The Design and Implementation of a Radiosity Renderer Alexandru Telea 2 Contents 1 Overview of this Thesis 5 2 The Radiosity Theory 7 2.1 Radiometry .............................. 7 2.1.1 Radiant energy (Q, [J]) ................... 7 2.1.2 Radiant flux (radiant power) (, [W]) ............ 8 2.1.3 Radiant flux density (E, M[W/m2]) ............. 8 2.1.4 Radiance (L, [W/m2sr]) ................... 9 2.1.5 Radiant intensity (I, [W/sr])................. 9 2.2 Photometry .............................. 10 2.2.1 Reflectance and Transmittance (ρ,[dimensionless]) ..... 10 2.2.2 Conclusions ......................... 11 2.3 Ideal Diffuse Reflectors ........................ 11 2.3.1 Conclusion .......................... 12 2.4 The Radiosity Theory ......................... 13 2.4.1 The Rendering Equation ................... 13 2.5 Overview of the Radiosity Process .................. 14 2.5.1 Radiosity Methods ...................... 14 2.5.2 Form Factors ......................... 15 2.6 The Structure of a Radiosity Renderer ................. 17 2.7 Solving the Radiosity Equation .................... 18 2.7.1 Full Radiosity and Progressive Refinement .......... 18 2.7.2 Form Factor Determination .................. 19 2.7.3 Substructuring ........................ 24 2.7.4 Adaptive Subdivision ..................... 25 3 The Design of a Radiosity Renderer 29 3.1 Design Overview ........................... 29 3.2 Modelling the Environment ...................... 30 3.2.1 Polygons ........................... 30 3.2.2 Patches ............................ 31 3.2.3 Elements ........................... 32 3.3 Form Factor Determination ...................... 33 3.3.1 General Presentation ..................... 33 3.3.2 Ray Casting Implementation ................. 36 3.3.3 Ray Occlusion Testing using Octrees ............. 39 3.3.4 Ray-Polygon Intersection ................... 41 3.4 Adaptive Receiver Subdivision .................... 42 3 4 CONTENTS 3.4.1 A Non Uniform Element Mesh Implementation ........ 46 3.4.2 Vertex Radiant Exitances Computation ............ 52 3.5 The Progressive Refinement Strategy ................. 57 3.6 An Overview of the Progressive Refinement Loop ........... 59 4 The Close Objects Buffer 61 4.1 Modelling Sharp Shadows with a Radiosity Renderer ......... 61 4.2 Sharp Shadows ............................ 63 4.3 The Close Objects Buffer ....................... 64 4.4 Building the Close Objects Buffer ................... 66 4.5 Using the Close Objects Buffer .................... 69 4.6 A Two-Level Close Object Buffer ................... 71 4.7 Conclusions ............................. 72 5 The Radiant Flux Hit Model 73 5.1 Introduction .............................. 73 5.2 The Radiant Flux Hit ......................... 73 6 Modelling and Viewing the Environment 77 6.1 Introduction .............................. 77 6.2 WINVIEW: A 3D Viewing Application ................ 77 6.2.1 Introduction ......................... 77 6.2.2 General Overview ...................... 77 6.2.3 User Guidelines ........................ 79 6.3 BUILD 3D: A 3D Modelling Application ............... 80 6.3.1 Transformations ....................... 85 6.3.2 Colors ............................ 85 6.3.3 Material properties ...................... 85 6.3.4 Comments .......................... 86 A The Radiosity Renderer User Guide 87 B The 3D File Format 93 C The TAKES File Format 95 DPlates 97 Chapter 1 Overview of this Thesis This thesis presents the design and the implementation of a radiosity renderer, starting from the theoretical assumptions that are made by the diffuse global illumination model and up to the final design and implementation steps. Besides the implementation of all the standard features of the most common radiosity renderers, some new methods for enhancing the rendering speed and quality of the result are presented, implemented and tested on sample scenes. Since most of the features of the renderer can be directly con- trolled by the user, the application can be used on a wide range of scenes and for ob- taining results of the desired quality level. The first part of this thesis (chapter 2) presents the theoretical basis of the radiosity method. Radiometric and photometric quantities are introduced, the rendering equation is described and particularized for the diffuse global illumination case. An overview of the radiosity process follows, presenting the basic steps performed by a radiosity ren- derer and introducing the various quantities and methods used within: form factors, pro- gressive refinement, substructuring, adaptive subdivision. The advantages and disad- vantages of most of the several techniques and models used in radiosity renderers are compared in order to determine a suitable model for the radiosity renderer that will be implemented. The second part of the thesis starts with chapter 3, presenting the major design lines of the radiosity renderer that will be implemented, based on the accuracy, speed and memory consumption considerations outlined in the first part. The way the environment to render is modelled is firstly presented (section 3.2), followed by a presentation of the method used for form factors computation (section 3.3), the method used for adaptive subdivision (section 3.4) and for progressive refinement (section 3.5). The next chapter (4) introduces a new method proposed for enhancing the sharp shadow rendering done with a radiosity method: the close objects buffer. Both the the- oretical motivation and the implementation of this technique are presented. Chapter 5 presents a postprocessing technique used for controlling the shadow smoothness. Chap- ter 6 presents the methods and the software implemented for modelling the scene to be rendered as well as the ones used for viewing the results. Specific data about the implementation of the various pieces of software used in the radiosity pipeline are presented in the Appendices, as well as plates showing several rendered scenes. 5 6 CHAPTER 1. OVERVIEW OF THIS THESIS Chapter 2 The Radiosity Theory 2.1 Radiometry There exist several photometric and radiometric terminologies used in computer graph- ics, sometimes being different from the ones encountered in illumination engineering. In order to avoid ambiguities in naming the physical quantities, the set of definitions in- troduced by [RP-16-1986, 1986] will be used. The radiometric and photometric mag- nitudes that will be subsequently used in this paper are briefly presented here. Radiometry measures light in any portion of the electromagnetic spectrum. From radiometric point of view, the light is considered as radiant energy that travels through space. The radiometric magnitudes that will be presented are radiant energy, radiant flux, radiant flux density (irradiance and radiant exitance), radiance and radiant inten- sity. These magnitudes have a physical significance (they can describe surfaces that emit,reflect and absorb light). Alternatively, the radiometric field theory describes light by means of a three-dimensional or five-dimensional ’photic field’ that gives the value of a quantity describing light in any point of the space and for any orientation [Moon and Spencer, 1981]. The main importance of the photic field model resides in the fact that it describes light totally independent from any physical surfaces. The physical quantities describing light are now intrinsic properties of the photic field. Consequently the knowledge of the photic field in all points of the space gives a complete knowledge of the lighting of that space for any position and orientation of the observer. The following definitions are valid both for the model considering physical surfaces as for the radiometric field model: 2.1.1 Radiant energy (Q, [J]) Radiant energy is the energy carried by light seen as electromagnetic waves. It is usually measured in joules or kilowatt-hours. Considering the light as electromagnetic waves, we can define the spectral radiant energy as being radiant energy per unit wavelength interval: dQ Qλ = (2.1) dλ For different wavelengths one gets different spectral radiant energies (that can be re- garded as density of radiant energy with respect to wavelength)(see equation (2.1)). 7 8 CHAPTER 2. THE RADIOSITY THEORY 2.1.2 Radiant flux (radiant power) (, [W]) dQ = (2.2) dt Radiant flux is the time rate of radiant energy flow. It is measured in watts. Similar to the spectral radiant energy, one can define the spectral radiant flux as being the radiant flux per unit wavelength interval (or, in other words, density of radiant power with respect to wavelength) d λ = (2.3) dλ 2.1.3 Radiant flux density (E, M[W/m2]) Radiant flux density is the radiant flux per unit area at a point on a real or imaginary arbitrarily oriented surface. Two cases are distinguished: the flux can arrive at the sur- face or can leave the surface (for a real surface, the flux can leave it due to reflection or emission). In the case the flux arrives at the surface, the radiant flux density is called irradiance, while in the case the flux leaves the surface the radiant flux density is called radiant exitance. Irradiance is defined as: irradiance radiant exitance (radiosity) Figure 2.1: Irradiance and radiant exitance d E = (2.4) dA where dAis the differential area receiving the radiant flux d. Radiant exitance is defined as: d M = (2.5) dA where, similarly, dAis the differential area from which the radiant flux d leaves. Both irradiance and radiant exitance are measured in watts per square meter. Similarly to the spectral radiant flux, we can define the spectral irradiance Eλ and the spectral