M. Sbert. The Use of Global Random Directions to Compute Radiosity. Global Monte Carlo Methods. PhD thesis, UPC, Barcelona, Spain, November 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to the incoming power of the element i. The Equation (1) is solved by probabilistic simulation of photon paths traveled by photons leaving light sources in the scene. Random walk global illumination solution was proposed by [Patta92] followed by number of MonteCarlo radiosity algorithms [Kelle97, Neuma97, Sbert97]. Importance driven extensions to continuous random walks, that concentrate most of the particle paths to the region of interest, have been discussed by Pattanaik and Mudur [Patta93a, Patta93b, Patta95] An extension of stochastic ray radiosity algorithm to take view importance into account was ....

Mateou Sbert. The Use of Global Random Directions to Compute Radiosity -- Global Monte-Carlo Techniques. PhD thesis, Universitat de Girona, 1997.

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M. Sbert. The use of global random directions to compute radiosity --- Global Monte Carlo techniques. PhD thesis, Universitat Politecnica de Catalunya, Barcelona, Spain, November 1996.

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M. Sbert. The Use of Global Random Directions to Compute Radiosity. Global Monte Carlo Methods. PhD thesis, Departament de Llenguatges i Sistemes Informatics, Barcelona, Spain, November 1996.

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Sbert M., "The use of global random directions to compute Radiosity. Global Monte Carlo Techniques". PhD. dissertation, Universitat Politcnica de Catalunya, Barcelona, March 1997.

.... crossing a source patch we can begin a new path transporting the correct quantity of energy (on the average) The global density of lines will be simulated through the surrounding of the scene by a sphere, and taking pairs of random points on its surface (there are also other possibilities, see [RPS51, Sbe97c]) The methods that solve radiosity through the use of a global density of lines have been called global Monte Carlo methods [SPP95] opposite to local Monte Carlo methods, that draw lines local to a patch or source. Global densities of lines have also been used by [BF89] and [Neu95] In [Pel95] ....

....covering paths [Rub81] as shown in figure 2(bottom) From this characteristics and from the fact that at any moment there are many paths alive in the simulation, we named this method multi path. 3 SOME RESULTS ABOUT THE FORM FACTOR MATRIX Here we present some theoretical results, obtained in [Sbe97c], which will be used in section 4 to justify the new technique presented in this paper. Let us first remember that F is a stochastic or probability matrix, because 8(i; j)F ij 0 and P j F ij = 1 for all i. A probability matrix is said to be aperiodic if it has no periodic state [Col74] a state ....

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Mateu Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. Ph.D. thesis, Universitat Polit`ecnica de Catalunya, Barcelona, March 1997. Available in http://ima.udg.es/~ mateu

.... distribution is 1:06, which is the same as in the first scene (that is, our heuristic for the extended first shot does not difference for the moment between the two cases) On this figure we see that the multi path methods are better than the local Monte Carlo method (as already demonstrated in [Sbe97b] for the first shot case) and the extended first shot method does not has any noticeable improvement over the first shot method. a) b) c) Figure 6: Images generated with the first shot (a) extended first shot (b) and local Monte Carlo (c) methods with 1.5 million lines 0 0.05 0.1 0.15 ....

M. Sbert. The use of global random directions to compute radiosity. global monte carlo methods. Ph.D. thesis. Universitat Polit`ecnica de Catalunya, Barcelona, 1997.

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M. Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. PhD. thesis, Universitat Politcnica de Catalunya (Barcelona, Spain), March

....and discussion In order to illustrate the feasibility of animation complexity measure, we compute C a and D e for nine sequences of frames, whose values are contained in table 1. In all cases, 10 5 global lines have been cast to obtain an approximated Monte Carlo solution for the form factors [13], by counting the number of intersections between pairs of segments wich are visible. The first two sequences (figures 1(a,b) show a moving square following two different paths. Figure 1(b) is more complex than the other one because the movement is produced in a more complex area (between the ....

SBERT, M. The use of global random directions to compute radiosity. Global Monte Carlo methods. PhD. thesis, Universitat Politecnica de Catalunya (Barcelona, Spain), March 1997. Available in http://ima.udg.es/ mateu. 6

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SBERT, M. The use of global random directions to compute radiosity. Global Monte Carlo methods. PhD. thesis, Universitat Politcnica de Catalunya (Barcelona, Spain), March 1997.

....F i h 1 : Fhn Gamma1 s R 2 i p i X h 1 Delta Delta Delta X h n Gamma1 X s F i h 1 : Fhn Gamma1 s E 2 s (6) because we have assumed R 2 i i 1 for all i. But we have X h 1 Delta Delta Delta X h n Gamma1 F i h 1 : Fhn Gamma1 s = F n ) is and in [15] it is proven that, whenever the Form Factor matrix is irreducible and aperiodic lim n 1 (F n ) is = As AT (7) where AT is the total area in the scene. We do not consider it geometrically meaningful for a Form Factor matrix to be periodic. If there are closed rooms, it is reducible with one ....

Mateu Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. Ph.D. thesis, Universitat Politecnica de Catalunya, Barcelona, March 1997. Available in http://ima.udg.es/ mateu

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Mateu Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. Ph.D. thesis, Universitat Politcnica de Catalunya, Barcelona, March 1997. Available in http://ima.udg.es/ mateu.

.... 2 Integral geometry and analogies for the form factor A very interesting result about the differential form factor between two spherical patches i and j on the surface of the same sphere, that is related to Integral Geometry can be found or derived from results of various authors ( 6] 10] [7]) Namely, that this form factor is F i j = A A S , where A S is the area of the sphere. This can be seen very easily considering figure 2. Since the two angles q are equal and r = 2R Delta cos q, the expression for the form factor becomes F i j = 1 A i Z A i Z A cos q i cos q j pr 2 V ....

Mateu Sbert. The Use of Global Random Directions to Compute Radiosity -- Global Monte Carlo Techniques. PhD thesis, Universitat Politecnica de Catalunya, Barcelona, Spain, November 1996.

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Mateu Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. Ph.D. thesis, Universitat Politècnica de Catalunya, Barcelona, March 1997. Available in http://ima.udg.es/ mateu.

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Mateu Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. Ph.D. thesis, Universitat Politècnica de Catalunya, Barcelona, March 1997. Available in http://ima.udg.es/ mateu.

....setting, a scene is composed by surfaces which are divided (discretized) into n p patches. The form factor F ij between patch i and patch j can be defined (for a planar patch i) as the fraction of lines that, exiting from i, have j as the nearest patch intersected (thus P np j=1 F ij = 1) [16, 14]. In this way, F ij can be considered as the probability of a line that exiting from i lands in j, and then the form factors from any patch form a probability vector. If we identify the lines connecting two patches with visibility, the form factor will thus give us the visibility between ....

....room. In the case of covered or hidden patches, we can simply suppress them and obtain a smaller and now irreducible form factor matrix. Some interesting properties can be proved by the form factor matrix. For the purpose of this paper we are mainly interested in the following two propositions [16]: Proposition 1 If the form factor matrix F is irreducible and aperiodic, then we have lim n 1 (F n ) ij A j AT , where A j is the area of patch j and A T = P np i=1 A i , for all the n p patches in the scene. Thus, as the equilibrium distribution for a Markov chain is defined as the ....

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Mateu Sbert. The use of global random directions to compute radiosity. Global Monte Carlo methods. Ph.D. thesis, Universitat Polit`ecnica de Catalunya, Barcelona, March 1997. Available in http://ima.udg.es/~ mateu.

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M. Sbert. The Use of Global Random Directions to Compute Radiosity. Global Monte Carlo Methods. PhD thesis, UPC, Barcelona, Spain, November 1996.

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Mateu Sbert. The Use of Global Random Directions to Compute Radiosity: Global Monte Carlo Techniques. PhD thesis, Universitat Politecnica de Catalunya, Barcelona, Spain, 1997.

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Sbert M.; The use of global random directions to compute radiosity - Global Monte Carlo techniques. Universitat Politcnica de Catalunya, Barcelona, Spain, 1997. http://ima.udg.es/~mateu/

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M. Sbert, The Use of Global Random Directions to Compute Radiosity { Global Monte-Carlo Techniques. PhD thesis, Universitat de Girona, (1997).

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Mateu Sbert. The Use Of Global Random Directions To Compute Radiosity. Global Monte Carlo Techniques. PhD thesis, Universitat Politecnica de Catalunya 1996

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