In this project, we implemented an XPBD solver in C++ with a basic renderer using freeglut and glew. Our implementation heavily relies on the Eigen library to manipulate 3D vector and matrices. We used an oriented-object approach to manipulate the meshes and the constraints. Please refer to the IMA904_report.pdf file for more details.
The roadmap for this project was to implement small scenes to play with the different constraints and their parameters. To see those scenes, go to the folder ./src, and enter in the terminal the commands described in the next subsections.
make spring
./spring
This will compile then execute the spring.cpp file which aims to display two particles linked by a distance constraint. One of this particle is fixed.
make cloth
./cloth
This will compile then execute the demo_cloth.cpp file which aimes to display a cloth with its top two vertices fixed.
make wall
./wall
This will compile then execute the wall.cpp file which displays one bouncing ball
make ball
./ball
This will compile then execute the ball.cpp file which displays a bunch of balls that are constrained to stay inside a box. The front face and the back face of the box are not displayed for clarity and visualisation purpose. User can add a ball to the scene by pressing F1.
make run
This will compile and execute main.cpp , the main scene of the project, which is basically a cloth balloon scene.
We designed a generic class Object with
mass, position, speed and color attributes. Those attributes will be
used to set and render the object in the space, but are not going to
be updated. Instead, each object will have a std::vector of Particle which will store its vertices. Those
vertices are the ones that are going to see their position and speed
updated to move the object.
Here are the different classes that inherits or are involved with the Object class:
A class implementing the particles which are going to be the core of the (X)PBD process.
A class representing a sphere. Basically it is a particule with a boundary radius.
A class representing a cloth, which is actually a rectangle of particles. This rectangle is subdivided in quads which are virtually subdivided in triangles.
A class representing a finite plane in the 3D space. It is useful to place walls in the scene
The floor of the scene.
The other important class is the Constraint which define the main attributes used to solve a constraint. Then, each subclass of constraints has its own attributes to do the calculation.
This tries to maintain two particles at a certain distance. It gives a similar effect than a spring between those two particles.
It makes a particle staying at a given position.
It is basically the inequality version of the distance constraint, and allows us to avoid the collision between two particles.
This constraint prevents a vertex q from entering the triangle formed by particles (p1,p2,p3).
It is the particular case of the penetration constraint when (p1,p2,p3) are not particles but static points of a given plane that acts like a wall or a floor.
We constraint the two half-triangles to keep the same angle.
Two adjacent triangles should keep the same bending energy overtime.