# Bullet Dealing with voronoi chunks spat out

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I call on the shatter function and it now has a series of chunks stored, and I can retrieve those to the main physics system. But do I hide the main object and re-construct the fragment pieces into some other brand new game objects or some sort?
Thanks
Jack

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• By kevinyu
Original Post: Limitless Curiosity
Out of various phases of the physics engine. Constraint Resolution was the hardest for me to understand personally. I need to read a lot of different papers and articles to fully understand how constraint resolution works. So I decided to write this article to help me understand it more easily in the future if, for example, I forget how this works.
This article will tackle this problem by giving an example then make a general formula out of it. So let us delve into a pretty common scenario when two of our rigid bodies collide and penetrate each other as depicted below.

From the scenario above we can formulate:
$$\(d = ((\vec{p1} + \vec{r1}) - (\vec{p2} + \vec{r2}) \cdot \vec{n}\$$
We don't want our rigid bodies to intersect each other, thus we construct a constraint where the penetration depth must be more than zero.
$$C: d>=0$$
This is an inequality constraint, we can transform it to a more simple equality constraint by only solving it if two bodies are penetrating each other. If two rigid bodies don't collide with each other, we don't need any constraint resolution. So:
if d>=0, do nothing else if d < 0 solve C: d = 0
Now we solve this constraint by calculating $\Delta \vec{p1},\Delta \vec{p2},\Delta \vec{r1},and \Delta \vec{r2}$ that cause the constraint above satisfied. This method is called the position-based method. This will satisfy the above constraint immediately in the current frame and might cause a jittery effect.
A much more modern and preferable method that is used in Box2d, Chipmunk, Bullet and my physics engine is called the impulse-based method. In this method, we derive a velocity constraint equation from the position constraint equation above.

We are working in 2D so angular velocity and the cross result of two vectors are scalars.
Next, we need to find $\Delta V$ or impulse to satisfy the velocity constraint. This $\Delta V$ is caused by a force. We call this force 'constraint force'. Constraint force only exerts a force on the direction of illegal movement in our case the penetration normal. We don't want this force to do any work, contribute or restrict any motion of legal direction.

$\lambda$ is a scalar, called Lagrangian multiplier. To understand why constraint force working on $$J^T$$ $J^{T}$ direction (remember J is a 12 by 1 matrix, so $J^{T}$ is a 1 by 12 matrix or a 12-dimensional vector), try to remember the equation for a three-dimensional plane.

Now we can draw similarity between equation(1) and equation(2), where $\vec{n}^{T}$ is similar to J and $\vec{v}$ is similar to V. So we can interpret equation(1) as a 12 dimensional plane, we can conclude that $J^{T}$ as the normal of this plane. If a point is outside a plane, the shortest distance from this point to the surface is the normal direction.

After we calculate the Lagrangian multiplier, we have a way to get back the impulse from equation(3). Then, we can apply this impulse to each rigid body.
Baumgarte Stabilization
Note that solving the velocity constraint doesn't mean that we satisfy the position constraint. When we solve the velocity constraint, there is already a violation in the position constraint. We call this violation position drift. What we achieve is stopping the two bodies from penetrating deeper (The penetration depth will stop growing). It might be fine for a slow-moving object as the position drift is not noticeable, but it will be a problem as the object moving faster. The animation below demonstrates what happens when we solve the velocity constraint.
[caption id="attachment_38" align="alignnone" width="800"]
So instead of purely solving the velocity constraint, we add a bias term to fix any violation that happens in position constraint.

So what is the value of the bias? As mentioned before we need this bias to fix positional drift. So we want this bias to be in proportion to penetration depth.

This method is called Baumgarte Stabilization and $\beta$ is a baumgarte term. The right value for this term might differ for different scenarios. We need to tweak this value between 0 and 1 to find the right value that makes our simulation stable.

Sequential Impulse
If our world consists only of two rigid bodies and one contact constraint. Then the above method will work decently. But in most games, there are more than two rigid bodies. One body can collide and penetrate with two or more bodies. We need to satisfy all the contact constraint simultaneously. For a real-time application, solving all these constraints simultaneously is not feasible. Erin Catto proposes a practical solution, called sequential impulse. The idea here is similar to Project Gauss-Seidel. We calculate $\lambda$ and $\Delta V$ for each constraint one by one, from constraint one to constraint n(n = number of constraint). After we finish iterating through the constraints and calculate $\Delta V$, we repeat the process from constraint one to constraint n until the specified number of iteration. This algorithm will converge to the actual solution.The more we repeat the process, the more accurate the result will be. In Box2d, Erin Catto set ten as the default for the number of iteration.
Another thing to notice is that while we satisfy one constraint we might unintentionally satisfy another constraint. Say for example that we have two different contact constraint on the same rigid body.

When we solve $\dot{C1}$, we might incidentally make $\dot{d2} >= 0$. Remember that equation(5), is a formula for $\dot{C}: \dot{d} = 0$ not $\dot{C}: \dot{d} >= 0$. So we don't need to apply it to $\dot{C2}$ anymore. We can detect this by looking at the sign of $\lambda$. If the sign of $\lambda$ is negative, that means the constraint is already satisfied. If we use this negative lambda as an impulse, it means we pull it closer instead of pushing it apart. It is fine for individual $\lambda$ to be negative. But, we need to make sure the accumulation of $\lambda$ is not negative. In each iteration, we add the current lambda to normalImpulseSum. Then we clamp the normalImpulseSum between 0 and positive infinity. The actual Lagrangian multiplier that we will use to calculate the impulse is the difference between the new normalImpulseSum and the previous normalImpulseSum
Restitution
Okay, now we have successfully resolve contact penetration in our physics engine. But what about simulating objects that bounce when a collision happens. The property to bounce when a collision happens is called restitution. The coefficient of restitution, denoted $C_{r}$, is the ratio of the parting speed after the collision and the closing speed before the collision.

The coefficient of restitution only affects the velocity along the normal direction. So we need to do the dot operation with the normal vector.

Notice that in this specific case the $V_{initial}$ is similar to JV. If we look back at our constraint above, we set $\dot{d}$ to zero because we assume that the object does not bounce back($C_{r}=0$).So, if $C_{r} != 0$, instead of 0, we can modify our constraint so the desired velocity is $V_{final}$.

We can merge our old bias term with the restitution term to get a new bias value.

// init constraint // Calculate J(M^-1)(J^T). This term is constant so we can calculate this first for (int i = 0; i < constraint->numContactPoint; i++) { ftContactPointConstraint *pointConstraint = &constraint->pointConstraint; pointConstraint->r1 = manifold->contactPoints.r1 - (bodyA->transform.center + bodyA->centerOfMass); pointConstraint->r2 = manifold->contactPoints.r2 - (bodyB->transform.center + bodyB->centerOfMass); real kNormal = bodyA->inverseMass + bodyB->inverseMass; // Calculate r X normal real rnA = pointConstraint->r1.cross(constraint->normal); real rnB = pointConstraint->r2.cross(constraint->normal); // Calculate J(M^-1)(J^T). kNormal += (bodyA->inverseMoment * rnA * rnA + bodyB->inverseMoment * rnB * rnB); // Save inverse of J(M^-1)(J^T). pointConstraint->normalMass = 1 / kNormal; pointConstraint->positionBias = m_option.baumgarteCoef * manifold->penetrationDepth; ftVector2 vA = bodyA->velocity; ftVector2 vB = bodyB->velocity; real wA = bodyA->angularVelocity; real wB = bodyB->angularVelocity; ftVector2 dv = (vB + pointConstraint->r2.invCross(wB) - vA - pointConstraint->r1.invCross(wA)); //Calculate JV real jnV = dv.dot(constraint->normal pointConstraint->restitutionBias = -restitution * (jnV + m_option.restitutionSlop); } // solve constraint while (numIteration > 0) { for (int i = 0; i < m_constraintGroup.nConstraint; ++i) { ftContactConstraint *constraint = &(m_constraintGroup.constraints); int32 bodyIDA = constraint->bodyIDA; int32 bodyIDB = constraint->bodyIDB; ftVector2 normal = constraint->normal; ftVector2 tangent = normal.tangent(); for (int j = 0; j < constraint->numContactPoint; ++j) { ftContactPointConstraint *pointConstraint = &(constraint->pointConstraint[j]); ftVector2 vA = m_constraintGroup.velocities[bodyIDA]; ftVector2 vB = m_constraintGroup.velocities[bodyIDB]; real wA = m_constraintGroup.angularVelocities[bodyIDA]; real wB = m_constraintGroup.angularVelocities[bodyIDB]; //Calculate JV. (jnV = JV, dv = derivative of d, JV = derivative(d) dot normal)) ftVector2 dv = (vB + pointConstraint->r2.invCross(wB) - vA - pointConstraint->r1.invCross(wA)); real jnV = dv.dot(normal); //Calculate Lambda ( lambda real nLambda = (-jnV + pointConstraint->positionBias / dt + pointConstraint->restitutionBias) * pointConstraint->normalMass; // Add lambda to normalImpulse and clamp real oldAccumI = pointConstraint->nIAcc; pointConstraint->nIAcc += nLambda; if (pointConstraint->nIAcc < 0) { pointConstraint->nIAcc = 0; } // Find real lambda real I = pointConstraint->nIAcc - oldAccumI; // Calculate linear impulse ftVector2 nLinearI = normal * I; // Calculate angular impulse real rnA = pointConstraint->r1.cross(normal); real rnB = pointConstraint->r2.cross(normal); real nAngularIA = rnA * I; real nAngularIB = rnB * I; // Apply linear impulse m_constraintGroup.velocities[bodyIDA] -= constraint->invMassA * nLinearI; m_constraintGroup.velocities[bodyIDB] += constraint->invMassB * nLinearI; // Apply angular impulse m_constraintGroup.angularVelocities[bodyIDA] -= constraint->invMomentA * nAngularIA; m_constraintGroup.angularVelocities[bodyIDB] += constraint->invMomentB * nAngularIB; } } --numIteration; }
General Step to Solve Constraint
In this article, we have learned how to solve contact penetration by defining it as a constraint and solve it. But this framework is not only used to solve contact penetration. We can do many more cool things with constraints like for example implementing hinge joint, pulley, spring, etc.
So this is the step-by-step of constraint resolution:
Define the constraint in the form $\dot{C}: JV + b = 0$. V is always $\begin{bmatrix} \vec{v1} \\ w1 \\ \vec{v2} \\ w2\end{bmatrix}$ for every constraint. So we need to find J or the Jacobian Matrix for that specific constraint. Decide the number of iteration for the sequential impulse. Next find the Lagrangian multiplier by inserting velocity, mass, and the Jacobian Matrix into this equation: Do step 3 for each constraint, and repeat the process as much as the number of iteration. Clamp the Lagrangian multiplier if needed. This marks the end of this article. Feel free to ask if something is still unclear. And please inform me if there are inaccuracies in my article. Thank you for reading.
NB: Box2d use sequential impulse, but does not use baumgarte stabilization anymore. It uses full NGS to resolve the position drift. Chipmunk still use baumgarte stabilization.
References
Allen Chou's post on Constraint Resolution A Unified Framework for Rigid Body Dynamics An Introduction to Physically Based Modeling: Constrained Dynamics Erin Catto's Box2d and presentation on constraint resolution Falton Debug Visualizer 18_01_2018 22_40_12.mp4
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• By -Tau-
Hello, I'm trying to use needBroadphaseCollision to filter collision between moveable objects and player. It works pretty well but there is one problem.

The idea is simple: If an object is still or does not move faster that a threshold, ignore collision with players physical body. In this case I use my own code to update player. If the speed of this object breaks that threshold, convert player to rag-doll and let Bullet do the update.
I'm using my own custom character controller as i couldn't use Bullets. My player is a ragdoll with btRigidBody bodyparts where linear and angular factors are set to 0 and these limbs are updated based on model animation as long as the player has control over their character. As soon as collision with a fast moving object happens, player loses control over their character, linear an angular factors are set to 1 and i let Bullet handle the ragdoll physics.

It works well for most objects but i have an object that uses btCompoundShape for its body. When this object is still, (it didn't move for a while) it works.
However when this object starts to move and doesn't break the speed threshold, it gets affected by players physical body (player starts to push this object around).
I added some debug variables and it seems that even when needBroadphaseCollision returns false, there are still contact points generated between player and this object.
What am i missing?

• I am a beginner in the Game Dev business, however I plan to build a futuristic MMO with some interesting mechanics.
However, I have some doubts about shooting mechanics that I chose for this game and would like to know your opinion on this. The mechanic goes as follows:
- Each gun would have it's damage-per-shot value
- Each gun would have it's shots-per-second value
- Each gun would have it's accuracy rating
Now the question is: how to calculate the output damage? I have three available options:
1) Calculate the chance of each shot hitting the target (per-shot accuracy)
2) Multiply the damage output of a weapon by it's accuracy rating (weapon with 50% accuracy deals 50% of it's base damage)
3) Don't use accuracy at all and just adjust the weapon damage output
Which of these three mechanics would you like to see in a game? Mind, this will be an MMO game, so it will have lock-on targets, AoE effects and all that jazz.

• My AI subsystem is completed dragged by the physics with objects with Gimpact proxies.. When you need to calculate stuff like bumps, it is very horrible...It is even worse than using compound vehicle methods...
Thanks
Jack

• I looked one of the the bullet physics samples which talks about the topic in height field. But however, when the height fields get rendered, the "DemoApplication" class calls the opengl shape drawer object which finally retrieves the display list of the collision shape, which is strongly coupled to opengl, I want to do the same thing with DirectX (D3DX at the moment, damn old, but hey).. How can I draw the height fields out? Is there a way to turn the display list into something recognizable by Direct3D 9?
Thanks
Jack