Jello Cube Simulation

Implemented on macOS 10.15.4, tested on both macOS and Ubuntu 20.04

link to project description page

What is this project?

It's a physically based simulation for a deformable jello cube.

Usage:

1. Type make to complete
2. Run with ```./jello some_world_file.w
3. During simulation press v to turn on full rendering of the cube. Press s to show/hide structural springs. Press b to show/hide bend springs. Press h to show/hide shear springs. Press 'i' to enter interactive mode. Further instructions for interactive mode are illustrated in terminal while running the program.
4. You can also use createWorld routine to create your own world file.

More Details about What I implemented for the Project

• Simulated the jello cube in a physics realistic way
• Added top and bottom walls to make the scene an enclosed world
• Changed lighting and material style to be more cyberpunk
• Implemented functionality that allow users to use arrow keys to move the scene. Left and right keys are for horizontally translate camera along a curve. Up and down are for vertically translate the camera along a curve. Press 'e' to reset.
• Created multiple different world files with non-homogeneous (in space) force fields Since force fields are just vector fields; and since vector fields can be defined as functions that maps R^3 to R^3, to create force fields, we just need to map all positions of points in the force field (i.e. (x,y,z) indecies) to some functions about (x,y,z). Here are force fields I created:

  1. strongerRotate.x It is the same motion with rotate.x but forces are stronger. Mapping function: F(x,y,z)=(-y/10)i+(x/10)j+0k

  2. pushToCenter.w This world file's force field has all forces pointing to origin (0,0,0). Hence, the cube will be eventurally pushed around the center of the world. Mapping function: f(x,y,z) = (2(-x)/(x^2+y^2+z^2))i +(2(-y)/(x^2+y^2+z^2))j +(2(-z)/(x^2+y^2+z^2))k

  3. accelerate.w This world file's force field have smaller forces at +y direction but larger forces at -y direction. As a result, putting the cube on furtherest +y direction creates an effect of acceleration. The cube first moves slowly then suddenly gets crazy, rotating and rushing to -y wall. Mapping function: f(x,y,z) = (-sin(x)/(x^2+y^2+z^2))i +(logb(y)/(x^2+y^2+z^2))j + 0k

• Implemented inclined plane collision:
  1. Implemented functionality to detect collision against the inclined plane on either sides.
  2. Implemented functionality to display inclined plane as a square by finding binormal vectors to the plane defined by normal [a,b,c] and linearly combine the binormal vectors to form four corners of the square.
  3. Use OpenGL blending function to make the inclined plane to be half transparent so that it is prettier
• Implemented mouse drag user interaction for pushing the cube
  1. With a .w file open, you can press 'i' to turn on interaction mode.
  2. Dragging up and down moves the cube up or down.
  3. Dragging left and right moves the cube on x-y plane. For this, four modes of directions of movement are implement. You can press 'i' to switch modes. 1> Mode 1 - Diagonal Drag of (-x,y,z) to (x,-y,z) 2> Mode 2 - Diagonal Drag of (x,y,z) to (-x,-y,z) 3> Mode 3 - Drag between Left and Right Walls 4> Mode 4 - Drag between Front and Back Walls
  4. Amount of forces added to the cube is determine by how far you have moved the mouse. The equation I used for calculating magnitude give a normalized force point is: sqrt(x-movement^2, y-movement^2)/20 * (1/dt)/1000 the dividing 20 part is for preventing force is too large that will destroy the cube's structure. And the (1/dt)/1000 magnify the force for smaller timesteps. For 0.001 timestep, (1/0.001)/1000=1. But for smaller timestep, the value of this part will always be greater than 1. This is a consideration that worlds with smaller timestep runs slow, so dragging effect is less obvious; magnifying force solves this problem.
  5. You will also see explanations about how to interact with the cube in the console ;)

Some Demos

1. Animation 1 is an execution with pushToCenter.w. Some additional forces from user push on (x,y) to (-x,-y) and plane and +z direction are added to create some dynamics. You can also observe the force field tries to move the cube around the center of the world.
   
2. Animation 2 is an execution with accelerate.w. It is mainly to show collisions with walls and the inclined plane. You can also observe the cube accelerates due to the forces given by force field.