I personally prefer Velocity Verlet for most simulations. In my experience with this method, it is quite suitable for pretty stiff equations. It seems like this "improved Euler" method is pretty similar to the Velocity Verlet one and relies on a class of integration methods known as predictor-corrector. You can read a lot of things on these methods nowadays, starting with David Baraff's "Large steps in cloth simulation" where the power of implicit methods really shines. Their downfall is that you:

1. have to approximate Jacobians or Hessians and then have to,
2. compute a fair amount of matrix inverses per frame.

So if you're not a math guru, you could get your fingers stuck. Just experiment with whichever method you want and then settle for the one that seems to perform best for you. Simple is not always better, but for interactive framerates I only know one word: compromise.

Some additional resources you might want to look at:

• Jakobsen's "Advanced Character Physics"
• James McCarthy's "Comparison of Simulation Techniques using Particle Systems"

Jakobsen is a sort of genius for coming up with such a simple idea for pretentious problem (his specialty is Cryptography if not mistaking, but he succeeded in proving the mathematical equivalence of his method to a class of Gauss-Seidel iterative algorithm, which is convergent). For simplicity, go for this first before delving deep into implicit methods.

I personally prefer Velocity Verlet for most simulations. In my experience with this method, it is quite suitable for pretty stiff equations. It seems like this "improved Euler" method is pretty similar to the Velocity Verlet one and relies on a class of integration methods known as predictor-corrector. You can read a lot of things on these methods nowadays, starting with David Baraff's "Large steps in cloth simulation" where the power of implicit methods really shines. Their downfall is that you:

1. have to approximate Jacobians or Hessians and then have to,
2. compute a fair amount of matrix inverses per frame.

So if you're not a math guru, you could get your fingers stuck. Just experiment with whichever method you want and then settle for the one that seems to perform best for you. Simple is not always better, but for interactive framerates I only know one word: compromise.

Some additional resources you might want to look at:

• Jakobsen's "Advanced Character Physics"
• James McCarthy's "Comparison of Simulation Techniques using Particle Systems"

Jakobsen is a sort of genius for coming up with such a simple idea for pretentious problem (his specialty is Cryptography if not mistaking, but he succeeded in proving the mathematical equivalence of his method to a class of Gauss-Seidel iterative algorithm, which is convergent). For simplicity, go for this first before delving deep into implicit methods.

LATER EDIT: I recently got a paper on this issue of using explicit integrators for soft or semi-rigid body simulation and what their performance and quality impact is. This paper should serve as a guide for choosing a certain integrator, depending on the scenario.

I personally prefer Velocity Verlet for most simulations. In my experience with this method, it is quite suitable for pretty stiff equations.. It seems like this "improved Euler" method is pretty similar to the Velocity Verlet one and relies on a class of integration methods known as predictor-corrector. You can read a lot of things on these methods nowadays, starting with David Baraff's "Large steps in cloth simulation" where the power of implicit methods really shines. Their downfall is that you 1) have to approximate Jacobians or Hessians and then have to 2) compute a fair amount of matrix inverses per frame.. So if you're not a math guru, you could get your fingers stuck. Just experiment with whichever method you want and then settle for the one that seems to perform best for you. Simple is not always better, but for interactive framerates I only know one word: compromise. You should, by the way, read Jakobsen's magisterial paper: http://www.pagines.ma1.upc.edu/~susin/files/AdvancedCharacterPhysics.pdf

http://www.cs.rpi.edu/~cutler/classes/advancedgraphics/F05/assignments/final_projects/mccarj7/index.html

Jakobsen is a sort of genius for coming up with such a simple idea for pretentious problem (his specialty is Cryptography if not mistaking, but he succeeded in proving the mathematical equivalence of his method to a class of Gauss-Seidel iterative algorithm, which is convergent). For simplicity, go for this first before delving deep into implicit methods.

I personally prefer Velocity Verlet for most simulations. In my experience with this method, it is quite suitable for pretty stiff equations. It seems like this "improved Euler" method is pretty similar to the Velocity Verlet one and relies on a class of integration methods known as predictor-corrector. You can read a lot of things on these methods nowadays, starting with David Baraff's "Large steps in cloth simulation" where the power of implicit methods really shines. Their downfall is that you:

1. have to approximate Jacobians or Hessians and then have to,
2. compute a fair amount of matrix inverses per frame.

So if you're not a math guru, you could get your fingers stuck. Just experiment with whichever method you want and then settle for the one that seems to perform best for you. Simple is not always better, but for interactive framerates I only know one word: compromise.

Some additional resources you might want to look at:

• Jakobsen's "Advanced Character Physics"
• James McCarthy's "Comparison of Simulation Techniques using Particle Systems"

Jakobsen is a sort of genius for coming up with such a simple idea for pretentious problem (his specialty is Cryptography if not mistaking, but he succeeded in proving the mathematical equivalence of his method to a class of Gauss-Seidel iterative algorithm, which is convergent). For simplicity, go for this first before delving deep into implicit methods.