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A Fast Voxel Traversal Algorithm for Ray Tracing
 In Eurographics ’87
, 1987
"... A fast and simple voxel traversal algorithm through a 3D space partition is introduced. Going from one voxel to its neighbour requires only two floating point comparisons and one floating point addition. Also, multiple ray intersections with objects that are in more than one voxel are eliminated. ..."
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Cited by 148 (5 self)
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A fast and simple voxel traversal algorithm through a 3D space partition is introduced. Going from one voxel to its neighbour requires only two floating point comparisons and one floating point addition. Also, multiple ray intersections with objects that are in more than one voxel are eliminated. Introduction In recent years, ray tracing has become the algorithm of choice for generating high fidelity images. Its simplicity and elegance allows one to easily model reflection, refraction and shadows. 1 Unfortunately, it has a major drawback: computational expense. The prime reason for this is that the heart of ray tracing, intersecting an object with a ray, is expensive and can easily take up to 95% of the rendering time. Unless some sort of intersection culling is performed, each ray must intersect all the objects in the scene, a very expensive proposition. There are two general strategies for intersection culling: hierarchical bounding volumes 1, 2, 3, 4 and space partitioning...
Interval Analysis For Computer Graphics
 Computer Graphics
, 1992
"... This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are ..."
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Cited by 132 (2 self)
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This paper discusses how interval analysis can be used to solve a wide variety of problems in computer graphics. These problems include ray tracing, interference detection, polygonal decomposition of parametric surfaces, and CSG on solids bounded by parametric surfaces. Only two basic algorithms are required: SOLVE, which computes solutions to a system of constraints, and MINIMIZE, which computes the global minimum of a function, subject to a system of constraints. We present algorithms for SOLVE and MINIMIZE using interval analysis as the conceptual framework. Crucial to the technique is the creation of "inclusion functions" for each constraint and function to be minimized. Inclusion functions compute a bound on the range of a function, given a similar bound on its domain, allowing a branch and bound approach to constraint solution and constrained minimization. Inclusion functions also allow the MINIMIZE algorithm to compute global rather than local minima, unlike many other numerica...
A survey of shadow algorithms
 IEEE Computer Graphics and Applications
, 1990
"... Essential to realistic and visually appealing images, shadows are difficult ta compute in most display environments. This survey characterizes the various types of shadows. It also describes most existing shadow algorithms and discusses their complexities, advantages, and shommings. We examine herd ..."
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Cited by 123 (3 self)
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Essential to realistic and visually appealing images, shadows are difficult ta compute in most display environments. This survey characterizes the various types of shadows. It also describes most existing shadow algorithms and discusses their complexities, advantages, and shommings. We examine herd shadows, soft shadbws, shadows of transparent objects, and shadows for complex modeling primitives. For each type, we examine shadow algorithms within various rendswing techniques. This survey attempts to provide readem with enough background and insight on the various rmthods to dow them to choose the algorithm best wpuited to their W. We also hope that our analysis will h&p identify the a m that need more research and point bo possible sotutkms. A shadowa region of relative darkness within an not necessarily attenuate the light it occludes. In fact, illuminated regionoccurs when an object totally or it can concentrate light. However, as is traditional in partially occludes the light. A transparent object does image synthesis, lve will consider a region to be in
Illumination from Curved Reflectors
, 1992
"... A technique is presented to compute the reflected illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat's principle, this is equivalent to finding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, i ..."
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Cited by 55 (0 self)
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A technique is presented to compute the reflected illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat's principle, this is equivalent to finding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, irradiance is computed from the Gaussian curvature of the geometrical wavefront. Techniques from optics, differential geometry and interval analysis are applied to solve these problems. CR Categories and Subject Descriptions: I.3.3 [ Computer Graphics ]: Picture/Image Generation; I.3.7 [ Computer Graphics ]: ThreeDimensional Graphics and Realism General Terms: Algorithms Additional Keywords and Phrases: Caustics, Differential Geometry, Geometrical Optics, Global Illumination, Interval Arithmetic, Ray Tracing, Wavefronts 1. Introduction Ray tracing provides a straightforward means for synthesizing realistic images on the computer. A scene is first modeled, usually by a collection of implici...
Practical Ray Tracing of Trimmed NURBS Surfaces
 Journal of Graphics Tools
, 2000
"... A system is presented for ray tracing trimmed NURBS surfaces. While approaches to components are drawn largely from existing literature, their combination within a single framework is novel. This paper also differs from prior work in that the details of an efficient implementation are fleshed out. T ..."
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Cited by 21 (1 self)
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A system is presented for ray tracing trimmed NURBS surfaces. While approaches to components are drawn largely from existing literature, their combination within a single framework is novel. This paper also differs from prior work in that the details of an efficient implementation are fleshed out. Throughout, emphasis is placed on practical methods suitable to implementation in general ray tracing programs. 1 Introduction The modeling community has embraced trimmed NURBS as a primitive of choice. The result has been a rapid proliferation in the number of models utilizing this representation. At the same time, ray tracing has become a popular method for generating computer graphics images of geometric models. Surprisingly, most ray tracing programs do not support the direct use of untessellated trimmed NURBS surfaces. The direct use of untessellated NURBS is desirable because tessellated models increase memory use which can be detrimental to runtime efficiency on modern architectures. ...
Ray tracing of subdivision surfaces
 In Rendering Techniques ’98 (Proceedings of the Eurographics Workshop
, 1998
"... Abstract. We present the necessary theory for the integration of subdivision surfaces into general purpose rendering systems. The most important functionality that has to be provided via an abstract geometry interface are the computation of surface points and normals as well as the ray intersection ..."
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Cited by 18 (0 self)
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Abstract. We present the necessary theory for the integration of subdivision surfaces into general purpose rendering systems. The most important functionality that has to be provided via an abstract geometry interface are the computation of surface points and normals as well as the ray intersection test. We demonstrate how to derive the corresponding formulas and how to construct tight bounding volumes for subdivision surfaces. We introduce envelope meshes which have the same topology as the control meshes but tightly circumscribe the limit surface. An efficient and simple algorithm is presented to trace a ray recursively through the forest of triangles emerging from adaptive refinement of an envelope mesh. 1
An Efficient and Stable Ray Tracing Algorithm for Parametric Surfaces
 Journal of Information Science and Engineering
, 2001
"... In this paper, we propose an efficient and stable algorithm for finding the raysurface intersections. Newton’s method and Bézier clipping are adapted to form the core of our algorithm. Ray coherence is used to find starting points for Newton iteration. We introduce an obstruction detection techniqu ..."
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Cited by 13 (0 self)
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In this paper, we propose an efficient and stable algorithm for finding the raysurface intersections. Newton’s method and Bézier clipping are adapted to form the core of our algorithm. Ray coherence is used to find starting points for Newton iteration. We introduce an obstruction detection technique to verify whether an intersection point found by using Newton’s method is the closest one. When Newton’s method fails to achieve convergence, we use Bézier clipping as the substitution to find the intersection points. This combination achieves significant improvement in tracing primary rays. A similar approach also successfully improves the performance in tracing secondary rays. Keywords: ray tracing, Newton’s method, Bézier clipping, parametric surfaces, ray coherence, Bézier surface
Ray Tracing Implicit Surfaces
 Siggraph 93 Course Notes: Design, Visualization and Animation of Implicit Surfaces
"... This is an overview of methods for ray tracing implicit surfaces, including the primary problem of intersecting a ray with an implicit surface, and the secondary problems of determining surface normals, and incorporating CSG operations and deformations. 1 Introduction An implicit surface is defined ..."
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Cited by 11 (0 self)
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This is an overview of methods for ray tracing implicit surfaces, including the primary problem of intersecting a ray with an implicit surface, and the secondary problems of determining surface normals, and incorporating CSG operations and deformations. 1 Introduction An implicit surface is defined by a function f : R 3 ! R that assigns a scalar value to each point in space. The surface is the set of points x j (x; y; z) 2 R 3 such that f(x) = 0: Let A be a closed solid described by the implicit function f: Then, for uniformity, we assume x 2 ffi A , f(x) ! 0 (1) x 2 @A , f(x) = 0 (2) x 2 R 3 \Gamma A , f(x) ? 0: (3) This states, via pointset topology, that the implicit function is negative inside the solid, zero on its surface, and positive outside. (This standard is the most common in recent implicit surface literature. Other examples include: [Ricci, 1974], where implicit functions were always positive, and unitvalued on the surface, less than one inside and greater t...
Improved Techniques for Ray Tracing Parametric Surfaces
 The Visual Computer
, 1990
"... Several techniques for acceleration of ray tracing parametric surfaces are presented. Some of these are entirely new to ray tracing, while others are improvements of previously known techniques. First a uniform spatial subdivision scheme is adapted to parametric surfaces. A new space and timeeff ..."
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Cited by 10 (0 self)
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Several techniques for acceleration of ray tracing parametric surfaces are presented. Some of these are entirely new to ray tracing, while others are improvements of previously known techniques. First a uniform spatial subdivision scheme is adapted to parametric surfaces. A new space and timeefficient algorithm for finding raysurface intersections is introduced. It combines numerical and subdivision techniques, thus allowing utilization of raycoherence and greatly reducing the average raysurface intersection time. Nonscanline sampling orders of the image plane are proposed that facilitate utilization of coherence. Finally, a method to handle reflected, refracted, and shadow rays in a more efficient manner is described. Results of timing tests indicating the efficiency of these techniques for various environments are presented.
Fast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic
"... Existing techniques for rendering arbitraryform implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for rootfinding are robust and general in the class of surfaces they support, but tr ..."
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Cited by 9 (4 self)
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Existing techniques for rendering arbitraryform implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for rootfinding are robust and general in the class of surfaces they support, but traditionally slow. Nonetheless, implemented efficiently using a stackdriven iterative algorithm and SIMD vector instructions, these methods can achieve interactive performance for common algebraic surfaces on the CPU. A similar algorithm can also be implemented stacklessly, allowing for efficient ray tracing on the GPU. This paper presents these algorithms, as well as an inclusionpreserving reduced affine arithmetic (RAA) for faster raysurface intersection. Shader metaprogramming allows for immediate and automatic generation of symbolic expressions and their interval or affine extensions. Moreover, we are able to render even complex forms robustly, in realtime at high resolution.