## Computational Methods for Realistic Image Synthesis

### BibTeX

@MISC{Shao_computationalmethods,

author = {Min-zhi Shao and My Parents and Ya-mei Zhong and Jian Shao Acknowledgments and Thank Professors Ruzena Bajcsy and Herman Gluck and Jerry Kazdan and Michael Palis and Min-zhi Shao},

title = {Computational Methods for Realistic Image Synthesis},

year = {}

}

### OpenURL

### Abstract

I owe a great deal to my advisor, Professor Norman Badler, for his guidance, support, and patience. Norm has provided an excellent environment in which to work. Without his open mind and flexibility, this work would never have been completed. I want to thank the other members of my doctoral committee: Professors David Ebert, Jean Gallier, Sampath Kannan, and Dimitris Metaxas, for their encouragement and helpful comments. I would like to take this opportunity to thank the faculties in the Computer and Information Science and the Mathematics Departments. In particular, I

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Citation Context ...0 ; i� i) dx 0 (2:32) where ; denotes the set of all surface points in the environment. The radiance equation was first introduced to computer graphics by Kajiya (who named it the rendering equation) =-=[41]-=- and Immel et al. [39]. In mathematics, it is a Fredholm integral equation of the second kind [22, p. 3]. Except for few simple environment settings, however, we do not have enough computing power to ... |

556 |
An improved illumination model for shaded display
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- 1980
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Citation Context ...46] were the most popular. Major research efforts were devoted to the visible surface determination for polygonal environments [58]. In an attempt to simulate the global illumination effects, Whitted =-=[63]-=- first introduced the ray tracing method to computer graphics. In this method, for 1each pixel on the raster display a ray is traced from the eye into the environment. In addition to the direct illum... |

429 |
T.: Illumination for computer generated pictures
- Phong
- 1975
(Show Context)
Citation Context ...in the environment is often ignored or specified by an ambient constant. Simple reflectance models such as the Lambertian model for diffuse reflection [32] and the Phong model for specular reflection =-=[46]-=- were the most popular. Major research efforts were devoted to the visible surface determination for polygonal environments [58]. In an attempt to simulate the global illumination effects, Whitted [63... |

400 |
Fast wavelet transforms and numerical algorithms
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Citation Context ...lt since shadows usually produce sharp edges which may not be represented by a small set of polynomial basis functions. When the basis functions are chosen to be the wavelet functions, Beylkin et al. =-=[10]-=- have shown that kernel functions satisfying very general smoothness conditions can be approximated to any finite precision with only O(n) elements where n is the dimension of the wavelet basis. It im... |

368 |
Distributed Ray Tracing
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- 1984
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Citation Context ...illumination contribution from other surfaces is added by recursively generating new rays in the mirror reflection whenever a ray strikes a surface. For non-mirror reflection, distributed ray tracing =-=[18]-=- extends this procedure by generating a bundle of new rays in accordance with the reflectance model. Despite often impressive pictures, the ray tracing model does not obey the energy conservation prin... |

368 | A rapid hierarchical radiosity algorithm
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- 1991
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Citation Context ...numerical solution to the radiosity equation (3.1) have progressed rapidly during the last decade. The numerical techniques developed to date include the shooting method [15], the hierarchical method =-=[14, 34]-=-, the higher order method [36, 64], and the wavelet method [31, 49]. With the general bidirectional reflectance distribution function, the surface radiance is no longer viewing angle independent. The ... |

355 | A Reflectance Model for Computer Graphics - Cook, Torrance - 1981 |

347 |
Theory for off-specular reflection from roughened surfaces
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Citation Context ...wise� (2:16) (x) dx = 1� (2:17) Z f( ) (x ; ) d = f(x): (2:18) The ideal specular reflection is often called the mirror reflection. 2.2.3 Torrance-Sparrow Reflectance Model The Torrance-Sparrow model =-=[59]-=- is a geometric reflectance model based on the ray theory of geometric optics. In this model, the surface is assumed to be composed of a collection of randomly oriented mirror-like micro facets. The w... |

337 | Multiresolution Analysis for Surfaces of Arbitrary Topological Type
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Citation Context ...ms of reflected and incident flux density ratios [29]. This representation tends to be more compact and accurate but lacks analytical expressions. New techniques, such as spherical wavelet algorithms =-=[43, 51]-=-, may be used to further compress the data. A direct motivation of this work is Arvo’s recent paper on irradiance tensors [5]. Due to the generalized Stokes’ theorem, the key result of the irradiance ... |

331 | Battaile B., "Modelling the interaction of light between diffuse surfaces
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- 1983
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Citation Context ...ht energy distribution, the ray tracing method does poorly in computing the global illumination effects. In order to model the interaction of light between diffusely reflecting surfaces, Goral et al. =-=[30]-=- introduced to computer graphics the radiosity method which was initially developed for radiative transfer computations. In this method, an environment is first discretized into a set of small surface... |

308 | Radiosity and Realistic Image Synthesis - Cohen, Wallace - 1993 |

308 | Introduction to applied mathematics - Strang - 1986 |

301 | D.: Fundamentals of Computer Aided Geometric Design - Hoschek, Lasser - 1993 |

270 |
The Hemi-Cube: A Radiosity Solution for Complex Environments
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Citation Context ...e converted into a double contour integral for the evaluation of form factors between unoccluded patches. Numerical form factor techniques for environments with occlusion include the hemi-cube method =-=[13]-=-, the analytical method [7], and the ray tracing method [61]. With the definition of form factor (3.4), Equation (3.3) may be rewritten as Bi = Ei + 19 nX i FijBj: (3:6) j=1Notice that for each patch... |

236 | A progressive refinement approach to fast radiosity image generation
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Citation Context ...7 7 5 : (3:7) The research in numerical solution to the radiosity equation (3.1) have progressed rapidly during the last decade. The numerical techniques developed to date include the shooting method =-=[15]-=-, the hierarchical method [14, 34], the higher order method [36, 64], and the wavelet method [31, 49]. With the general bidirectional reflectance distribution function, the surface radiance is no long... |

229 | Spherical wavelets: efficiently representing functions on the sphere
- Schroder, Sweldens
- 1995
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Citation Context ...ms of reflected and incident flux density ratios [29]. This representation tends to be more compact and accurate but lacks analytical expressions. New techniques, such as spherical wavelet algorithms =-=[43, 51]-=-, may be used to further compress the data. A direct motivation of this work is Arvo’s recent paper on irradiance tensors [5]. Due to the generalized Stokes’ theorem, the key result of the irradiance ... |

215 | Ray tracing volume densities
- KAJIYA, HERZEN
- 1984
(Show Context)
Citation Context ...represent bidirectional reflectance distribution functions (BRDFs) [12, 62], incident radiance functions [12], reflected radiance functions [55], and scattering radiance functions in volume densities =-=[40]-=-. Because the basis functions are globally supported over the entire unit sphere, the spherical harmonic representation is often prone to the Gibbs phenomenon [56, p. 272], especially for discontinuou... |

199 | A characterization of ten hidden-surface algorithms
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Citation Context ...for diffuse reflection [32] and the Phong model for specular reflection [46] were the most popular. Major research efforts were devoted to the visible surface determination for polygonal environments =-=[58]-=-. In an attempt to simulate the global illumination effects, Whitted [63] first introduced the ray tracing method to computer graphics. In this method, for 1each pixel on the raster display a ray is ... |

179 |
Numerical methods
- Björck, Dahlquist
- 1974
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Citation Context ...: Conventional shooting method. 461.0 2000 0.8 800 0.6 400 0.4 200 100 0.2 Total patches: 1080 38 [light patches: 38] Patch vertices: 2282 0.0 0 500 1000 1500 2000 2500 (a) = 100 1.00 0.98 0.96 0.94 =-=[20]-=- [100] [200] [300] [500] 0.92 0.90 2000 0.88 0.86 0.84 Total patches: 1080 0.82 [light patches: 38] Patch vertices: 2282 0.80 0 500 1000 1500 2000 2500 (b) = 20, 100, 200, 300, 500, and the convention... |

154 |
The Scattering of Electromagnetic Waves from Rough Surfaces
- Beckmann, Spizzichino
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Citation Context ...e oriented in bisection direction w. The Gaussian distribution 2 ; D = ce m2 (2:23) where c is an arbitrary constant was used in [59]. Cook and Torrance [17] suggested using the Beckmann distribution =-=[8]-=- D = 1 4m 2 cos 4 tan2 ; e m2 (2:24) in their improved model for computer graphics. In distributions (2.23) and (2.24), m denotes the root-mean-square slope of micro facets. Small values of m signify ... |

153 | A Comprehensive Physical Model for Light Reflection
- He, Torrance
- 1991
(Show Context)
Citation Context ...s from very smooth to very rough. It is more general than geometric reflectance models such as the Torrance-Sparrow model which has a considerably simpler mathematical expression. Recently, He et al. =-=[35]-=- proposed a comprehensive physical reflectance model for computer graphics. It builds upon and extends the BeckmannSpizzichino model by including the polarization, masking, and shadowing effects. The ... |

148 | Wavelet radiosity - GORTLER, SCHRÖDER, et al. - 1993 |

140 |
Predicting Reflectance Functions from Complex Surfaces
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Citation Context ...nt to use them to describe and manipulate direction-dependent functions. In computer graphics, spherical harmonics have been used to represent bidirectional reflectance distribution functions (BRDFs) =-=[12, 62]-=-, incident radiance functions [12], reflected radiance functions [55], and scattering radiance functions in volume densities [40]. Because the basis functions are globally supported over the entire un... |

139 |
A global illumination solution for general reflectance distributions
- Sillion, Arvo, et al.
- 1991
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Citation Context ...on for solving the radiance equation (2.29). The numerical techniques developed to date include the global cube method [39], the two-pass method [60], the form factor method [52], the shooting method =-=[55]-=-, the hierarchical method [6], and the wavelet method [50]. The Monte Carlo method is another research avenue for the nondeterministic solution to this general global illumination problem [41]. It is ... |

137 |
A two-pass solution to the rendering equation: A synthesis of ray tracing and radiosity methods
- Wallace, Cohen, et al.
- 1987
(Show Context)
Citation Context ...extended to include directional hemisphere discretization for solving the radiance equation (2.29). The numerical techniques developed to date include the global cube method [39], the two-pass method =-=[60]-=-, the form factor method [52], the shooting method [55], the hierarchical method [6], and the wavelet method [50]. The Monte Carlo method is another research avenue for the nondeterministic solution t... |

130 |
Continuous shading of curved surfaces
- Gouraud
(Show Context)
Citation Context ...s. The illumination of light from other surfaces in the environment is often ignored or specified by an ambient constant. Simple reflectance models such as the Lambertian model for diffuse reflection =-=[32]-=- and the Phong model for specular reflection [46] were the most popular. Major research efforts were devoted to the visible surface determination for polygonal environments [58]. In an attempt to simu... |

127 | The zonal method for calculating light intensities in the presence of a participating medium - Rushmeier, Torrance - 1987 |

123 |
A radiosity method for non-diffuse environments
- Immel, Cohen, et al.
- 1986
(Show Context)
Citation Context ...where ; denotes the set of all surface points in the environment. The radiance equation was first introduced to computer graphics by Kajiya (who named it the rendering equation) [41] and Immel et al. =-=[39]-=-. In mathematics, it is a Fredholm integral equation of the second kind [22, p. 3]. Except for few simple environment settings, however, we do not have enough computing power to solve such high dimens... |

115 |
Bidirectional Reflection Functions from Surface Bump Maps
- Cabral, Max, et al.
- 1987
(Show Context)
Citation Context ...nt to use them to describe and manipulate direction-dependent functions. In computer graphics, spherical harmonics have been used to represent bidirectional reflectance distribution functions (BRDFs) =-=[12, 62]-=-, incident radiance functions [12], reflected radiance functions [55], and scattering radiance functions in volume densities [40]. Because the basis functions are globally supported over the entire un... |

107 |
A Ray Tracing Algorithm for Progressive Radiosity
- Wallace, Elmquist, et al.
- 1989
(Show Context)
Citation Context ...n of form factors between unoccluded patches. Numerical form factor techniques for environments with occlusion include the hemi-cube method [13], the analytical method [7], and the ray tracing method =-=[61]-=-. With the definition of form factor (3.4), Equation (3.3) may be rewritten as Bi = Ei + 19 nX i FijBj: (3:6) j=1Notice that for each patch i in the environment, we can derive such an equation. There... |

102 |
Greenberg D.: Discontinuity Meshing for Accurate Radiosity
- Lischinski, Tampieri
- 1992
(Show Context)
Citation Context ...more stable than the monomials [24, 25]. In high quality radiosity solutions, they should be a natural choice for piecewise basis functions over triangular elements generated by discontinuity meshing =-=[36, 42]-=- or isolux meshing [4]. To evaluate the kernel projections in the radiosity method, the Gaussian quadratures [20, p. 302] may be used. They have also been derived for simplexes [33]. The formulas can ... |

99 |
An efficient radiosity approach for realistic image synthesis
- Cohen, Grenberg, et al.
- 1986
(Show Context)
Citation Context ...numerical solution to the radiosity equation (3.1) have progressed rapidly during the last decade. The numerical techniques developed to date include the shooting method [15], the hierarchical method =-=[14, 34]-=-, the higher order method [36, 64], and the wavelet method [31, 49]. With the general bidirectional reflectance distribution function, the surface radiance is no longer viewing angle independent. The ... |

91 | Improving radiosity solutions through the use of analytically determined form-factors - Baum, Rushmeier, et al. - 1989 |

88 | Computational Methods for Integral Equations - Delves, Mohamed - 1985 |

74 |
Simulating Global Illumination Using Adaptive Meshing
- Heckbert
- 1991
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Citation Context ...y equation (3.1) have progressed rapidly during the last decade. The numerical techniques developed to date include the shooting method [15], the hierarchical method [14, 34], the higher order method =-=[36, 64]-=-, and the wavelet method [31, 49]. With the general bidirectional reflectance distribution function, the surface radiance is no longer viewing angle independent. The idea of spatial surface discretiza... |

72 |
Galerkin radiosity: A higher order solution method for global illumination
- Zatz
- 1993
(Show Context)
Citation Context ...y equation (3.1) have progressed rapidly during the last decade. The numerical techniques developed to date include the shooting method [15], the hierarchical method [14, 34], the higher order method =-=[36, 64]-=-, and the wavelet method [31, 49]. With the general bidirectional reflectance distribution function, the surface radiance is no longer viewing angle independent. The idea of spatial surface discretiza... |

61 | Wavelength dependent reflectance functions
- Gondek, Meyer, et al.
- 1994
(Show Context)
Citation Context ...ooth basis functions. Recently, a hierarchical geodesic sphere construction with adaptive subdivision has been proposed to approximate the BRDFs in terms of reflected and incident flux density ratios =-=[29]-=-. This representation tends to be more compact and accurate but lacks analytical expressions. New techniques, such as spherical wavelet algorithms [43, 51], may be used to further compress the data. A... |

59 | A Hierarchical Illumination Algorithm for Surfaces with Glossy Reflection
- Aupperle, Hanrahan
- 1993
(Show Context)
Citation Context ...uation (2.29). The numerical techniques developed to date include the global cube method [39], the two-pass method [60], the form factor method [52], the shooting method [55], the hierarchical method =-=[6]-=-, and the wavelet method [50]. The Monte Carlo method is another research avenue for the nondeterministic solution to this general global illumination problem [41]. It is assumed in the radiance equat... |

54 | The irradiance Jacobian for partially occluded polyhedral sources
- Arvo
- 1994
(Show Context)
Citation Context ...als [24, 25]. In high quality radiosity solutions, they should be a natural choice for piecewise basis functions over triangular elements generated by discontinuity meshing [36, 42] or isolux meshing =-=[4]-=-. To evaluate the kernel projections in the radiosity method, the Gaussian quadratures [20, p. 302] may be used. They have also been derived for simplexes [33]. The formulas can be made symmetric in b... |

51 |
An Experimental Evaluation of Computer Graphics Imagery
- Meyer, Rushmeier, et al.
- 1986
(Show Context)
Citation Context ... generalization to the radiosity method in this regard leads to the zonal method [38, 48] which includes the emission, absorption, and scattering of light within the participating media. Meyer et al. =-=[45]-=- have conducted a comprehensive study of the physical and perceptual aspects of the radiosity method. In their physical study, the spectral 20reflectance of the materials and the spectral and directi... |

48 | Fitting Scattered Data on Sphere-like Surfaces using Spherical Splines
- Alfeld, Neamtu, et al.
- 1996
(Show Context)
Citation Context ...e spherical Bernstein polynomials of degree n over domain 4abc B n n! i�j�k (u� v� w) = i!j!k! uiv j w k � i + j + k = n (5:16) and Bn i�j�k (u� v� w) =0 if any of i, j, k is negative. It is shown in =-=[2, 3]-=- that they are homogeneous trivariate basis functions and possess virtually all of the properties of the classical planar Bernstein polynomials, despite the results in [11]. However, formulas (5.7) an... |

48 | Linear Algebra and its Applications. Harcourt Brace Jonanovich - Strang - 1988 |

41 | Wavelet projections for radiosity
- Schröder, Gortler, et al.
- 1993
(Show Context)
Citation Context ...rapidly during the last decade. The numerical techniques developed to date include the shooting method [15], the hierarchical method [14, 34], the higher order method [36, 64], and the wavelet method =-=[31, 49]-=-. With the general bidirectional reflectance distribution function, the surface radiance is no longer viewing angle independent. The idea of spatial surface discretization, however, may be extended to... |

40 | Introduction to Applied Mathematics (WellesleyCambridge - Strang - 1986 |

37 | Applications of irradiance tensors to the simulation of nonlambertian phenomena
- ARVO
- 1995
(Show Context)
Citation Context ...vironment settings. The difficulty essentially comes from the lack of computing power in solving higher dimensional radiance integral equations for environments beyond a few toy boxes. Recently, Arvo =-=[5]-=- presented an analytic method for computing direct illumination effects involving directional area light sources and surfaces ranging from diffuse to nearly-specular. The entire computation is based o... |

37 | On the numerical condition of polynomials in bernstein form - Farouki, Rajan - 1987 |

35 | Bernstein-Bézier polynomials on spheres and sphere-like surfaces
- Alfeld, Neamtu, et al.
- 1996
(Show Context)
Citation Context ...� w) are called the spherical barycentric coordinates of spherical point p with respect to a, b, c. They were first introduced by Möbius in the last century and rediscovered recently by Alfeld et al. =-=[2]-=-, from where we adopt the definitions. The equations in (5.12) also give a geometric interpretation of the spherical barycentric coordinates, i.e., u = volume (Ofp� b� cg) volume (Ofa� b� cg) � volume... |

34 |
On the numerical condition of polynomials
- Farouki, Rajan
- 1987
(Show Context)
Citation Context ... (Bézier triangle) are extremely important in surface design, data fitting and interpolation, and elsewhere. It has been shown that numerically they are inherently much more stable than the monomials =-=[24, 25]-=-. In high quality radiosity solutions, they should be a natural choice for piecewise basis functions over triangular elements generated by discontinuity meshing [36, 42] or isolux meshing [4]. To eval... |

32 |
Triangular Bernstein-Bézier patches, Computer Aided Geometric Design
- Farin
- 1986
(Show Context)
Citation Context ...area (4abc) = 1 2 ax bx cx ay by cy 1 1 1 (5:4) is the projected area of 4abc on the xy plane. The uniquely defined (u� v� w) are called the barycentric coordinates of point p with respect to a, b, c =-=[23]-=-; see Figure 5.1. With the geometric interpretation from the equations in (5.3), it is clear that barycentric coordinates are intrinsic, i.e., they only depend on the relative position of point p in 4... |

27 |
Algorithms for polynomials in Bernstein form
- Farouki, Rajan
- 1988
(Show Context)
Citation Context ... (Bézier triangle) are extremely important in surface design, data fitting and interpolation, and elsewhere. It has been shown that numerically they are inherently much more stable than the monomials =-=[24, 25]-=-. In high quality radiosity solutions, they should be a natural choice for piecewise basis functions over triangular elements generated by discontinuity meshing [36, 42] or isolux meshing [4]. To eval... |