# Feature guide » Collision detection

Collection of simple shapes for high performance collision detection.

The essential thing in collision detection is to define a complex object with collection of simple shapes, for which it is easy to detect collisions. The library is contained in Shapes namespace, see its documentation for more information about building and usage with CMake.

These shapes can be either one-, two- or three-dimensional and they can be grouped together using various operations.

## Available shapes

Magnum provides a set of simple shapes for collision detection, similarly to what is found in many other collision detection libraries. Additionally some shapes are provided in inverted form — e.g. inverted box detects collisions on outside instead of inside, which might be useful for example to create bounds around platformer game level.

### One-dimensional shapes

Because of numerical instability it's not possible to detect collisions of line and point. Collision of two lines can be detected only in 2D.

### Two-dimensional shapes

• Shapes::Plane — Infinite plane, defined by position and normal (3D only)

### Three-dimensional shapes

The easiest (and most efficient) shape combination for detecting collisions is point and sphere, followed by two spheres. Computing collision of two boxes is least efficient.

## Creating shape compositions

Shapes can be composed together using one of three available logical operations: AND, OR and NOT. These operations are mapped to `&&`, `||` and `!` operators, so for example creating negation of logical OR of line segment and point is simple as this:

```Shapes::LineSegment3D segment;
Shapes::Point3D point;

Shapes::Composition3D composition = !(segment || point);```

### Providing simplified version of shape for better performance

If there are many shapes composed together, it might hurt performance of collision detection, because it might be testing collision with more shapes than necessary. It's then good to specify simplified version of such shape, so the collision detection is done on the complex one if and only if collision was detected with the simplified shape. It is in fact logical AND using the `&&` operator — the collision is initially detected on first (simplified) shape and then on the other:

```Shapes::Sphere3D sphere;
Shapes::Box3D box;
Shapes::AxisAlignedBox3D simplified;

Shapes::Composition3D composition = simplified && (sphere || box);```

## Detecting shape collisions

Shape pairs which have collision occurence detection implemented can be tested for collision using the `%` operator. The operator returns boolean describing whether the collision happened or not. Example:

```Shapes::Point3D point;
Shapes::Sphere3D sphere;

bool collide = point % sphere;```

As this is useful for e.g. menu handling and simple particle systems, for serious physics you often need more information like contact point, separation normal and penetration depth. For shape pairs which have implemented this detailed collision detection you can use the `/` operator, which returns Shapes::Collision object. Note that unlike with the `%` operator mentioned above, this operation is not commutative. See Shapes::Collision class documentation for more information about the returned data. Example:

```const Shapes::Collision3D c = point/sphere;
if(c) {
Vector3 translation = c.separationNormal()*c.separationDistance();
// translate point by translation...
}```

## Integration with scene graph

Shape can be attached to object in the scene using Shapes::Shape feature. In conjunction with Shapes::ShapeGroup you can use Shapes::Shape::collides() and Shapes::Shape::collision() similarly to the `%` and `/` operators above. Please note that the shape group caches the absolute transformations of all shapes and thus you need to explicitly call Shapes::ShapeGroup::setClean() before computing the collisions if you did any modifications to the objects in the scene.

Scenegraph-flavored equivalent to the above code:

```Shapes::ShapeGroup3D shapes;
Object3D& a;
auto aShape = new Shapes::Shape<Shapes::Sphere3D>(a, {{}, 23.0f}, &shapes);

Object3D& b;
auto bShape = new Shapes::Shape<Shapes::Point3D>(b, {{1.0f, 0.2f, 3.0f}}, &shapes);

// Translate point so the objects no longer collide
shapes.setClean();
if(aShape->collides(*bShape)) {
const Shapes::Collision3D c = aShape->collision(*bShape);
b.translate(c.separationNormal()*c.separationDistance());
}```

There is also Shapes::ShapeGroup::firstCollision() function which returns arbitrary first collision for given shape in whole group (or `nullptr`, if there isn't any collision).

You can also use DebugTools::ShapeRenderer to visualize the shapes for debugging purposes. See also Using the scene graph for introduction.