Realistic Plant Leaf Animation Using Position-based Dynamics

In the real world,plants are an important part of natural scenes.Plants can show various postures when interacting with the natural environment,such as swaying when they interact with the wind,or bending and deforming when branches and leaves are crushed.The key to the realistic animation simulation of plants lies in its branches and leaves.The realistic of the leaves is very important for the overall effect of the dynamic simulation of plants.The existing plant animation research only focuses on the whole,and the simulation research on the details of plant organs such as leaves is not in-depth.And traditional simulation algorithms take a long time to solve the equation of motion,and cannot perform real-time simulation interaction.Therefore,how to construct an efficient,stable and realistic plant leaf simulation method is an urgent problem to be solved in plant animation simulation.Based on the analysis of classical plant leaf animation simulation methods,this thesis studies a leaf animation simulation method based on position constraints,which has the advantages of high efficiency,stability and easy control.Combining the extended position-based dynamics with the proposed vein constraint construction method,the simulation algorithm is improved and optimized to achieve better animation effects.The main work is as follows:(1)Plant leaf geometric constraints construction and processing.Work around the realistic leaf model to study and analyze the difference between the structure of plant leaves and ordinary simulated objects.A realistic leaf model is reconstructed using an image-based reconstruction method,A realistic leaf model is reconstructed using an image-based method,and the skeleton support of the veins is considered when the leaf is deformed by external force.The position-based geometric constraint method is used to control the deformation coefficient of the leaf vein independently,and based on the idea of non-uniform distribution of the constraint coefficient,a realistic leaf animation is generated with the leaf vein as the skeleton.(2)Construction and solution of plant leaf dynamics system.The leaf mesh is processed using a triplet and the dynamic model of the leaf is constructed.A plant leaf simulation system is constructed with the leaf dynamics model as the core,and the Gauss-Seidel iteration method of nonlinear projection is used to solve the constraint equation of the system.The position-based method and the implicit Euler method are combined to improve the the secondorder Backward Differentiation Formula(BDF2)method,and the motion deformation state of the leaf is updated by the improved BDF2 integral method.The improved BDF2 method can reduce the numerical damping of the system and accelerate the speed of system convergence.(3)Simulation system improvements and optimizations.In order to solve the problem that the traditional position-based method is affected by the system iterations and time step when simulating leaf animation,an extended position-based dynamic method is proposed.The extended position-based method considers the force in the physical sense,simulates the elastic potential energy through geometric constraints,and then derives the elastic potential energy to obtain the elastic force of the system,and introduces the Lagrange multiplier to eliminate the influence of the time step.On this basis,the traditional position-based method and the extended position-based method are optimized respectively using the small step method.The designed animation simulation experiment results for multiple groups of leaves such as tulipifera,maple and cherry trees show that the combination of the position constraint-based leaf simulation method and the realistic leaf model can realize the realism of the support of the leaf vein skeleton,so as to simulate the realistic leaf animation.Combining the non-uniformly distributed distance constraint coefficient and bending constraint coefficient can simulate different motion deformation,and is suitable for different kinds of plant leaves.The method in this thesis combines the extended position-based method to solve the problem that the leaf stiffness is affected by the number of iterations and the time step.After using the small step algorithm to optimize the system,a fast and stable interactive simulation is better achieved.