Physically Based Modelling And Simulation

As digital modeling technology develops and computational power of CPUs and GPUs grows rapidly,people are seeking for sophisticated object models and more phys-ically real animations.Physically based simulation has emerged in the late eighties out of the need to make animations more physically plausible and to free animator from explicitly specifying the motion of complex passively moving objects.It becomes a significant and active research field in computer graphics and is applied widely in com-puter aided geometry design,computer vision,animated film,virtual reality,3D print-ing,medical apparatus,and so on.Physically based simulation techniques allow users to make real object models which meet the specified physical properties and reduce the labor and time costs.With the development of digital geometry processing and appli-cation of numerical solution to differential equation in computer animations,more and more physically based simulation and modeling problems get solved.For the flower blooming simulation,earlier methods are either based on stop-motion frame-by-frame modeling or based on complicated plant growth parameters in simulations.These methods usually cost a lot of time and labors,they not only require users to have experienced skills in modeling software but also need users to master much botanical knowledge and limit the possibilities of users.We present a boundary-dominant flower blooming simulation method which based on the biological observations that flower opening is usually driven by a boundary-dominant morpholog-ical transition in a curved petal.In this method we take a petal as a thin plate and apply mass-spring system which includes stretching energy and bending energy to simulate its physical motion.We use in-plane growth to induce the petal to open outwards and em-ploy out-of-plane growth to assist to control the curvature of opening petals.With some suitable hypothesis we reduce the growth parameters into a growth curve,which sim-plifies the parameter setting process,to control the blooming simulation.Our method allows the angle between petal and receptacle to increase automatically and produces convincing flower opening animations.In addition,our method can generate waves on petal boundaries,making flower more beautiful and natural.Optionally,our method can use connected springs,which connect vertices on different flower bud model,to simulate the forbidding force at initial blooming stage to produce pop-up opening ef-fects.In Chapter 4 we provide a method based on planar hydrodynamic particles to sim-ulate motion of water puddle.Water puddle is a natural phenomenon and usually has visible height.A small amount of water under attraction of molecules accumulates and forms the puddle membrane.For puddle's simulation,earlier methods usually take days to complete a scene or rely on accurate puddle mesh surface to make simulation sys-tem fast and stable.In our method,we use planar hydrodynamic particles to drive the motion of water puddle.Coupling physical factors,such as puddle area and gravity,with static puddle's Yong-Laplace equation,we take the puddle simulation as an en-ergy minimization problem.Since the final energy is quadratic we only need to solve a positive definite sparse linear system in each simulation iteration,enabling interactive application.Besides,we use stable smoothed particle hydrodynamics in the plane,so our method is unconditionally stable.For a given scene,it is relatively easy to run the simulation forwards in time,how-ever,it is usually difficult to solve an inverse problem in dynamic modeling and simu-lation.In Chapter 5 we present a method for deformable object modeling based on elas-tic micro-structure.The cardiovascular stent structure inspires us to design basic elas-tic micro-structures,which we call as basic elements,to synthesize deformable object shapes.We are trying to solve an inverse problem that given source and target shapes which basic elements are needed to synthesize the source shape with the requirement that source shape can be deformed into target shape with some external constraints.We form this problem as an energy minimization and use genetic algorithm to optimize ba-sic elements for source shape,making the source shape deform into target shape as close as possible.The selection of basic elements in genetic algorithm is equivalent to select different elastic micro-structures,and the optimization is guaranteed to be monotone decreasing.