Software Requirements Specification for Game Physics Alex Halliwushka, Luthfi Mawarid, and Olu Owojaiye September 29, 2021 Contents 1 Reference Material 3 1.1 Table of Units ................................... 3 1.2 Table of Symbols ................................. 3 1.3 Abbreviations and Acronyms .......................... 5 2 Introduction 6 2.1 Purpose of Document ............................... 6 2.2 Scope of Requirements .............................. 7 2.3 Characteristics of Intended Reader ....................... 7 2.4 Organization of Document ............................ 7 3 General System Description 7 3.1 System Context .................................. 7 3.2 User Characteristics ............................... 8 3.3 System Constraints ................................ 8 4 Specific System Description 8 4.1 Problem Description ............................... 8 4.1.1 Terminology and Definitions ....................... 9 4.1.2 Goal Statements ............................. 9 4.2 Solution Characteristics Specification ...................... 9 4.2.1 Assumptions ............................... 10 4.2.2 Theoretical Models ............................ 10 4.2.3 General Definitions ............................ 14 4.2.4 Data Definitions ............................. 18 4.2.5 Instance Models ............................. 32 4.2.6 Data Constraints ............................. 38 4.2.7 Properties of a Correct Solution ..................... 38 1 5 Requirements 39 5.1 Functional Requirements ............................. 39 5.2 Non-Functional Requirements .......................... 39 6 Likely Changes 40 7 Unlikely Changes 40 8 Off-The-Shelf Solutions 40 9 Traceability Matrices and Graphs 41 10 Values of Auxiliary Constants 45 11 References 45 2 1 Reference Material This section records information for easy reference. 1.1 Table of Units The unit system used throughout is SI (Système International d’Unités). In addition to the basic units, several derived units are also used. For each unit, the Table of Units lists the symbol, a description and the SI name. Symbol Description SI Name J energy joule kg mass kilogram m length metre N force newton rad angle radian s time second Table 1: Table of Units 1.2 Table of Symbols The symbols used in this document are summarized in the Table of Symbols along with their units. Throughout the document, symbols in bold will represent vectors, and scalars otherwise. The symbols are listed in alphabetical order. For vector quantities, the units shown are for each component of the vector. Symbol Description Units 퐚 m Acceleration s2 퐚 푡 m ( ) Linear acceleration s2 퐚 m 푗 J-Th Body’s Acceleration s2 퐶R Coefficient of restitution – 푑푗 Distance Between the J-Th Particle and the Axis of Rotation m 퐝 Distance between the center of mass of the rigid bodies m 퐝̂ Unit vector directed from the center of the large mass to the center m of the smaller mass ‖퐝‖ Euclidean norm of the distance between the center of mass of two m bodies ‖퐝‖2 Squared distance m2 퐅 Force N 3 Symbol Description Units 퐅1 Force exerted by the first body (on another body) N 퐅2 Force exerted by the second body (on another body) N 퐅퐠 Force of gravity N 퐅푗 Force Applied to the J-Th Body at Time T N 퐺 m3 Gravitational constant kgs2 퐠 m Gravitational acceleration s2 ℎ Height m 퐈 Moment of inertia kgm2 2 퐈A Moment of Inertia of Rigid Body A kgm 2 퐈B Moment of Inertia of Rigid Body B kgm 퐉 Impulse (vector) Ns 푗 Impulse (scalar) Ns 퐾퐸 Kinetic energy J 퐿 Length m 푀 Mass of the Larger Rigid Body kg 푚 Mass kg 푚1 Mass of the first body kg 푚2 Mass of the second body kg 푚A Mass of Rigid Body A kg 푚B Mass of Rigid Body B kg 푚푗 Mass of the J-Th Particle kg 푚푇 Total Mass of the Rigid Body kg 퐧 Collision normal vector m ‖퐧‖ Length of the normal vector m 푃 퐸 Potential energy J 퐩 Position m 퐩CM Center of Mass m 퐩푗 Position Vector of the J-Th Particle m 퐫 Position vector m 푡 Time s 푡c Denotes the time at collision s 퐮 Displacement m 퐮(푡) Linear displacement m 4 Symbol Description Units ‖퐮AP*퐧‖ Length of the Perpendicular Vector to the Contact Displacement m Vector of Rigid Body A ‖퐮BP*퐧‖ Length of the Perpendicular Vector to the Contact Displacement m Vector of Rigid Body B 퐮OB Displacement vector between the origin and point B m 퐯 m Velocity s 퐯 푡 m ( ) Linear velocity s Δ퐯 m Change in velocity s 퐯AP m Velocity of the Point of Collision P in Body A s 퐯BP m Velocity of the Point of Collision P in Body B s 퐯 m 1 Velocity of the First Body s 퐯 m 2 Velocity of the Second Body s 퐯 m A Velocity at Point A s 퐯 m B Velocity at Point B s 퐯 AB m f Final Relative Velocity Between Rigid Bodies of A and B s 퐯 AB m i Initial Relative Velocity Between Rigid Bodies of A and B s 퐯 m 푗 Velocity of the J-Th Body s 퐯 m O Velocity at Point Origin s 훼 rad Angular acceleration s2 훼 rad 푗 J-Th Body’s Angular Acceleration s2 휃 Angular displacement rad 흉 Torque Nm 흉푗 Torque applied to the j-th body Nm 휔 rad Angular velocity s 휙 Orientation rad Table 2: Table of Symbols 1.3 Abbreviations and Acronyms Abbreviation Full Form 2D Two-Dimensional 3D Three-Dimensional 5 Abbreviation Full Form A Assumption CM Centre of Mass DD Data Definition GD General Definition GS Goal Statement Game Physics game physics library IM Instance Model LC Likely Change ODE Ordinary Differential Equation R Requirement SRS Software Requirements Specification TM Theoretical Model UC Unlikely Change Uncert. Typical Uncertainty Table 3: Abbreviations and Acronyms 2 Introduction Due to the rising cost of developing video games, developers are looking for ways to save time and money for their projects. Using an open source physics library that is reliable and free will cut down development costs and lead to better quality products. The following section provides an overview of the Software Requirements Specification (SRS) for Game Physics. This section explains the purpose of this document, the scope of the requirements, the characteristics of the intended reader, and the organization of the document. 2.1 Purpose of Document The primary purpose of this document is to record the requirements of the game physics library. Goals, assumptions, theoretical models, definitions, and other model derivation information are specified, allowing the reader to fully understand and verify the purpose and scientific basis of Game Physics. With the exception of system constraints, this SRS will remain abstract, describing what problem is being solved, but not how to solve it. This document will be used as a starting point for subsequent development phases, in- cluding writing the design specification and the software verification and validation plan. The design document will show how the requirements are to be realized, including decisions on the numerical algorithms and programming environment. The verification and validation plan will show the steps that will be used to increase confidence in the software documen- tation and the implementation. Although the SRS fits in a series of documents that follow the so-called waterfall model, the actual development process is not constrained in any way. 6 Even when the waterfall model is not followed, as Parnas and Clements point out [8], the most logical way to present the documentation is still to “fake” a rational design process. 2.2 Scope of Requirements The scope of the requirements includes the physical simulation of 2D rigid bodies acted on by forces. 2.3 Characteristics of Intended Reader Reviewers of this documentation should have an understanding of rigid body dynamics and high school calculus. The users of Game Physics can have a lower level of expertise, as explained in Sec:User Characteristics. 2.4 Organization of Document The organization of this document follows the template for an SRS for scientific computing software proposed by [6] and [10]. The presentation follows the standard pattern of presenting goals, theories, definitions, and assumptions. For readers that would like a more bottom up approach, they can start reading the instance models and trace back to find any additional information they require. The goal statements are refined to the theoretical models and the theoretical models to the instance models. 3 General System Description This section provides general information about the system. It identifies the interfaces between the system and its environment, describes the user characteristics, and lists the system constraints. 3.1 System Context Fig:sysCtxDiag shows the system context. A circle represents an entity external to the software, the user in this case. A rectangle represents the software system itself (Game Physics). Arrows are used to show the data flow between the system and its environment. The interaction between the product and the user is through an application programming interface. The responsibilities of the user and the system are as follows: • User Responsibilities – Provide initial conditions of the physical state of the simulation, rigid bodies present, and forces applied to them. – Ensure application programming interface use complies with the user guide. 7 Figure 1: System Context – Ensure required software assumptions are appropriate for any particular problem the software addresses. • Game Physics Responsibilities – Determine if the inputs and simulation state satisfy the required physical and system constraints. – Calculate the new state of all rigid bodies within the simulation at each simulation step. – Provide updated physical state of all rigid bodies at the end of a simulation step. 3.2 User Characteristics The end user of Game Physics should have an understanding of first year programming concepts and an understanding of high school physics. 3.3 System Constraints There are no system constraints. 4 Specific System Description This section first presents the problem description, which gives a high-level view ofthe problem to be solved.