Comparison Supplement to Incremental Potential Contact ...5 HOUDINI We test Houdini with the simple chain example. Each link is a torus with outer radius 1.25 and inner radius 0.28

Comparison Supplement to Incremental Potential Contact: Intersection-and Inversion-free, Large-Deformation Dynamics

MINCHEN LI, University of Pennsylvania & Adobe ResearchZACHARY FERGUSON and TESEO SCHNEIDER, New York UniversityTIMOTHY LANGLOIS, Adobe ResearchDENIS ZORIN and DANIELE PANOZZO, New York UniversityCHENFANFU JIANG, University of PennsylvaniaDANNY M. KAUFMAN, Adobe ResearchACM Reference Format:Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, DenisZorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman. 2020.Comparison Supplement to Incremental Potential Contact: Intersection-and Inversion-free, Large-Deformation Dynamics. ACM Trans. Graph. 39, 4,Article 49 (July 2020), 7 pages. https://doi.org/10.1145/3386569.3392425

1 COMSOLScene Setup. We set up a simple scene to illustrate issues we

encounter for contact modeling in COMSOL. See Figures 1 top andmiddle, for our initial positions where we have, from left to right,a fixed rectangle (0.2 × 0.7m), two free squares (0.5 × 0.5m), and amoving rectangle (0.2× 0.7m) with symmetric boundary conditionsin the y-direction. We impose displacement boundary conditionson the right-most rectangle of −0.6m, use densities of 1000kg/m3

and a linear material model with E = 1000Pa and ν = 0.4. Weexperimented with different discretizations and applications of theboundary conditions. With a quad model we apply the boundaryconditions incrementally (−0.6s) with s going from zero to one, andsteps of size 0.01, while with a triangle mesh we applied steps of0.005. The first four figures in Figure 1 show respectively the initialconfigurations and the solutions for these two experiments, thelast figure shows increased failure if we simply apply the boundaryconditions directly without incremental loading.

Discussion. In COMSOL, we initially attempted to simulate dy-namic contacts. However, the contact formulation is documented asbeing strictly valid only for stationary problems [?, Time-DependentContact Analysis, Page 199]. We then attempted to solve a simplerstationary problem. We take two cubes compressed by two rectan-gle, again, as above, one fixed, and one displaced. After an extensivecorrespondence with COMSOL technical support (see Additional

Authors’ addresses: Minchen Li, University of Pennsylvania & Adobe Research,[email protected]; Zachary Ferguson; Teseo Schneider, New York University;Timothy Langlois, Adobe Research; Denis Zorin; Daniele Panozzo, New York Univer-sity; Chenfanfu Jiang, University of Pennsylvania; Danny M. Kaufman, Adobe Research,[email protected].

Permission to make digital or hard copies of all or part of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for components of this work owned by others than ACMmust be honored. Abstracting with credit is permitted. To copy otherwise, or republish,to post on servers or to redistribute to lists, requires prior specific permission and/or afee. Request permissions from [email protected].© 2020 Association for Computing Machinery.0730-0301/2020/7-ART49 $15.00https://doi.org/10.1145/3386569.3392425

Material), we were told to apply a few necessary “tricks”: (i) sincethe problem is symmetric, it is better to cut it in half and imposesymmetry boundary conditions; (ii) the mesh on the destinationobject should be twice as fine as the mesh on the source objectalong all contact interface boundaries; (iii) the scene should be de-signed so that there are no initial gaps between the objects thatare in contact (no changing contact sets); (iv) the system shouldbe solved applying an auxiliary sweep with small parametric steps,and so apply the displacement incrementally. Applying all of theseadditional customized tricks we were able to solve the simulationwith both COMSOL’s penalty and augmented Lagrangian options.Our experiments, agreeing with COMSOL technical support, showthat the number of parametric steps that must be applied dependon the mesh size, with different values (larger or smaller) leadingto reasonable solutions or not that must be discovered per example.For both simulations penetration is expected, more, we observe forthe penalty method, as intersection is how contact pressure devel-ops in the solver. Additionally, we learned that it is never a goodidea to have corners being a part of a contact boundaries, as thecorners will be numerically singular and cause penetration betweenthe contact boundaries. Thus, according to COMSOL guidelines1corners should be filleted.

2 ANSYSScene Setup. We again set up two simple problems to test contact

modeling in ANSYS. For the first example we generate a “C”-shapedmesh (formed from 5 10×10×10mm cubes) supported on the bottomand a dropped cube (10 × 10 × 10mm) subject to gravity 981mm/s2.For the second example we placed a large cube (14 × 14 × 14mm)with fixed support on the bottom and placed a smaller cube on top(10 × 10 × 10mm), beveled at 1mm; both were subject to gravity of100mm/s2. Both set ups apply densities of 10−6kg/mm3 and neo-Hookean material with E = 0.01MPa and ν = 0.4. Figure 2 showsthe two set ups and the resulting simulation failures. Note for thesecond experiment the spacing between the two objects is 1mm,from the plot on the bottom we see that the top, falling cube has amaximum displacement of more than 1.4mm for an implicit timestep, and 1.02mm for an explicit time step.

Discussion. ANSYS provides explicit (through its explicit dynam-ics modules) and implicit (through its transient structural module)

1https://www.comsol.com/support/knowledgebase/1102

ACM Trans. Graph., Vol. 39, No. 4, Article 49. Publication date: July 2020.

https://doi.org/10.1145/3386569.3392425

https://doi.org/10.1145/3386569.3392425

https://www.comsol.com/support/knowledgebase/1102

49:2 • Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman

Fig. 1. Experiment setup (first and third figure) and results (second andfourth figure) of our COMSOL experiment. Disabling the incremental ap-plication of the boundary conditions leads to massive penetrations (lastfigure).

numerical time-integration options. The two models are fundamen-tally different in the way they handle collisions, but they both allowfor small inter-penetrations. The explicit module is mostly auto-matic both in how it detects possible contact pairs and then resolvesthem. The results of the simulations are reasonable, although they docontain some small penetrations. The implicit module, is more com-plex, requires identifying contact pairs and much hand- tweaking ofmany exposed parameters in order to gain a successful simulation.This is true even for a simple scenario where two cubes are colliding.Here the default parameters do not produce a reasonable solution.

Fig. 2. First and second Ansys experiment (first and third image). All exper-iments all have inter-penetration. The second-to-last image applies implicittime-stepping, and the last one explicit time-stepping.

For such simple scenarios ANSYS technical support advised us toapply explicit dynamics and did not provide us with a reasonableset of parameters to fix the implicit simulation.


Comparison Supplement to Incremental Potential Contact: Intersection- and Inversion-free, Large-Deformation Dynamics • 49:3

Fig. 3. Utopia setup coarse and fine mesh (first two image). Closeup on thetwo failures (third image has self-penetration because of large time stepand fourth image has oscillations that prevent the solver the continue) forthe coarse mesh.

Fig. 4. Left: SOFA is able to simulate a five link even with large timesteps.Right: As we add more links, decreasing time steps down to 10−4s, we areunable to find a time step that will not break the chain.

3 UTOPIA [?]Scene Setup. To investigate Utopia we set up a simulation with a

large 10 × 10 × 10m block with fixed displacement on the bottomand a small cube 1 × 1 × 1m with a half-sphere on the bottom andprescribed −1.5N force on the top flat face. See Figure 3. Both objectshave the same neo-Hookean material parameters: density 1kg/m3,λ = 10Pa, µ = 10Pa. in Figure 3 we show the initial set up and theresulting penetration and oscillations for the coarse mesh version.Note that oscillations disappear for the fine mesh and penetrationsdecrease as we go to smaller time steps. We tested time steps of 0.5,0.05, 0.01, and 0.001s.

Discussion. Utopia applies a parallel mortar algorithm for FE con-tact modeling. Like several other engineering FEM codes, UTOPIArequires a priori manual marking of all possible paired mesh bound-ary regions that can be treated for contact resolution. Such markingcould be automated, see e.g, Yang and Laursen [?]). Note that evenwith automated pairing the mortar approach does not yet extendfor more general collisions in regions that would involve more thantwo distinct surface regions. We tested the UTOPIA implementa-tion [?] with a simple didactic experiment in which we drop anelastic sphere under gravity upon an elastic cube with its bottomDOF fixed. At larger time steps, we observe large scale volume in-tersections. These contact errors then reduce but do not disappearas time step decreases. These issues are not surprising as mortarmethods enforce contact constraints in a weak sense and so allowintersections.

4 SOFAWe modify the the chain example provided with SOFA, replacingthe ring mesh with simple, low-resolution tori (∼500 tetrahedra).Table 1 shows the material settings used. Changing any of these

Fig. 5. We test SOFA on a five link chain with three varying stiffnesses, allwith a fixed timestep of 10−3s. Left: Young’s Modulus of 100 fails, Middle:Young’s Modulus of 1000 works, Right: Young’s Modulus of 10000 fails.

parameters can result in different levels of failure (see Figure 5 foran example of changing material stiffness).

Elasticity Model linearYoung’s Modulus 1000Poisson’s Ratio 0.3Mass 5.0

Table 1. SOFA FEM parameter values

5 HOUDINIWe test Houdini with the simple chain example. Each link is a toruswith outer radius 1.25 and inner radius 0.28. The links are duplicatedwith a transform downwards of 1.62 and a rotation of 90 degrees.One ring at the top is added as a static surface collider. Parametervalues that were changed from default Houdini parameters for theFEM solver are shown in Table 2 and values for the vellum solverare shown in Table 3. The scene was set to 24 FPS.

Damping Ratio 0.5Shape Stiffness 387Volume Stiffness 384Repulsion 1e11Friction 0.1Substeps 14Collision Passes 16

Table 2. Houdini FEM parameter values

6 SQP BENCHMARKThe table at the bottom of this document summarizes the results ofour benchmark comparison of different SQP-type contact handlingmethods. For each scene we vary the time step size, constraint offset,constraint type, and solve the problem as both a fully nonlinearproblem at each time step and a quadratic approximation (Linearizedelasticity) of the energy with nonlinear constraints. See our mainpaper for details.

Additionally, we also initially tested two active-set update strate-gies: the first being to clear the active set and rebuild it upon everyiteration and the second, applied successfully in recent methods[??] incrementally adds newly detected collisions to the active set.



Cloth Node Struts Node Solver NodeMass Calculate Varying Direction Jitter 2 Substeps 40Thickness Calculate Uniform Constraints Per Point 80Stretch Stiffness 1000000 Stretch Stiffness 1e-9Bend Stiffness 1e-4 Compression Stiffness 10000

Table 3. Houdini Vellum parameter values that were changed from default

Fig. 6. Intersections. Severity of intersections affect usability of simulationresults. Left: Examining a chain drop the results look correct until we lookinside the top ring. It is clear the fixed ring has started to intersect thetop FEM ring. These small intersections can build in to larger constraintdrift and eventually pass-through of the rings. Middle: At first glance theresults of this mat twist appear fine, but when we look closely there areseveral small intersections hidden in the folds of the mat (22 in total). Right:An extreme case of intersections where the two tetrahedron meshes havealmost completely overlapped.

We found that the latter performed significantly better across ourbenchmark so we restrict our results here to the latter.

In the table we document results of each simulation as either: 1)intersecting: the simulation fails with some amount of intersection(see Figure 6 for examples of minor andmajor intersections); 2) blow-up: the simulation blows up due to rapid growth in energy and/ordisplacement during the optimization (see Figure 7 for examples);3) incomplete: the simulation is unable to complete in the giventime limit of four hours, or 4) successful: the simulation successfullycompletes with none of the aforementioned failures. Note that IPCis the only method to succeed across all simulations.

6.1 IntersectionsSQP-type optimizations can result in intersection for a variety ofreasons, but they are commonly generated in cases where the timestep is too large (leading to poor linearization of constraints) or theconstraint offset is too small (allowing slight solver inaccuraciesto generate drift and intersections). While possible in lucky cases,recovering from intersections is generally rare on it sown and ofcourse challenging to fix algorithmically.

Not all intersections are alike, however. Minor intersections whilenot physical are commonly ignored as they do not affect visualquality. Figure 6 shows examples of both minor and egregious in-tersections.

6.2 Optimization blow-upOptimization “blow-up” occurs when the objective energy or searchdirection of the optimization increases at alarming rates due tonumerical difficulties. Studying the results of our sweep, we findthat blow-ups more often occur with large time steps where a large

Fig. 7. Explosions. Top: Two different examples (left and right) with theirtime steps right before the SQP optimization starts to fail with increasinglylarge displacements. Bottom: An intermediate state for each example duringthe SQP optimization “blow-up”.

number of constraints may be activated at once. This can create adifficult, if not numerically infeasible, optimization problems andlikewise instability due to lack of line search.We also note the large amount of blow-ups when applying the

single quadratic approximation per time step. While faster to opti-mize, this method is a poor approximation of the nonlinear elasticityenergy and leads to increased energy values. Again, the problem isworsened in all cases by the lack of line-search to find a step lengththat sufficiently decreases the energy.

6.3 Poor convergence and subsequent timeoutIn our benchmark, SQP-type methods struggle to handle moderatelylarge scenes. We attribute this poor performance to 1) large numbersof constraints when the constraint offsets are enabled – this, in turn,can lead to infeasibility in the QP solve and so subsequent solvefails; and 2) oscillating optimization iterations largely resulting fromlack of line-search. When the underlying QP solver fails, we chooseto clear and build a new active set. While this helps in some cases, itoften results in more QP fails and a stagnant optimization. Conver-gence could be improved with a line-search along the constrainedsearch directions, but suitable merit-functions for line search hereremain an open and ongoing area of research.


Key: Sequential Quadratic Programming Quadratic Programming with Nonlinear Constraints IPC

Finishes successfully PassProjected Gap

ConstraintsVolume Based

ConstraintsCCD Distance

Based ConstraintsProjected Gap



Based ConstraintsUnable to finish in four hours Timeout

Energy or displacement blow up Blow-Up

Intersections Intersecting Constraint Offset

1e-2 1e-3 1e-4 1e-5 1e-2 1e-3 1e-4 1e-5 1e-2 1e-3 1e-4 1e-5 1e-2 1e-3 1e-4 1e-5 1e-2 1e-3 1e-4 1e-5 1e-2 1e-3 1e-4 1e-5

Mesh Point vs CO Triangle

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1e-2 Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-UpIntersectingBlow-UpTimeoutTimeoutBlow-Up Blow-UpPass Pass Pass Pass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpPass Pass Pass Pass Blow-UpPass Pass Blow-UpIntersectingBlow-UpBlow-Up Pass Pass IntersectingPass Pass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpPass Pass Pass TimeoutPass Blow-UpBlow-Up Blow-UpPass Pass Blow-Up Pass Pass Pass IntersectingPass

1e-5 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass

Mesh Triangle vs CO Point

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1e-2 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingBlow-UpBlow-UpBlow-UpIntersectingIntersectingBlow-UpBlow-UpIntersectingBlow-UpBlow-UpIntersectingBlow-Up Pass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpPass Pass Pass Blow-UpBlow-UpIntersectingPass Pass Pass Pass Pass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Timeout Pass Pass Pass Blow-Up Pass Pass Pass IntersectingPass


Mesh Edge vs CO Edge

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1e-2 Blow-UpPass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingPass Pass Pass Pass Blow-UpBlow-UpBlow-UpBlow-Up Pass Pass Pass Pass Pass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-Up Pass Blow-UpPass Blow-Up Pass Pass Pass IntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingPass Pass Blow-UpBlow-Up Pass Pass IntersectingIntersectingPass


Mesh Point vs Mesh Triangle

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1e-2 Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpIntersectingIntersectingBlow-UpBlow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass IntersectingPass Pass Pass Pass Pass Pass Pass IntersectingBlow-UpBlow-UpIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-4 Pass Pass Pass Pass Blow-UpPass Pass Pass Pass Pass Pass IntersectingIntersectingIntersectingIntersectingBlow-Up IntersectingBlow-UpIntersectingTimeout IntersectingIntersectingIntersectingIntersectingPass


Mesh Edge vs Mesh Edge

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1e-2 Pass Blow-UpPass Blow-Up Pass Pass Pass Pass IntersectingIntersectingIntersectingIntersectingBlow-UpBlow-UpIntersectingBlow-Up Blow-UpIntersectingIntersectingBlow-Up IntersectingBlow-UpIntersectingIntersectingPass

1e-3 Pass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass IntersectingIntersectingPass Pass IntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass Pass IntersectingIntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpBlow-UpIntersectingTimeout IntersectingBlow-UpIntersectingBlow-Up Pass Blow-UpIntersectingIntersectingPass


Tet vs Tet

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1e-2 Blow-UpBlow-UpBlow-UpBlow-Up Pass IntersectingIntersectingBlow-Up Blow-UpIntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-UpIntersectingIntersectingBlow-UpTimeoutBlow-Up IntersectingIntersectingIntersectingIntersectingPass

1e-3 Pass IntersectingBlow-UpBlow-Up Pass Pass IntersectingIntersectingPass Pass IntersectingIntersectingBlow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingPass


Cube vs Plane

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1e-2 Blow-UpPass Pass Pass Pass Pass Pass Pass IntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-Up IntersectingIntersectingIntersectingBlow-Up IntersectingIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpPass Pass Pass IntersectingIntersectingIntersectingIntersectingTimeoutIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-4 Pass Pass Pass Pass IntersectingIntersectingPass Pass Blow-UpPass Pass Pass IntersectingIntersectingBlow-UpIntersectingTimeoutIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-5 IntersectingIntersectingPass Pass IntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingPass IntersectingBlow-UpBlow-UpIntersectingIntersectingTimeoutIntersectingBlow-UpIntersectingBlow-UpIntersectingIntersectingIntersectingPass

Cube vs Cube CO

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1e-2 Blow-UpPass Blow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpIntersectingBlow-UpIntersectingBlow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpIntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-3 Blow-UpBlow-UpBlow-UpPass Blow-UpBlow-UpBlow-UpTimeout Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpIntersectingBlow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpIntersectingBlow-Up Pass

1e-4 Blow-UpPass Blow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpTimeoutIntersectingIntersectingBlow-UpBlow-UpIntersectingBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpIntersectingBlow-UpIntersectingPass

1e-5 Blow-UpBlow-UpBlow-UpPass Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpIntersectingIntersectingTimeout Blow-UpBlow-UpTimeoutTimeout Blow-UpIntersectingIntersectingIntersectingPass

Tet vs Cube

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1e-2 Blow-UpPass IntersectingIntersectingPass Pass Pass IntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass IntersectingPass Pass Pass IntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-4 Pass Pass Pass Pass IntersectingIntersectingPass Pass Pass Pass Pass IntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingPass


Aligned Tet vs Cube

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1e-2 Pass IntersectingBlow-UpIntersectingPass Pass Blow-UpBlow-Up Pass Blow-UpIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Blow-UpBlow-Up IntersectingTimeoutBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-4 Pass Pass Blow-UpIntersectingIntersectingIntersectingPass Pass Pass Pass IntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-Up IntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass















Cube vs Cube

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1e-2 Blow-UpPass Blow-UpBlow-Up IntersectingPass Pass Pass IntersectingIntersectingIntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass IntersectingIntersectingPass Pass IntersectingPass IntersectingIntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingBlow-Up IntersectingTimeoutIntersectingIntersectingPass

1e-4 Pass Pass Pass Pass IntersectingIntersectingPass Pass Pass Blow-UpPass IntersectingIntersectingIntersectingBlow-UpIntersectingTimeoutTimeoutIntersectingBlow-Up Blow-UpBlow-UpIntersectingIntersectingPass


Aligned Cube vs Cube

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1e-2 Blow-UpBlow-UpIntersectingBlow-Up TimeoutBlow-UpIntersectingIntersectingBlow-UpIntersectingBlow-UpIntersectingBlow-UpIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-3 Blow-UpPass IntersectingIntersectingPass Pass Pass Blow-Up IntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpTimeoutIntersectingIntersectingPass

1e-4 Pass Pass Blow-UpBlow-Up IntersectingPass Pass Pass IntersectingPass IntersectingIntersectingBlow-UpBlow-UpIntersectingBlow-Up Blow-UpIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass


Five Cube Pyramid

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1e-2 Blow-UpBlow-UpBlow-UpTimeout Blow-UpBlow-UpIntersectingBlow-Up Blow-UpBlow-UpBlow-UpIntersectingTimeoutIntersectingBlow-UpBlow-Up IntersectingIntersectingIntersectingBlow-Up Blow-UpBlow-UpIntersectingIntersectingPass

1e-3 IntersectingPass Pass IntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpPass IntersectingIntersectingTimeoutIntersectingTimeoutIntersectingIntersectingIntersectingIntersectingTimeout TimeoutIntersectingIntersectingIntersectingPass

1e-4 Pass Pass Blow-UpPass IntersectingIntersectingIntersectingIntersectingBlow-UpPass Pass IntersectingIntersectingIntersectingBlow-UpBlow-Up IntersectingIntersectingIntersectingIntersectingTimeoutIntersectingIntersectingIntersectingPass

1e-5 TimeoutPass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass Blow-UpPass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass Pass

Five Cube Stack

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1e-2 Blow-UpTimeoutIntersectingBlow-Up TimeoutIntersectingBlow-UpTimeout Blow-UpBlow-UpIntersectingIntersectingTimeoutIntersectingIntersectingBlow-Up TimeoutIntersectingIntersectingBlow-Up IntersectingIntersectingIntersectingIntersectingPass

1e-3 IntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingPass IntersectingIntersectingBlow-UpIntersectingIntersectingTimeoutBlow-UpIntersectingBlow-Up IntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass



Cubes in a Corner

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1e-2 IntersectingIntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-3 Blow-UpBlow-UpIntersectingBlow-Up Pass IntersectingBlow-UpIntersectingPass IntersectingIntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingTimeoutIntersectingBlow-UpIntersectingBlow-UpIntersectingBlow-UpIntersectingPass

1e-4 IntersectingTimeoutPass Pass IntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpBlow-UpTimeoutTimeout IntersectingIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingPass


Tets in a Corner

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1e-2 Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingBlow-Up Blow-UpBlow-UpIntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-Up Pass

1e-3 Blow-UpBlow-UpPass IntersectingPass IntersectingPass IntersectingIntersectingIntersectingPass IntersectingTimeoutIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass

1e-4 Blow-UpPass Pass Pass Blow-UpPass Pass Pass IntersectingPass Pass IntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingIntersectingIntersectingIntersectingPass


Erleben's Spikes

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1e-2 Pass Blow-UpIntersectingIntersectingPass Pass IntersectingIntersectingPass IntersectingIntersectingIntersectingPass IntersectingIntersectingBlow-Up Pass Blow-UpBlow-UpIntersectingPass IntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingIntersectingPass Blow-UpBlow-UpIntersectingPass Pass Pass IntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingPass


Erleben's Spike and Wedge

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1e-2 Blow-UpPass Pass Pass Pass Pass IntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingBlow-UpIntersectingIntersectingIntersectingBlow-UpBlow-UpBlow-UpBlow-Up IntersectingIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass Pass Pass Pass Pass IntersectingBlow-UpPass Pass Pass Pass Pass IntersectingIntersectingPass Blow-UpIntersectingIntersectingPass Pass IntersectingIntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass IntersectingPass Pass Pass Pass Blow-UpBlow-UpIntersectingPass IntersectingTimeoutIntersectingPass TimeoutPass IntersectingPass


Erleben's Wedges

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1e-2 Blow-UpBlow-UpBlow-UpPass Blow-UpPass Pass Pass Blow-UpIntersectingBlow-UpIntersectingBlow-UpBlow-UpIntersectingPass Blow-UpBlow-UpBlow-UpPass Pass IntersectingTimeoutIntersectingPass

1e-3 Blow-UpBlow-UpPass Blow-Up Blow-UpBlow-UpPass Pass IntersectingBlow-UpIntersectingPass Blow-UpPass Blow-UpBlow-Up Blow-UpBlow-UpPass Blow-Up Pass Pass IntersectingIntersectingPass

1e-4 Blow-UpBlow-UpPass Pass Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpIntersectingTimeoutPass Blow-UpIntersectingBlow-UpTimeout Blow-UpBlow-UpBlow-UpTimeout Blow-UpBlow-UpIntersectingTimeout Pass


Erleben's Spike in a Hole

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1e-2 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingBlow-UpPass Blow-UpIntersectingBlow-UpBlow-UpIntersectingTimeout Blow-UpIntersectingIntersectingIntersectingPass

1e-3 Blow-UpPass Pass Pass Pass Pass Pass Pass Blow-UpPass Pass Pass Pass Blow-UpBlow-UpBlow-Up Blow-UpIntersectingPass IntersectingPass Pass Pass Pass Pass

1e-4 Blow-UpPass Pass Pass Pass Pass Pass Pass Blow-UpPass Pass Pass Blow-UpBlow-UpPass Pass Pass TimeoutPass Pass Blow-UpBlow-UpPass Pass Pass

1e-5 Pass Pass Pass Pass TimeoutTimeoutPass Pass Pass Pass Pass Pass Blow-UpBlow-UpPass Pass Blow-UpTimeoutIntersectingPass Blow-UpIntersectingIntersectingPass Pass














Erleben's Spike in a Crack

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1e-2 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingPass Pass Pass Blow-Up Pass Pass Blow-UpBlow-Up Pass Pass IntersectingIntersectingPass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-UpPass Blow-UpPass Blow-UpPass Blow-UpPass Pass Pass IntersectingIntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass TimeoutPass TimeoutBlow-Up TimeoutPass Pass Timeout TimeoutPass IntersectingIntersectingPass

1e-5 TimeoutPass Pass Pass TimeoutPass Pass Pass TimeoutPass Pass Pass Blow-UpPass Pass Pass IntersectingIntersectingPass Pass TimeoutPass Pass Pass Pass

Erleben's Wedge in a Crack

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1e-2 IntersectingPass IntersectingIntersectingPass Pass IntersectingIntersectingBlow-UpPass IntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingPass Blow-UpPass IntersectingBlow-UpIntersectingIntersectingIntersectingPass

1e-3 Pass Pass Pass IntersectingBlow-UpPass Pass IntersectingBlow-UpPass Pass IntersectingBlow-UpBlow-UpPass Pass Blow-UpPass Blow-UpBlow-Up Pass Pass Blow-UpIntersectingPass

1e-4 Pass Pass Pass Pass Blow-UpPass Pass Pass Pass Pass Pass Pass Pass Blow-UpPass Blow-Up Blow-UpPass TimeoutPass Pass Pass Pass IntersectingPass

1e-5 Pass Pass Pass Pass Blow-UpPass Pass Pass TimeoutPass Pass Pass Blow-UpPass Pass Pass TimeoutIntersectingPass Timeout Blow-UpPass Pass Pass Pass

Erleben's Sliding Spike

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1e-2 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingIntersectingPass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass

1e-3 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-Up Pass Pass Pass Pass Pass Pass Pass Pass Pass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Blow-Up Pass Pass TimeoutBlow-Up Pass Pass Pass Timeout Pass


Erleben's Sliding Wedge

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1e-3 Pass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingPass

1e-4 Pass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingPass Pass Pass IntersectingBlow-UpPass Pass IntersectingPass Pass Pass IntersectingPass


Erleben's Cliff Edges

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1e-2 Blow-UpBlow-UpBlow-UpPass Blow-UpBlow-UpBlow-UpPass Blow-UpBlow-UpIntersectingBlow-Up Blow-UpIntersectingBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpIntersectingIntersectingIntersectingPass

1e-3 Blow-UpPass Pass Pass Pass Blow-UpPass Pass Blow-UpBlow-UpPass IntersectingBlow-UpBlow-UpBlow-UpIntersectingBlow-UpBlow-UpIntersectingBlow-Up Blow-UpIntersectingBlow-UpIntersectingPass

1e-4 Blow-UpPass Pass Pass Blow-UpBlow-UpBlow-UpPass Blow-UpPass IntersectingPass Blow-UpBlow-UpBlow-UpTimeout Blow-UpBlow-UpPass Blow-Up IntersectingIntersectingIntersectingIntersectingPass

1e-5 TimeoutBlow-UpPass Pass TimeoutBlow-UpTimeoutTimeout Blow-UpBlow-UpPass Pass Blow-UpBlow-UpIntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingBlow-UpBlow-UpIntersectingIntersectingPass

Erleben's Internal Edges

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1e-2 Blow-UpBlow-UpPass Pass Blow-UpBlow-UpPass Pass IntersectingIntersectingPass Pass Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpIntersectingIntersectingIntersectingBlow-UpIntersectingPass

1e-3 Pass Blow-UpPass Pass Pass Pass Pass IntersectingPass Blow-UpPass Pass Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpIntersectingIntersectingPass

1e-4 Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass Pass IntersectingBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Blow-UpBlow-UpBlow-UpBlow-Up Pass

1e-5 Pass Pass Pass Pass TimeoutPass Pass Pass Pass Pass Pass Pass Blow-UpBlow-UpBlow-UpIntersectingBlow-UpBlow-UpBlow-UpBlow-Up Blow-UpIntersectingIntersectingTimeout Pass

Chain

Tim

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1e-2 TimeoutBlow-UpTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout Blow-UpTimeoutIntersectingIntersectingTimeoutTimeoutTimeoutIntersectingTimeoutBlow-UpIntersectingIntersectingPass

1e-3 Blow-UpTimeoutTimeoutIntersectingIntersectingIntersectingTimeoutTimeout TimeoutTimeoutTimeoutIntersectingTimeoutBlow-UpTimeoutTimeout IntersectingIntersectingTimeoutTimeout Blow-UpBlow-UpIntersectingIntersectingPass

1e-4 TimeoutTimeoutTimeoutIntersectingTimeoutIntersectingTimeoutIntersectingTimeoutTimeoutTimeoutIntersectingBlow-UpBlow-UpBlow-UpBlow-Up TimeoutIntersectingIntersectingIntersectingBlow-UpTimeoutTimeoutIntersectingPass

1e-5 TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout Pass

Rod vs Plane

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1e-2 TimeoutBlow-UpBlow-UpTimeout TimeoutBlow-UpBlow-UpIntersectingTimeoutTimeoutTimeoutTimeout TimeoutBlow-UpBlow-UpTimeout TimeoutBlow-UpBlow-UpBlow-Up TimeoutBlow-UpBlow-UpBlow-Up Pass

1e-3 TimeoutTimeoutTimeoutIntersectingTimeoutTimeoutTimeoutTimeout TimeoutTimeoutIntersectingIntersectingTimeoutTimeoutTimeoutTimeout TimeoutTimeoutIntersectingIntersectingTimeoutBlow-UpIntersectingIntersectingPass



Cow Head vs Plane

Tim

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1e-2 Blow-UpTimeoutTimeoutBlow-Up TimeoutBlow-UpTimeoutIntersectingTimeoutTimeoutBlow-UpBlow-Up TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutBlow-UpBlow-UpBlow-Up Pass

1e-3 TimeoutTimeoutTimeoutIntersectingTimeoutIntersectingIntersectingIntersectingTimeoutIntersectingIntersectingIntersectingTimeoutBlow-UpTimeoutTimeout TimeoutBlow-UpIntersectingTimeout Blow-UpBlow-UpTimeoutTimeout Pass

1e-4 Blow-UpTimeoutIntersectingIntersectingTimeoutTimeoutTimeoutIntersectingTimeoutTimeoutIntersectingIntersectingTimeoutBlow-UpTimeoutIntersectingTimeoutIntersectingTimeoutTimeout TimeoutBlow-UpBlow-UpIntersectingPass

1e-5 Blow-UpTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutTimeoutTimeout Pass

Mat Twist

Tim

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1e-2 TimeoutTimeoutTimeoutBlow-Up TimeoutTimeoutTimeoutTimeout TimeoutTimeoutIntersectingIntersectingTimeoutBlow-UpTimeoutTimeout TimeoutTimeoutTimeoutTimeout TimeoutTimeoutBlow-UpTimeout Pass

1e-3 TimeoutBlow-UpIntersectingIntersectingTimeoutIntersectingIntersectingIntersectingTimeoutBlow-UpIntersectingIntersectingTimeoutBlow-UpBlow-UpTimeout TimeoutIntersectingTimeoutTimeout TimeoutTimeoutTimeoutIntersectingPass

1e-4 TimeoutTimeoutIntersectingIntersectingTimeoutTimeoutTimeoutIntersectingTimeoutIntersectingIntersectingIntersectingTimeoutBlow-UpTimeoutTimeout Timeoutblow-upIntersectingTimeout TimeoutTimeoutTimeoutBlow-Up Pass

1e-5 TimeoutIntersectingIntersectingTimeout TimeoutIntersectingIntersectingIntersectingTimeoutIntersectingIntersectingIntersectingTimeoutIntersectingTimeoutIntersectingTimeoutTimeoutTimeoutIntersectingTimeoutIntersectingTimeoutIntersectingPass



Documents

Comparison Supplement to Incremental Potential Contact ...5 HOUDINI We test Houdini with the simple chain example. Each link is a torus with outer radius 1.25 and inner radius 0.28