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R. dell’Erba
18.1 Introduction
It is well known that time evolution of a material particles system is determined by
Newton’s dynamics laws; however, in recent years, especially with the evolution of
computer graphics driven by videogames applications, there has been great interest
in studying the evolution of a particle system whose motion is simply determined
by their relative position in a frame, without solving the differential equations of
dynamics. The name of this method is position-based dynamics (PBD) (Bender
et al. 2015; Bender et al. 2014). This method does not determine forces and solve
differential equations but use a position-based approach, where the new position
of a particle is determined by its neighbor’s positions and can be easily be used to
describe complex object behavior. The physically based simulation of deformable
solids has been an active research topic of computer graphics since many years:
The aim is to simulate the behavior of real materials to achieve graphically realistic
results. The credibility requirements of user interfaces in videogames have generated
a technology, user interface physic, where physical principles are partially enforced
through ad hoc heuristics assumptions and are often implemented without the usual
calculus. The PBD methods result in a physically plausible behavior of the continuum
but suffer from limitations, modeling complex material properties and describing
interactions between heterogeneous bodies (Macklin et al. 2016). But this approach
has many practical applications. For example, a touch screen phone contact list can
be scrolled, by fingers, with a motion based on velocity and list length. Reaching the
end of the list, the motion will bounce as if a collision occurred. The user feels such
behavior very realistic even if the effects are heuristically reproduced and are not a
solution of Newton’s law. Aim of the PBD is not to compute physical process but to
generate visually plausible simulation results with low computational cost (Bender
et al. 2014), sacrificing some accuracy, with respect of solution of heavy equations
by finite element methods (FEM). Some other disadvantages of PBD include low
fidelity, poor adaptability and low interactivity. Therefore, sometimes, a physics
engine, working through integration techniques that are based on Newton’s laws
of motion, is added. The advantage of using PBD is in computational simplicity
and time machine leading to results similar to those obtainable with FEM but in
a much shorter time; it also provides a useful point of view that could be able to
help in understanding what features are important in the deformation without solving
differential equations. They are fast, robust, simple, efficient and easily configurable.
In the beginning, simulations for videogame applications widely used continuum
mechanical methods, solving FEM. Classical methods are based on discretization
(Lagrangian or Eulerian) of Newton’s second law and formulate forces for each
mechanical effect. To obtain robust simulations, very small time steps are required
by these methods; therefore, they cannot be used in interactive situations owing to
the large machine time used. In spite of this, still now, the first approach to simulate
deformable objects by continuum mechanics is to discretize equations and to solve
them using numerical integration. This can be done in several ways, but many of
R. dell’Erba
18.1 Introduction
It is well known that time evolution of a material particles system is determined by
Newton’s dynamics laws; however, in recent years, especially with the evolution of
computer graphics driven by videogames applications, there has been great interest
in studying the evolution of a particle system whose motion is simply determined
by their relative position in a frame, without solving the differential equations of
dynamics. The name of this method is position-based dynamics (PBD) (Bender
et al. 2015; Bender et al. 2014). This method does not determine forces and solve
differential equations but use a position-based approach, where the new position
of a particle is determined by its neighbor’s positions and can be easily be used to
describe complex object behavior. The physically based simulation of deformable
solids has been an active research topic of computer graphics since many years:
The aim is to simulate the behavior of real materials to achieve graphically realistic
results. The credibility requirements of user interfaces in videogames have generated
a technology, user interface physic, where physical principles are partially enforced
through ad hoc heuristics assumptions and are often implemented without the usual
calculus. The PBD methods result in a physically plausible behavior of the continuum
but suffer from limitations, modeling complex material properties and describing
interactions between heterogeneous bodies (Macklin et al. 2016). But this approach
has many practical applications. For example, a touch screen phone contact list can
be scrolled, by fingers, with a motion based on velocity and list length. Reaching the
end of the list, the motion will bounce as if a collision occurred. The user feels such
behavior very realistic even if the effects are heuristically reproduced and are not a
solution of Newton’s law. Aim of the PBD is not to compute physical process but to
generate visually plausible simulation results with low computational cost (Bender
et al. 2014), sacrificing some accuracy, with respect of solution of heavy equations
by finite element methods (FEM). Some other disadvantages of PBD include low
fidelity, poor adaptability and low interactivity. Therefore, sometimes, a physics
engine, working through integration techniques that are based on Newton’s laws
of motion, is added. The advantage of using PBD is in computational simplicity
and time machine leading to results similar to those obtainable with FEM but in
a much shorter time; it also provides a useful point of view that could be able to
help in understanding what features are important in the deformation without solving
differential equations. They are fast, robust, simple, efficient and easily configurable.
In the beginning, simulations for videogame applications widely used continuum
mechanical methods, solving FEM. Classical methods are based on discretization
(Lagrangian or Eulerian) of Newton’s second law and formulate forces for each
mechanical effect. To obtain robust simulations, very small time steps are required
by these methods; therefore, they cannot be used in interactive situations owing to
the large machine time used. In spite of this, still now, the first approach to simulate
deformable objects by continuum mechanics is to discretize equations and to solve
them using numerical integration. This can be done in several ways, but many of