CS 5643 Assignment #2: Position-based Dynamics

• Part1: Tuesday Mar 17, 2015 (midnight)
  
• Final: Friday Mar 27, 2015 (midnight)

• Getting started: Start by familiarizing yourself with the starter code, and modify it to support the position-based dynamics time-stepping scheme, as described in the PBD paper.
• Representing constraints: You should implement a Constraint class or interface to represent equality and inequality Constraints, and their associated stiffness value. Design your representation so that it can support what you need to do in later steps.
  
• Particle-plane collision constraints: To keep the particles from passing through the floor, or leaving the container, you need to implement position-based collision response with the computational cell boundaries. For now, modify the inner position-correction iteration so that the particle position are kept from leaving the box when bouncing around under the influence of gravity. You can implement each using a general particle-plane inequality constraint (with strength k=1), and then later reuse it for other plane constraints.
  
• Cloth constraints: Following section 4 of [PBD], implement the core constraints and constraint gradients needed for (1) edge-based stretching constraints, and then (2) bending constraints. Formulae for evaluating nontrivial gradients are available in the paper's Appendix.  You should represent each piece of cloth in your simulation using a Cloth Object, with associated simulation parameters and constraints. Cloth vertex/particle mass should be computed using the density of the cloth, rho, times 1/3 of the sum of the surrounding triangle areas.  Implement the position updates associated with stretch and bend constraints, using iterative Gauss-Seidel updates. Make sure to support multiple constraint passes per time-step for best results.
  
• Damping: Implement the "rigid damping" approximation (described in section 3.5) to shed energy from individual cloth objects. While you could just implement a simple damping force, such as f = -c*v, or a velocity-scaling filter (e.g., "v *= 0.9999"), these trivial models produce an "underwater" damping effect, whereas the "rigid damping" model does not damp rigid-body motion.
• Attachment constraints: Pin constraints should be implemented, so that vertices can be fixed in space and/or attached to other moving objects. This can be achieved using position-level updates, and by setting the particle inverse mass value, w, to zero, i.e., giving it infinite mass. You should provide an example with cloth suspended in space, e.g., a rectangular piece of cloth hanging from two corners.
• Generate basic cloth animations to demonstrate completion of Part I: Use your simulator to animate the triangle mesh examples provided in the starter code. Dump your frames and generate a movie file, or perform a video screen capture, or better, so that we can see your results easily as the output of Part I.
  
• Submit your code and video results on CMS under Part I: Including videos is important to demonstrate your progress. You do not need to include a writeup for your Part I submission.
  

  >> Part II (due Fri, Mar 27): After you get the basic simulator working, next you will (a) first add two additional constraints then (b) try something more personalized.

• Interaction constraints: Implement a position-level mouse constraint to allow you to pull on cloth vertices. Your simulation should remain stable during the interaction. You will need to need to support particle picking, by finding the particle closest to your mouse position. This can be implemented in many ways, but probably the easiest is to determine the line associated with your mouse position/ray, and then scan all particles to find the particle closest to that line using 3D geometry. The mouse particle goal position can be determined by mouse position changes in the parallel view plane.
• Balloon constraints: To simulate closed objects with air inside, such as a inflatable ball, implement the "cloth balloon" constraint (see section 4.4).
• Do at least one of the following:
  
• Animate something interesting... please: Use your simulator to implement at least one nontrivial animation scenario. You can use the OBJ mesh loader to load a variety of meshes that you can either build, or download (e.g., from TurboSquid), to help you build an interesting scenario. Setting initial positions and velocities of your objects, can be used to create interesting setups, e.g., crash scenarios, running objects through gears, etc.
• Collisions with rigid obstacles can be approximated using local vertex-plane constraints as described in the paper. In order to detect collisions for purposes of generating time-step-specific constraints, you should use a spatial acceleration data structure, such as a bounding volume hierarchy (BVH) or (uniform) spatial subdivision. Robust collision responses with rigid obstacles will enable you to implement challenging scenarios (such as the example shown in Figure 1).  Alternately, collisions with volumetric rigid obstacles can be implemented robustly if you can tell if a vertex is inside or outside the object, since then you can then detect and "push" vertices to the surface during the constraint projection phase. Implicit function definitions (such as for a sphere), or signed distance fields, can be useful representations for volumetric objects.
• Cloth self-collisions can be approximated as described in the paper. However, these can be more complicated to get working properly, and are not a required part of the project. Only implement self-collision constraints last, after you have finished other parts of the assignment and still want an extra challenge.
• Just add water: If you are feeling ambitious, you can combine your cloth simulator with the previous Particle Based Fluids implementation from assignment #1, which is also in the cs5643.particles package. You will need to implement fluid-cloth particle collisions to ensure that fluid particles do not pass through the cloth, and that contact-based momentum is transferred between cloth and fluid particles. You might also try implementing some of the approaches from "Unified Particle Physics."
  
• Interactive modification of simulation parameters (such as constraint "stiffness," or cloth density, gravity, etc.) can be implemented using GUI sliders, etc., and can enable fun interactions. 
• Hand-in using CMS: Submit everything for Part II final submission:
  
• A brief written document (in txt or PDF) that details what you did, your findings, and who you discussed the assignment with, etc.  
  
• Any comparisons or analysis/results demonstrating the behavior of your implementation.
• Citation: 
  
• Include the names of everyone that you discussed the assignment with.
• Include citations of external resources (books, webpages, etc.) that you used in your R&D.
  
• Documented software implementation derived from the Java starter code, or based on an analogous framework in another language, e.g., C++.
• Your creative simulation artifacts, videos, images, etc.   
• We will run your software to evaluate your implementation, and/or ask you to provide a demo. However including videos that demonstrate the requested features, and interesting behavior are strongly encouraged.
  
• If you are working with a partner, be sure to form a two-person group, and submit your zip file as a group.
• Regarding requests for extensions because "I have another deadline on that day," etc.: Please start early, and budget your time to do the many things you need to do. The deadline is not when you do your work, it's when you relax.
• Late days will be granted at a default 5%/day penalty. Please plan ahead to minimize unnecessary deductions.

• M. Müller, B. Heidelberger, M. Hennix, J. Ratcliff, Position Based Dynamics, Proceedings of Virtual Reality Interactions and Physical Simulations (VRIPhys), pp 71-80, Madrid, November 6-7 2006, Best Paper Award, PDF, (video), (slides)
• Jos Stam, Nucleus: Towards a Unified Dynamics Solver for Computer Graphics, 2009 Conference Proceedings: IEEE International Conference on Computer-Aided Design and Computer Graphics, pp. 1-11, 2009. (related talk)
  
• T. Jakobsen, Advanced Character Physics, Game Developer Conference, 2001.
• Miles Macklin, Matthias Müller, Nuttapong Chentanez, Tae-Yong Kim: Unified Particle Physics for Real-Time Applications, ACM Transactions on Graphics (SIGGRAPH 2014), 33(4) [Slides] [Preprint] [Video] [Project Page]