9,785 research outputs found
Ray casting implicit fractal surfaces with reduced affine arithmetic
A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray. The method is also efficient due to a modification in the affine arithmetic representation that introduces a condensation step at the end of every non-affine operation. We show that our method is able to retain the tight estimation capabilities of affine arithmetic for ray casting implicit surfaces made from procedural noise functions while being faster to compute and more efficient to store
Topological correction of hypertextured implicit surfaces for ray casting
Hypertextures are a useful modelling tool in that they
can add three-dimensional detail to the surface of otherwise
smooth objects. Hypertextures can be rendered as implicit
surfaces, resulting in objects with a complex but well
defined boundary. However, representing a hypertexture as
an implicit surface often results in many small parts being
detached from the main surface, turning an object into a
disconnected set. Depending on the context, this can detract
from the realism in a scene where one usually does not
expect a solid object to have clouds of smaller objects floating around it. We present a topology correction technique, integrated in a ray casting algorithm for hypertextured implicit surfaces, that detects and removes all the surface components that have become disconnected from the main surface. Our method works with implicit surfaces that are C2 continuous and uses Morse theory to find the critical points of the surface. The method follows the separatrix lines joining the critical points to isolate disconnected components
Progressive refinement rendering of implicit surfaces
The visualisation of implicit surfaces can be an inefficient task when such surfaces are complex and highly detailed. Visualising a surface by first converting it to a
polygon mesh may lead to an excessive polygon count. Visualising a surface by direct ray casting is often a slow procedure. In this paper we present a progressive refinement renderer for implicit surfaces that are Lipschitz continuous. The renderer first displays a low resolution estimate of what the final image is going to be and, as the computation progresses, increases the quality of this estimate at an interactive frame rate. This renderer provides a quick previewing facility that significantly reduces the design cycle of a new and complex implicit surface. The renderer is also capable of completing an image faster than a conventional implicit surface rendering algorithm based on ray casting
Implicit yield function formulation for granular and rock-like materials
The constitutive modelling of granular, porous and quasi-brittle materials is
based on yield (or damage) functions, which may exhibit features (for instance,
lack of convexity, or branches where the values go to infinity, or false
elastic domains) preventing the use of efficient return-mapping integration
schemes. This problem is solved by proposing a general construction strategy to
define an implicitly defined convex yield function starting from any convex
yield surface. Based on this implicit definition of the yield function, a
return-mapping integration scheme is implemented and tested for elastic-plastic
(or -damaging) rate equations. The scheme is general and, although it
introduces a numerical cost when compared to situations where the scheme is not
needed, is demonstrated to perform correctly and accurately.Comment: 19 page
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