This chapter focuses on springs and joints. A spring will exert some force on one or more objects to create a spring like motion. A joint is a constraint that limits the motion of rigidbodies. Throughout the chapter, we will cover the following topics:
Particle Modifications
Springs
Cloth
Physics System Modifications
Joints
Springs are one of the most powerful tools in any physics engine. On the surface, it may seem like they are only useful for creating oscillating motions, but we can use springs to model soft bodies or even cloth! In this chapter, we will learn how to use the spring formula to build soft body objects. By the end of the chapter, we will have a full cloth simulation working!
Up until this chapter, every rigidbody enjoyed having six degrees of freedom for motion. At the end of this chapter, we will introduce a way to constrain that motion using joints. In this chapter, we will build a simple distance joint that will remove a degree of freedom from a pair of rigidbodies.
In this chapter, we will attach particles to springs to create a point mass system. A point mass system contains a number of points that have mass, but not volume. A particle fits this description perfectly. However, as it is, the Particle class does not expose all the functions that we need to achieve this. In order to develop the point mass system, we need to make a few modifications to the Particle class we developed in Chapter 14, Constraint Solving.
In this section, we will make several modifications to the public API of the Particle class. We will introduce setter functions for the mass and friction of particles. We will also introduce getter functions for the velocity and inverse mass of particles. Finally, we will implement a function to add an impulse to particles.
Springs are important to build realistic objects. In the real world, we use springs everywhere, from watches to the suspension of cars. In games, we can use springs to model these same interactions, or to simulate more complex systems, such as rigidbodies.
Every spring has a Resting Length, sometimes called the spring's Equilibrium. Equilibrium describes the length of a resting spring, that is, when the spring is not contracted or stretched. When a spring is contracted or stretched away from its equilibrium, the spring will try to pull back to its resting length with a force equivalent to the difference of its current length and resting length. This describes Hooke's Law. Mathematically, Hooke's Law is expressed by the following equation:
In this equation, F is the force exerted by the spring, k is the spring constant, and x is the difference between the current length and resting length of the spring. The spring constant represents the strength of the spring, that is, how stiff or...
We can use springs to model interesting soft body objects. Unlike a rigidbody, a soft body can change its shape. In this section, we will use springs to simulate cloth. Cloth is implemented as a point mass system. In a point mass system, every vertex of a mesh is represented by a particle. Every particle is attached to other particles by springs to force the object to maintain its shape.
If we arrange all the particles representing the vertices of a cloth in a grid, we can connect every row and column using springs. These springs are the structural springs of the cloth:
This, however, is not enough for an accurate simulation. If we set any one of the particles to have infinite mass so that it does not move, the cloth will collapse into a rope. We can improve the structural integrity of the cloth by adding shear springs. Shear springs connect every particle to its neighbors diagonally:
Having both structural and shear springs makes the cloth behave as expected in the scenario where one...
In the last section of this chapter, we will build a stable Cloth class. This class contains a set of particles and three spring systems. For the cloth to actually work, we have to call its physics simulation functions every frame. In this section, we will add cloth support to the PhysicsSystem.
In this section, we will make several modifications to the PhysicsSystem class to add support for cloth simulation.
Perform the following steps to add cloth support to our physics system:
Include the Cloth.h header file in PhysicsSystem.h. Add a vector of Cloth pointers to the PhysicsSystem class. Add a function to register a new cloth into the vector and a function to clear the vector:
// Start of file unchanced
#include "Cloth.h"
class PhysicsSystem {
protected:
// Previous member variable declarations unchanged
std::vector<Cloth*> cloths;
public:
// Previous member functions unchanged
void AddCloth(Cloth* cloth);
void...In three dimensions, an object has six degrees of freedom. Three degrees of freedom come from translation and an additional three come from orientation. A constraint takes away one or more degrees of freedom. A joint is a type of constraint that limits the degrees of freedom between two objects. There are several common types of joints:
Several simple joints can be combined to create more complex joints. We can use joints to model hinges for doors, ragdolls that represent characters, or to simply stick objects to each other.
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