P. Heckbert and P. Hanrahan, "Beam Tracing Polygonal Objects," Computer Graphics (Proc. Siggraph), Vol. 18, No. 3, July 1984, pp. 119-127.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....ray tracing acceleration schemes that were devised over the years [4] In particular, Haines [6] describes an approach, referred to as the light buffer, specifically to accelerate the casting of shadow rays. There were also a few alternative approaches to shadow ray casting, such as casting beams [9] and cones [1] but these approaches are not as general as ray casting, since they impose limiting assumptions on the geometry of the objects in the scene. Radiosity and other finite element based global illumination methods typically perform very large amounts of point to area and area to area ....

P. S. Heckbert and P. Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119--128, July 1984.

....image signal will have the same probability distribution for any set of sampling positions [18] This argument applies to quasirandom samples (such as samples from a Halton sequence [15] as well. An alternative are methods that trace extended ray volumes such as cone tracing or beam tracing [3, 10, 11, 16, 25]. These methods do not shoot infinitesimally small rays into the scene but larger cones with a crosssection corresponding to a pixel in the image. These techniques render anti aliased images using only one ray per pixel. However, they suffer from a different kind of complexity problem: In a highly ....

....artifacts. 2 Related Work Cone beam tracing techniques: Cone tracing [3, 16] calculates the interaction of ray cones through each pixel with the scene geometry. The technique is able to render antialiased images and to approximate effects such as soft shadows and blurry reflections. Beam tracing [10, 11] starts with the view frustum as initial beam and successively clips it to polygonal objects to generate sub beams. Shinya et al. discuss models for the interaction of pencils of rays with reflecting and refracting surfaces [25] A more general and robust model of the interactions between beams ....

Heckbert, P., Hanrahan, P.: Beam Tracing Polygonal Objects. In: SIGGRAPH 84 Proceedings, 119-127, 1984.

....RAY TRACING USING K D TREES Donald Fussell and K. R. Subramanian The University of Texas at Austin Austin, Texas 78712 1188 TR 88 07 March 1988 Fast Ray Tracing Using K D Trees Donald Fussell K. R. Subramanian Abstract A hierarchical search structure for ray tracing based on k d trees is introduced. This data structure can handle the variety of surfaces commonly used in computer graphics. Algorithms to ....

....depending on the effects we are trying to model (reflection, transmission, shadows, penumbras etc) Considerable effort has gone into making this process very efficient. Bounding volumes [18] 22] 23] 14] search structures [8] 9] 13] item buffers [22] shadow buffers [11] and ray coherence [1] 121120] all have drastically reduced this cost. Bounding volumes are advantageous because they provide a quick non intersection test for objects. Using tight bounding volumes improves the chances of intersecting the object inside the volume, but then increases the bounding volume intersection cost. ....

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Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119-127, July 1984.

....Another disadvantage of path tracing is that the results are dependent on a particular receiver position, and thus these methods are not directly applicable in virtual environment applications where either the source or receiver is moving continuously. 4.1. 3 Beam Tracing Beam tracing methods [25, 52] classify propagation paths from a source by recursively tracing pyramidal beams (i.e. sets of rays) through the environment (see Figure 11) Briefly, for each beam, polygons in the environment are considered for intersection with the beam in front to back visibility order (i.e. such that no ....

....beam is constructed by mirroring the transmission beam over the polygon s plane, and possibly other beams are formed to model other types of scattering. This method has been used in a variety of application areas, including acoustic modeling [25, 37, 38, 39, 85, 110, 129] global illumination [18, 36, 46, 48, 52, 130], radio wave propagation [34, 33] and visibility determination [40, 55, 79, 116] Original Beam Reflection Beam Transmission S S a b c Figure 11: Beam tracing method. As compared to image source methods, the advantage of beam tracing is that fewer virtual sources must be considered ....

P. Heckbert and P. Hanrahan. Beam tracing polygonal objects. ACM Computer Graphics, SIGGRAPH '84 Proceedings, 18(3):119--127, July 1984.

....and differentials for arbitrary sampled paths. Section 4 shows how to compute the path gradient and Section 5 demonstrates applications. 2 Related work Several researchers have tried to exploit coherence in the neighborhood of a path by tracking some kind of footprint. In beam tracing [7] a ray is extended to a beam with a polygonal footprint. Intersections with and reflection from objects (polygonal only) fragment the beam in smaller pieces. Lighting calculations can be done coherently over the beam. Cone tracing [1] uses a conical approximation of the footprint. Both approaches ....

Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119--127, July 1984.

....about its neighborhood, these algorithms are prone to aliasing or noise. The common solution is supersampling, averaging the evaluation of many paths. This is expensive, and researchers have tried to exploit coherence in the neighborhood of the rays to reduce aliasing or noise. Beam tracing [6], Cone tracing [1] and pencil tracing [11] all extend a ray to a finite width. Lighting calculations can be done coherently over the extent of the ray, but intersection, reflection and refraction calculations are much more difficult. The combination of physically based BRDF s with these methods is ....

Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119--127, July 1984.

....scene objects are subdivided or not used. This system achieves good results in combining object space and temporal coherence, but no reflections or refractions are allowed, and the scene must remain static, limiting its utility for animation. 15 2. 4 Beam Tracing Heckbert and Hanrahan observed [32] that scenes containing reflections from planar surfaces could be rendered by simply mirroring the observer s location and orientation and generating the reflection by rendering the scene from the new point of view. Beam Tracing held the promise of not repeatedly calcu lating the direction of ....

Heckbert, .S., and Hanrahan, P., "Beam Tracing Polygonal Objects" Computer Graphics, 18:119-127, Siggraph '84

....surface with the refracted caustic. Arvo [1] used backward ray tracing to calculate the position of photons emitted from a light source incident on an object in a scene. Interestingly, he treats texture maps as data structures by using them to accumulate illumination. Heckbert and Hanrahan [9] leveraged the spatial coherence of polygonal objects by reflecting and refracting beams from the visible surfaces in the view frustum, starting at the eye point. The reverse approach was taken up by Watt [26] who calculated the caustics on the bottom of a swimming pool using backward beam ....

Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. In SIGGRAPH '84 Proceedings, pages 119--127, July, 1984.

....area. This technique can only support constant shaded polygons and box filtering, and is not entirely successful at removing aliasing artifacts. By scaling the filter, Catmull could approximate motion blur but without proper interpenetration or occlusion. Extensions of area sampling include beam [11] and cone sampling [1] which are generalizations of ray tracing. Duff [5] extended Catmull s approach by replacing the area computation with a contour integral. He also describes several optimizations that exploit the coherence of scan conversion. In theory, Duff s technique can handle any ....

Heckbert, Paul S. and Pat Hanrahan. Beam Tracing Polygonal Objects. Computer Graphics (SIGGRAPH '84 Proceedings), 18(3):119--127, July 1984.

....to the shading computation, path finding operation is much more expensive. Therefore, many ray tracing acceleration techniques have concentrated on reducing the cost of ray casting by exploiting various kinds of coherence between rays. This has been done by casting bundles of rays, such as beams [41] and cones [3] employing a fixed grid [32] or adaptive 3D spatial hierarchy of scene objects [34] and directional techniques [6] A good summary of these techniques can be found in Arvo and Kirk [7] Besides the above techniques used to accelerate the generation of a single ray traced image, ....

Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119--127, July 1984.

....of the integration domain into components that can be solved efficiently and accurately. Traditionally, four approaches have been used to address this problem: finite or boundary element methods [16, 26, 11] recursive ray tracing [22, 36] Monte Carlo path tracing [18, 28] and beam tracing [10, 24, 14, 17]. All four methods have been used for both sound and light. For validation, the common problems are: 1) defining a quantitative measure of accuracy, and (2) understanding the causes of simulation errors. The first problem is generally addressed in acoustics with statistical measures of impulse ....

P. Heckbert and P. Hanrahan. Beam tracing polygonal objects. Computer Graphics (SIGGRAPH 84), 18(3):119--127, July 1984.

....well for high order reflections, and is best used in combination with a statistical technique to generate the reverberant late reflections. Beam Tracing Methods Recently the beam tracing techniques developed by Heckbert for use in graphical rendering have been adapted for modelling sound fields[35]. Beam tracing considers tracing beams of constant solid angle whether they be triangular, square (often refered to as pyramidal beams) or circular (cone tracing) in cross section. Unlike rays, which are considered to have infinitesimal cross sectional area beams grow in their dimensions the ....

P. S. Heckbert and P. Hanrahan. Beam tracing polygonal objects. Computer Graphics (Proceedings SIGGRAPH '84), 18(3):119--127, 1984.

....of computation. Another disadvantage of ray tracing is that the results are dependent on a particular receiver position, and thus these methods are not directly applicable in interactive applications where either the source or receiver can move. 2. 4 Beam Tracing Methods Beam tracing methods [27, 28] classify propagation paths from a source by recursively tracing pyramidal beams (i.e. sets of rays) through the environment (see Figure 4) Briefly, for each beam, polygons in the environment are considered for intersection with the beam in front to back visibility order (i.e. such that no ....

....the shadow region, a transmission beam is constructed matching the shadow region, and a reflection beam is constructed by mirroring the transmission beam over the polygon s plane. This method has been used in a variety of applications, including acoustic modeling [27, 8, 29, 30, 31] illumination [32, 33, 34, 35, 28, 36], visibility determination [37, 38, 39] and radio propagation prediction [40, 41] The primary advantage of beam tracing is that it leverages geometric coherence, since each beam represents an infinite number of potential ray paths emanating from the source location. It does not suffer from the ....

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P. Heckbert and P. Hanrahan. Beam tracing polygonal objects. ACM Computer Graphics, SIGGRAPH'84 Proceedings, 18(3):119--127, July 1984.

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P. Heckbert and P. Hanrahan, "Beam Tracing Polygonal Objects," Computer Graphics (Proc. Siggraph), Vol. 18, No. 3, July 1984, pp. 119-127.

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Paul S. Heckbert and Pat Hanrahan. Beam Tracing Polygonal Objects. In Computer Graphics (Proceedings of ACM SIGGRAPH 84), volume 18, pages 119--127. ACM. 96

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P. Heckbert, P. Hanrahan, "Beam Tracing Polygonal Objects," Computer Graphics, Vol. 18, No. 3, (1984),pp. 11-127.

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Paul S. Heckbert and Pat Hanrahan. Beam Tracing Polygonal Objects. In Computer Graphics (Proceedings of ACM SIGGRAPH 84), volume 18, pages 119--127. ACM. 346

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Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics, 18(3):119--127, July 1984.

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P. Heckbert and P. Hanrahan, "Beam tracing polygonal objects ", in Proc. SIGGRAPH 1984, pp. 119--127, (July 1984).

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Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. In SIGGRAPH '84 Proceedings, pages 119--127, July, 1984.

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P.S. Heckbert and P. Hanrahan. Beam tracing polygonal objects. In Computer Graphics (SIGGRAPH '84 Proceedings) , volume 18, pages 119--127, July 1984.

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Heckbert, P. S., and Hanrahan, P., "Beam Tracing Polygonal Objects", Computer Graphics (proceedings of SIGGRAPH), 18(3), July 1984, pp. 119--127.

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P. Heckbert and P. Hanrahan. Beam tracing polygonal objects. ACM Computer Graphics, SIGGRAPH'84 Proceedings, 18(3):119--127, July 1984.

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Paul S. Heckbert and Pat Hanrahan. Beam tracing polygonal objects. Computer Graphics (Proc. ACM SIGGRAPH Conf.), 18(3). pp. 119--127 (1984).

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Heckbert, P. a nd Hanrahan, P., "Beam Tracing Polygonal Objects," Computer Graphics, 18(3), pp. 119-127 (July 1984).

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