A Progressive Refinement Approach for the Visualisation of Implicit Surfaces (original) (raw)

Implicit surface visualisation using Adaptive Raymarching

Indirect methods for visualisation of implicit surfaces use triangulated mesh for object shape aproximation. The overall visualisation quality thus depends on the degree of surface tessalation. Direct visualization approach by Raytracing based methods requires computation of an object-ray intersection point which is problematic and computationally expensive. The article discusses Adaptive Raymarching as an implicit surface realtime visualisation method which uses distance functions for object modeling. The knowledge of distance to the closest surface based on distance functions at each spatial point in the scene allows us to adaptively optimize ray marching distance to the maximal possible length each step, thus lowers amout of calculation steps for the object-ray intersection evaluation. Disadvantages of the aformentioned approach such as a rapid increase of ray steps along surface edges are discussed in the article. Function descriptions for distance estimation of basic quadrics are presented along with an advanced shading algorithm including ambient occlusion estimation and usage of CSG operation for advanced modeling purposes.

Interactive Pen-and-Ink Rendering for Implicit Surfaces

2005

: An implicit surface model visualized using a smooth-shaded triangle mesh (a) and a pen-and-ink drawing (b). The generated silhouettes (d) are much smoother than base mesh (c) and render at interactive rates. Suggestive contours (e) add important additional detail.

Frustum casting for progressive, interactive rendering

1998

E cient visible surface determination algorithms have long been a fundamental goal of computer graphics. We discuss the well-known ray casting problem: given a geometric scene description, a synthetic camera, and a viewport which discretizes the camera lm plane into pixels, ray casting identi es the visible surface at each pixel, i.e., that scene primitive which is rst encountered by a n eye r a y directed through the pixel center. Interactive rendering systems have not ordinarily been based on ray casting, due to its computational cost. Instead, the dominant method for achieving interactive rendering is hardware-assisted rasterization and depth bu ering of polygons, often produced by static or dynamic tesselation of higher-level objects. Modern polygon rasterization architectures are extremely powerful, having undergone an extensive development path. Several trends indicate, however, that alternatives to polygon rasterization and depth bu ering deserve examination in the design of future interactive rendering systems. The rst trend is the number and breadth of proposed algorithmic and hardware methods to lessen transformation, rasterizer and depth bu er load while viewing models of high complexity. A second, related trend is that geometric models are, increasingly often, larger than ordinary physical memories, lending greater importance to memory coherence considerations. Finally, general purpose processors have grown very powerful, enabling exible, dynamic retargeting of computational resources to di ering subtasks while maintaining responsiveness. A rendering system based on such processors could have signi cant advantages over dedicated hardware. In light of the above, we explored an alternative, general rendering architecture based on ray casting. In seeking to build an interactive software ray caster, we studied existing visible surface algorithms. Combining three such algorithms, we synthesized frustum casting, a novel algorithm for per-pixel visible surface identi cation in general scenes. The algorithm samples discretely, but operates in object space, and is exact and e cient. We demonstrate a prototype software renderer based on frustum casting, which a c hieves interactivity through just-in-time" sampling, and progressive image improvement through deferral of intersection and shading operations. Frustum casting well addresses the technological trends listed above. We believe that it and other ray-based rendering methods may be practically incorporable by designers of future high-performance rendering architectures.

Hierarchical implicit surface refinement

Proceedings. Computer Graphics International 2001, 2001

A novel method of hierarchical implicit modeling is presented, in which an implicit object is modeled by using a hierarchy of implicit surfaces. The hierarchy provides both layered local refinement and global deformation. Local refinement allows the introduction of higher-level detailed surfaces. Global deformation changes the overall shape of the surface while maintaining the integrity of surface details. The model is gradually refined by introducing appropriate new primitives in the specified surface areas. Refinement constraints, such as local surface area and level of the surface (within the hierarchy) are designed to be applied to the implicit object so as to achieve finer control over the local surface. The method provides a dynamic representation of implicit surfaces and can be used not only in modeling complex implicit objects, but also in animating the surfaces and simulating the deformations of various objects.

Iterative methods for visualization of implicit surfaces on gpu

2007

The ray-casting of implicit surfaces on GPU has been explored in the last few years. However, until recently, they were restricted to second degree (quadrics). We present an iterative solution to ray cast cubics and quartics on GPU. Our solution targets efficient implementation, obtaining interactive rendering for thousands of surfaces per frame. We have given special attention to torus rendering since it is a useful shape for multiple CAD models. We have tested four different iterative methods, including a novel one, comparing them with classical tessellation solution. Fig. 1. The faces of two bounding boxes are used to trigger the fragment shader responsible for rendering the tori.

Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces

Sphere tracing is a new technique for rendering implicit surfaces that uses geometric distance. Sphere tracing marches along the ray toward its first intersection in steps guaranteed not to penetrate the implicit surface. It is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Sphere tracing requires only a bound on the magnitude of the derivative, robustly avoiding problems where the derivative jumps or vanishes. It is an efficient direct visualization system for the design and investigation of new implicit models. Sphere tracing efficiently approximates cone tracing, supporting symbolicprefiltered antialiasing. Signed distance functions for a variety of primitives and operations are derived.

GPU-based rendering of sparse low-degree implicit surfaces

Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia, 2006

Implicit surface is a well-known surface representation. Geometric details of an object can be represented using less surface primitives than other representations such as polygonal meshes. In this paper, we propose a fast and a direct rendering method of SLIM (Sparse Low-degree IMplicit) surfaces using recent programmable GPUs. Our approach establishes a direct rendering of implicit surfaces based on the ray casting approach. Geometric processes such as an intersection between a ray and an implicit surface and blending for PU (Partition of Unity) are performed in the fragment program on GPUs. For large models, a hierarchical structure of a SLIM surface can be used for LOD rendering or view frustum culling to speed up the rendering. We demonstrate that highly parallel processing using GPUs enables efficient rendering of implicit surfaces.

Point Based Rendering of Implicit 4-Dimensional Surfaces

Computer Graphics, Imaging and Visualisation (CGIV 2007), 2007

We present a point based rendering algorithm that uses hyper-cubes to perform spatial subdivision in a 4D volume. A 4D function interval exclusion test is used to speed up the rendering of 4D Implicit surfaces in this hyper-volume. A 4D orthonormal basis function is used to define a 4D camera, which projects isometric or perspective views onto a plane in 4D for viewing. The technique requires evaluations of 4D implicit surface functions and gradients to render shaded images. The technique also allows for hidden surface elimination using a z-buffer modified for use in a 4D space. We give examples of its use in rendering some 4D surfaces and discuss problems with the technique. The algorithm can be generalised to higher dimensions.

DigitalSculpture: a subdivision-based approach to interactive implicit surface modeling

Graphical Models, 2005

This paper presents DigitalSculpture, an interactive sculpting framework founded upon isosurfaces extracted from recursively subdivided, 3D irregular grids. Our unique implicit surface model arises from an interpolatory, volumetric subdivision scheme that is C 1 continuous across the domains defined by arbitrary 3D irregular grids. We assign scalar coefficients and color to each control vertex and allow these quantities to participate in the volumetric subdivision of irregular grids. In the subdivision limit, a virtual sculpture is obtained by extracting the zero-level from the volumetric, scalar field defined over the irregular grid. This novel shape geometry extends concepts from solid modeling, recursive subdivision, and implicit surfaces; facilitates many techniques for interactive sculpting; permits rapid, local evaluation of iso-surfaces; and affords level-of-detail control of the sculpted surfaces. (K.T. McDonnell). www.elsevier.com/locate/gmod Graphical Models 67 (2005) 347-369

Interactive techniques for implicit modeling

ACM SIGGRAPH Computer Graphics, 1990

Recent research has demonstrated the usefulness of implicit surfaces for modeling geometric objects. The interactive design of such surfaces has not, however, received the same attention as has the design of parametric surfaces. Principally this is due to the difficulty of controlling the shape of implicit surfaces while displaying the changes quickly enough for use within an interactive design environment. This paper describes progress towards interactive control of implicit surfaces and introduces new techniques useful to the designer.