Introduction
Soft body physics is a complex and fascinating area of game development that deals with the simulation of deformable objects. Unlike rigid bodies, which do not change shape, soft bodies can bend, stretch, and compress, making them ideal for simulating objects like cloth, jelly, or even human tissue.
Key Concepts
- Deformable Objects
- Definition: Objects that can change shape in response to forces.
- Examples: Cloth, rubber, jelly, and organic tissues.
- Mesh Representation
- Vertices and Edges: Soft bodies are often represented as a mesh of interconnected vertices and edges.
- Springs and Damping: Springs can be used to simulate the elastic properties of the material, while damping helps to simulate energy loss over time.
- Physics Models
- Mass-Spring Model: Uses masses connected by springs to simulate elasticity.
- Finite Element Method (FEM): A more advanced technique that divides the object into smaller elements and solves the physics equations for each element.
Practical Example: Mass-Spring Model
Step-by-Step Implementation
-
Define the Mesh:
- Create a grid of vertices connected by springs.
- Each vertex has a mass and can move in response to forces.
-
Apply Forces:
- Gravity, wind, and user interactions can be applied to the vertices.
- Calculate the forces acting on each vertex.
-
Update Positions:
- Use numerical integration (e.g., Euler or Verlet integration) to update the positions of the vertices based on the forces.
-
Collision Detection and Response:
- Detect collisions with other objects and adjust the positions of the vertices to prevent interpenetration.
Code Example
import numpy as np
class SoftBody:
def __init__(self, width, height, mass, stiffness, damping):
self.width = width
self.height = height
self.mass = mass
self.stiffness = stiffness
self.damping = damping
self.vertices = np.zeros((width, height, 2)) # 2D positions
self.velocities = np.zeros((width, height, 2)) # 2D velocities
self.forces = np.zeros((width, height, 2)) # 2D forces
def apply_gravity(self, g):
self.forces[:, :, 1] += self.mass * g
def update(self, dt):
# Apply forces and update velocities
self.velocities += (self.forces / self.mass) * dt
# Damping
self.velocities *= (1 - self.damping)
# Update positions
self.vertices += self.velocities * dt
# Reset forces
self.forces.fill(0)
# Example usage
soft_body = SoftBody(width=10, height=10, mass=1.0, stiffness=0.5, damping=0.1)
soft_body.apply_gravity(9.81)
soft_body.update(0.01)Explanation
- Vertices: Represent the positions of the points in the soft body.
- Velocities: Track the movement speed of each vertex.
- Forces: Accumulate the forces acting on each vertex.
- apply_gravity: Adds gravitational force to each vertex.
- update: Updates the positions and velocities of the vertices based on the forces.
Practical Exercise
Task
Create a simple soft body simulation using the mass-spring model. Implement collision detection with a static plane.
Steps
- Define a grid of vertices connected by springs.
- Apply gravitational force to the vertices.
- Implement collision detection with a plane.
- Update the positions and velocities of the vertices.
Solution
import numpy as np
class SoftBody:
def __init__(self, width, height, mass, stiffness, damping):
self.width = width
self.height = height
self.mass = mass
self.stiffness = stiffness
self.damping = damping
self.vertices = np.zeros((width, height, 2)) # 2D positions
self.velocities = np.zeros((width, height, 2)) # 2D velocities
self.forces = np.zeros((width, height, 2)) # 2D forces
def apply_gravity(self, g):
self.forces[:, :, 1] += self.mass * g
def apply_spring_forces(self):
for i in range(self.width):
for j in range(self.height):
if i > 0:
self.add_spring_force(i, j, i-1, j)
if i < self.width - 1:
self.add_spring_force(i, j, i+1, j)
if j > 0:
self.add_spring_force(i, j, i, j-1)
if j < self.height - 1:
self.add_spring_force(i, j, i, j+1)
def add_spring_force(self, i1, j1, i2, j2):
pos1 = self.vertices[i1, j1]
pos2 = self.vertices[i2, j2]
delta = pos2 - pos1
distance = np.linalg.norm(delta)
force = self.stiffness * (distance - 1) * (delta / distance)
self.forces[i1, j1] += force
self.forces[i2, j2] -= force
def update(self, dt):
self.apply_spring_forces()
self.velocities += (self.forces / self.mass) * dt
self.velocities *= (1 - self.damping)
self.vertices += self.velocities * dt
self.forces.fill(0)
def handle_collisions(self, plane_y):
for i in range(self.width):
for j in range(self.height):
if self.vertices[i, j, 1] < plane_y:
self.vertices[i, j, 1] = plane_y
self.velocities[i, j, 1] = 0
# Example usage
soft_body = SoftBody(width=10, height=10, mass=1.0, stiffness=0.5, damping=0.1)
soft_body.apply_gravity(9.81)
for _ in range(100):
soft_body.update(0.01)
soft_body.handle_collisions(plane_y=0)Explanation
- apply_spring_forces: Adds forces between connected vertices to simulate elasticity.
- add_spring_force: Calculates and applies the spring force between two vertices.
- handle_collisions: Detects and resolves collisions with a static plane.
Common Mistakes and Tips
- Numerical Stability: Ensure the time step (
dt) is small enough to maintain stability in the simulation. - Damping: Proper damping is crucial to prevent the system from oscillating indefinitely.
- Collision Handling: Ensure that collision response is robust to prevent vertices from penetrating the collision plane.
Conclusion
Soft body physics adds a layer of realism to video games by simulating deformable objects. Understanding the principles of mesh representation, mass-spring models, and collision detection is essential for implementing soft body physics. By practicing with simple examples and gradually increasing complexity, you can master the techniques needed to create realistic soft body simulations in your games.
Physics of Video Games
Module 1: Introduction to Physics in Video Games
Module 2: Kinematics and Dynamics
- Uniform Rectilinear Motion (URM)
- Uniformly Accelerated Rectilinear Motion (UARM)
- Newton's Laws
- Circular Motion
Module 3: Collisions and Responses
Module 4: Rigid Bodies Physics
- Introduction to Rigid Bodies
- Rigid Bodies Simulation
- Interactions between Rigid Bodies
- Constraints and Joints