Install

git clone --recursive git@github.com:tt6746690/fast_support_reduction.git

# profiling: minitrace + chrome tracing 
#       https://github.com/hrydgard/minitrace
#       https://www.chromium.org/developers/how-tos/trace-event-profiling-tool

# dependencies
brew install cgal

mkdir build && cd build

# brew install ninja
cmake -GNinja ..

# openmp
export OMP_NUM_THREADS=4

# mesh file generator: tetrahedralize the input surface mesh and generate bbw weights for each corresponding tet
./mesh_file_generator dinosaur
input files: ../dinosaur.obj ../dinosaur.tgf
output file: ../data/dinosaur.mesh ../data/dinosaur.dmat


# run
./support_reduction \
    -d ../data/ \
    -f bb-bunny \
    -b 5 \
    -i 1 \
    -p 1 \
    -r 10 \
    -a 90 \
    -c 20 \
    -e 1000

# debugging
lldb support_reduction
process launch -- -d ../data/ -f bb-bunny -b 5 -i 1 -p 1 -r 50 -a 90 -c 20

Layout

.
├── CMakeLists.txt
├── README.md
├── abstract                    // extended abstract
├── cmake
├── data                        // source and destination directory for mesh, weights, ...
├── libigl
├── makefile
├── matlab
├── papers
├── src                         // source code
├── bbw.cpp                     // for generating bounded biharmonic weights and remeshing
├── support_reduction.cpp       // run program
└── visualize.cpp               // visualize self-interesection

self-intersection with shader

• GPU-accelerated evaluation of self-intersection volume
  • problem
    • given a water-tight mesh and projection direction
    • framebuffer width and height, for controlling how accurate the computation is
    • return self-intersecting volume
  • preparation
    • find bounding box of the mesh
    • determine orthographic projection around the bounding box of the mesh Peel off front-most fragment of mesh along an orthographic viewing direction aligned with the inverse of printing direction (i.e. projection direction). The near/far plane of orthographic projection are faces of the bounding box of the mesh. For each fragment, record

TODO

• low priority
  • optimized forward kinematics in shaders
  • depth counter algorithm for self intersection volume computation

meeting

before March 22

• coefficient

  • tune to be fixed
  • account for volume / surface
  • one way to test things work: scale mesh by 100x and see result is invariant

• support generation

  • meshmixer generates support
  • varied for different software / other scenario

• the cool part

  • joint based character deformation

• how to push forward to a publication

  • make things fast
  • dont worry about support reduction
    • varied by software used
    • probably material/context specific algorithm/technique for support reduction and so a general black box is not easy to be motivated.
  • make this about posing sculptures: take into account physics of material
    • print out cement ... need to make sure it does not fracture
  • impl detail
    • remove overhang
    • add self-balancing (center of mesh project into convex hull)
      • surface intergrall to determine mass center volumetrically
    • add load+stress
      • linear elasticity
      • stress is a linear function of displacement
      • KV = KMT where V=MT
        • K given beforehand
        • KM is 6n x m can be put in vertex shader?
      • need to account for things not covered by the first rig
        • another rig?
      • need to account for fracture in interior?
        • enough to render stress on boundary ?
        • need to dig with this later
    • interface for
      • hints for intersection, position of stress
      • then option for global optimization

• todo

  • understand physics of stress field
    • ask sarah on physics based stuff.
  • rendering based speed up

March 22

• faster stress computation
  • GPU accelerated Jacobi solver
  • voxel representation of mesh
    • no matrix assembly since its on a grid
    • solving linear system Ax=b with iterative solver on CPU first then GPU
      • shader (cross platform) vs. cuda
  • reference 2d jacobi solver for poisson equation ... on CPU/GPU
• ui
  • find closest quaternion to match screen space drag, or
  • github repo given ImGuizmo
• engineering
  • cmake release/debug mode

May 23

• what have we done so far
  • goal
    • a design tool to allow artistics to deform figures by their skeleton
    • be able to visualize yield stress on surface as they make edit
    • explore deformations with good properties with global optimization
  • global optimization
    • reduced space (skeleton) enabling possibility of global optimization
    • objective function capturing requirements:
      • minimize supporting material used
      • able to stand (center of mass inside support polygon)
      • will not break (yield criterion > material-specific yield stress)
      • local distortion (arap energy)
  • stress visualization (need real time)
    • explored
      • iterative methods like jacobi, SOR (can control number of iterations)
      • hexahedron element over axis-aligned grids (element stiffness K constant)
    • later
      • multigrid on cuda

June 4

• forget about the continuous derivation for shape gradient
  • variational surface cutting has a different formulation from our problem
• discrete setting for solving the PDE-contrained optimization problem
  • convert the constraints into K(d)u=f(d) using FEM, where d is the design parameter (in our case the vertex positions)
  • take derivative of K and f with respect to d
  • look into automatic differentiation
• refer to Bernhard Thomaszewski's papers to get a better sense regarding how the method works
• the ultimate goal doesn't change
  • object function: min E_{ARAP}(X_{input mesh},X(T))+E_{stress}(X_{input mesh},X(T))
• next step
  • start with a simple 2D cantilever example
    • linear FEM stiff material
    • nonlinear FEM soft material
    • treat X as a function of T (apply LBS)

June 6

• the deformed volumetric mesh might be of bad quality due to LBS
  • not suitable to do FEM based on this
  • need to confirm in both 2D and 3D
• use auto diff to compute the partial derivative of K with respect to T
• in each frame voxelize the deformed tet mesh
• do trilinear interpolation over the bbw weights field for each grid point
  • to get the variable back to T

June 20

• instead of doing voxelization, use fixed grid

  • look at ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics
  • the approach that is used here (tet <-> hex) is similar to what is commonly used in CFD
  • ask Michael Tao for details

• dK(p)/dp * u has equivalent result as d(K(p)*u)/dp

  • u is simply a few numbers u = Kf
  • the difference is the complexity -> the sparsity of K

• stan is good

• questions

  • continuous optimization (whether or not use gradient ...)
    • consider arap energy direction ?
    • min_\Omega ( \min_u \int_\Omega E(u,X) dx))
      • \Omega is the domain
    • https://nmwsharp.com/media/cea_tutorial.pdf
    • hard constraints (make it stand)
      • global optimization use hard constaints
      • then use gradient for different initial points.
    • do not penalize small values of stress
      • can design functions that is continuous
        • (0 infeasible, grows very quickly for feasible)
    • need to consider the feasible set ... (should be good)
    • todo
      • do continous optimization on arap+fracture energy
      • how do you derive gradients
        • derivation of gradient of fracture u with respect to X
          • https://nmwsharp.com/media/cea_tutorial.pdf
      • do 2d shape optimization
        • on simple coarse domain, the rod that sticks out of wall
        • expect points close to wall expand
    • hybrid global optimization methods
      • design gallery: probably better to use global methods
    • what is the thing we want to compute gradient of ?
      • in the want to compute gradient with respect to euler angle
      • X(\theta) where X is the surface
  • is it a good idea to go with multigrid ?
    • pro: O(n) complexity
  • can we do weekly meetings ?
  • interpolation problem is fixed
    • do a screenshot to show it's done

• thoughts

  • at first identify your problem rather than jumping into the problem i.e. what the problem it is
  • look into the closest work, try to understand their work and make comparisons