicit function, a volume dataset, or a polygonal mesh. Our simulation combines and extends previous work in developmental models and constrained particle systems. Key Words: particle systems, developmental models, data amplification, constraints, texture mapping, bump mapping, displacement mapping 1 Introduction For several years computer graphics researchers and practitioners have been grappling with the problem of creating and displaying surfaces having an organic appearance. Texture maps, bump maps, and related methods often attain the appearanc...

We present an efficient and robust algorithm for finding points of collision between time-dependent parametric and implicit surfaces. The algorithm detects simultaneous collisions at multiple points of contact. When the regions of contact form curves or surfaces, it returns a finite set of points uniformly distributed over each contact region. Collisions can be computed for a very general class of surfaces: those for which inclusion functions can be constructed. Included in this set are the familiar kinds of surfaces and time behaviors encountered in computer graphics. We use a new interval approach for constrained minimization to detect collisions, and a tangency condition to reduce the dimensionality of the search space. These approaches make interval methods practical for multi-point collisions between complex surfaces. An interval Newton method based on the solution of the interval linear equation is used to speed convergence to the collision time and location. This method is mor...

In this paper we present methods to smoothly interpolate orientations, given N rotational keyframes of an object along a trajectory. The methods allow the user to impose constraints on the rotational path, such as the angular velocity at the endpoints of the trajectory. We convert the rotations to quaternions, and then spline in that non-Euclidean space. Analogous to the mathematical foundations of flat-space spline curves, we minimize the net "tangential acceleration" of the quaternion path. We replace the flat-space quantities with curved-space quantities, and numerically solve the resulting equation with finite difference and optimization methods. 1 Introduction The problem of using spline curves to smoothly interpolate mathematical quantities in flat Euclidean spaces is a well-studied problem in computer graphics [bartels et al 87], [kochanek&bartels 84]. Many quantities important to computer graphics, however, such as rotations, lie in non-Euclidean spaces. In 1985, a method to...