# Comparing Positions

This may be obvious to many (I'm guessing the skill level of people on coderwall is quite high), but considering I just signed up and had gone over explaining this to someone (I seem to have shared this multiple times), here goes.

If you've got two position vectors you wish to "compare", you should use distance (in fact squared distance), instead of a component-wise equality check. As an example - a game character (position) and a specific position in space - "Has the character reached the origin (0, 0, 0) of the world?".

I often see the naive implementation when someone complains about certain game-play code not working.

Pseudo:

```
// Class Vector3 skeleton below if needed.
Vector3 position; // player position
Vector3 destination; // target/destination position
// ...
// Naive check
if(position==destination) {
onTargetReached();
}
```

This is likely to "not work", since your *position* is updating based on a *speed* or *velocity* vector and taking into account *deltaTime* (all of them being *floats* or *doubles*). The quotes around *not work* are placed because the computer does **exactly** what you program it to and nothing else. A reason to use distance is because of the (discrete) time step, *position* may never actually reach *destination* (you may skip over it in one frame(or calculation/simulation step) to another). Another reason is that floating point numbers may have accuracy issues.

The distance to use would depend on your scale - if you ever studied mathematics, physics, statistics etc, you may have come across the term standard error or epsilon. Think of the distance as an acceptable measurement error or "close enough". So if your system scale or the units are 1 float unit = 1m and the problem you're solving (code you're writing) isn't affected by anything smaller than a centimeter, you could use 0.01 as your *epsilon* value.

```
// Check using distance
const float kEpsilon = 0.01f;
if( (position-destination).magnitude() < kEpsilon ) {
onTargetReached();
}
```

This changes your question to "Has the character reached *close enough* to the origin (0, 0, 0) of the world?". Make sure this change is appropriate to your code base - if you're at NASA or CERN where the accuracy may be more important than speed, walk away from here.

To make this even better, you could use squared distance. "What?! Add more instructions to square both sides of the condition/inequality?"

**SIDE** For comparing just two floats (rather than vectors), it may be appropriate for you to do so in your application (probably not for you if you code for a bank!):

```
float a, b;
// ... (system specific operations assigning values to a and b)
// Replace:
// if(a==b)
// with
if( (a-b)*(a-b) < kEpsilon*kEpsilon )
```

**END SIDE**

The answer to that is - a multiplication requires fewer instructions as compared to a square root which is required in finding the magnitude of a vector. So your check should be:

```
// Check using squared distance (helper defined below)
const float kEpsilonSq = 0.01f*0.01f;
if( (position-destination).sqMagnitude() < kEpsilonSq ) {
onTargetReached();
}
```

Plus, most Vector classes that you come across probably already have a *lenSquared* or *sqMagnitude* equivalent (look for them if you start working with on an existing code base or a project with a new engine etc); if you're writing your own, you now know what it's good for. Note that if you do come across some code which doesn't have a magnitude squared method built in, you should add one. If you can't (no access to source), just use length if that's all that's available - there's no point squaring the magnitude if you've already calculated it.

Finally when it comes to optimization, only optimize something which would benefit the overall performance. Don't go around changing all places in your (existing) code base to do this unless it's in a function that gets called a *lot* - such as an *update*/*step* function called every frame. Otherwise it may not be worth the time you spend replacing all usages. Optimization should be balanced with readability. For a new code base you could use squared distance everywhere from a "good practice" standpoint.

```
// Skeleton for Vector3 for those that may need it for better understanding
class Vector3 {
float x, y, z;
// Magnitude (or length) of the vector.
float magnitude() {
return sqrtf( this.sqMagnitude() );
}
// For more details, see http://en.wikipedia.org/wiki/Magnitude_%28mathematics%29
float sqMagnitude() {
return (x*x+y*y+z*z);
}
Vector3 operator-(const Vector &other) {
return Vector3(x-other.x, y-other.y, z-other.z);
}
bool operator==(const Vector &other) {
return (x==other.x && y==other.y && z==other.z);
}
// More class details omitted
// ...
};
```

#### Written by Pranav Tekchand

#### Related protips

#### 1 Response

thank you for the advice... :)