Building models with implicit surfaces

Implicit surfaces are defined, and the problem of producing pictures of them is examined. The steps involved in building models using the implicit method are explained. The advantages of the implicit approach over the usual parametric approach are discussed     

Implicit Decals: Interactive Editing of Repetitive Patterns on Surfaces

Texture mapping is an essential component for creating 3D models and is widely used in both the game and the movie industries. Creating texture maps has always been a complex task and existing methods carefully balance flexibility with ease of use. One difficulty in using texturing is the repeated placement of individual textures over larger areas. In this paper, we propose a method which uses decals to place images onto a model. Our method allows the decals to compete for space and to deform as they are being pushed by other decals. A spherical field function is used to determine the position and the size of each decal and the deformation applied to fit the decals. The decals may span multiple objects with heterogeneous representations. Our method does not require an explicit parametrization of the model. As such, varieties of patterns, including repeated patterns like rocks, tiles and scales can be mapped. We have implemented the method using the GPU where placement, size and orientation of thousands of decals are manipulated in real time.     

Visualization of connectivity in octree based models

An interesting problem in the oil and gas industry is the visualization of the movement of oil and gas in porous media. An example of such a medium is a rock sample with some distribution of holes (pores) connected by channels (pore throats), the solid parts of the rock are called grains. In our work we have simulated the porous medium using a pointer-based octree, representing these pores and grains. This data structure allows us to model the connectivity of the pores and thus visualize fluid penetration within the medium. Whereas earlier models represent a serious simplifications or two dimensional homogeneous layers, our model provides us with a statistically accurate distribution in three dimensions and a more accurate representation of the connectivity. In this paper we present our data structure and the techniques which were used to create models of porous media and their porous networks. Next, we present algorithms for connectivity in octrees and we show how to apply them to modelling and visualization of fluid penetration in porous media.     

The visualization of knots and braids

We describe a new method for modelling braids and certain classes of knots and links, and how they may be visualized. The method uses generalized cylinders built around a bicubic spline centre line. We also show how multi-stranded, recursive, hawser laid ropes can be modelled using related techniques.     

Field functions for implicit surfaces

The use of 3D computer generated models is a rapidly growing part of the animation industry. But the established modelling techniques, using polygons or parametric patches, are not the best to define characters which can change their shape as they move. A newer method, using iso-surfaces in a scalar field, enables us to create models that can make the dynamic shape changes seen in hand animation. We call such modelsSoft Objects.From the user's point of view, a soft object is built from primitive key objects that blend to form a compound shape. In this paper, we examine some of the problems of choosing suitable keys and introduce some new field functions that increase the range of shapes available as keys.     

Implicit Blending Revisited

Blending is both the strength and the weakness of functionally based implicit surfaces (such as F‐reps or soft‐objects). While it gives them the unique ability to smoothly merge into a single, arbitrary shape, it makes implicit modelling hard to control since implicit surfaces blend at a distance, in a way that heavily depends on the slope of the field functions that define them. This paper presents a novel, generic solution to blending of functionally‐based implicit surfaces: the insight is that to be intuitive and easy to control, blends should be located where two objects overlap, while enabling other parts of the objects to come as close to each other as desired without being deformed. Our solution relies on automatically defined blending regions around the intersection curves between two objects. Outside of these volumes, a clean union of the objects is computed thanks to a new operator that guarantees the smoothness of the resulting field function; meanwhile, a smooth blend is generated inside the blending regions. Parameters can automatically be tuned in order to prevent small objects from blurring out when blended into larger ones, and to generate a progressive blend when two animated objects come in contact.     

Computational Aesthetics

Guest Editors Bruce Gooch and Brian Wyvill discuss computational aesthetics and the articles that comprise their special issue.     

Two-dimensional Potential Fields for Advanced Implicit Modeling Operators

Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free‐form curve to define the profile of the blend region between implicit primitives. The use of a free‐form implicit curve, controlled point‐by‐point in the Euclidean user space, allows us to group boolean composition operators with sharp transitions or smooth free‐form transitions in a single modeling metaphor. This idea is generalized for the creation, sculpting and manipulation of volume objects, while providing the user with simplicity, controllability and freedom in implicit modeling. ACM CSS: I.3.5 Computational Gemoetry and Object Modeling—Curve, surface, solid, and object representations     

Modeling a Murex cabritii sea shell with a structured implicit surface modeler

BlobTree , and its application to the generation of a complex and visually accurate biological model of the sea shell Murex cabritii. Since the model is purely procedurally defined and does not rely on polygon mesh operations, it is resolution independent and can be rendered directly using ray tracing. An interface has been built for the BlobTree using an interpreted programming language (Python). The language interface readily allows a user to procedurally describe the shell based on numeric data taken from the actual object. Published online: 15 March 2002