A Little Math for your Big Ideas

Vectors, Physics and Floating

Ziba Scott / @popcannibal

Let's make things...

float
and drag
but only underwater parts
and account for surface area
on waves
and have a thousand!

Rigidbodies

Gravity pulls down

Let's go the other way.

                            
                                    rigidbody.AddForce(I want it to go up)

VECTORS

A vector is

Direction + Magnitude

Easily confused with a position

Tremendously useful

Vector3


Vector3 force = new Vector3(0,20,0);
rigidbody.AddForce(force);

Float
Drag
Underwater Center
Surface Area
Waves
Speed

Let's make the water push back

Opposite of a vector

                
        RigidBody.AddForce(rigidbody.velocity * -1 * viscosity);

Float
Drag
Underwater Center
Surface Area
Waves
Speed

We need to know:

Where are the corners of this object?
What corners are under water?
What's the center of those corners?


                    BoxCollider b = go.GetComponent
                        ();
                        Vector3 size = b.size;


                    BoxCollider b = go.GetComponent
                        ();
                        Vector3 size = b.size;

Local Space

                
localDuckButt = new Vector3(2.3,0,0);
worldDuckButt = duck.Transform.TransformPoint(localDuckButt);
Debug.Log(worldDuckButt); // (-1,1,0)

Float
Drag
Underwater Center
Surface Area
Waves
Speed

Cross products!

Vector3 v1 = Vector3.Cross(forwardVelocity, Vector3.up);

Vector3 v1 = Vector3.Cross(forwardVelocity, Vector3.up); Vector3 v2 = Vector3.Cross(forwardVelocity, v1);

                
Vector3 pointOutFront = position + (velocityDirection * 10);

for (float x = -width; x <= width; x += 1)
{
  for (float y = -width; y <= width; y += 1)
  {
    Vector3 start =  pointOutFront + (v1 * x) + (v2 * y);
    if (Physics.Raycast(start, -velocityDirection, out hit, 10))
    {
            Push it!
    }            
  }
}

Float
Drag
Underwater Center
Surface Area
Waves
Speed

Compare against every point! 50 times a second! Yay!

Float
Drag
Underwater Center
Surface Area
Waves
Speed

Compute fewer things
Don't trigger garbage collection
Threads

Deep Profiler

Compute fewer things

Break the water mesh into multiples

Compute fewer things

Vector3.magnitude has a square root

Vector3.sqrMagnitude is cheaper

Compute fewer things

raycast methods are not equal


Physics.Raycast(myRay, out hit, distance, layerMask); // 35% slower!

Physics.Raycast(start, direction, out hit, distance, layerMask)

Garbage collection

New has a cost!
Accessing mesh data always copies!
foreach allocates

Deep Profiler

Threading

ThreadPool makes some things super easy

                
ThreadPool.QueueUserWorkItem(myObject.MyMethod, threadNumber);

but it does have a tiny allocation!

Threading

No Unity api calls

No Rigidbody!
No Raycasts!
No Meshfilters!
No Transform!

                
l2w = transform.localToWorldMatrix;

// later, in a thread

worldPosition =  l2w.MultiplyPoint(point);

Conclusion

Vectors are direction + magnitude
Force and velocity are vectors
Transform.TransformPoint(localSpacePoint)
Vector3.Cross(v1, v2) == Perpendicular
Deep profiler