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				<div class="heading" style="text-align:center">Incremental Potential Contact:<br/>Intersection- and Inversion-free Large Deformation Dynamics</div>
				<br />
				<div class="subheading" style="margin-top:-8pt;text-align:center;font-size:13pt">
					<a href="http://www.seas.upenn.edu/~minchenl/" target="_blank">Minchen Li</a><sup>1,2</sup>,&nbsp;
					<a href="https://zferg.us" target="_blank">Zachary Ferguson</a><sup>3</sup>,&nbsp;
					<a href="http://web.uvic.ca/~teseo/" target="_blank">Teseo Schneider</a><sup>3</sup>,&nbsp;
					<a href="http://langlo.is/" target="_blank">Timothy Langlois</a><sup>2</sup>,&nbsp;
					<a href="https://cims.nyu.edu/gcl/denis.html" target="_blank">Denis Zorin</a><sup>3</sup>,&nbsp;
					<a href="https://cims.nyu.edu/gcl/daniele.html" target="_blank">Daniele Panozzo</a><sup>3</sup>,&nbsp;
					<br />
					<a href="https://www.seas.upenn.edu/~cffjiang/" target="_blank">Chenfanfu Jiang</a><sup>1</sup>,&nbsp;
					<a href="http://dannykaufman.io/" target="_blank">Danny M. Kaufman</a><sup>2</sup>
					<br />
					<div style="margin-top:6pt;"><sup>1</sup>University of Pennsylvania,&nbsp; <sup>2</sup>Adobe Research,&nbsp; <sup>3</sup>New York University</text></div>
					<div class="subheading" style="margin-top:8pt;"><span style="font-style: italic">ACM Transactions on Graphics (SIGGRAPH), 2020</span></div>
				</div>
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					<img src="file/IPC-teaser.jpg" style="padding:3pt; width:99%">
					<div class="text" style="text-align:left; font-size:10pt; margin-top:10pt">
						<p class="text">
							<b>Squeeze out:</b> Incremental Potential Contact (IPC) enables high-rate time stepping, here with h = 0.01s, of extreme nonlinear elastodynamics with
							contact that is intersection- and inversion-free at all time steps, irrespective of the degree of compression and contact. Here a plate compresses and then
							forces a collection of complex soft elastic FE models (181K tetrahedra in total, with a neo-Hookean material) through a thin, codimensional obstacle tube. The
							models are then compressed entirely together forming a tight mush to fit through the gap and then once through they cleanly separate into a stable pile.
						</p>
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				</div>
				<div class="regularHeader" style="margin-bottom:15px;text-align:left;">Paper</div>
				<div class="text">
					<p class="text">
						<b><a href="file/IPC-paper-fullRes.pdf" target="_blank"> Paper (PDF) </a></b>
						&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
						<b><a href="file/IPC-paper-350ppi.pdf" target="_blank"> Low res (PDF) </a></b>
					</p>
				</div>
				<div class="regularHeader" style="text-align:left;">Abstract</div>
				<div class="text" align="center">
					<p class="text">
						Contacts weave through every aspect of our physical world, from daily
						household chores to acts of nature. Modeling and predictive computation of
						these phenomena for solid mechanics is important to every discipline concerned with the motion of mechanical systems, including engineering and
						animation. Nevertheless, efficiently time-stepping accurate and consistent
						simulations of real-world contacting elastica remains an outstanding computational challenge. To model the complex interaction of deforming solids
						in contact we propose Incremental Potential Contact (IPC) – a new model
						and algorithm for variationally solving implicitly time-stepped nonlinear
						elastodynamics. IPC maintains an intersection- and inversion-free trajectory
						regardless of material parameters, time step sizes, impact velocities, severity
						of deformation, or boundary conditions enforced.
					</p>
					<p class="text">
						Constructed with a custom nonlinear solver, IPC enables efficient resolution of time-stepping problems with separate, user-exposed accuracy
						tolerances that allow independent specification of the physical accuracy of
						the dynamics and the geometric accuracy of surface-to-surface conformation.
						This enables users to decouple, as needed per application, desired accuracies
						for a simulation’s dynamics and geometry.
					</p>
					<p class="text">
						The resulting time stepper solves contact problems that are intersectionfree (and thus robust), inversion-free, efficient (at speeds comparable to or
						faster than available methods that lack both convergence and feasibility),
						and accurate (solved to user-specified accuracies). To our knowledge this
						is the first implicit time-stepping method, across both the engineering and
						graphics literature that can consistently enforce these guarantees as we vary
						simulation parameters.
					</p>
					<p class="text">
						In an extensive comparison of available simulation methods, research
						libraries and commercial codes we confirm that available engineering and
						computer graphics methods, while each succeeding admirably in custom-tuned regimes, often fail with instabilities, egregious constraint violations
						and/or inaccurate and implausible solutions, as we vary input materials,
						contact numbers and time step. We also exercise IPC across a wide range
						of existing and new benchmark tests and demonstrate its accurate solution
						over a broad sweep of reasonable time-step sizes and beyond (up to h=2s)
						across challenging large-deformation, large-contact stress-test scenarios
						with meshes composed of up to 2.3M tetrahedra and processing up to 498K
						contacts per time step. For applications requiring high-accuracy we demonstrate tight convergence on all measures. While, for applications requiring
						lower accuracies, e.g. animation, we confirm IPC can ensure feasibility and
						plausibility even when specified tolerances are lowered for efficiency.
					</p>
				</div>
				<div class="regularHeader" style="margin-bottom:15px;text-align:left;">Video</div>
				<div class="text" align="center">
					<p class="text">
						<b><a href="https://www.bilibili.com/video/BV1964y1275C/" target="_blank">Main video (MP4, 126 MB)</a></b>
						<br/> <br/>
						<iframe width="560" height="315" src="https://www.youtube.com/embed/y96jk-eUCgI" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen style="-webkit-box-shadow: 1px 1px 3px 3px rgba(0, 0, 0, 0.2)"></iframe>
						<br/> <br/> <br/>
						<b><a href="file/IPC-supplemental-video.mp4" target="_blank">Supplemental Video (MP4, 64.7 MB)</a></b>
						<br/> <br/>
						<iframe width="560" height="315" src="https://www.youtube.com/embed/sX5qQEDvHVU" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen style="-webkit-box-shadow: 1px 1px 3px 3px rgba(0, 0, 0, 0.2)"></iframe>
					</p>
				</div>
				<div class="regularHeader" style="margin-bottom:15px;text-align:left;">Source Code and Data</div>
				<div class="text">
					<p class="text">
						<b><a href="https://github.com/ipc-sim/IPC" target="_blank">Codebase</a></b>
						&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
						<b><a href="https://github.com/ipc-sim/ipc-toolkit" target="_blank">Toolkit</a></b>
					</p>
				</div>
				<div class="regularHeader" style="margin-bottom:15px;text-align:left;">BibTex</div>
				<div class="text">
					<p class="text">
						@article{Li2020IPC,<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;author  = {Minchen Li and Zachary Ferguson and Teseo Schneider and Timothy Langlois and<br />
						&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Denis Zorin and Daniele Panozzo and Chenfanfu Jiang and Danny M. Kaufman},<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;title   = {Incremental Potential Contact: Intersection- and Inversion-free Large Deformation Dynamics},<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;journal = {ACM Trans. Graph. (SIGGRAPH)},<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;year    = {2020},<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;volume = {39},<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;number = {4},<br/>
						&nbsp;&nbsp;&nbsp;&nbsp;articleno = {49}<br/>
						}
					</p>
				</div>
				<div class="regularHeader" style="margin-bottom:15px;text-align:left;">Supplemental Documents</div>
				<div class="text">
					<p class="text">
						<b><a href="file/IPC-supplement-A-technical.pdf" target="_blank">Supplement A: Technical Details (PDF) </a></b> <br/>
						<b><a href="file/IPC-supplement-B-comparisons.pdf" target="_blank">Supplement B: Comparison Details (PDF) </a></b><br/>
						<b><a href="file/IPC-supplement-C-statistics.pdf" target="_blank">Supplement C: Statistics (PDF) </a></b><br/>
					</p>
				</div>

				<div class="regularHeader" style="margin-bottom:15px;text-align:left;">Results</div>
				<div align="center" style="clear:none; margin-top:15px">
					<img src="file/IPC-golf.jpg" style="padding:3pt; width:89%">
					<div class="text" style="text-align:left; font-size:10pt; margin-top:10pt">
						<p class="text">
							<b>High-speed impact test:</b> Top: we show key frames from a highspeed
							video capture of a foam practice ball fired at a fixed plate. Matching
							reported material properties (0.04m diameter, E = 107Pa, ν = 0.45, ρ =
							1150kg/m3) and firing speed (v0 = 67m/s), we apply IPC to simulate the
							set-up with Newmark time stepping at h = 2e−5s to capture the highfrequency
							behaviors. Middle and bottom: IPC-simulated frames at times
							corresponding to the video frames showing respectively, visualization of the
							simulated velocity magnitudes (middle) and geometry (bottom).
						</p>
					</div>
				</div>
				<br />
				<div align="center" style="clear:none; margin-top:15px">
					<img src="file/IPC-squishyBall.jpg" style="padding:3pt; width:89%">
					<div class="text" style="text-align:left; font-size:10pt; margin-top:10pt">
						<p class="text">
							<b>Squishy ball scaling test:</b> Simulated by IPC, an elastic squishy ball toy
							model (688K nodes, 2.3M tets) is thrown at a glass wall. The left three frames
							show side views before, at, and after the moment of maximal compression
							during impact. The right-most frame then shows the view behind the glass
							during the moment of maximal compression, highlighting how all of the
							toy’s intricately intertwined tendrils remain intersection free.
						</p>
					</div>
				</div>
				<br />
				<div align="center" style="clear:none; margin-top:15px">
					<img src="file/IPC-codimRoller.jpg" style="padding:3pt; width:89%">
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						<p class="text">
							<b>Codimensional collision tests:</b> Here we simulate collisions with codimensional moving obstacles using only the mesh edge segments (left) or even just the mesh vertices (right) for the rotating roller. For these extremely
							challenging tests IPC continues robust simulation exhibiting tight compliant
							shapes in contact regions pressed by the sharp obstacles.
						</p>
					</div>
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