Haarbach, Adrian, Tolga Birdal, and Slobodan Ilic. "Survey of higher order rigid body motion interpolation methods for keyframe animation and continuous-time trajectory estimation." 2018 International Conference on 3D Vision (3DV). IEEE, 2018:
Since animation techniques are best explored interactively, we provide our web and C++ applications to interact with and visualize Euclidean, orientation and rigid body motion interpolation methods that produced all our figures and runtime evaluations as well as an overview table of all methods: http://adrian-haarbach.de/interpolation-methods.
The src directory contains the C++ implementation of our trajectory representations which uses Eigen3/{Dense,Geometry} as templated Matrix and Quaternion basis and GLFW for the visualization.
The following methods are provided
Euclidean interpolation:
- LERP
- cubic Bezier Spline based on ttk592/spline
- cubic B-Spline in Matrix basis and cumulative form
Orientation interpolation:
- QLB/LERPN (Quaternion Linear Blending == renormalized LERP)
- SLERP in SU(2)
expq,logqofQuaternionMapping.hfrom hengli/vmas-ros-pkg/calibration/hand_eye_calibration - SQUAD (Shoemake '87)
- RQBEz (Renormalized quaternion Bezier curve)
- Cumulative B-spline curve (CuBsp) in SU(2) (Kim, Kim, Shin '95)
Rigid body motion interpolation based on cubic B-Spline in combination with:
- R(3)xSO(3)/SPLIT interpolation
- DH (Dual Quaternion) based on
DualQuaternion.hfrom hengli/vmas-ros-pkg/calibration/hand_eye_calibration - SE(3) based on
sophus/se3.hppfrom strasdat/Sophus
Install dependencies via homebrew package manager:
brew install cmake eigen glfwInstall dependencies via apt:
sudo apt install cmake libeigen3-dev libglfw3-devgit checkout https://github.com/adrelino/interpolation-methods.git
cd interpolation-methods
git submodule update --initmkdir build && cd build
cmake ../src
makegit clone https://github.com/emscripten-core/emsdk.git
cd emsdk
git pull
./emsdk update-tags
./emsdk install latest
./emsdk activate latest
source ./emsdk_env.sh
cd ..Then build
mkdir build-web && cd build-web
cmake ../src -DEIGEN3_INCLUDE_DIR=/usr/include/eigen3 -DCMAKE_TOOLCHAIN_FILE="../emsdk/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake"
makeserve the file either using node or python
npx http-server
python2 -m SimpleHTTPServer 8080
Then open http://localhost:8080.
To reproduce the 3D visualizations and runtime experiments from sections 4, 5 and 6 of the paper.
This will display the rotation part of the trajectories on the surfaces of a unit quaternions sphere.
./app_runtime/vis-orientation
This allows e.g. to generate
Figure 4: Comparison of orientation interpolation methods on the surface of the sphere S^2 and by the norm of their angular velocity su(2).
This will display the rotation part of the trajectories as an animated camera frustrum and the translation part as a line in 3D Euclidean space.
./app_visualization/vis-rigid 
This allows e.g. to generate
Figure 5: Interpolation of two poses / Figure 6: Trajectory from 4 poses
To re-run the runtime experiments, run
./app_runtime/rigid-pairwise
...
===== TIMINGS ===== multip ===== ops=10001
name nsec max min SPLIT #means
QLB+LERP 11.98 0.06 1.00 0.13 1000
DLB 22.76 0.11 1.90 0.26 1000
SPLIT 88.84 0.44 7.42 1.00 1000
ScLERP 131.27 0.64 10.96 1.48 1000
SE3Up 204.00 1.00 17.03 2.30 1000 and
./app_visualization/vis-rigid
...
===== TIMINGS ===== Trajectories ===== ops=10001
name nsec max min CuBsp #means
DLFus 175.94 0.24 1.00 0.50 10
CuBsp 353.50 0.48 2.01 1.00 10
ScFus 448.13 0.61 2.55 1.27 10
SQUAD 643.04 0.87 3.65 1.82 10
SpFus 738.24 1.00 4.20 2.09 10 This allows e.g. to generate
Table 2: Runtime for pairwise (left) and higher order (right) rigidbody motion interpolation.