The division by zero is indeed a problem with this approach. E.g. the Ember raytracer just uses FLT_MIN if one of the direction elements is zero (at least in one of their older versions). Another option is to use the Separating Axis Test (SAT) for ray/box instead. This will not clip the ray though, but only provide a boolean answer whether the ray intersects the box. I use this in most of my tree traversals as I found it faster and more robust.
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Dirk Gregorius
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#5313392 problem with ray/box intersection in GLSL
Posted by Dirk Gregorius on Today, 10:12 AM
#5313385 When should I use int32_t ranther than int
Posted by Dirk Gregorius on Today, 09:17 AM
You are correct about the warning. You can cast the to integer, but this is ugly as well . We don't use the STL at work and I also don't use it personally and the size type is int. I think Mike Acton formulated it perfectly at the C++ conference a while ago. "The STL doesn't solve our problems".
I totally agree with you on the strong typing! Personally I believe that code should be written for *readability*. This helps with maintaining large code bases over decades. It also helps with managing complexity. It helps with productivity since you enable more team members to work on a larger number of problem in the code base. auto is orthogonal to all of this in my opinion. E.g.
int x = 5;
This is clear. I read over this and I now know that x is a signed integer.
auto x = 5;
What type is x now? Can I write x = 5 or will this overflow. The int specifier is somewhat redundant from the perspective of the compiler, but for a programmer this is useful information. Sure, we know that 5 is int, but not every programmer on a team is a language expert. I am not saying auto is not useful. Personally I use it for lambda's and if I use STL for some of iterator types, but currently auto is truly overused in the suggestions and explanations I am reading. And the ferrous example above shows perfectly how it easily can lead to misunderstandings.
#5313122 When should I use int32_t ranther than int
Posted by Dirk Gregorius on 28 September 2016  05:07 PM
#5313058 Turning a Physics degree into Game Development material
Posted by Dirk Gregorius on 28 September 2016  10:52 AM
I actually took a very similar route. I studied constructional engineering in college and discovered my joy in programming when I was about half through my classes. Changing my major wasn't an option so I specialized in Computational Engineering and taught myself all about programming in my spare time myself. My first job in the industry was writing a physics engine for the PS3 so my specialization helped me actually a lot. So there are quite a few possibilities for you like Havok/MS or PhysX/nVidia to get a foot into the industry with you background. There are also quite a few game studios looking for people with background in physics.
For me personally I decided I wanted to become a physics/collision/animation specialist as this fitted my background well. I also got interested in tools programming recently. It seems popular to write 'an engine' as a student, but from my experience this is the least interesting problem to solve. It is better to take a more specialized (kind of unsolved) problem and add that to Unity or Unreal and show this in portfolio. On the other hand you say you want to make a game. So if you are more interested in the design process this would be a more orthogonal to your education, but I don't believe this would be a problem. I recommend to figure out in what part of the development process you are interested and then become good at it. Your education will not be the reason if you don't succeed in my opinion.
#5312167 Question about Jacobian in Joint Constraint formula
Posted by Dirk Gregorius on 23 September 2016  02:34 PM
It looks nearly correct. I think you just have the signs and dimension a bit mixed up. Here is how to derive the constraint.
// Position constraint
C = pb  pa
// Velocity constraint (is the time derivative of the position constraint)
dC/dt = pb/dt  pa/dt
= vb + wb x rb  va  wa x ra
= vb  rb x wb  va + ra x wa
= vb  skew( rb ) * wb  va + skew( ra ) * wa
The velocity constraint has a special form:
dC/dt = del_C / del_x * dx /dt + del_C / del_t = J * v + del_C / del_t
If the velocity constraint doesn't depend explicitly on time (del_C / del_t = 0)  which it doesn't in our case  this simply becomes.
dC/dt = J * v
So finally we can find the Jacobian by inspection:
J = [ 1 skew( ra ) 1 skew( rb ) ]
There are a couple of things here. v the the linear velocity at the center of mass and w (read omega) is the angular velocity. r are the offset vectors (lever arms) from the center of mass to the constrained points and skew( r ) is the cross product matrix such that r x w = skew( r ) * w. Also note that '1' is not a vector, but the identity matrix. The Jacobian is a 3 x 12 matrix. If you build the effective mass matrix Me^1 = J * W * JT the result will be a 3x3 matrix. You can solve the constraint as 3D block using e.g. sequential impulses. Also for clarification del_ is the *partial* derivative. If you are interested in the math check here: https://en.wikipedia.org/wiki/Total_derivative
There were plenty of great talks about this at the GDC Physics tutorial over the last years. In particular I would check out the talks by Erin Catto and Richard Tongue. You can find all presentations here: http://box2d.org/downloads/
#5312005 Question about Jacobian in Joint Constraint formula
Posted by Dirk Gregorius on 22 September 2016  06:26 PM
Your observation is absolutely correct. Choosing a constraint function such that the Jacobian is not defined if the constraint error is zero (C = 0) is a very poor choice. For exactly the reasons you describe. Usually a distance constraint is formulated like C = pb  pa  L. If L is reasonable large the Jacobian will be fine. Also note that the correct constraint to hold two points coincident is C = pb  pa. The later is 2d/3d constraint (hence the bold notation).
The reason is that the 1d distance constraint is not only a poor choice because it is undefined when C = 0. Let's assume we actually had a small displacement and get a valid Jacobian. The constraint can only handle forces along the offset vector of the two connected points. If you apply a force orthogonal to that direction the constraint will not handle this as expected and the objects will drift apart until the constraint will handle this in the next frame.
#5311102 3D Manipulators/Gizmos in DirectX
Posted by Dirk Gregorius on 16 September 2016  12:12 PM
What you are looking for is called 'Direct Manipulation'. I liked this resource: http://www.codeproject.com/Articles/35139/InteractiveTechniquesinThreedimensionalScenes
There was also a Sigraph course 2002: https://www.siggraph.org/s2002/conference/courses/crs20.html
It was downloadable, but I cannot find it anymore. Maybe your GoogleFu is better than mine. Otherwise PM me and I send you the PDF
#5311099 Continous collision for plane of triangles vs AABB
Posted by Dirk Gregorius on 16 September 2016  12:04 PM
1) Conservative Advancement (B.Mirtich)
2) Bracketed Advancement (E. Catto)
3) Convex Cast (G. v. d. Bergen)
4) Special case version using continuous SAT
They all use basically the same idea. The first two require a stable version of GJK to compute distance inside the loop. If you have only linear movement (no rotation) CA is great as the root finding is trivial. For CCD with rotation CA has problems and might iterate forever and even might not find a solution. This is solved in bracketed advancement. A pathological example would be an icehockey pug spinning in place.
If you are not into this topic a lot what I am saying might not make sense to you. This is a pretty large topic and here are some suggestions for reading:
1) B. Mirtich's PhD explaining CA: http://www.kuffner.org/james/software/dynamics/mirtich/index.html
2) E. Catto's GDC presentations: http://box2d.org/files/GDC2013/ErinCatto_GDC2013.zip
3) Gino has a couple of great presentation here: http://dtecta.com/publications
In particular:
Ray Casting against General Convex Objects with Application to Continuous Collision Detection: http://dtecta.com/papers/unpublished04raycast.pdf
Continuous Collision Detection of General Convex Objects under Translation: http://dtecta.com/papers/gdc2005_Gino_vandenBergen.pps
4) There might be special version for swept AABB vs triangle. I would check Christer Ericson's book: 'RealTime Collision Detection'
HTH,
Dirk
#5311038 Continous collision for plane of triangles vs AABB
Posted by Dirk Gregorius on 16 September 2016  12:26 AM
#5309581 Quaternion multiplication
Posted by Dirk Gregorius on 05 September 2016  07:41 PM
Let's define a quaternion like this:
struct Quaternion { Vector3 v; float s; };
Then the quaternion product is defined as:
Quaternion operator*( const Quaternion& q1, const Quaternion& q2 ) { Quaternion result; result.v = cross( q1.v, q2.v )+ q1.s * q2.v + q2.s * q1.v; result.s = q1.s * q2.s  dot( q1, q2 ); return result; }
Both your functions are equivalent. The vector'ish form is just less usual in literature in my experience. If you write the definition above componentwise you will get the same result!
#5308938 Resolving and Remembering Collisions
Posted by Dirk Gregorius on 31 August 2016  07:30 PM
Here is how continuous physics works in a nutshell. We start with the general discrete solver step:
1) You integrate external forces (e.g. gravity)
2) You solve the joint and contact constraints
3) You integrate the velocities to find the new positions
Of course we might have tunneled right now. So in a continuous solver the new positions are tentative and we now enter the continuous part of the solver:
1) For each shape you build the swept AABB and add it into the broadphase.
2) For each contact you compute and cache the TOI
3) You advance the bodies to the minimum TOI, build the contacts and solve them
4) You invalidate the cached TOI for the involved bodies and recompute them
5) Repeat from 3) until you have reached the end of the timestep
I left out a lot of detail, but this is the general idea. Note that you still need to run the normal contact phase before entering the continuous phase.
So to answer you question. Yes, of course you need to compute the contact at each TOI.
HTH,
Dirk
#5308403 Resolving and Remembering Collisions
Posted by Dirk Gregorius on 28 August 2016  07:22 PM
After you compute a TOI you need to make sure to move the shapes 'close enough' such that the contact generation doesn't fail. E.g. the classical error is to advance the shapes to the determined TOI and when running the contact creation routine you end up an empty manifold. This will lead to the object tunneling out of the world even though you determined the correct TOI. In order to to handle this my contact creation routing considers shapes withing some margin touching and builds the manifold. I use an adjusted SAT which can handle small separations.
For me the major source of failure in the TOI computation using any form of conservative advancement was the GJK. If you run a GJK with some epsilon tolerance to support e.g. quadric shapes you run into a numerical nightmare with 32bit floating precision. So in Rubikon I only support spheres, capsules, hulls and meshes and the GJK implementation continues until it doesn't make any absolute progress getting me as close as possible. With this I haven't seen any numerical problems in practice. Note that spheres can be handled as points and capsules as segments and the radius is handled afterwards.
Erin's GJK and TOI actually address these problems, though they might not be explicitly mentioned here:
http://box2d.org/files/GDC2013/ErinCatto_GDC2013.zip
http://box2d.org/files/GDC2010/GDC2010_Catto_Erin_GJK.pdf
I gave a presentation a GDC on contact creating in general which might also be helpful:
http://media.steampowered.com/apps/valve/2015/DirkGregorius_Contacts.pdf
Finally I recommend studying the Box2D continuous physics solution. It addresses a lot of problems with continuous physics. You will find a great example of substepping there as well which I didn't discuss in my answer here.
HTH,
Dirk
#5305644 need a algorithm to update skin mesh global AABB
Posted by Dirk Gregorius on 13 August 2016  11:52 AM
Usually the artists also define a worstcase AABB which gets exported with the model. This AABB would fully contain the model in every possible pose. You really don't want to update the AABB at runtime.
#5303892 How To Correctly Caluclate Compression Speed For Damping?
Posted by Dirk Gregorius on 03 August 2016  08:07 PM
I would think the relative velocity along the spring axis.
#5302835 Stackoverflow And Money
Posted by Dirk Gregorius on 27 July 2016  07:34 PM
This is a solid pay, but you can make 23 times of this in the US as programmer (base salary, bonus and stocks).